Church encoding

en-noun

Church encoding (countable and uncountable, plural Church encodings)

(mathematics) A means of representing data and operators in the lambda calculus, by forming them into a mathematical structure embedded in the lambda calculus.


anentropy

anentropy (countable and uncountable, plural anentropies)

The advantages of the RHA method are that it is flexible and can deal with all variants of phoscorites, including diopside and phlogopite-bearing varieties, as well as the continuous series through to carbonatite (Table 2.4) and other related rocks. It gives a measure of complexity of composition and of minor components in the entropy and anentropy values.

2004, F. Wall, A. N. Zaitsev, Phoscorites and Carbonatites from Mantle to Mine, →ISBN, page 66:

Here, R is rank formula of composition – a sequence of components by reduction of their value (contents); Н is Shannon information entropy – complexity measure; А – anentropy – measure of purity; Т – tolerance – measure of ultrapurity.

2012 March, Томас Георгиевич Петров, S.V. Moshkin, “RHA (Т)-System for Coding of Discrete Distributions and Their Alteration Processes”, in Proceedings of the 3rd International Multi-Conference on Complexity, Informatics and Cybernetics IMCIC-2012:

(statistics, countable and uncountable) A measure of the simplicity or purity of a distribution.


artificial general intelligence

artificial general intelligence (countable and uncountable, plural artificial general intelligences)

artificial general intelligences (plural)

Used as early as 1997, by Mark Gubrud in a discussion of the implications of fully automated military production and operations, and popularized by Ben Goertzel around 2002.

The real question, I think, is not whether the field as a whole is in any real danger of another AI winter but, rather, whether progress remains limited to narrow AI or ultimately expands to Artificial General Intelligence as well.

2015, Martin Ford, The Rise of the Robots, Oneworld:

artificial intelligence
artificial intelligence

Artificial intelligence
artificial intelligence#English

(artificial intelligence) Artificial intelligence which matches or exceeds the intelligence and capabilities of human beings.

Ben Goertzel
artificial general intelligence


horodisk

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In this paper we study the geometry and the topology of unbounded domains in the Hyperbolic Space #92;mathbb#123;H#125;ⁿ supporting a bounded positive solution to an overdetermined elliptic problem. Under suitable conditions on the elliptic problem and the behaviour of the bounded solution at infinity, we are able to show that symmetries of the boundary at infinity imply symmetries on the domain itself. In dimension two, we can strengthen our results proving that a connected domain #92;Omega#92;subset#92;mathbb#123;H#125;² with C² boundary whose complement is connected and supports a bounded positive solution u to an overdetermined problem, assuming natural conditions on the equation and the behaviour at infinity of the solution, must be either a geodesic ball or, a horodisk or, a half-space determined by a complete equidistant curve or, the complement of any of the above example.

2015, José M. Espinar, Alberto Farina, Laurent Mazet, “f-extremal domains in hyperbolic space”, in arXiv:


hypercover

(mathematics) A certain generalisation of a cover obtained iteratively


inversibility

Particle in Coulomb like potential is revisited and the problem of inversibility and hermicity of inverse coordinate operator is solved..

2015, M. I. Samar, V. M. Tkachuk, “Exactly solvable problems in the momentum space with a minimum uncertainty in position”, in arXiv:

(mathematics) Alternative form of invertibility


offshell

Working at next-to-leading order in QCD we show that carefully selected ratios of offshell regions to onshell regions in the reconstructed top and antitop invariant mass spectra are, \emph{independently} of the coupling g#95;#123;tbW#125;, sensitive to the top-quark width.

2015, Stefan Liebler, Gudrid Moortgat-Pick, Andrew S. Papanastasiou, “Probing the top-quark width through ratios of resonance contributions of e⁺e⁻→W⁺W⁻b̄b”, in arXiv:

(mathematics, physics) That does not conform to classical physics.


smooth function

smooth function (plural smooth functions)

Any ANALYTIC FUNCTION is smooth. But a smooth function is not necessarily analytic.

2003, Eric W. Weisstein, CRC Concise Encyclopedia of Mathematics, →ISBN, page 419:

(mathematics) a function that has derivatives of all finite orders everywhere in its domain.


polyquadratic

If E does not have complex multiplication (CM), by results of Ribet and Elkies concerning fields of definition of elliptic #92;mathbb#123;Q#125;-curves E is isogenous to a curve defined over a polyquadratic extension of #92;mathbb#123;Q#125;.

2015, Francesc Fité, Xavier Guitart, “Fields of definition of elliptic k-curves and the realizability of all genus 2 Sato--Tate groups over a number field”, in arXiv:

(mathematics) Involving multiple quadratic equations or functions


pseudoapproximation

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(mathematics) An approximation where the error of approximation is greater than ε because calculation of a true approximation is not feasible.


reductivity

There are three parts and each contains some new ingredients: first, we generalized Matsushima's reductivity result to conic setting by Hormander's L^2 estimate; second, we constructed a new continuity path for Kaehler cone metrics; third, Bando-Mabuchi's bifurcation technique was explored to this path at Kaehler-Einstein cone metrics..

2015, Long Li, Kai Zheng, “A continuity method approach to the uniqueness of Kaehler-Einstein cone metrics”, in arXiv:

(mathematics) The condition of being reductive


semibent

As applications of this construction, we show several series of linear codes over f#95;#123;2ᵗ#125; with two or three weights by using bent, semibent, monomial and quadratic Boolean function f..

2015, Can Xiang, Keqin Feng, Chunming Tang, “A Construction of Linear Codes over f_2ᵗ from Boolean Functions”, in arXiv:

(mathematics) Having a Walsh transform that contains only the values {0, ±2(n+1)/2}, when n is odd.


tridegree

We construct a counter-example to Viro's conjecture in tridegree (4,4,2) and a family of real algebraic surfaces of tridegree (2k,2l,2) in (#92;mathbb#123;CP#125;¹)³ with asymptotically maximal first Betti number of the real part.

2015, Arthur Renaudineau, “Real algebraic surfaces with many handles in (ℂℙ¹)³”, in arXiv:

(mathematics, of a polynomial) The condition of being cubic


uniformisable

Finally, equivalently uniformisable topological spaces are considered..

2015, Farshad Omidi, MohammadReza Molaei, “On U-equivalence spaces”, in arXiv:

(mathematics) Alternative form of uniformizable


cocompletion

We show that j satisfies this condition if and only if j presents #92;mathcal#123;V#125; as a free cocompletion of #92;mathcal#123;J#125; with respect to the weights for left Kan extensions along j, and so we call such systems of arities eleutheric.

2015, Rory B. B. Lucyshyn-Wright, “Enriched algebraic theories and monads for a system of arities”, in arXiv:

(mathematics) A full embedding whose image is a cocomplete category and for which every functor with a cocomplete image has an extension to a cocontinuous functor that is unique up to natural isomorphism.


hyperideal

Moreover, there are only four hyperbolic honeycombs with material vertices and material cells (the cells are entirely inside of hyperbolic space), eleven with ideal vertices or cells (the cells touch the boundary of hyperbolic space in some way), and all others have either hyperideal vertices or hyperideal cells (the cells go outside of the boundary of hyperbolic space in some way).

2015, Roice Nelson, Henry Segerman, “Visualizing Hyperbolic Honeycombs”, in arXiv:

(mathematics) An ideal of a semihypergroup.


hyperspecial

We give an expository overview over recent results on the global structure and geometry of the Newton stratification of the reduction modulo p of Shimura varieties of Hodge type with hyperspecial level structure.

2015, Eva Viehmann, “On the geometry of the Newton stratification”, in arXiv:

(mathematics) Pertaining to a hyperspecial subgroup.


rackoid

Our main objective are large classes of examples, including a Lie rackoid integrating the Dorfman bracket without the cocycle term of the standard Courant algebroid..

2015, Camille Laurent-Gengoux, Friedrich Wagemann, “Lie rackoids”, in arXiv:

(mathematics) A specific form of groupoid


selfdistributive

Its main ingredient is a selfdistributive product on the manifold of bisections of a smooth precategory. We show that the tangent algebroid of a Lie rackoid is a Leibniz algebroid and that Lie groupoids gives rise via conjugation to a Lie rackoid.

The aim of this text is to survey some aspects of selfdistributive algebra, with a special emphasis on the involved word problems.

2019, Petr Vojtěchovský, Murray R. Bremner, J. Scott Carter, Nonassociative Mathematics and its Applications, page 70:

(mathematics) Having the property (of an operation) of being distributive with respect to itself. Thus, an operator ◦ is left selfdistributive iff x◦(y◦z) = (x◦y)◦(x◦z), and is right selfdistributive iff (x◦y)◦z = (x◦z)◦(y◦z), for all x, y, z.


semicoercive

As a model example we consider a unilateral semicoercive contact problem with nonmonotone friction and provide numerical results for benchmark tests..

2015, Nina Ovcharova, Joachim Gwinner, “Semicoercive Variational Inequalities - From Existence to Numerical Solution of Nonmonotone Contact Problems”, in arXiv:

(mathematics) Continuous and symmetric but with a nonzero kernal.


ambitwistor

We obtain all the type II supergravity constraints in the pure spinor ambitwistor string by imposing consistency of local worldsheet gauge symmetries..

2015, Osvaldo Chandia, Brenno Carlini Vallilo, “On-shell type II supergravity from the ambitwistor pure spinor string”, in arXiv:

(mathematics, physics) A form of complex null geodesic


autoparallel

(mathematics) A curve having a parallel tangent vector field.


autoparallel

(mathematics) Having a parallel tangent vector field.


fibering

We show the existence of multiple solutions for suitable range of #92;lambda by analyzing the fibering maps and the corresponding Nehari manifold.

2015, Jacques Giacomoni, Pawan Kumar Mishra, Konijeti Sreenadh, “Critical growth fractional systems with exponential nonlinearity”, in arXiv:


hyperhoneycomb

Simple examples are hyperhoneycomb and stripy-honeycomb lattices, which are realized in #92;beta-Li#95;#123;2#125;IrO#95;#123;3#125; and #92;gamma-Li#95;#123;2#125;IrO#95;#123;3#125;, respectively.

2015, Motohiko Ezawa, “Loop-nodal and Point-nodal Semimetals in Three-dimensional Honeycomb Lattices”, in arXiv:

(mathematics) A three-dimensional analog of a honeycomb structure


macroprocess

Multiple bits moving in macroprocess join triplet macrounits which logically organize information networks encoding units in structures enclosing triplet code.

2015, Vladimir S. Lerner, “The impulse observations of random process generate information binding reversible micro and irreversible macro processes in Observer: regularities, limitations, and conditions of self-creation”, in arXiv:

(mathematics) Relatively large-scale process


microprocess

Memorized information binds reversible microprocess within impulse with irreversible information macroprocess.

(mathematics) Relatively small-scale process


biinvariant

In this paper we give explicit calculations of the Laplace operator's spectrum for smooth real or complex functions on all connected compact simple Lie groups of rank 3 with biinvariant Riemannian metric and establish a connection of these formulas with the number theory and ternary and binary quadratic forms..

2015, Valera Berestovskii, Irina Zubareva, Victor Svirkin, “The spectrum of the Laplace operator on connected compact simple Lie groups of rank 3”, in arXiv:

(mathematics) Both left-invariant and right-invariant.


convolutional neural network

convolutional neural network (plural convolutional neural networks)

(machine learning) A neural network in which the connectivity pattern between its neurons is modelled on the organization of the animal visual cortex.


hypernetwork

The properties of the hypernetwork model are summarized as three aspects: glocality, compositionality and self association based on randomness and recall.

2010, Byoung-Tak Zhang, PRICAI 2010: Trends in Artificial Intelligence, →ISBN:

We obtain the stationary average hyperedge hyperdegree distribution of the hypernetwork by the characteristic equation.

2015, Jin-Li Guo, “Bose-Einstein Hypernetworks”, in arXiv:

(mathematics) A probabilistic graphical model based on hypergraph models and inspired by biological systems.


hypervirtual

In detail: to a monad T on a hypervirtual double category #92;mathcalK several hypervirtual double categories T-#92;mathsf#123;Alg#125;#95;#123;(v,w)#125; of T-algebras are associated, [...].

2015, Seerp Roald Koudenburg, “A double-dimensional approach to formal category theory”, in arXiv:

(mathematics, of a virtual double category) Having additional cells with nullary target.


peanosphere

We give bijections between bipolar-oriented (acyclic with unique source and sink) planar maps and certain random walks, which show that the uniformly random bipolar-oriented planar map, decorated by the "peano curve" surrounding the tree of left-most paths to the sink, converges in law with respect to the peanosphere topology to a #92;sqrt#123;4#47;3#125;-Liouville quantum gravity surface decorated by an independent Schramm-Loewner evolution with parameter #92;kappa#61;12 (i.e., SLE#95;#123;12#125;).

2015, Richard Kenyon, Jason Miller, Scott Sheffield, David B. Wilson, “Bipolar orientations on planar maps and SLE₁₂”, in arXiv:

(mathematics) the scaling limit of random planar maps equipped with a collection of loops coming from a critical FK model.


pseudoumbilical

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We also characterize the pseudoumbilical ones in terms of soliton curves for the inverse curve shortening flow and minimal Legendrian immersions in odd-dimensional spheres.

2015, Ildefonso Castro, Ana M. Lerma, “Homothetic solitons for the inverse mean curvature flow”, in arXiv:

(mathematics) Umbilical in the direction of the mean curvature vector field everywhere.


subdifferentially

In 2001, Burke and Overton characterize the regular subdifferential of the spectral abscissa and show that the spectral abscissa is subdifferentially regular in the sense of Clarke on the set of matrices with nonderogatory eigenvalues.

2015, James V. Burke, Julia Eaton, “Variational Analysis Convexly Generated Spectral Max Functions”, in arXiv:

(mathematics) With respect to subderivatives


comonoidal

A polyad is a lax functor from a small category (its source) to the bicategory of categories, and a Hopf polyad is a comonoidal polyad whose fusion operators are invertible.

2015, Alain Bruguières, “Hopf polyads”, in arXiv:


eigenaxis

Important generalizations for linear decision boundaries are shown to be encoded within a dual statistical eigenlocus of principal eigenaxis components.

2015, Denise M. Reeves, “Resolving the Geometric Locus Dilemma for Support Vector Learning Machines”, in arXiv:

(mathematics) An eigenvector of an axis of rotation


eigenlocus

(mathematics) A locus of a point that moves about an eigenaxis


indicability

A short chapter outlines a proof that the group of PL homeomorphisms of the n-dimensional cube (fixed on the boundary) is left-orderable; a property conjectured to be true for the group of homeomorphisms in dimension two. We present a new proof that local indicability of a group is equivalent to the existence of a "Conradian" left-ordering.

2015, Adam Clay, Dale Rolfsen, “Ordered groups and topology”, in arXiv:

(mathematics) The condition of being indicable


multicosimplicial

We apply these results to various situations, and in particular show that certain important subdiagrams of a fibrant multicosimplicial object are fibrant..

2015, Philip S. Hirschhorn, Ismar Volic, “Functors between Reedy model categories of diagrams”, in arXiv:

(mathematics) Pertaining to a generalization of a cosimplicial space to diagrams of spaces that are cosimplicial in each direction.


nonexplosion

The conditions are practical and in the meanwhile sharp; e.g., the one for nonexplosion is necessary if the state space is in addition locally compact and the Q-function satisfies weak Feller-type and local boundedness conditions.

2015, Yi Zhang, “On the nonexplosion and explosion for nonhomogeneous Markov pure jump processes in Borel spaces”, in arXiv:

(mathematics) The absence of combinatorial explosion


pseudohyperbolic

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In this elementary classroom note, we are interested in the collection of the pseudohyperbolic disks D#95;#92;rho(x,r) (with fixed radius r and variable hyperbolic centers -1lt;xlt;1) and determine explicitely^([sic]) with function theoretic tools the enveloppe^([sic]) of these disks..

2015, Raymond Mortini, Rudolf Rupp, “On a family of pseudohyperbolic disks”, in Elem. Math., volume 70, pages 153–160:


semiacyclic

We provide an example of a tournament on nine vertices that can not be made semiacyclic, yet it may be represented as a dominance graph of coins, if we also allow coins that display their smaller side with greater probability.

2015, Gábor Hetyei, “Efron's coins and the Linial arrangement”, in arXiv:

(mathematics) Having no ascending cycles


transiso

We have also discussed the completeness of transiso graphs for the groups of order less than 32..

2015, Laxmi Kant Mishra, Brajesh Kumar Sharma, “On Transiso Graphs of Groups of order less than 32”, in arXiv:

(mathematics) Pertaining to a graph on a finite group whose vertices are the subgroups of a specified order and for which two vertices are adjacent if the sets of all normalized right transversals for each corresponding subgroup contain at least one common element.


eigensymbol

Since this method allows to generate a Jacobi eigenform directly from a given modular eigensymbol without reference to the whole ambient space of Jacobi forms it makes it possible to compute Jacobi Hecke eigenforms of large index.

2016, Nathan C. Ryan, Nicolás Sirolli, Nils-Peter Skoruppa, Gonzalo Tornaría, “Computing Jacobi Forms”, in arXiv:

(mathematics) The symbol for an eigenvector.


semicovering

In this paper, by reviewing the concept of semicovering maps, we present some conditions under which a local homeomorphism becomes a semicovering map.

2016, Majid Kowkabi, Behrooz Mashayekhy, Hamid Torabi, “When Is a Local Homeomorphism a Semicovering map?”, in arXiv:

(mathematics) A projection that has the property that for any projection onto its image, it is possible to find a corresponding projection onto its domain such that locally constant regions about a point projected onto the image have locally constant images in the domain.


superproper

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The main result of the present paper asserts that the moduli superstack classifying pointed stable log twisted #92;text#123;SUSY#125;#95;1 curves may be represented by a log superstack whose underlying superstack is a superproper and supersmooth Deligne-Mumford superstack.

2016, Yasuhiro Wakabayashi, “Moduli of log twisted cal N=1 SUSY curves”, in arXiv:


superscheme

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In the present paper, we prove that a locally noetherian superscheme X#92;circledS may be reconstructed (up to certain equivalence) category-theoretically from the category of noetherian superschemes over X#92;circledS.

2016, Yasuhiro Wakabayashi, “Categorical representation of superschemes”, in arXiv:


supershadow

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Specifically we employ the supershadow formalism to study the four-point correlator #92;langle#92;Phi#95;1#92;Phi#95;2#92;Phi#95;3#92;Phi#95;4#92;rangle, in which the four scalars #92;Phi#95;i have arbitrary scaling dimensions and R-charges with the only constraint from R-symmetry invariance of the four-point function.

2016, Zhijin Li, Ning Su, “The Most General 4𝒟 cal N=1 Superconformal Blocks for Scalar Operators”, in arXiv:


superstack

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Consequently, this moduli superstack forms a smooth compactification different from the compactification proposed by P.


ultradifferentiability

A characterization of the scalar type spectral generators of Beurling type Carleman ultradifferentiable C#95;0-semigroups is established, the important case of the Gevrey ultradifferentiability is considered in detail, the implementation of the general criterion corresponding to a certain rapidly growing defining sequence is observed..

2016, Marat V. Markin, “On the generation of Beurling type Carleman ultradifferentiable C_0-semigroups by scalar type spectral operators”, in arXiv:

(mathematics) The condition of being ultradifferentiable


bicommutant

In this article, we prove that every unitary fusion category gives an example of a bicommutant category.

2015, André Henriques, David Penneys, “Bicommutant categories from fusion categories”, in arXiv:

(mathematics) A double commutant (that commutes with the elements of two subgroups)


bipartization

We relate the problem of computing the classical value of single-party anti-correlation XOR games to finding the edge bipartization number of a graph, which is known to be MaxSNP hard, and connect the computation of the classical value of more general XOR-d games to the identification of specific cycles in the graph.

2015, Piotr Gnaciński, Monika Rosicka, Ravishankar Ramanathan, Karol Horodecki, Michał Horodecki, Paweł Horodecki, Simone Severini, “Linear game non-contextuality and Bell inequalities - a graph-theoretic approach”, in arXiv:

(mathematics) The removal of vertices from a graph in order to make it bipartite


hypercohomology

This leads to a physical interpretation of the hypercohomology groups from the perspective of the Coulomb branch, as well as an interpretation for the spectral sequences used to compute them..

2015, Kenny Wong, “Spectral Sequences and Vacua in N = 2 Gauged Linear Quantum Mechanics with Potentials”, in arXiv:

(mathematics) The dual of a hyperhomology.


hyperradial

For the case of zero-range, regularized pseudo-potential interactions, we find that the system is nearly separable in hyperspherical coordinates and that, away from a set of narrow avoided crossings, the full energy eigenspectrum as a function of the 2D s-wave scattering length is well described by ignoring coupling between adiabatic hyperradial potentials.

2015, Seth T. Rittenhouse, Andrew Wray, B. L. Johnson, “Hyperspherical approach to the three-bosons problem in 2D with a magnetic field”, in arXiv:


hyperradius

hyperradius (plural hyperradii or hyperradiuses)

hyperradii (plural)
hyperradiuses (plural)

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hyperfield

(mathematics) A field in which the operation of addition is multivalued


hyperskewness

This, together with the result for the second cumulant, leads to the hyperskewness value #92;widetilde#123;S#125;#61;0.0835.

2015, Tapas Singha, Malay K. Nandy, “Hyperskewness of (1+1)-dimensional KPZ Height Fluctuations”, in arXiv:

(mathematics) A central moment of the fifth order.


isovorticed

In this paper we describe necessary and sufficient conditions on the vorticity function of a 2D ideal flow on a surface with or without boundary, for which there exists a steady flow among isovorticed fields.

2015, Anton Izosimov, Boris Khesin, “Characterization of steady solutions to the 2D Euler equation”, in arXiv:

(mathematics, physics) Having the same vorticity


quasizero

It has been suggested by lattice simulations, however, that a symmetry of mesons in the light quark sector upon the quasizero mode truncation from the quark propagators is actually higher than SU(4), because the states from a singlet and a 15-plet irreducible representations of SU(4) are also degenerate.

2015, L. Ya. Glozman, “SU(4) * SU(4) bilocal symmetry of Coulombic confinement and emergent symmetry in QCD”, in arXiv:


semicuspidal

Real semicuspidal strata are well-understood.

2015, Alexander Kleshchev, Robert Muth, “Affine zigzag algebras and imaginary strata for KLR algebras”, in arXiv:

(mathematics) Pertaining to a singularity that is not smooth.


semidirected

We extend AMP chain graphs by (i) relaxing the semidirected acyclity constraint so that only directed cycles are forbidden, and (ii) allowing up to two edges between any pair of nodes.

2015, Jose M. Peña, “Alternative Markov Properties for Acyclic Directed Mixed Graphs”, in arXiv:

(mathematics) Alternative form of semidirect


unparametrized

For many metrics the tangent space T#95;c#92;operatorname#123;Imm#125;(S¹,#92;mathbbR²) at each curve c splits into vertical and horizontal components (with respect to the projection onto the shape space B#95;i(S¹,#92;mathbbR²)#61;#92;operatorname#123;Imm#125;(S¹,#92;mathbbR²)#47;#92;operatorname#123;Diff#125;(S¹) of unparametrized curves and with respect to the metric G).

2015, Martin Bauer, Philipp Harms, “Metrics with prescribed horizontal bundle on spaces of curve”, in arXiv:

(mathematics) Alternative form of unparameterized


contactomorphism

In this expository article I will review some constructions of bi-invariant metrics on the contactomorphism group, and how these metrics are related to some other global rigidity phenomena in contact topology which have been discovered in the last few years, in particular the notion of orderability (due to Eliashberg and Polterovich) and an analogue in contact topology (due to Eliashberg, Kim and Poltorovich) of Gromov's symplectic non-squeezing theorem..

2015, Sheila Sandon, “Bi-invariant metrics on contactomorphism groups”, in arXiv:

(mathematics) An isomorphism in the contact category.


equilogical

We show that the two models of extensional type theory, those given by the category of equilogical spaces and by the effective topos, are homotopical quotients of categories of 2-groupoids..

2015, Giuseppe Rosolini, “The category of equilogical spaces and the effective topos as homotopical quotients”, in arXiv:

Cartesian closed categories
Cartesian closed category

(mathematics) Pertaining to topological spaces that are Cartesian closed categories.


permutizer

Given a finite group G, we introduce the \textit{permutability degree} of G, as Gwhere\mathcal{L}(G)isthesubgrouplatticeofGandP_G(X)thepermutizerofthesubgroupXinG,thatis,thesubgroupgeneratedbyallcyclicsubgroupsofGthatpermutewithX\in \mathcal{L}(G)$.

2015, Daniele Ettore Otera, Francesco G. Russo, “Permutability degrees of finite groups”, in arXiv:

(mathematics) A subgroup of all cyclic subgroups that permute with another


subdirect

We also show that the most general partially ordered plausibility calculus embeddable in a ring can be represented as a set of extended probability distributions or, in algebraic terms, is a subdirect sum of ordered fields.

2015, Stefan Arnborg, Gunnar Sjödin, “What is the plausibility of probability?(revised 2003, 2015)”, in arXiv:

(mathematics) Describing a subalgebra of a direct product


superquadratic

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In this paper, we construct the Rabinowitz-Floer homology for the coupled Dirac system \begin{equation*} \left\{ \begin{aligned} Du=\frac{\partial H}{\partial v}(x,u,v)\hspace{4mm} {\rm on} \hspace{2mm}M,\\ Dv=\frac{\partial H}{\partial u}(x,u,v)\hspace{4mm} {\rm on} \hspace{2mm}M, \end{aligned} \right. \end{equation*} where M is an n-dimensional compact Riemannian spin manifold, D is the Dirac operator on M, and H#58;#92;SigmaM#92;oplus#92;SigmaM#92;to#92;mathbb#123;R#125; is a real valued superquadratic function of class C¹ with subcritical growth rates.

2015, Wenmin Gong, Guangcun Lu, “Existence results for coupled Dirac systems via Rabinowitz-Floer theory”, in arXiv:

(mathematics) Describing an extension of a quadratic function related to the superellipsoid


ditopological

Actually a soft ditopological space is a soft set with two independent structures on it - a soft topology and a soft co-topology.

2015, Tugbahan Simsekler Dizman, Alexander Sostak, Saziye Yuksel, “Soft Ditopological Spaces”, in arXiv:


ditopology

(topology) A dichotomous topology; A topology that includes two structures: one describing the properties related to openness of sets, the other describing the properties related to closedness of sets.


equibipartite

Kettle, Tur\'{a}n Numbers of multiple and equibipartite forests, Combin.

2015, Long-Tu Yuan, Xiao-Dong Zhang, “The Turan Number of Disjoint Copies of Paths”, in arXiv:

(mathematics) Having vertices that can be divided into two equal independent sets


hyperinvariant

In this note we describe the lattice of hyperinvariant subspaces of V.

2015, Pudji Astuti, Harald K. Wimmer, “Hyperinvariant subspaces of locally nilpotent linear transformations”, in arXiv:

(mathematics) Invariant for any transformation that commutes with a specified endomorphism.


icosagrid

We call this quasicrystal the Fibonacci modified icosagrid quasicrystal.

2015, Fang Fang, Klee Irwin, “An Icosahedral Quasicrystal as a Golden Modification of the Icosagrid and its Connection to the E8 Lattice”, in arXiv:


isoperiodic

An isoperiodic plot shows the periods of different attractors in parameter space.

2008, Yin Shan, Applications of Complex Adaptive Systems, →ISBN:

In this paper we study the dynamics and topology of the isoperiodic foliation defined on the Hodge bundle over the moduli space of genus g#92;geq 2 curves.

2015, Gabriel Calsamiglia, Bertrand Deroin, Stefano Francaviglia, “A transfer principle: from periods to isoperiodic foliations”, in arXiv:


properad

If a properad #92;mathcalP is in addition equipped with a map from the properad governing Lie bialgebras (or graded versions thereof), then we define a notion of #92;mathcalP-graph complex, of stable #92;mathcalP-graph complex and a certain operad, that is in good cases an E#95;d operad.

2015, Sergei Merkulov, Thomas Willwacher, “Props of ribbon graphs, involutive Lie bialgebras and moduli spaces of curves”, in arXiv:


semiorthogonal

For del Pezzo surfaces of degree at least 5, we construct explicit semiorthogonal decompositions by subcategories of modules over semisimple algebras arising as endomorphism algebras of vector bundles and we show how to retrieve information about the index of the surface from Brauer classes and Chern classes associated to these vector bundles..

2015, Asher Auel, Marcello Bernardara, “Semiorthogonal decompositions and birational geometry of del Pezzo surfaces over arbitrary fields”, in arXiv:

(mathematics, category theory) Having the property that every subcategory is in the set of orthogonal subcategories of every higher order subcategory.

(mathematics, matrix algebra) Either columnwise orthogonal (having the property that M'M is an identity matrix) or rowwise orthogonal (having the property that MM' is an identity matrix).


subface

LL-Q1860 (eng)-Flame, not lame-subface.wav

At each iteration, our methods first identify a face of an orthant and then either perform an exact line search along the direction of the negative projected minimum-norm subgradient of the objective function or execute a CG subroutine that conducts a sequence of CG iterations until a CG iterate crosses the boundary of this face or an approximate minimizer of over this face or a subface is found.

2015, Zhaosong Lu, Xiaojun Chen, “Generalized Conjugate Gradient Methods for ℓ₁ Regularized Convex Quadratic Programming with Finite Convergence”, in arXiv:


subprop

Using a new prop of ribbon graphs and the fact that it contains the prop of involutive Lie bialgebras as a subprop we find new algebraic structures on the classical ribbon graph complex computing H#92;bullet(#92;mathcalM#95;#123;g,n#125;).

(mathematics) A prop (structure that supports a theory) that is part of another prop.


bilattice

We show that for a linear space of operators #123;#92;mathcalM#125;#92;subseteq#123;#92;mathcalB#125;(H#95;1,H#95;2) the following assertions are equivalent. (i) #123;#92;mathcalM#125; is reflexive in the sense of Loginov--Shulman. (ii) There exists an order-preserving map 1 on a bilattice Bil(#123;#92;mathcalM#125;) of subspaces determined by #123;#92;mathcalM#125;, with P#92;leq#92;psi#95;1(P,Q) and Q#92;leq#92;psi#95;2(P,Q), for any pair (P,Q)#92;inBil(#123;#92;mathcalM#125;), and such that an operator T#92;in#123;#92;mathcalB#125;(H#95;1,H#95;2) lies in #123;#92;mathcalM#125; if and only if #92;psi#95;2(P,Q)T#92;psi#95;1(P,Q)#61;0 for all (P,Q)#92;inBil(#123;#92;mathcalM#125;).

2015, Janko Bračič, Lina Oliveira, “A characterization of reflexive spaces of operators”, in arXiv:

(mathematics, computing) A structure B = (S,⊑₁ ,⊑₂) in which S is a non-empty set, and ⊑₁ and ⊑₂ are partial orderings each giving S the structure of a lattice, determining thus for each of the two lattices the corresponding operations of meet and join.


multicommutator

Our proof exploits the limited smoothness of the symbol of the multicommutator via a new multilinear multiplier theorem for symbols of restricted smoothness which lie locally in certain Sobolev spaces.

2015, Loukas Grafakos, Danqing He, Hanh Van Nguyen, Lixin Yan, “Multicommutators and Multiplier Theorems”, in arXiv:


pseudohermitian

This enables straightforward and explicit calculation of the pseudohermitian invariants of the embedding which are also CR invariant.

2015, Sean N. Curry, A. Rod Gover, “CR embedded submanifolds of CR manifolds”, in arXiv:

(mathematics) Having the Hermitian properties except that the eigenvalues may be complex and the eigenvectors need not be orthogonal.


subtorus

It is evident from the proof of Theorem 2 that the subtorus M is selected randomly and uniformly over the collection of all k-dimensional coordinate subtori.

2014, Bo'az Klartag, Emanuel Milman, Geometric Aspects of Functional Analysis: Israel Seminar (GAFA) 2011-2013, page 130:

(mathematics) A smaller torus-shaped structure within a larger torus.


pseudorepresentation

More generally, we prove that the structures of the Frobenius-semisimplifications of the Weyl modules attached to a collection of pure representations are rigid if these pure representations lift to Weil-Deligne representations over domains containing #92;mathcal#123;O#125; and the traces of these lifts are parametrized by a pseudorepresentation over #92;mathcal#123;O#125;..

2015, Jyoti Prakash Saha, “Variation of Weyl modules in p-adic families”, in arXiv:

(mathematics) Given a group G and a commutative ring R, a tuple of maps (a,d,x), where a,d:G→R and x:GxG→R, are a pseudorepresentation if they satisfy the relations one would expect if a(g) and d(g) were the diagonal entries of a two dimensional representation |a(g)b(g)|\|c(g)d(g)| and if x was given by x(g,g^′)=b(g)c(g^′).


subfan

The problem is motivated by the wish to compute tropical varieties over the p-adic numbers, which are the intersection of a subfan of a Gr\"obner fan as studied in this paper by some affine hyperplane, as shown in a forthcoming paper..

2015, Thomas Markwig, Yue Ren, “Gröbner Fans of x-homogeneous Ideals in Rt[x]”, in arXiv:

(mathematics) A subset of a fan (part of a tree).


Belyi's theorem

It is a result of G. V. Belyi, from 1979.

(mathematics) A theorem stating that any non-singular algebraic curve defined by algebraic number coefficients represents a compact Riemann surface which is a ramified covering of the Riemann sphere, ramified at three points only.


Perron's formula

(mathematics) A formula for calculating the sum of an arithmetical function by means of an inverse Mellin transform.


Mellin transform

Mellin transform (plural Mellin transforms)

Named after Finnish mathematician Hjalmar Mellin.

This chapter is concerned with the theory and applications of the Mellin transform. We derive the Mellin transform and its inverse from the complex Fourier transform. This is followed by several examples and the basic operational properties of Mellin transforms.

1995, Lokenath Debnath, Integral Transforms and Their Applications, CRC Press, page 211:

2005, Robb J. Muirhead, Aspects of Multivariate Statistical Theory, John Wiley & Sons, page 303,
If X is a positive random variable with density function f(x), the Mellin transform M(s) gives the (s-l)th moment of X. Hence Theorem 8.2.6 gives the Mellin transform of W evaluated at s=h+1; that is,
M(h+1)=E(Wʰ).
The inverse Mellin transform gives the density function of W.

In Chapters 2 and 7, the Mellin transform of the exponential function and the inverse Mellin transform of the Gamma function play key roles in demonstrating the equivalence of the modular relation and the functional equation. In proving the identities in this chapter, Mellin transforms also play central roles.

2008, Bruce C. Berndt, Marvin I. Knopp, Hecke's Theory of Modular Forms and Dirichlet Series, World Scientific, page 115:

mathematical analysis
mathematical analysis

(mathematical analysis, number theory, statistics) An integral transform that may be regarded as the multiplicative version of the two-sided Laplace transform.


Skewes' number

Named after South African mathematician Stanley Skewes.

(number theory) Any of several extremely large numbers used as upper bounds for the smallest natural number x for which π(x)> operatorname li(x), where π is the prime-counting function and li is the logarithmic integral function. These bounds have since been improved by others.


antidominant

We make use of the Orr-Shimozono formula for the nonsymmetric Macdonald polynomials in order to prove that the t#61;#92;infty specialization of the nonsymmetric Macdonald polynomials are equal to the characters of the generalized Weyl modules corresponding to the antidominant weights.

2015, Evgeny Feigin, Ievgen Makedonskyi, “Generalized Weyl modules, alcove paths and Macdonald polynomials”, in arXiv:

(mathematics) Having the property that all mappings yield a value no smaller than itself.


antidominance

(mathematics) The condition of being antidominant


bitrade

(mathematics) Either of two elements of a permutation group that trade places with each other.


covincular

In this paper we count the number of permutations simultaneously avoiding a vincular and a covincular pattern, both of length 3.

2015, Christian Bean, Anders Claesson, Henning Ulfarsson, “Simultaneous Avoidance of a Vincular and a Covincular Pattern of Length 3”, in arXiv:


graphex

We call the triple (I,S,W) a graphex, in analogy to graphons, which characterize the (dense) exchangeable graphs on #92;mathbb#123;N#125;.

2015, Victor Veitch, Daniel M. Roy, “The Class of Random Graphs Arising from Exchangeable Random Measures”, in arXiv:

(mathematics) A form of exchangeable graphon


propelinear

In the paper a classification of the propelinear structures on the Nordstrom-Robinson code is obtained and the question of extension of these structures to propelinear structures of the Hamming code, that contains the Nordstrom-Robinson code.

2015, I. Yu. Mogilnykh, “On the extention^([sic]) of propelinear structures of Nordstrom-Robinson code to Hamming code”, in arXiv:

(mathematics) A code C is propelinear if, for every codeword x in C, there exists a coordinate permutation Pₓ such that x + Pₓ (C) = C and, for any codewords x, y, z, and c in C, if x + Pₓ(y) = z, then P_z(c) is the composition of the permutations Pₓ and P_y(c).


versality

We consider families of curve-to-curve maps that have no singularities except those of genus 0 stable maps and that satisfy a versality condition at each singularity.

2015, Maxim Kazarian, Sergey Lando, Dimitri Zvonkine, “Universal cohomological expressions for singularities in families of genus 0 stable maps”, in arXiv:

(mathematics) The condition of being versal


secretary problem

secretary problem (plural secretary problems)

(probability theory) The problem of selecting the best out of n applicants for a position, under the condition that all applicants are interviewed in random order, the quality of the applicants is not known before interviewing, and once rejected an applicant cannot be recalled.


bihermitian

In a forthcoming paper, we use these algebroids to derive results about bihermitian manifolds, also known as generalized Kahler manifolds..

2015, Steven Gindi, “Algebroids and Twistor Spaces”, in arXiv:

(mathematics) Hermitian in x for every y and hermitian in y for every x.


endograph

Based on above results, we give characterizations of relatively compact sets, totally bounded sets and compact sets in (F#95;#123;USCB#125;(#92;mathbb#123;R#125;ᵐ),H#95;#123;#92;rmend#125;), where H#95;#123;#92;rmend#125; is the endograph metric.

2015, Huan Huang, “Characterizations of endograph metric and Γ-convergence on fuzzy sets spaces”, in arXiv:


hyperhamiltonian

We also discuss the properties of hyperhamiltonian dynamics in this respect..

052901 (26pp), Giuseppe Gaeta, Miguel Angel Rodriguez, “Canonical transformations for hyperkahler structures and hyperhamiltonian dynamics”, in J. Math. Phys., volume 052901:

(mathematics) Containing a closed circuit that visits one vertex exactly twice and all other vertices exactly once.


microformal

They act on oscillatory wave functions, whose algebra extends the algebra of formal power series in Planck's constant. In the classical limit, quantum microformal morphisms reproduce, as the main term of the asymptotic, the nonlinear pullbacks of functions with respect to `classical' microformal morphisms.

2015, Theodore Voronov, “Quantum microformal morphisms of supermanifolds: an explicit formula and further properties”, in arXiv:

(mathematics) "Thickened" using formal canonical relations between the cotangent bundles of smooth manifolds.


nonbidiagonal

We consider generic linear perturbations of a nonbidiagonal class of static black-hole solutions in massive (bi)gravity.

2015, Eugeny Babichev, Richard Brito, Paolo Pani, “Linear stability of nonbidiagonal black holes in massive gravity”, in arXiv:


prefundamental

This allows, in particular, to relate q-oscillator and prefundamental representations..

2015, H. Boos, F. Göhmann, A. Klümper, Kh. S. Nirov, A. V. Razumov, “Oscillator versus prefundamental representations”, in arXiv:

(mathematics) Given a group G that acts on a set P, a subset P is prefundamental for G if, for any g in G, gB is in B only if g is 1.


pseudoholomorphic

We set up an algebraic framework for the study of pseudoholomorphic discs bounding nonorientable Lagrangians, as well as equivariant extensions of such structures arising from a torus action. First, we define unital cyclic twisted A#95;#92;infty algebras and prove some basic results about them, including a homological perturbation lemma which allows one to construct minimal models of such algebras.

2015, Amitai Zernik, “Equivariant A-infinity algebras for nonorientable Lagrangians”, in arXiv:


semipositive

The purpose of this short note is to give a remark on the decomposition theorem for direct images of canonical sheaves tensorized with Nakano semipositive vector bundles.

2015, Taro Fujisawa, “A remark on the decomposition theorem for direct images of canonical sheaves tensorized with semipositive vector bundles”, in arXiv:

(mathematics) Having a dual that is nonnegative.

(mathematics) Having all elements nonnegative where at least one is positive.


unidenticality

Such a difference in lifetimes expresses the unidenticality of masses, energies and momenta of axial-vector photons of the different components.

2015, Rasulkhozha S. Sharafiddinov, “An Axial Vector Photon in a Mirror World”, in arXiv:

(mathematics) The condition of being unidentical


octilinear

As the problem of finding planar octilinear drawings of minimum number of bends is NP-hard, in this paper we focus on upper and lower bounds.

2015, Michael A. Bekos, Michael Kaufmann, Robert Krug, “On the Total Number of Bends for Planar Octilinear Drawings”, in arXiv:

(mathematics) Composed of horizontal, vertical and/or diagonal (45 degrees) line segments only


multideviation

In Part I, I introduce the multideviation framework and then use it to prove an important theorem: the Bell distributions can be generated from the set of joint distributions over all observables by deeming specific degrees of freedom unobservable.

2015, Brandon Fogel, “Multideviations: The hidden structure of Bell's theorems”, in arXiv:

(mathematics) A generalization of standard deviation to higher orders.

(statistics) A distance of more than two standard deviations from the mean.


multifractional

We propose a wavelet-based approach to construct consistent estimators of the pointwise H\"older exponent of a multifractional Brownian motion, in the case where this underlying process is not directly observed.

2015, Sixian Jin, Qidi Peng, Henry Schellhorn, “Estimation of the Pointwise Hölder Exponent of Hidden Multifractional Brownian Motion Using Wavelet Coefficients”, in arXiv:

(mathematics) Involving multiple fractions.


ambitoric

We use the methods of \cite{ambitoric2} to show that on a compact symplectic toric 4-orbifold with second Betti number equal to 2, K-polystability is also a sufficient condition for the existence of (toric) conformally K\"ahler, EM metrics, and the latter are explicitly described as ambitoric in the sense of \cite{ambitoric1}.

2015, Vestislav Apostolov, Gideon Maschler, “Conformally Kähler, Einstein-Maxwell Geometry”, in arXiv:

(mathematics) toric but having opposite orientations


biconservative

We give the complete classification of biconservative hypersurfaces with diagonalizable shape operator.

2015, Abhitosh Upadhyay, Nurettin Cenk Turgay, “Biconservative hypersurfaces in a pseudo-Euclidean spaces”, in arXiv:

(mathematics) Satisfying the equation A(grad H) = -H grad H for the mean curvature function H and the Weingarten operator A.


bivariational

For the latter case, the bivariational Lagrangian formulation becomes more than a convenient mathematical tool, since it facilitates a faster convergent perturbation series than the simpler energy expansion..

2015, Kasper Kristensen, Janus Juul Eriksen, Devin A. Matthews, Jeppe Olsen, Poul Jørgensen, “A view on coupled cluster perturbation theory using a bivariational Lagrangian formulation”, in arXiv:

(mathematics) Pertaining to interactions between functionals.


groundset

In this paper we consider the relation between the number of sparse paving matroids s(n,r) and the number of matroids m(n,r) on a fixed groundset of size n of fixed rank r.

2015, Rudi Pendavingh, Jorn van der Pol, “Enumerating matroids of fixed rank”, in arXiv:

(mathematics) A vector space upon which matroids may be paved


multidifferential

We extended this formulation to the multidifferential ones, and consider their infinite order jet prolongation.

2015, G. Sardanashvily, A. Zamyatin, “Deformation quantization on jet manifolds”, in arXiv:

(mathematics) Pertaining to any of various constructions based on multiple differential equations or operators.


pinscape

Besides measurement of the critical current density j#95;c and of creep rates S, the ac magnetic response provides valuable information on the pinscape which is different from that obtained through j#95;c or S, with the Campbell penetration depth #92;lambda#95;#123;#92;rm#92;scriptscriptstyleC#125; defining a characteristic quantity well accessible in an experiment.

2015, R. Willa, V. B. Geshkenbein, G. Blatter, “Probing the pinscape in type-II superconductors via Campbell penetration”, in arXiv:

(mathematics) A two-dimensional lattice.


pseudocollarable

Answering a question going back to Gromov, we show that, for an open, polyhedral contractible manifold M of dimension at least 6, the following conditions are equivalent: - M admits a geodesically complete CAT(0) metric; - M can be collapsed; - M is pseudocollarable. This yields many new contractible manifolds that admit CAT(0) metrics, and it shows that the CAT(0) property of a contractible manifold is purely determined by a condition at infinity, and shows that contractible manifolds of the Whitehead type can never admit a complete CAT(0) metric.

2015, Karim A. Adiprasito, Louis Funar, “Hyperbolicity of contractible manifolds”, in arXiv:

(mathematics) Such that there exists a neighborhood that is homeomorphic to a product, but this homeomorphism may not preserve all the desired structures or conditions that a true collar neighborhood would.


quasinilpotent

The particular case of algebra-valued circular elements is considered; as an application, the polar decomposition of the quasinilpotent DT-operator is described..

2015, March Boedihardjo, Ken Dykema, “Algebra-valued R-diagonal elements”, in arXiv:

(mathematics) Of a bounded operator over a Hilbert space, having a spectrum containing only 0.


superreflexivity

LL-Q1860 (eng)-Flame, not lame-superreflexivity.wav

Some results for these families of graphs are parallel to each other, for example superreflexivity of Banach spaces can be characterized both in terms of binary trees (Bourgain, 1986) and diamond graphs (Johnson-Schechtman, 2009).

2015, Siu Lam Leung, Sarah Nelson, Sofiya Ostrovska, Mikhail Ostrovskii, “Distortion of embeddings of binary trees into diamond graphs”, in arXiv:

(mathematics) The condition of being superreflexive


traciality

Also, a condition for traciality of a trace on B composed with the B-valued conditional expectation is given in terms of B-valued cumulants..

2015, Ken Dykema, “Canonical random variables for multivariate, algebra-valued distributions”, in arXiv:

(mathematics) The condition of being tracial


ultrahyperbolic

Ricci-flat metrics of the ultrahyperbolic signature which enjoy the l-conformal Galilei symmetry are constructed.

2015, D. Chernyavsky, A. Galajinsky, “Ricci-flat spacetimes with l-conformal Galilei symmetry”, in arXiv:

(mathematics) Pertaining to an ultrahyperbolic equation.


eigenstep

(mathematics) An iteration step whose size is related to an eigenvalue


semiconvex

We also prove the first quantitative estimates on convergence of the discrete gradient flow or "JKO scheme" outside of the semiconvex case.

2015, Katy Craig, “Nonconvex gradient flow in the Wasserstein metric and applications to constrained nonlocal interactions”, in arXiv:

(mathematics, of a function, f) Having the property that for every compact subset of the domain, there exists a constant C such that f(x) + ½C|x|² is convex on the subset.


cominuscule

We show how to reduce the nonlinear Wei-Norman equations, expressing the solution of a linear system of non-autonomous equations on a Lie algebra, to a hierarchy of matrix Riccati equations using the cominuscule induction.

2015, J. Gutt, S. Charzyński, M. Kuś, “Wei-Norman equations for classical groups via cominuscule induction”, in Differential Geometry and its Applications, volume 42:

(mathematics) Pertaining to an associated simple root that occurs with coefficient 1 in the highest root of a subgroup.


hyperexpansive

As a consequence hyperexpansive multiplication operators are investigated..

2015, Yousef Estaremi, “Unbounded weighted conditional type operators on L^p spaces”, in arXiv:

(mathematics) Pertaining to a class of operators closely related to the theory of negative definite functions on abelian semigroups.


plactic

We obtain as a corollary that plactic monoids for any semisimple Lie algebra satisfy homological finiteness properties..

2015, Nohra Hage, “Finite convergent presentations of plactic monoids for semisimple lie algebras”, in arXiv:

(mathematics) Based on all words in the alphabet of positive integers modulo Knuth equivalence.


subpower

Using a result of Dranishnikov and Smith we prove that, under some conditions, the asymptotic power dimension of a proper metric space coincides with the dimension of its subpower corona.

2015, Jacek Kucab, Michael Zarichnyi, “Remarks on asymptotic power dimension”, in arXiv:

(mathematics) A type of function such that for every exponent a, there is a small integer ε such that for any positive value x less than ε, its image lies between xᵃ and x⁻ᵃ .

(mathematics) A natural number x, with the property that x = bⁱy for some y that is not multiple of b.


contramodule

(mathematics) A contraderived category of module


quermassintegral

compound

German <i class="Latn mention" lang="de">Quermaße</i>


coquasitriangular

Our construction unifies quasitriangular and coquasitriangular Hom-Hopf algebras and Hom-Yetter-Drinfeld modules.

2015, Daowei Lu, “The braided monoidal structure on the category of Hom-type Doi-Hopf modules”, in arXiv:

(mathematics) dual to something quasitriangular.


microsupport

A greater number of elements may be detected by means of a thin pyrographite or glassy carbon microsupport (cross section 0.1-0.5 mm2), which is introduced into a high-temperature flame such as acetylene/nitrous oxide.

1978, American Laboratory - Volume 10, page 20:

This structure is in contrast to asymmetric membranes in which thin salt barrier is formed during gelation and consist of the same material as the underlying microsupport.

1980, Anthony Delyannis, E Delyannis, Proceedings of the 7th International Symposium on Fresh Water from the Sea.:

A salient feature of the approach is the assessment of the microsupport effect at the mostly sharp toe and root notches of the welded joints according to the Neuber microstructural support hypothesis.

1998, Dieter Radaj, Cetin Morris Sonsino, Fatigue Assessment of Welded Joints by Local Approaches, →ISBN, page 122:

The data reported here show that Dielectric spectroscopy can detect the uptake of serum proteins by the microsupport following the latter exposure to complete growth medium.

2013, R. E. Spier, J. B. Griffiths, W. Berthold, Animal Cell Technology: Products of Today, Prospects for Tomorrow, →ISBN:

(mathematics) Extremely localized structural support.

We show that many interesting spaces -- including all positroid strata and wild character varieties -- are moduli of constructible sheaves on a surface with microsupport in a Legendrian link.

2015, Vivek Shende, David Treumann, Harold Williams, Eric Zaslow, “Cluster varieties from Legendrian knots”, in arXiv:

(mathematics) A closed involutive cone in the cotangent bundle of codirections in which the cohomology of the object does not propagate.


polysymplectic

In our numerical experiments the polysymplectic integrator appears to be an order of magnitude more precise and approximately 2.5 times faster at long propagation times than the pseudo-spectral method..

2015, Monika E. Pietrzyk, Igor V. Kanatchikov, “On the Polysymplectic Integrator for the Short Pulse Equation”, in arXiv:


precanonical

We also argue that the normalizability of precanonical wave functions with respect to the scalar product, which involves an operator-valued invariant measure on the space of spin connection coefficients, leads to the quantum avoidance of curvature singularities.

2015, I.V. Kanatchikov, “On the "Spin-Connection Foam" Picture of Quantum Gravity from Precanonical Quantization”, in arXiv:

(mathematics) In raw form, before conversion to a canonical form.


prodiscrete

Since G can be viewed as a closed subgroup of the Tychonoff product of continuum many copies of the integers Z, this provides an example of a group described in the title, thereby answering Problem 11 from J.Galindo, L.Recorder-N\'{u}\~{n}ez, M.Tkachenko, Reflexivity of prodiscrete topological groups, J.

2015, Maria Vincenta Ferrer, Salvador Hernández, Dmitri Shakhmatov, “A countable free closed non-reflexive subgroup of Z^c”, in arXiv:

(mathematics) Isomorphic to the limit of a filtered projective system of discrete groups.


pseudolocality

LL-Q1860 (eng)-Flame, not lame-pseudolocality.wav

The result has two main consequences: First, it implies that singularities in Ricci flows with bounded scalar curvature have codimension #92;geq 4 and, second, it establishes a general form of the Hamilton-Tian Conjecture, which is even true in the Riemannian case. In the course of the proof, we will also establish the following results: L#123;plt;4#125; curvature bounds, integral bounds on the curvature radius, Gromov-Hausdorff closeness of time-slices, an #92;varepsilon-regularity theorem for Ricci flows and an improved backwards pseudolocality theorem..

2015, Richard H. Bamler, “Compactness properties of Ricci flows with bounded scalar curvature”, in arXiv:

(mathematics) The condition of being pseudolocal


coorbit

As special cases, this includes embeddings into Sobolev spaces of (homogeneous and inhomogeneous) Besov spaces, (#92;alpha)-modulation spaces, shearlet smoothness spaces and also of a large class of wavelet coorbit spaces, in particular of shearlet-type coorbit spaces. Precisely, we will show that under extremely mild assumptions on the covering #92;mathcal#123;Q#125;#61;#92;left(Q#95;#123;i#125;#92;right)#95;#123;i#92;inI#125;, we have #92;mathcal#123;D#125;#92;left(#92;mathcal#123;Q#125;,L#123;p#125;,Y#92;right)#92;hookrightarrowW#123;k,q#125;(#92;mathbb#123;R#125;#123;d#125;) as soon as p#92;leqq and Y#92;hookrightarrow#92;ell#95;#123;u#123;#92;left(k,p,q#92;right)

2016, Felix Voigtlaender, “Embeddings of Decomposition Spaces into Sobolev and BV Spaces”, in arXiv:

(mathematics, physics) The dual of an orbit


diagonalness

We show how a fully diagonal interaction at the similarity cutoff #92;lambda#92;rightarrow 0 may be obtained from the eigenvalues of the hamiltonian and quantify the diagonalness by means of operator norms.

2016, E. Ruiz Arriola, S. Szpigel, V. S. Timoteo, “Fixed points of the SRG evolution and the on-shell limit of the nuclear force”, in arXiv:

(mathematics) The condition of being diagonal


pluriharmonic

The transformation law of the Q-prime curvature under scaling is given in terms of a differential operator, called the P-prime operator, acting on the space of CR pluriharmonic functions.

2016, Yuya Takeuchi, “Q-prime curvature and scattering theory on strictly pseudoconvex domains”, in arXiv:

(mathematics) Locally the real part of a holomorphic function of several complex variables.


pseudocontractive

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In this paper, we propose two novel parallel hybrid methods for finding a common element of the set of solutions of a finite family of generalized equilibrium problems for monotone bifunctions #92;left#92;#123;f#95;i#92;right#92;#125;#95;#123;i#61;1#125;ᴺ and #92;alpha - inverse strongly monotone operators #92;left#92;#123;A#95;i#92;right#92;#125;#95;#123;i#61;1#125;ᴺ and the set of common fixed points of a finite family of (asymptotically) #92;kappa- strictly pseudocontractive mappings #92;left#92;#123;S#95;j#92;right#92;#125;#95;#123;j#61;1#125;ᴹ in Hilbert spaces.

2016, Dang Van Hieu, “Parallel hybrid methods for generalized equilibrium problems and asymptotically strictly pseudocontractive mappings”, in arXiv:

(mathematics) Satisfying the equation ||Tx - Ty|| <= ||x - y|| - α * ||x - y||² where T is the mapping that is pseudocontractive, x and y are points in the metric space, ||.|| denotes the norm in the metric space, and α is a constant.


kilopixel

NIKA2 (New IRAM KID Array 2) is a camera dedicated to millimeter wave astronomy based upon kilopixel arrays of Kinetic Inductance Detectors (KID).

2016, M. Calvo, A. Benoit, A. Catalano, J. Goupy, A. Monfardini, N. Ponthieu, E. Barria, G. Bres, M. Grollier, G. Garde, J.-P. Leggeri, G. Pont, S. Triqueneaux, R. Adam, O. Bourrion, J.-F. Macías-Pérez, M. Rebolo, A. Ritacco, J.-P. Scordilis, D. Tourres, C. Vescovi, F.-X. Désert, A. Adane, G. Coiffard, S. Leclercq, S. Doyle, P. Mauskopf, C. Tucker, P. Ade, P. André, A. Beelen, B. Belier, A. Bideaud, N. Billot, B. Comis, A. D'Addabbo, C. Kramer, J. Martino, F. Mayet, F. Pajot, E. Pascale, L. Perotto, V. Revéret, L. Rodriguez, G. Savini, K. Schuster, A. Sievers, R. Zylka, “The NIKA2 instrument, a dual-band kilopixel KID array for millimetric astronomy”, in arXiv:


letterplace

We investigate resolutions of letterplace ideals of posets.

2016, Alessio D'Ali, Gunnar Fløystad, Amin Nematbakhsh, “Resolutions of letterplace ideals of posets”, in arXiv:

(mathematics) The occurrence of a letter at a specific place; a pair of values that includes one letter and one place.


metrize

en-verb

metrize (third-person singular simple present metrizes, present participle metrizing, simple past and past participle metrized)

metrizes (present singular third-person)
metrizing (participle present)
metrized (participle past)
metrized (past)

(mathematics) To associate with an appropriate metric space.


multistack

We show that the Hartmanis--Stearns problem can be solved in a satisfactory way for the class of multistack machines.

2016, Boris Adamczewski, Julien Cassaigne, Marion Le Gonidec, “On the computational complexity of algebraic numbers: the Hartmanis--Stearns problem revisited”, in arXiv:

(mathematics, computing) Employing multiple stacks


permutahedral

This result stems from high-dimensional lattice geometry and exploits properties of the permutahedral lattice, a well-studied structure in discrete geometry. Building on the same geometric concept, we also present a lower bound result on the size of an approximate filtration: we construct a point set for which every (1#43;#92;epsilon)-approximation of the \v{C}ech filtration has to contain n#123;#92;Omega(#92;log#92;logn)#125; features, provided that #92;epsilonlt;#92;frac#123;1#125;#123;#92;log#123;1#43;c#125;n#125; for c#92;in(0,1)..

2016, Aruni Choudhary, Michael Kerber, Sharath Raghvendra, “Polynomial-Sized Topological Approximations Using The Permutahedron”, in arXiv:

(mathematics) Relating to a permutahedron


predimension

We also demonstrate how Hrushovski's predimension arises in this general context as a natural geometric notion and use it as one of our main tools..

2016, Boris Zilber, “Analytic Zariski structures and non-elementary categoricity”, in arXiv:

(mathematics) The result of a function on a group of sets, where the function satisfies three conditions: (1) it returns 0 for the empty set; (2) if one set is contained in another set, the function always returns a value that is less than or equal to the result for the containing set; (3) the result for the union of two sets is less than or equal to the sum of the results for each of those sets individually minus the result for their intersection.


quasifinite

We give a sufficient condition under which the moduli space of morphisms between logarithmic schemes is quasifinite under the moduli space of morphisms between the underlying schemes.

2016, Jonathan Wise, “Uniqueness of minimal morphisms of logarithmic schemes”, in arXiv:


semivalue

(game theory) A function on a vector space of all coalitional games which verifies linearity, anonymity, positivity, and inessential games.


superregular

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Given a a times b, a larger than or equal to b, superregular matrix over a field, we show that if all of its rows are nonzero then any linear combination of its columns, with nonzero coefficients, has at least a-b+1 nonzero entries.

2016, P. J. Almeida, D. Napp, R. Pinto, “Superregular matrices and applications to convolutional codes”, in arXiv:


pseudoanalytical

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We use the method of pseudoanalytical continuation to obtain the characterization of these spaces in terms of polynomial approximations.

2016, Alexander Rotkevich, “Constructive description of Hardy-Sobolev spaces in ℂⁿ”, in arXiv:

(mathematics) Relying on simplifying assumptions in order to create a less complex alternative to a full analytical approach.


superconic

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Moreover, the superconic curves are represented in explicit form while Greynolds' superconic curves are in implicit form..

2016, Sunggoo Cho, “Explicit Superconic Curves”, in arXiv:

(mathematics) Describing any of several extensions of conic curves and equations


supernumber

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Modular arithmetic considerations on the calendar supernumber give the position of the Calendar Round at the Mayan origin of time, the Long Count Calendar date 0.0.0.0.0 4 Ahau 8 Cumku.

2016, Thomas Chanier, “Solution of the Mayan Calendar Enigma”, in arXiv:

(mathematics) A generalization of a complex number in a commutative superalgebra


bispanning

And for all remaining bispanning graphs, we prove a composition method at a vertex of degree three, wherein the unique exchange graph is constructed from the exchange graphs of three reduced bispanning graphs.

2016, Timo Bingmann, “On the Structure of the Graph of Unique Symmetric Base Exchanges of Bispanning Graphs”, in arXiv:

(mathematics) Having a partition of the edge set into two spanning trees.


quasitrace

Our results are achieved through applications of the techniques developed in \cite{BR} and \cite{R}. We also note that, whenever the first Conjecture holds for some unital A and extreme boundary of the the^([sic]) quasitrace simplex of A is finite, then every dimension function of A is lower semicontinuous and DF(A) is affinely homeomorphic to the quasitrace simplex of A.

2016, Kaushika De Silva, “A note on two Conjectures on Dimension funcitons of C^*-algebras”, in arXiv:


superslice

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The Kinoshita-Terasaka knot K_(KT), illustrated in Fig. 1 is the first example of a superslice, which has been know at latest in 1970 by R.H. Fox, F. Hosokawa, T. Yangawa and others.

2012, M.E. Bozhüyük, Topics in Knot Theory, →ISBN, page 69:

(mathematics) A knot for which there is an almost identical trivial knot.


superslice

Answering a question of Livingston-Meier, we find smoothly slice (in fact doubly slice) knots in the 3-sphere with Alexander polynomial equal to 1 that are not smoothly superslice..

2016, Daniel Ruberman, “On smoothly superslice knots”, in arXiv:

(mathematics, of a knot) Having the property of being a superslice.


stevedore's knot

en-noun

stevedore's knot (plural stevedore's knots)

(mathematics) A knot made from a single loop that crosses itself three times


toroidalization

Unlike Ax-Kochen's proof, ours does not use any notions from mathematical logic and is based on weak toroidalization of morphisms.

2016, Jan Denef, “Geometric proofs of theorems of Ax-Kochen and Ersov”, in arXiv:

(mathematics) Conversion to toroidal form


bimeromorphic

This implies that every K\"ahler threefold of Kodaira dimension zero admits an algebraic approximation after a suitable bimeromorphic modification.

2016, Patrick Graf, “Algebraic approximation of Kähler threefolds of Kodaira dimension zero”, in arXiv:

(mathematics) Isomorphic outside thin analytic sets.


cosymplectic

Several examples are given and classification results are obtained in dimension five for cosymplectic, K-cosymplectic and coK\"ahler Lie algebras..

2016, Giovanni Calvaruso, Antonella Perrone, “Cosymplectic and α-cosymplectic Lie algebras”, in arXiv:

(mathematics) Symplectic and having a closed contact form as well.


multihomogenous

We refine and extend quantitative bounds, on the fraction of nonnegative polynomials that are sums of squares, to the multihomogenous case.

2016, Alperen Ergur, “Multihomogenous Nonnegative Polynomials and Sums of Squares”, in arXiv:

(mathematics) Pertaining to a sum of terms whose monomials all have the same multidegree


quasibialgebra

We prove the existence of a quasi-Coxeter, quasitriangular quasibialgebra structure on the enveloping algebra of g, which binds the quasi-Coxeter structure underlying the Casimir connection of g and the quasitriangular quasibialgebra one underlying its KZ equations.

2016, Valerio Toledano-Laredo, “Quasi-Coxeter quasitriangular quasibialgebras and the Casimir connection”, in arXiv:

(mathematics) A generalization of a bialgebra that allows for a weaker form of coassociativity.


semiabelian

The second theorem establishes the finiteness of III^{2}(F,G) for a certain class of semiabelian varieties G over a global field F..

2016, Cristian D. Gonzalez-Aviles, “On Tate-Shafarevich groups of 1-motives”, in arXiv:


superhomogeneous

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eikonalization

eikonalization (countable and uncountable, plural eikonalizations)

We derive an explicit rule for when eikonalization is valid, and provide a direct connection to the picture of multiple Wilson lines crossing a shockwave.

2016, Ira Z. Rothstein, Iain W. Stewart, “An Effective Field Theory for Forward Scattering and Factorization Violation”, in arXiv:

(mathematics) conversion to eikonal form


subfractal

We find that the zeros of the lower and upper topological pressure functions are lower and upper bounds, respectively, for the Hausdorff, packing, lower and upper box dimensions of the subfractal..

2016, Elizabeth Sattler, “Fractal dimensions of subfractals induced by sofic subshifts”, in arXiv:


substack

In particular, we give necessary and sufficient conditions for the existence of Poincar\'e bundles over the universal curve of an open substack of the rigidification, generalizing a result of Mestrano-Ramanan..

2016, Roberto Fringuelli, “The Picard group of the universal moduli space of vector bundles over ̄ℳ_g”, in arXiv:


pseudomonoid

(mathematics) A structure similar to a monoid that supports associativity and an identity element, but does not include all the constraints that are required to qualify as a monoid.


quasicentroid

The main results are: for all 3-Lie algebra A, 1) the generalized derivation algebra GDer(A) is the sum of quasiderivation algebra QDer(A) and quasicentroid Q#92;Gamma(A); 2) quasiderivations of A can be embedded as derivations in a larger algebra; 3) quasiderivation algebra QDer(A) normalizer quasicentroid, that is, #91;QDer(A),Q#92;Gamma(A)#93;#92;subseteqQ#92;Gamma(A); 4) if A contains a maximal diagonalized tours T, then QDer(A) and Q#92;Gamma(A) are diagonalized T-modules, that is, as T-modules, (T,T) semi-simplely acts on QDer(A) and Q#92;Gamma(A), respectively..

2016, Ruipu Bai, Qiyong Li, Kai Zhang, “Generalized derivations of 3-Lie algebras”, in arXiv:


biquotient

An infinite family of six-dimensional simply connected biquotients whose second Betti number is three, different from Totaro's biquotients, is considered and it is proved that none of biquotient from this family is geometrically formal..

2016, Svjetlana Terzic, “Geometric formality of rationally elliptic manifolds in small dimensions”, in Glasnik of the Section of Natural Sciences, volume Montenegrin Academy of:

(mathematics) The base space of a principal bundle with a homogeneous space as total space.


coamoeba

Our results include an explicit description of the space of coamoebas, a relation between connected components of the coamoeba complement and critical points of the polynomial, an upper bound on the area of a planar coamoeba, and a recovered bound on the number of positive solutions of a fewnomial system..

2016, Jens Forsgård, “Coamoebas of polynomials supported on circuits”, in arXiv:

(mathematics) The graph of the real part of the logarithms of a polynomial equation under the argument mapping.


treeable

(mathematics) That can be represented as a tree (graph)


assosymmetric

We prove that assosymmetric algebras under Jordan product are Lie triple.

2016, A.S. Dzhumadil'daev, “Assosymmetric algebras under jordan product”, in arXiv:

(mathematics) (more or less) associative and also symmetric


centroaffine

In fact the curve is generated by a chain structure, and depending on this chain structure, we could study some geometric properties for a space centroaffine discrete curve in #92;R³ by the centroaffine curvatures and torsion..

2016, Yun Yang, “The Frenet-Serret formulas of a discrete centroaffine curve”, in arXiv:

(mathematics) Relating to the centre of an affine space


gyroaddition

From this we prove the structure theorem that every transitive action of a gyrogroup can be realized as a gyrogroup action by left gyroaddition.

2016, Teerapong Suksumran, “Gyrogroup actions: A generalization of group actions”, in arXiv:

(mathematics) A gyrovector space addition.


hypoplactic

Finally, the quasi-crystal structure is applied to prove some new results about the hypoplactic monoid..

2016, Alan J. Cain, António Malheiro, “Crystallizing the hypoplactic monoid: from quasi-Kashiwara operators to the Robinson--Schensted-type correspondence for quasi-ribbon tableaux”, in arXiv:

(mathematics) Analogous to plactic, generalized to the theory of noncommutative symmetric functions.


quadriculated

We consider the problem of counting and classifying domino tilings of a quadriculated torus.

2016, Fillipo Impellizieri, “Domino Tilings of the Torus”, in arXiv:

(mathematics) covered with a checkerboard pattern


subgyrogroup

We then prove that under a certain condition, a gyrogroup G acts transitively on the set G#47;H of left cosets of a subgyrogroup H in G in a natural way.

(mathematics) A subset of a gyrogroup that satisfies the gyrogroup axioms.


autotopism

This includes {determining} when two such semifields are isotopic and the order of the autotopism group..

2016, Daniele Bartoli, Jurgen Bierbrauer, Gohar Kyureghyan, Massimo Giulietti, Stefano Marcugini, Fernanda Pambianco, “A family of semifields in characteristic 2”, in arXiv:

(mathematics) A full group fixing any ordered pair of components of the spread of a vector space over a prime field.


nefness

We also get some general results under nefness and relative semi-ampleness assumptions..

2016, Lei Zhang, “Subadditivity of Kodaira dimensions for fibrations from minimal models to projective varieties of general type”, in arXiv:

(algebraic geometry) The quality of being nef.


semiampleness

(algebraic geometry) The quality of being semiample.


semiample

(algebraic geometry) Having a positive multiple that is generated by global sections.


negative binomial distribution

negative binomial distribution (plural negative binomial distributions)

negative binomial distributions (plural)

(statistics) A discrete probability distribution of the number of successes in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of failures (denoted r) occurs.


bitensor

This requires a careful analysis of how changes of the spin supplementary condition are related to shifts of the body's representative worldline and transformations of the body's multipole moments, and we employ bitensor calculus for a precise framing of this analysis.

2016, Justin Vines, Daniela Kunst, Jan Steinhoff, Tanja Hinderer, “Canonical Hamiltonian for an extended test body in curved spacetime: To quadratic order in spin”, in arXiv:

(mathematics) A tensorial function of pairs of points.


paracomposition

To obtain this result, we establish global, quantitative results for the paracomposition theory of Alinhac..

2016, Quang-Huy Nguyen, “A sharp Cauchy theory for the 2D gravity-capillary waves”, in arXiv:

(mathematics) An extension of the paralinearization of non-smooth functions, used to flatten pairs of surfaces by changing variables.


superunitary

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We then deduce the description of the generalized superunitary dual of Heisenberg groups. As applications, we build the group Fourier transformation on Heisenberg supergroups, prove the associated Parseval theorem, and construct Metaplectic representations..

2016, Axel de Goursac, Jean-Philippe Michel, “Superunitary Representations of Heisenberg Supergroups”, in arXiv:


conharmonically

Secondly, we study conditions for (T#123;#92;ast#125;M,#123;#125;#92;bar#123;g#125;#95;#123;#92;nabla,c#125;) to be semi-symmetric, Ricci semi-symmetric, #92;widetilde#123;Z#125; semi-symmetric or locally conharmonically flat with respect to the metric connection #37;#92;widetilde#123;#92;nabla#125;.

2016, Lokman Bilen, Aydin Gezer, “On metric connections with torsion on the cotangent bundle with modified Riemannian extension”, in arXiv:


quasianalytical

Here, we present the theory for UDG-FEM forward modeling, its validation using quasianalytical solutions in multi-layer sphere models and an evaluation of the new method in a comparison with a discontinuous Galerkin (DG-FEM) method on hexahedral and on conforming tetrahedral meshes.

2016, Andreas Nüßing, Carsten H. Wolters, Heinrich Brinck, Christian Engwer, “The Unfitted Discontinuous Galerkin Method for Solving the EEG Forward Problem”, in arXiv:


subprincipal

Then we prove the well-posedness of the Cauchy problem in all Gevrey classes assuming, on the double characteristic manifold, that the ratio of the imaginary part of the subprincipal symbol to the real eigenvalue of the Hamilton map is bounded and that the sum of the real part of the subprincipal symbol and the modulus of the imaginary eigenvalue of the Hamilton map is strictly positive..

2016, Tatsuo Nishitani, “On the Cauchy problem for differential operators with double characteristics, transition from effective to non-effective characteristics”, in arXiv:


cohomologous

Let (X,#92;omega) be a compact K\"ahler manifold and #92;mathcalH the space of K\"ahler metrics cohomologous to #92;omega.

2016, Robert J. Berman, Tamás Darvas, Chinh H. Lu, “Regularity of weak minimizers of the K-energy and applications to properness and K-stability”, in arXiv:

(mathematics) Relating to, or part of a cohomology


cosection

Provided #92;mathcal#123;R#125; admits a cosection cutting out a 1-dimensional subscheme, we prove that the generating function of these Euler characteristics is equal to M(q)#123;2e(X)#125; times a polynomial of degree c#95;3(#92;mathcal#123;R#125;).

2016, M. Kool, A. Gholampour, “Rank 2 wall-crossing and the Serre correspondence”, in arXiv:

(mathematics) The left inverse of a morphism.


gyroaverage

The gyroaverage operator has been reformulated and is now expressed as a matrix-vector product and a cache-friendly algorithm has been setup.

2016, F Rozar, C Steiner, G Latu, M Mehrenberger, V Grandgirard, Julien Bigot, T Cartier-Michaud, Jean Roman, “Optilization of the gyroaverage operator based on hermite interpolation”, in arXiv:

(mathematics) The average over a gyroperiod; a gyrophase average.


gyroaverage

en-verb

gyroaverage (third-person singular simple present gyroaverages, present participle gyroaveraging, simple past and past participle gyroaveraged)

gyroaverages (present singular third-person)
gyroaveraging (participle present)
gyroaveraged (participle past)
gyroaveraged (past)

The difference being that Eq. (5.9) is discrete and we cannot gyroaverage over the phase.

1990, Scott Edward Parker, Particle Simulation of Bounded Plasmas with a Wide Range of Space and Time Scales:

(mathematics) To calculate the gyroaverage.


semistationary

These solutions can in turn estimate so called volatility modulated Volterra (VMV) processes and L\'{e}vy semistationary (LSS) processes, which is a class of processes that have been employed to model turbulence, tumor growth and electricity forward and spot prices.

2016, Fred Espen Benth, Heidar Eyjolfsson, “Simulation of volatility modulated Volterra processes using hyperbolic stochastic partial differential equations”, in Bernoulli, volume 22, pages 774–793:

(mathematics) Having the same properties over time, although possibly showing different behavior in stability intervals.


proregular

Then adic reduction to the diagonal holds: A#92;otimes#123;L#125;#95;#123;A#92;hat#123;#92;otimes#125;#123;L#125;#95;#123;K#125;A#125;(M#92;hat#123;#92;otimes#125;#123;L#125;#95;#123;K#125;N)#92;congM#92;otimes#123;L#125;#95;AN. (2) Let A be a commutative ring, let a#92;subseteqA be a weakly proregular ideal, let M be an A-module, and assume that the a-adic completion of A is noetherian (if A is noetherian, all these conditions are always satisfied).

2016, Liran Shaul, “Adic reduction to the diagonal and a relation between cofiniteness and derived completion”, in arXiv:

(mathematics) Having the property that the inverse systems of the Koszul cohomology modules satisfy the Inverse limit#Mittag-Leffler condition.)


bitslice

We represent these vectors in bitslice format.

2016, Shixiong Xu, David Gregg, “Customizable Precision of Floating-Point Arithmetic with Bitslice Vector Types”, in arXiv:

(mathematics, computing) Alternative form of bit slice


bit slice

(mathematics, computing) Any of a group of variable-length words that may be combined to form computable lengths of bits of any length


idempotented

In particular, we obtain a new and geometric construction of the idempotented quantum affine #92;mathfrak#123;gl#125; and its canonical basis..

2016, Zhaobing Fan, Chun-Ju Lai, Yiqiang Li, Li Luo, Weiqiang Wang, “Affine flag varieties and quantum symmetric pairs”, in arXiv:


perfectoid

(mathematics) Of a field: being a complete topological field whose topology is induced by a nondiscrete valuation of rank 1.

Our method is based on the theory of perfectoid spaces introduced by P.

2016, Junyi Xie, “The dynamical Manin-Mumford conjecture for periodic points of lifts of Frobenius”, in arXiv:

(mathematics) Composed of perfectoid fields.


polytorus

(mathematics) The set of all vectors of a given dimension such that each element of the vector is within a radius r of the corresponding element of a central vector.


schemoid

We also apply the main result to a schemoid constructed from a Hamming scheme..

2016, Yasuhide Numata, “On functors between categories with colored morphisms”, in arXiv:

(category theory) A generalization of an association scheme from the point of view of small categories.


subsemiring

The following dichotomy is shown: If a finite semiring is such that (i) the multiplicative semigroup is solvable and (ii) it does not contain a subsemiring with an additive identity 0 and a multiplicative identity 1#92;neq 0, then the circuit evaluation problem for the semiring is in #92;mathsf#123;DET#125;#92;subseteq#92;mathsf#123;NC#125;².

2016, Moses Ganardi, Danny Hucke, Daniel König, Markus Lohrey, “Circuit Evaluation for Finite Semirings”, in arXiv:

(mathematics) A subset of a semiring that is also a semiring under the same operations as the original semiring.


superdialgebra

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We complete the problem of finding the universal central extension in the category of Leibniz superalgebras of #92;mathfrak#123;sl#125;(m,n,D) when m#43;n#92;geq 3 and D is a superdialgebra, solving in particular the problem when D is an associative algebra, superalgebra or dialgebra.

2016, Xabier García-Martínez, Manuel Ladra, “Universal central extensions of superdialgebras of matrices”, in arXiv:


permuton

Introduced by Carlos Hoppen, Yoshiharu Kohayakawa, Carlos Gustavo Moreira, Balázs Ráth and Rudini Menezes Sampaio in their 2011 paper, "Limits of permutation sequences", with the name "limit permutation".
The term "permuton" was coined by Roman Glebov, Andrzej Grzesik, Tereza Klimošová and Daniel Kráľ in their 2013 paper, "Finitely forcible graphons and permutons", from permute, to resemble graphon.

In the recent terminology of permutons, our work can be interpreted as the convergence of uniform random separable permutations towards a "Brownian separable permuton"..

2016, Frédérique Bassino, Mathilde Bouvel, Valentin Féray, Lucas Gerin, Adeline Pierrot, “The Brownian limit of separable permutations”, in arXiv:

(mathematics, physics) A probability measure Φ on the σ-algebra of Borel sets of the unit square [0,1]² such that Φ has uniform marginals (that is, Φ ([α, β] × [0,1]) = Φ ([0,1] × [α, β]) = β − α for every 0 ≤ α ≤ β ≤ 1).


selfconjugate

Interestingly, some of the solutions are not selfconjugate, which puts the model in sharp contrast to one of the model's limiting cases, the Heisenberg xxx spin chain.

2016, Rob Klabbers, “Thermodynamics of Inozemtsev's Elliptic Spin Chain”, in arXiv:

(mathematics, physics) Alternative form of self-conjugate


cocyclic

In this paper we show that to a unital associative algebra object (resp. co-unital co-associative co-algebra object) of any abelian monoidal category C endowed with a symmetric 2-trace one can attach a cyclic (resp. cocyclic) module, and therefore speak of the (co)cyclic homology of the (co)algebra "with coefficients in the trace".

2016, Mohammad Hassanzadeh, Masoud Khalkhali, Ilya Shapiro, “Monoidal Categories, 2-Traces, and Cyclic Cohomology”, in arXiv:


hyperarchimedean

(mathematics) Having all its homomorphic images be Archimedean.


hypercuboid

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(geometry) An analog of a cuboid in four or more dimensions

nadkvádr

analogue of a cuboid in four or more dimensions


quasihyperarchimedian

Reemplacing {0} with the whole ideal of infinitesimals yields a weaker notion of archimedian element that we call "quasiarchimedian", and characterize quasihyperarchimedian MV-algebras (which are in a sense non semisimple hyperarchimedian algebras) as those algebras with compact maximal spectrum.

2016, Eduardo J. Dubuc, Jorge Zilber, “Some remarks on infinitesimals in MV-algebras”, in arXiv:


nonbetweenness

The nonbetweenness function nbet(n) is the minimum number of total orderings such that for any three distinct objects a, b and c, there is an ordering in which b is not between a and c.

2016, Ross Atkins, “Betweenness and Nonbetweenness”, in arXiv:

(mathematics) The condition of not being between two other objects (in position or value)


pseudodimension

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Our algorithms rely on random sampling and their analysis leverages on Rademacher averages and pseudodimension, fundamental concepts from statistical learning theory.

2016, Matteo Riondato, Eli Upfal, “ABRA: Approximating Betweenness Centrality in Static and Dynamic Graphs with Rademacher Averages”, in arXiv:

(mathematics) The largest cardinality (or infinite) of a set of points (in a function class) that can be shattered.


semiarc

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subpacking

For a library of polyominoes of consisting only of polyominoes of the form 1#92;timesk, we give an upper bound on the the^([sic]) number which m must exceed to ensure a subpacking always exists..

2016, Jacob Turner, “On Subpackings of Polyomino Packings”, in arXiv:


ultrahomogeneous

We show that if #92;Gamma is ultrahomogeneous, then #92;operatorname#123;Aut#125;(#92;Gamma) has 2-generated dense subgroups, and that under certain conditions given f#92;in#92;operatorname#123;Aut#125;(#92;Gamma) there exists g#92;in#92;operatorname#123;Aut#125;(#92;Gamma) such that the subgroup generated by f and g is dense.

2016, J. Jonušas, J. D. Mitchell, “Topological 2-generation of automorphism groups of countable ultrahomogeneous graphs”, in arXiv:

(mathematics) Such that every isomorphism between finitely generated substructures extends to an automorphism of itself.


eigencomponent

(mathematics) A component of an eigenvector


quasiprimitive

In this paper we study the structure of quasiprimitive and biquasiprimitive 2'-elusive permutation groups, extending earlier work of Giudici and Xu on elusive groups.

2016, Timothy C. Burness, Michael Giudici, “Permutation groups and derangements of odd prime order”, in arXiv:


anafunctor

(mathematics) A generalized functor that does not employ the axiom of choice


disintegrability

Then a topological characterization of the subclasses of extensions satisfying the further properties of full disintegrability and full strong conglomerability is given and their envelopes are studied..

2016, Davide Petturiti, Barbara Vantaggi, “Envelopes of conditional probabilities extending a strategy and a prior probability”, in arXiv:

(topology) The condition of being disintegrable


nebentypus

For K an imaginary quadratic field with discriminant -D#95;K and associated quadratic Galois character #92;chi#95;K, Kojima, Gritsenko and Krieg studied a Hermitian Maass lift of elliptic modular cusp forms of level D#95;K and nebentypus #92;chi#95;K via Hermitian Jacobi forms to Hermitian modular forms of level one for the unitary group U(2,2) split over K.

2016, Tobias Berger, Krzysztof Klosin, “A p-adic Hermitian Maass lift”, in arXiv:

(mathematics) The character χ, as applied to a modular form.


quasilocally

Energy is at best defined quasilocally in general relativity.

2016, Nezihe Uzun, “Quasilocal energy exchange and the null cone”, in arXiv:


ribbonlength

We end the paper with a discussion of projection stick number and ribbonlength..

2016, Elizabeth Denne, Mary Kamp, Rebecca Terry, Xichen, “Ribbonlength of folded ribbon unknots in the plane”, in arXiv:

(mathematics) The length of a ribbon (in a ribbon knot)


ballean

Unknown. Perhaps a blend of ball + Boolean.

We show that each cellular ordinal ballean can be represented as a #92;gamma-comb.

2016, I.V. Protasov, K.D. Protasova, “The comb-like representations of cellular ordinal balleans”, in arXiv:

(mathematics) The asymptotical counterpart of a ball (inside surface of a sphere)


overpartition

Recently, Shen studied the arithmetic properties of #92;ell-regular overpartition function #92;overline#123;A#125;#95;#92;ell(n), which counts the number of overpartitions of n into parts not divisible by #92;ell.

2016, Shane Chern, “Remarks on ℓ-regular overpartitions”, in arXiv:

(mathematics) An overpartition of n is a non-increasing sequence of natural numbers whose sum is n in which the first occurrence of a number may be overlined.


submarkovian

A result by Liskevich and Perelmuter from 1995 yields the optimal angle of analyticity for symmetric submarkovian semigroups on L#95;p, 1lt;plt;#92;infty.

2016, Markus Haase, Peer Christian Kunstmann, Hendrik Vogt, “On the numerical range of generators of symmetric L_∞-contractive semigroups”, in arXiv:


submultiplicative

The partition functions of these models may satisfy a variety of super- or submultiplicative inequalities, and these may be reduced to a subadditive relation by taking logarithms, and changing signs, if necessary.

2016, EJ Janse van Rensburg, “Subadditivity in models of interacting lattice clusters”, in arXiv:

(mathematics) Having the property ‖AB‖≤‖A‖‖B‖


supermultiplicative

In this manuscript, the function p#95;n#92;#35;(m) into #92;mathbbN, with (n,m)#92;in#123;#92;mathbbN#125;², is assumed to satisfy the supermultiplicative inequality p#95;#123;n#95;1#125;#92;#35;(m#95;1)p#95;#123;n#95;2#125;#92;#35;(m#95;2)#92;leqp#95;#123;n#95;1#43;n#95;2#125;#92;#35;(m#95;1#43;m#95;2).


microergodic

Then consistency and asymptotic distribution for the microergodic parameters are established.

2016, Velandia Daira, Bachoc François, Bevilacqua Moreno, Gendre Xavier, Loubes Jean-Michel, “Maximum likelihood estimation for a bivariate Gaussian process under fixed domain asymptotics”, in arXiv:


subriemannian

Our results can be seen as a first step for developing the calculus of variations on the singular space of horizontal curves (in this direction we prove a subriemannian Minimax principle and discuss some applications)..

2016, Andrei A. Agrachev, Francesco Boarotto, Antonio Lerario, “Homotopically Invisible Singular Curves”, in arXiv:


Yule-Simon distribution

Named after Udny Yule and Herbert A. Simon. Simon originally called it the Yule distribution.

(statistics) A certain discrete probability distribution.


coarea

The main tool is a general coarea inequality satisfied by packing energies of maps..

2016, P Pansu, “On the quasisymmetric Hölder-equivalence problem for Carnot groups”, in arXiv:


cofiber

The aim of this paper is to prove the following results stated in [GP1]: for any k-smooth scheme X and any n#92;geq 1 the map of simplicial pointed sheaves (-,#92;mathbbA¹#92;rfloor#92;mathbbG#95;m)#123;#92;wedgen#125;#95;#43;#92;toTⁿ induces a Nisnevich local level weak equivalence of S¹-spectra $M#95;#123;fr#125;(X#92;times(#92;mathbbA¹#92;rfloor#92;mathbbG#95;m)#123;#92;wedgen#125;)#92;toM#95;#123;fr#125;(X#92;timesTⁿ)andthesequenceofS^1-spectraM#95;#123;fr#125;(X#92;timesTⁿ#92;times#92;mathbbG#95;m)#92;toM#95;#123;fr#125;(X#92;timesTⁿ#92;times#92;mathbbA¹)#92;toM#95;#123;fr#125;(X#92;timesT#123;n#43;1#125;)$ is locally a homotopy cofiber sequence in the Nisnevich topology..

2016, Grigory Garkusha, Alexander Neshitov, Ivan Panin, “Framed motives of relative motivic spheres”, in arXiv:

(mathematics) The coequalizer of a mapping.


hyperbent

In this paper we introduce generalized hyperbent functions from F#95;#123;2ⁿ#125; to Z#95;#123;2ᵏ#125;, and investigate decompositions of generalized (hyper)bent functions.

2016, Thor Martinsen, Wilfried Meidl, Sihem Mesnager, Pantelimon Stanica, “Decomposing generalized bent and hyperbent functions”, in arXiv:

(mathematics) Pertaining to a boolean function on the field F_(2ⁿ) such that f(xᵏ) is bent for every k co-prime with 2ⁿ - 1.


subdivergence

The contribution from #92;mathcal#123;E#125;#95;#123;D²#92;mathcal#123;R#125;⁴#125;, the coefficient function of an amplitude that vanishes onshell, arises from a two loop nested subdivergence of the three loop amplitude..

2016, Anirban Basu, “Non--analytic terms from nested divergences in maximal supergravity”, in arXiv:


bireversible

It has been proved that, for a connected automaton of size at most~3, or when the automaton is not bireversible, the generated group cannot be Burnside infinite.

2016, Thibault Godin, Ines Klimann, “Connected reversible Mealy automata of prime size cannot generate infinite Burnside groups”, in arXiv:

(mathematics) reversible under the action of two linear involutions


comodernism

We show comodernism for two main families of lattices that were not previously known to be shellable: the order congruence lattices of finite posets, and a weighted generalization of the k-equal partition lattices. We also exhibit many examples of (co)modernistic lattices that were already known to be shellable.

2016, Jay Schweig, Russ Woodroofe, “A broad class of shellable lattices”, in arXiv:

(mathematics) The property of being the dual of something modernistic.


comodernistic

Thus, the relation between comodernistic lattices and solvable groups resembles, in several respects, that between supersolvable lattices and supersolvable groups..

(mathematics) Relating to, or exhibiting comodernism


conormality

Moreover, relative coobservability is weaker than conormality, which is also closed under set union; unlike conormality, relative coobservability imposes no constraint on disabling unobservable controllable events..

2016, Kai Cai, Renyuan Zhang, W.M. Wonham, “Relative Coobservability in Decentralized Supervisory Control of Discrete-Event Systems”, in arXiv:

(mathematics) The condition of being conormal


biadjoint

Its extension is a theory in which the NLSM Goldstone bosons interact with a cubic biadjoint scalar.

2016, Freddy Cachazo, Peter Cha, Sebastian Mizera, “Extensions of Theories from Soft Limits”, in arXiv:

(mathematics) adjoint in two different ways


bilaplacian

In this work we show that in any dimension the rescaled odometer converges to the continuum bilaplacian field on the unit torus..

2016, Alessandra Cipriani, Rajat Subhra Hazra, Wioletta M. Ruszel, “Scaling limit of the odometer in divisible sandpiles”, in arXiv:


rdf

Although the maximum difference in structure is obtained in the partial radial distribution function (rdf) of the B type of particles, the rdf of AA pairs and AB pairs give rise to the differences in the entropy and dynamics.

2016, Atreyee Banerjee, Manoj Kumar Nandi, Srikanth Sastry, Sarika Maitra Bhattacharyya, “Effect of total and pair configurational entropy in determining dynamics of supercooled liquids over a range of densities”, in arXiv:

radial distribution function
radial distribution function

(mathematics) radial distribution function


cobraided

Moreover, necessary and sufficient conditions for (A#92;natural#95;RB,#92;alpha#92;otimes#92;beta) to be a cobraided Hom-Hopf algebra are given..

2016, Tianshui Ma, Haiying Li, Tao Yang, “Cobraided Smash Product Hom-Hopf Algebras”, in Colloquium Mathematicum, volume 134, pages 75–92:

(mathematics) Having a braided coalgebra.


disconjugate

The aim of this paper consists on the study of the following fourth-order operator: \begin{equation}\label{Ec::T4} T[M]\,u(t)\equiv u^{(4)}(t)+p_1(t)\,u"'(t)+p_2(t)\,u"(t)+M\,u(t)\,,\ t\in I \equiv [a,b]\,, \end{equation} coupled with the two point boundary conditions: \begin{equation}\label{Ec::cf} u(a)=u(b)=u"(a)=u"(b)=0\,. \end{equation} So, we define the following space: \begin{equation}\label{Ec::esp} X=\left\lbrace u\in C^4(I)\quad\mid\quad u(a)=u(b)=u"(a)=u"(b)=0 \right\rbrace \,. \end{equation} Here p#95;1#92;inC³(I) and p#95;2#92;inC²(I). By assuming that the second order linear differential equation \begin{equation}\label{Ec::2or} L_2\, u(t)\equiv u"(t)+p_1(t)\,u'(t)+p_2(t)\,u(t)=0\,,\quad t\in I, \end{equation} is disconjugate on I, we characterize the parameter's set where the Green's function related to operator T#91;M#93; in X is of constant sign on I#92;timesI.

2016, Alberto Cabada, Lorena Saavedra, “Constant sign Green's function for simply supported beam equation”, in arXiv:

(mathematics) Having at most one fewer zeros (including multiplicities) than the dimension of the problem space.


branch cut

(topology, complex analysis) A curve in the complex plane such that it is possible to define a single analytic branch of a multi-valued function on the plane minus that curve.


bianalytic

This paper studies analytic maps between free spectrahedra, and under certain irreducibility assumptions on the convex sets, classifies all those that are bianalytic.

2016, Meric Augat, J. William Helton, Igor Klep, Scott McCullough, “Bianalytic Maps Between Free Spectrahedra”, in arXiv:


epipolar

A third pair of matching epipolar lines, needed to compute the fundamental matrix, is found from lines incident to the epipoles. We validate our method using real-world images and compare it to state-of-the-art methods.

2016, Gil Ben-Artzi, Tavi Halperin, Michael Werman, Shmuel Peleg, “Two Points Fundamental Matrix”, in arXiv:


epipole

(mathematics) The intersection of two polar lines


fibonomial

While this result is not new, our method of proof is new and suggests a conjecture for the divisibility of a fibonomial coefficient by a general prime p.

2016, Jeremiah Southwick, “A Conjecture concerning the Fibonomial Triangle”, in arXiv:


frequentaneous

The proposed frequentaneous time and Fourier transform based time-frequency distribution contains only those frequencies which are present in the Fourier spectrum.

2016, Pushpendra Singh, “Time-Frequency analysis via the Fourier Representation”, in arXiv:

(mathematics, physics) Related to frequency and phase (of a wave)