multimaximal

A multimaximal coupling is one that is a maximal coupling of any subset of the random variables being coupled.

2016, Ehtibar N. Dzhafarov, Janne V. Kujala, “Contextuality-by-Default 2.0: Systems with Binary Random Variables”, in arXiv:


pseudofunction

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Using local pseudofunction boundary behavior enables us to relax boundary requirements to a minimum.

2016, Gregory Debruyne, Jasson Vindas, “Complex Tauberian theorems for Laplace transforms with local pseudofunction boundary behavior”, in arXiv:


pseudomeasure

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Most of our results are proved under one-sided Tauberian hypotheses; in this context, we also establish new boundedness theorems for Laplace transforms with pseudomeasure boundary behavior.

(mathematics) A distribution that can be extended to a continuous functional.


quasilinearization

The algorithms involve solving one inexpensive problem on coarse grid and solving on fine grid one linear problem obtained by quasilinearization of the differential equation about an interpolant of the computed solution on the coarse grid.

2016, Ivanka Tr. Angelova, Lubin G. Vulkov, “Two-grid algorithms for singularly perturbed reaction-diffusion problems on layer adapted meshes”, in arXiv:


superchiral

In the close vicinity of a chiral nanostructure, the circular dichroism of a biomolecule could be greatly enhanced, due to the interaction with the local superchiral fields.

2016, S. Hamed Shams Mousavi, Sajanlal R. Panikkanvalappil, Mostafa A. El-Sayed, Ali A. Eftekhar, Ali Adibi, “Large Enhancement of Circular Dichroism Using an Embossed Chiral Metamaterial”, in arXiv:

(mathematics, physics) (of a field) having chiral density much higher than circularly polarized light, particularly with respect to ultrasensitive detection


supercloseness

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We discuss also anisotropic problems, semilinear equations, supercloseness and a combination technique..

2016, Hans-Goerg Roos, “Error estimates in balanced norms of finite element methods on Shishkin meshes for reaction-diffusion problems”, in arXiv:

(mathematics) The condition of being superclose


uniruledness

In particular we give criteria for uniruledness and rational connectedness of components of D..

2016, Yuan Wang, “Rational curves on hypersurfaces”, in arXiv:

(mathematics) The condition of being uniruled


pseudounitary

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We present a novel representation of the Lorentz group, the geometric version of which uses "reversions" of a sphere while the algebraic version uses pseudounitary 2x2 matrices over complex numbers and quaternions, and Clifford algebras in general.

2016, Jerzy Kocik, “Cromlech, menhirs and celestial sphere: an unusual representation of the Lorentz group”, in arXiv:

(mathematics) Preserving Hermitian indefinite forms.


topologicality

Switching off magnetism by atomic substitution and ensuring that the electronic structure becomes two-dimensional is sufficient for topologicality to arise in such a system.

2016, J. L. Lado, V. Pardo, “Dirac topological insulator in the d_(z²) manifold of a honeycomb oxide”, in arXiv:

(topology) The condition of being topological


supercode

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We also find a BCH--like bound from the minimum distance of the original supercode.

2016, Heeralal Janwa, Fernando L. Piñero, “On Parameters of Subfield Subcodes of Extended Norm-Trace Codes”, in arXiv:

(mathematics) The larger code that a subcode is part of


kernelizability

In this way, we obtain fixed-parameter tractability and polynomial kernelizability results, with the central parameter being the maximum vertex degree.

2016, Robert Bredereck, Vincent Froese, Marcel Koseler, Marcelo Garlet Millani, André Nichterlein, Rolf Niedermeier, “A Parameterized Algorithmics Framework for Digraph Degree Sequence Completion Problems”, in arXiv:

(mathematics) The condition of being kernelizable


permanental

We explore some properties of a recent representation of permanental vectors which expresses them as sums of independent vectors with components that are independent gamma random variables..

2016, Michael B. Marcus, Jay Rosen, “Permanental random variables, M-matrices and α-permanents”, in arXiv:

(mathematics) Related to, or composed of permanents


quasilattice

Here we prove that reflection quasilattices only exist in dimensions two, three and four, and we prove that there is a unique reflection quasilattice in dimension four: the "maximal reflection quasilattice" in terms of dimensionality and symmetry.

2016, Latham Boyle, Paul J. Steinhardt, “Reflection Quasilattices and the Maximal Quasilattice”, in arXiv:

(mathematics) A non-periodic structure that exhibits long-range order without translational symmetry.


subratio

We carried out a numerical experiment and obtained more precise upper estimate on the Steiner subratio: we have shown that it is less than 0.857..

2016, Alexander Ivanov, Alexey Tuzhilin, “Gromov--Hausdorff Distance, Irreducible Correspondences, Steiner Problem, and Minimal Fillings”, in arXiv:


bosonification

en-noun

bosonification (countable and uncountable, plural bosonifications)

Tropical curve counting is related to an algebra of operators on the Fock space by means of bosonification.

2016, Renzo Cavalieri, Paul Johnson, Hannah Markwig, Dhruv Ranganathan, “A graphical interface for the Gromov--Witten theory of curves”, in arXiv:

(mathematics, physics) Synonym of bosonization


conull

Moreover, if the combinatorial structure on X is "induced" by the #91;0#59;1#93;-shift action of a countable group #92;Gamma, then, even without any local finiteness assumptions, there is a Borel choice for f which satisfies the constraints on an invariant conull set (i.e., with #92;epsilon#61;0).

2016, Anton Bernshteyn, “Measurable versions of the Lovász Local Lemma and measurable graph colorings”, in arXiv:


cpsd

We show that a graph is cpsd if and only if it has no odd cycle of length at least 5 as a subgraph.

2016, Anupam Prakash, Jamie Sikora, Antonios Varvitsiotis, Zhaohui Wei, “Completely positive semidefinite rank”, in arXiv:

(mathematics) Initialism of completely positive semidefinite.


elliptope

coined in: M. Laurent and S. Poljak, On a positive semidefinite relaxation of the cut polytope, Linear Algebra Appl., 223/224, (1995), 439-461

In particular, we use a known lower bound on the size of matrix representations of extremal quantum correlations which we apply to high-rank extreme points of the n-dimensional elliptope. Lastly, we study cpsd-graphs, i.e., graphs G with the property that every doubly nonnegative matrix whose support is given by G is cpsd.

(mathematics) The set of all real, square symmetric matrices whose diagonal entries are all equal to one and whose eigenvalues are all non-negative.


excedance

A number i for which π(i) ≥ i is called a weak excedance of π, while a number i for which π(i) > i is called an excedance of π.

1997, Richard P. Stanley, Enumerative Combinatorics, 2nd edition, volume 1, page 23:

(mathematics, combinatorics) A position in a permutation occupied by a value greater than the position number.


hypocoercive

By further developing the generalized #92;Gamma-calculus for hypoelliptic operators, we prove hypocoercive estimates for a large class of Kolmogorov type operators which are defined on non necessarily totally geodesic Riemannian foliations.

2016, Fabrice Baudoin, Camille Tardif, “Hypocoercive estimates on foliations and velocity spherical Brownian motion”, in arXiv:

(mathematics) Hypoelliptic and converging to regularity.


metabelianization

We provide evidence of exactly five non-isomorphic extensions H of G having the required relation rank d(2,H)=3 and derived length dl(H)=3 whose metabelianization #92;frac#123;H#125;#123;H#125; is isomorphic to G.

2016, Daniel C. Mayer, “Three stage towers of 5-class fields”, in arXiv:

(mathematics) Conversion to, or viewing as metabelian form


subsymplectic

We shall prove that any alternate module is subsymplectic, i.e. if (A,#92;phi) has a Lagrangian of cardinal n then there exists an abelian group B of order n such that (A,#92;phi) is a submodule of the standard symplectic module B#92;timesB#42;.

2016, Clement Guerin, “Alternate modules are subsymplectic”, in arXiv:


hyperexponential

In this context, Avanzi et al. [4] solved the case with i.i.d. hyperexponential jumps; they showed the optimality of a (periodic) barrier strategy where dividends are paid at dividend-decision times if and only if the surplus is above some level.

2016, José-Luis Pérez, Kazutoshi Yamazaki, “On the optimality of Periodic barrier strategies for a spectrally positive Lévy process”, in arXiv:

(mathematics, of an element "x") Having the property that δ(x)/x is in a specified set for all logarithmic derivatives δ.

(mathematics) Pertaining to a hyperexponential distribution.


pseudonumerical

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We introduce a pseudonumerical range and study an enclosure of this set.

2016, Christian Engström, Axel Torshage, “Enclosure of the Numerical Range of a Class of Non-Selfadjoint Rational Operator Functions”, in arXiv:

(mathematics) Being a factor-object of an algebraicly numerical object.


ultramatricial

If the involutive structure is not considered, our result implies that K#95;0#123;gr#125; completely classifies graded ultramatricial algebras over any graded field A. If the grading is trivial and the involutive structure is not considered, we obtain some well known results as corollaries..

2016, Roozbeh Hazrat, Lia Vas, “K-theory Classification of Graded Ultramatricial Algebras with Involution”, in arXiv:

(mathematics) Isomorphic to a countable direct limit of matricial algebras.


superdroplet

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However, it is shown that the use of interpolation schemes such as the cloud-in-cell algorithm is detrimental in connection with superparticle or superdroplet approaches.

2016, Xiang-Yu Li, A. Brandenburg, N. E. L. Haugen, G. Svensson, “Eulerian and modified Lagrangian approaches to multi-dimensional condensation and coagulation”, in arXiv:


paracomplex

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(topology) Pertaining to the category of all metric spaces and all CW-complexes.

Applications include complex, paracomplex and symplectic geometries..

2016, Giovanni Calvaruso, Gabriela P. Ovando, “From almost (para)-complex structures to affine structures on Lie groups”, in arXiv:


pseudodual

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We also present analogous results in two limiting cases of special interest, namely for the non-Abelian T-dual of the PCM and for the pseudodual model..

2016, George Georgiou, Konstantinos Sfetsos, Konstantinos Siampos, “All-loop correlators of integrable λ-deformed σ-models”, in arXiv:


antilimit

(mathematics) The result produced by the formula for the limit of a parameterized series applied to any parameter values in which the series is not convergent.


bipower

In this paper we study the effects of noise on the bipower variation (BPV), realized volatility (RV) and testing for co-jumps in high-frequency data under the small noise framework.

2016, Daisuke Kurisu, “Power variations and testing for co-jumps: the small noise approach”, in arXiv:

(statistics) An alternative to variance; a measure of variability based on summing the product of adjacent data points rather than summing the squares of data points.


bitopological

We study tightness properties and selective versions of separability in bitopological function spaces endowed with set-open topologies..

2016, Alexander V. Osipov, Selma Özçağ, “Variations of selective separability and tightness in function spaces with set open topologies”, in arXiv:

(mathematics) Equipped with two distinct arbitrary topologies.


conatural

Tensor products of copies of the natural and the conatural representations are injective objects in this category.

2016, Dimitar Grantcharov, Vera Serganova, “Tensor representations of q(∞)”, in arXiv:

(mathematics) Being the dual of a natural entity.


hypertranscendence

We also indicate how these results have consequences both in the theory of automatic sets, leading to a new proof of Cobham's Theorem, and in the Galois theories of linear difference and differential equations, leading to hypertranscendence results..

2016, Reinhard Schäfke, Michael F. Singer, “Consistent systems of linear differential and difference equations”, in arXiv:

(mathematics) The condition of being hypertranscendental


quasicentral

The condition is equivalent to the existence of quasicentral approximate unit with respect to the Macaev norm relative to the left regular representation of the group and has been studied by the author in connection with perturbation questions for Hilbert space operators.

2016, Dan-Virgil Voiculescu, “A remark about supramenability and the Macaev norm”, in arXiv:


supercoset

It would be remarkable that the supercoset construction works well, even if the resulting backgrounds are not maximally supersymmetric.

2016, Hideki Kyono, Kentaroh Yoshida, “Supercoset construction of Yang-Baxter deformed AdS₅×S⁵ backgrounds”, in arXiv:


supramenable

We show that a finitely generated group G which satisfies a certain condition with respect to the Macaev norm is supramenable.

(mathematics) Having the property that any nonempty subset has a finitely additive left-invariant measure that maps that subset to 1.


cogalois

We show that, in the present form, there does not exist a cogalois theory for Drinfeld modules of rank or class number larger than one.

2016, Marco Antonio Sánchez-Mirafuentes, Julio Cesar Salas-Torres, Gabriel Villa-Salvador, “Cogalois theory and Drinfeld modules”, in arXiv:

(mathematics) Pertaining to the correspondence between subfields of a radical field extension with subgroups of a cogroup that is a Galois group.


cosemisimple

Let V be a braided vector space of diagonal type with a principal realization in the category of Yetter-Drinfeld modules of a cosemisimple Hopf algebra H and such that the Nichols algebra #92;mathfrak#123;B#125;(V) is finitely presented.

2016, Iván Angiono, Agustín García Iglesias, “Liftings of Nichols algebras of diagonal type II. All liftings are cocycle deformations”, in arXiv:

(mathematics) dual to something semisimple.


subhypergraph

More precisely, let H be a k-uniform k- partite hypergraph with some ordering on parts as V1, V2,..., Vk. such that the subhypergraph generated on union of V1, V2,..., Vk-1 has a unique perfect matching.

2016, Reza Jafarpour-Golzari, “A generalization of hall's theorem for k-uniform k-partite hypergraphs”, in arXiv:

Next, Meunier [Colorful subhypergraphs in Kneser hypergraphs, The Electronic Journal of Combinatorics, 2014] improved their result by proving that any properly colored general Kneser hypergraph #123;#92;rmKG#125;ʳ(#123;#92;mathcalH#125;) contains a large colorful r-partite subhypergraph provided that r is prime.

2016, Meysam Alishahi, “Colorful Subhypergraphs in Uniform Hypergraphs”, in arXiv:


bidouble

We give explicit examples of surfaces X with Kodaira dimension 1 and 2 obtained as double cover of K3 surfaces and we describe some of them as bidouble cover of rational surfaces.

2016, Alice Garbagnati, “Smooth double covers of K3 surfaces”, in arXiv:

(mathematics) Acting as a finite flat Galois morphism with Galois group (Z/2)²-.


cocenter

As a consequence, we obtain a new criterion on the supersingular representation: a (virtual) representation is supersingular if and only if its character vanishes on the non-supersingular part of the cocenter..

2016, Xuhua He, Sian Nie, “Cocenters and representations of pro-p Hecke algebras”, in arXiv:

(mathematics) The cokernel of a homomorphism.


endobifunctor

Motivated by topology, we develop a general theory of traces and shadows in an endobicategory, which is a bicategory #92;mathbfC with an endobifunctor #92;Sigma#92;colon#92;mathbfC#92;to#92;mathbfC.

2016, Anna Beliakova, Krzysztof Karol Putyra, Stephan Martin Wehrli, “Quantum Link Homology via Trace Functor I”, in arXiv:

(mathematics) A bifunctor between a bicategory and itself.


superextension

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As a corollary, every constant scalar curvature Kähler supermanifold has a unique superextension to a Kähler-Einstein supermanifold of one higher fermionic dimension.

2016, J.P. Ang, Martin Rocek, John Schulman, “Kahler-Einstein and Kahler scalar flat supermanifolds”, in arXiv:


affinoid

We prove that the geometric etale fundamental group of a (geometrically connected) rigid smooth p-adic affinoid curve (resp. of a formal fibre of a p-adic curve) is a direct factor of a certain profinite free group.

2016, Mohamed Saidi, “Etale fundamental groups of affinoid p-adic curves and formal fibres of p-adic curves”, in arXiv:


bidiscrete

From the relation between bidiscrete systems and biorthogonal systems, we obtain some results about biorthogonal systems in Banach spaces of the form C(K)..

2016, Clayton Suguio Hida, “Two Cardinal Inequalities about Bidiscrete Systems”, in arXiv:

(mathematics) Both groupoidal and posetal.


coarray

In this paper, we derive a simplified asymptotic mean square error (MSE) expression for the MUSIC algorithm applied to the coarray model, which is applicable even if the source number exceeds the sensor number.

2016, Mianzhi Wang, Arye Nehorai, “Coarrays, MUSIC, and the Cramér Rao Bound”, in arXiv:

(mathematics) The mapping of an array into a cogroup.

(signal processing) The set of vector differences between the transmit and receive arrays.


coresolution

In this paper, we prove that every module has a #92;mathcal#123;W#125;-injective coresolution and we study the dimensions of right orthogonal class of pure projective modules.

2016, Arunachalam Umamaheswaran, “Coresolutions and dimensions of right orthogonal class of pure projective modules”, in arXiv:

(mathematics) An object in a comodule or other dual to an abelian object that has a specified property.


irredundance

From ir- + redundance or irredundant + -ance.

Todorcevic concerning the irredundance in Boolean algebras and we prove that for every maximal irredundant family #92;mathcal#123;F#125;#92;subsetC(K), there is a #92;pi-base #92;mathcal#123;B#125; for K with , a result analogous to the McKenzie Theorem for Boolean algebras in the context of compact spaces.

(mathematics) The condition of being irredundant


superterzatic

We use several known and new results to shed light on the concepts of superterzatic functions..

2016, Flavia-Corina Mitroi-Symeonidis, “On the Jensen functional and superterzaticity”, in arXiv:


infinitesimalization

The infinitesimalization of the connection D is a Cartan connection #92;nabla on the Lie algebroid of G, a notion already studied elsewhere by the author.

2016, Anthony D. Blaom, “Cartan connections on Lie algebroids and their integrability”, in arXiv:

(mathematics) conversion or extension to infinitesimal form


pseudointersection

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We investigate which filters on #92;omega can contain towers, that is, a modulo finite descending sequence without any pseudointersection (in #91;#92;omega#93;#92;omega).

2016, Jörg Brendle, Barnabás Farkas, Jonathan Verner, “Towers in filters, cardinal invariants, and Luzin type families”, in arXiv:

(mathematics) A set for which the number of elements that are not in the intersection (of two infinite sets) is finite.


quasidefinite

The transformation theory is finally discussed in the context of the 2D non-Abelian Toda lattice hierarchy, understood as the theory of continuous transformations of quasidefinite sesquilinear forms.

2016, Carlos Álvarez-Fernández, Gerardo Ariznabarreta, Juan C. García-Ardila, Manuel Mañas, Francisco Marcellán, “Transformation theory and Christoffel formulas for matrix biorthogonal polynomials on the real line”, in arXiv:


quasitau

This approach allows for the finding of perturbed quasitau and Baker matrices..


quasimeasure

Motivated by the Arzel\`a-Ascoli theorem for Cᵇ(X,E), where X is an^([sic]) Euclidean space and E an arbitrary Banach space, we construct a quasimeasure for this space and study its properties.

2016, Mateusz Krukowski, “Darbo-type theorem for quasimeasure of noncompactness”, in arXiv:

(mathematics) A nonnegative increasing semiadditive set function defined on a ring of sets that is continuous above the origin and takes its values in the extended domain of real numbers.


Cayley's theorem

(group theory) The theorem stating that every group G is isomorphic to a subgroup of the symmetric group acting on G.


anticoercive

(mathematics) Characteristic of a mapping of elements that tends toward negative infinity as the magnitude of the element tends toward positive infinity.


deconfusion

The current deconfusion approach operates on some given premises.

2004, Dragos Datcu, L.J.M. Rothkrantz, AIBO Robot as a soccer and rescue game player:

The OF coefficients are calculated, and the deconfusion parameters are derived.

2011 June, David Jäckel, Jan Müller, Muhammad Usman Khalid, Urs Frey, Doublas Bakkum, Andreas Hierlemann, “High-density microelectrode array system and optimal filtering for closed-loop experiments”, in Solid-State Sensors, Actuators and Microsystems Conference:

A deconfusion analysis of the deep Spitzer photometry available suggests that these galaxies exhibit strong rest-frame optical nebular emission lines (EW_0(H_beta + [OIII]) > 600A).

2016, R.A.A. Bowler, J.S. Dunlop, R.J. McLure, D.J. McLeod, “Unveiling the nature of bright z ~ 7 galaxies with the Hubble Space Telescope”, in arXiv:

(mathematics) A statistical technique, similar to independent component analysis, for separating correlated data.


hyperreflexive

In contrast to the subspaces of all C-symmetric operators, we show that the subspaces of all skew-C symmetric operators are reflexive and even hyperreflexive with the constant #92;kappa(#92;Cˢ)#92;leqslant 3..

2016, Chafiq Benhida, Kamila Kliś-Garlicka, Marek Ptak, “Skew-symmetric operators and reflexivity”, in arXiv:

(mathematics) Having a bounded local distance of operators in a nested algebra or reflexive subspace


antispecial

We show that, if quantum logic and categorical quantum mechanics are formalized in the same framework, then the antispecial law of categorical quantum mechanics corresponds to the natural requirement of effect algebras that the units are each other's unique complements, and that the modularity law corresponds to the Frobenius condition.

2016, Dusko Pavlovic, Peter-Michael Seidel, “(Modular) effect algebras are equivalent to (Frobenius) antispecial algebras”, in arXiv:


cubization

cubization (countable and uncountable, plural cubizations)

We present a procedure of group cubization: It results in a group whose some features resemble the ones of a given group, and which acts without fixed points on a CAT(0) cubical complex.

2016, Damian Osajda, “Group cubization”, in arXiv:


hemimetric

Without exploiting structural constraints of the hemimetric polytope, learning the distances between each pair of items requires #92;Theta(n²) queries.

2016, Adish Singla, Sebastian Tschiatschek, Andreas Krause, “Actively Learning Hemimetrics with Applications to Eliciting User Preferences”, in arXiv:

(mathematics) An abstraction of distance; a function, d, with two arguments that satisfies d(x,x) = 0 and d(x, y) + d(y,z) ≥ d(x,z) (the triangle inequality) for all x,y,z in the domain.


hyporeflexive

In the present paper it will be shown that power partial isometries are always hyporeflexive and 2--hyperreflexive.

2016, Kamila Piwowarczyk, Marek Ptak, “2--hyperreflexivity and hyporeflexivity of power partial isometries”, in arXiv:

(mathematics) Pertaining to an algebra W such that W = W′ ∩ Alg LatW.


transcorrelation

Here, we present a study that assesses and compares two contrasting `universal' explicitly correlated approaches that fit into the FCIQMC framework; the #91;2#93;#95;#123;R12#125; method of Valeev {\em et al.}, and the explicitly correlated canonical transcorrelation approach of Yanai {\em et al}.

2016, Jennifer Kersten, George H. Booth, Ali Alavi, “Assessment of Multireference Approaches to Explicitly Correlated Full Configuration Interaction Quantum Monte Carlo”, in arXiv:

(mathematics) A space- and time-averaged correlation.


codimensional

We then show how the sole knowledge of this spectral gap in weighted spaces implies the finite codimensional non radial stability of these solutions for smooth well localized initial data using energy bounds.

2016, Charles Collot, Pierre Raphael, Jeremie Szeftel, “On the stability of type I blow up for the energy super critical heat equation”, in arXiv:


equiregularity

Moreover, we study for geodesics in the Goursat and Cartan group the set of times of loss of equiregularity..

2016, Isidro H. Munive, “Sub-Riemannian curvature of rank-two distributions”, in arXiv:

(mathematics) The condition of being equiregular


equiregular

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mathematical analysis
mathematical analysis

(mathematical analysis) Containing elements that are both outer regular and inner regular and which have inverses that are also both outer regular and inner regular.

(geometry) Having both all sides equal length and all angles equal.


overcone

In the second approach we try to find good subdivision points in an approximating overcone that is faster to compute..

2016, Winfried Bruns, Richard Sieg, Christof Söger, “The subdivision of large simplicial cones in Normaliz”, in arXiv:

(mathematics) A morphism from a diagonal overfunctor to the base category of the overcategory.


semiforbidden

The IEL component is presented in different emission lines, including the permitted lines \lya\ #92;lambda1216, \civ\ #92;lambda1549, semiforbidden line \ciii\ #92;lambda1909, and forbidden lines \oiii\ #92;lambda#92;lambda4959, 5007.

2016, Zhenzhen Li, Hongyan Zhou, Lei Hao, Shufen Wang, Tuo Ji, Bo Liu, “Strong Optical and UV Intermediate-Width Emission Lines in the Quasar SDSS J232444.80-094600.3: Dust-Free and Intermediate-Density Gas at the Skin of Dusty Torus ?”, in arXiv:

(mathematics, physics) Partially forbidden


superderivative

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We distinguish non-degenerate operators as those with an invertible top coefficient in the expansion in the superderivative D.

2016, Simon Li, Ekaterina Shemyakova, Theodore Voronov, “Differential operators on the superline, Berezinians, and Darboux transformations”, in arXiv:

(mathematics) A generalization of a derivative that can be applied to a superfunction.


ultradifferential

We give new and simpler proofs of more general results for the inverse and implicit function theorem as well as the existence theorem for ode's in classes of ultradifferential functions.

2016, Jürgen Pöschel, “A new approach to ultradifferentiable functions”, in arXiv:

(mathematics) A generalization of a differential that is calculated over an ultradistribution.


antidirected

(mathematics) Such that the canonical mapping is injective.

A digraph D is antistrong if it contains an antidirected (x,y)-trail starting and ending with a forward arc for every choice of x,y#92;inV(D).

2016, Jorgen Bang-Jensen, Stephane Bessy, Bill Jackson, Matthias Kriesell, “Antistrong digraphs”, in arXiv:

(graph theory) Having arcs that alternate between forward and backward arcs.


antistrong

Finally, we study arc-decompositions of antistrong digraphs and pose several problems and conjectures.

(mathematics) Containing an antidirected (x, y)-trail starting and ending with a forward arc for every choice of x and y.


epimorphicity

We also obtain epimorphicity criteria for subgroups of affine algebraic groups, which generalize a result of Bien and Borel..

2016, Michel Brion, “Epimorphic subgroups of algebraic groups”, in arXiv:

(mathematics) The condition of being epimorphic


isochronicity

Using the correction of a vector field to characterize isochronicity and explicit computations of this quantity for polynomial vector fields, wa are able to describe a very large class of nonisochronous Hamiltonian system of even degree of degree arbitrary large.

2016, Jacky Cresson, Jordy Palafox, “Isochronous centers of polynomial Hamiltonian systems and a conjecture of Jarque and Villadelprat”, in arXiv:

(mathematics) The condition of being isochronic


semidihedral

In previous joint work with Holm we used K\"ulshammer ideals to distinguish classes with respect to these parameters in case of algebras of dihedral and semidihedral type.

2016, Alexander Zimmermann, “Külshammer ideals of algebras of quaternion type”, in arXiv:


coconform

en-verb

coconform (third-person singular simple present coconforms, present participle coconforming, simple past and past participle coconformed)

coconforms (present singular third-person)
coconforming (participle present)
coconformed (participle past)
coconformed (past)

Such matroids are said to conform or coconform to the template.

2016, Kevin Grace, Stefan H. M. van Zwam, “Templates for Binary Matroids”, in arXiv:

(mathematics) To conform by both a structure its dual.


cographic

A binary frame template is a device for creating binary matroids from graphic or cographic matroids.


cospan

This extra structure arises from a lax symmetric monoidal functor F#92;colon#92;mathbf#123;C#125;#92;to#92;mathbf#123;D#125;; we use this functor to "decorate" each cospan with apex N#92;in#92;mathbf#123;C#125; with an element of F(N).

2016, Kenny Courser, “A bicategory of decorated cospans”, in arXiv:


multicorn

The main results of the article show that the dynamically natural straightening map from a 'baby multicorn', either in multicorns of even degree or in the real cubic locus, to the original multicorn is discontinuous at infinitely many explicit parameters.

2016, Hiroyuki Inou, Sabyasachi Mukherjee, “Discontinuity of straightening in antiholomorphic dynamics”, in arXiv:

(mathematics) The connectedness locus in the space of antiholomorphic unicritical polynomials; The set of parameters for which the Julia set is connected.


quasihyperbolic

We prove that for a bounded domain #92;Omega#92;subset#92;mathbbRⁿ which is Gromov hyperbolic with respect to the quasihyperbolic metric, especially when #92;Omega is a finitely connected planar domain, the Sobolev space W#123;1,#92;,#92;infty#125;(#92;Omega) is dense in W#123;1,#92;,p#125;(#92;Omega) for any 1#92;leplt;#92;infty.

2016, Pekka Koskela, Tapio Rajala, Yi Ru-Ya Zhang, “A density problem for Sobolev spaces on Gromov hyperbolic domains”, in arXiv:


unicritical

The proof of discontinuity of straightening maps is carried out by showing that all non-real umbilical cords of the multicorns wiggle, which settles a conjecture made by various people including Hubbard, Milnor, and Schleicher. We also prove some rigidity theorems for polynomial parabolic germs, which state that one can recover unicritical holomorphic and antiholomorphic polynomials from their parabolic germs..

(mathematics) Having a single critical point.


duplicial

Explicitly, our main aims are: 1) To study how the cyclic homology of associative algebras and of Hopf algebras in the original sense of Connes and Moscovici arises from a distributive law, and to clarify the role of different notions of bimonad in this generalisation. 2) To extend the procedure of twisting the cyclic homology of a unital associative algebra to any duplicial object defined by a distributive law. 3) To study the universality of Bohm and Stefan's approach to constructing duplicial objects, which we do in terms of a 2-categorical generalisation of Hochschild (co)homology. 4) To characterise those categories whose nerve admits a duplicial structure..

2016, Paul Slevin, “2-categories and cyclic homology”, in arXiv:

(mathematics) Defined by two associative operations that have a coassociative coproduct.


hypercentral

The results of our model (the combination of our proposed hypercentral Potential and generalized GR mass formula to description of the spectrum) show that the strange and non-strange baryons spectra are in general fairly well reproduced.

2016, Nasrin Salehi, “Light Baryons Mass in a Non-Relativistic Quark Model within an Hypercentral Power Low Potential”, in arXiv:

(mathematics) Pertaining to the continuation of a lower central series to infinite ordinal numbers via transfinite recursion.


loopspace

Ravenel's: "Infinite loopspace theorists, where are you?", or more prosaically: Can one start from the notion of Ring Spectrum Representing [Formal Group Laws] (the functor) and arrive at Complex Cobordism? Our answer is a tentative "sort-of"..

2016, Jesse C. McKeown, “Complex Cobordism vs. Representing Formal Group Laws”, in arXiv:

(mathematics) A function space of continuous functions that map from the unit interval to a space from x₀ to x₁, all of which map 0 to x₀ and 1 to x₁.


pronilfactor

Specifically, if H is a group (subject to very mild topological assumptions) and (H,X) is a minimal dynamical system, then we give a simple characterization of the maximal pronilfactor of X.

2016, Yonatan Gutman, Freddie Manners, Péter P. Varjú, “The structure theory of Nilspaces III: Inverse limit representations and topological dynamics”, in arXiv:

(mathematics) An ergodic nilspace X/R(X) such that there exists an element x of X and a homomorphism H such that (H,X) is a nilsystem.


subdiagonal

(3) From R, we obtain the set of points #92;mathbb#123;R#125;#92;tbinom#123;n#125;#123;2#125; whose coordinates are the subdiagonal entries of the corresponding matrices:

2010, Martin Aigner with Günter M. Ziegler, chapter 16, in Proofs from THE BOOK, 4th edition, Delhi, India: Springer (India), published 2013, page 97:

(mathematics) Said of an entry of a square matrix: that it lies anywhere in the lower triangular area below the main diagonal of the matrix.


subdiagonal

(mathematics) The diagonal of a matrix that lies directly below and to the left of the main diagonal.


trichotomic

This treatment is based upon assuming the existence of the overall joint probability distributions for the measurement outcomes pertaining to the relevant trichotomic observables, satisfying the locality condition, and yielding the measurable marginal probabilities.

2016, Debarshi Das, Shounak Datta, Suchetana Goswami, A. S. Majumdar, Dipankar Home, “Probing quantum nonlocality of bipartite entangled qutrit states by generalising Wigner's argument”, in arXiv:


triharmonic

We consider the triharmonic operator subject to homogeneous boundary conditions of intermediate type on a bounded domain of the N-dimensional Euclidean space.

2016, José Arrieta, Francesco Ferraresso, Pier Domenico Lamberti, “Boundary homogenization for a triharmonic intermediate problem”, in arXiv:

partial differential equation
partial differential equation

(mathematics) Describing a class of sixth-order partial differential equations which arises in areas of continuum mechanics


biorthonormal

Based on the exact solution, we find that the spatially modulated real and complex fields rearrange the phase boundaries from that of the ordinary Ising model, which can be characterized by the Chern numbers defined in the context of Dirac and biorthonormal inner products, respectively..

2016, C. Li, G. Zhang, Z. Song, “Chern number in Ising models with spatially modulated real and complex fields”, in arXiv:

(mathematics, of two sets) Orthonormal and having elements that are each orthogonal to all but exactly one element in the other set.


pluriclosed

We show global existence and convergence results for the pluriclosed flow on manifolds for which certain naturally associated tensor bundles are globally generated..

2016, Jeffrey Streets, “Pluriclosed flow on manifolds with globally generated bundles”, in arXiv:


polysphere

Such a problem is generalized to an estimation of concentric, co-dimension 1, subspheres of a polysphere.

2016, Sungkyu Jung, “Inference on subspheres model for directional data”, in arXiv:


semidiscretization

For a large class of fully nonlinear parabolic equations, which include gradient flows for energy functionals that depend on the solution gradient, the semidiscretization in time by implicit Runge-Kutta methods such as the Radau IIA methods of arbitrary order is studied.

2016, Peer C. Kunstmann, Buyang Li, Christian Lubich, “Runge-Kutta time discretization of nonlinear parabolic equations studied via discrete maximal parabolic regularity”, in arXiv:


rationalification

We proceed by passing to the normalization and then gluing along the conductor in an appropriate rationalification or log-canonicalization of the normalization of X..

2016, Jeremy Berquist, “Demi-Normal Surface Singularities”, in arXiv:

(mathematics, physics) Conversion to rational form


smoothability

en-noun

smoothability (countable and uncountable, plural smoothabilities)

It allows us to describe an open subset of n#92;timesn#92;timesn tensors of minimal border rank in terms of smoothability of commutative algebras.

2016, Markus Bläser, Vladimir Lysikov, “On degeneration of tensors and algebras”, in arXiv:

(mathematics) The condition of being smoothable


snoidal

Second, we prove the spectral stability of the cnoidal waves against same-period perturbations (in a certain parameter range), and provide an alternate proof of this (known) fact for the snoidal waves, which does not rely on complete integrability.

2016, Stephen Gustafson, Stefan Le Coz, Tai-Peng Tsai, “Stability of periodic waves of 1D cubic nonlinear Schrödinger equations”, in arXiv:


subrecursive

We also prove computability of F\o lner sets for a group that is extension of an amenable group with solvable word problem by a finitely generated group with computable F\o lner sets with subrecursive distortion function.

2016, Matteo Cavaleri, “Computability of Følner sets”, in arXiv:

(mathematics) Able to be expressed in a language or by a set of operations that is a proper subset of the expressiveness of a Turing machine.


superbialgebra

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

Then, by making use of the automorphism supergroup of the Lie superalgebra (#123;#92;calC#125;³#43;#123;#92;calA#125;), the Lie superbialgebra structures on the Lie superalgebra (#123;#92;calC#125;³#43;#123;#92;calA#125;) are obtained and classified into inequivalent 31 families.

2016, A. Eghbali, A. Rezaei-Aghdam, “Lie superbialgebra structures on the Lie superalgebra (cal C³+cal A) and deformation of related integrable Hamiltonian systems”, in arXiv:


biderivation

We extend to the category of crossed modules of Leibniz algebras the notion of biderivation via the action of a Leibniz algebra.

2016, José Manuel Casas, Rafael F. Casado, Xabier García-Martínez, Emzar Khmaladze, “Actor of a crossed module of Leibniz algebras”, in arXiv:

(mathematics) A bilinear mapping which is a derivation in each variable separately.


sublaplacian

Let #92;mathsfG be a Carnot group of homogeneous dimension M and #92;Delta its horizontal sublaplacian.

2016, Marius Mantoiu, “Spectral Analysis for Perturbed Operators on Carnot Groups”, in arXiv:


subsymmetry

Then, we give the scalar potential of the theory where the A#95;#123;3#125; discrete subsymmetry is used to avoid the so-called sequestering problem.

113005 (2016), R. Ahl Laamara, M.A Loualidi, E.H Saidi, “Type II seesaw supersymmetric neutrino model for θ₁₃≠0”, in Phys. Rev. D, volume 113005:


superperiodic

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

However, their description of the low-energy dynamics of twisted bilayer graphene is restricted to the extended zone scheme and therefore neglects the effects of the superperiodic structure.

247401 (2016), M. Van der Donck, F. M. Peeters, B. Van Duppen, “Comment on "Creating in-plane pseudomagnetic fields in excess of 1000 T by misoriented stacking in a graphene bilayer"”, in Phys. Rev. B, volume 247401:


biequivalent

We define strict and weak duality involutions on 2-categories, and prove a coherence theorem that every bicategory with a weak duality involution is biequivalent to a 2-category with a strict duality involution.

2016, Michael Shulman, “Contravariance through enrichment”, in arXiv:

(mathematics, of two entities A and B) Both left equivalent and right equivalent; Having the property that there exists a pair of mappings M₁ (A->B) and M₂ (B->A) such that M₁M₂(A) is equivalent to applying the unity operator to A and M₂ M₁(B) is equivalent to applying the unity operator to B.


dreibein

Three orthonormal vectors #92;hat#123;l#125;, #92;hat#123;e#125;#123;(1)#125; and #92;hat#123;e#125;#123;(2)#125; form the dreiben - a local physical coordinate frame of the A-phase vacuum.

1992, G. E. Volovik, Exotic Properties of Superfluid 3He, page 21:

This is shown for the following canonical sectors: i) a conformally invariant generic description where the spinor field and the dreibein are locally rescaled; ii) a specific configuration for the Dirac fermion consistent with its spin, where Weyl symmetry is exchanged by time reparametrizations; iii) the vacuum sector 1, which is of interest for perturbation theory.

2016, Alfredo Guevara, Pablo Pais, Jorge Zanelli, “Dynamical Contents of Unconventional Supersymmetry”, in arXiv:


pseudoalgebra

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


transjective

We characterize the indecomposable transjective modules over an arbitrary cluster-tilted algebra that do not lie on a local slice, and we provide a sharp upper bound for the number of (isoclasses of) these modules..

2016, Ibrahim Assem, Ralf Schiffler, Khrystyna Serhiyenko, “Modules over cluster-tilted algebras that do not lie on local slices”, in arXiv:

(mathematics) Corresponding to shifts of preprojective and preinjective modules.


anticommutating

Besides the usual off-shell nilpotent and absolutely anticommutating (anti-)BRST symmetry transformations, we discuss the off-shell nilpotent and absolutely anticommutating (anti-)co-BRST symmetry transformations for this specific 2D theory.

2016, N. Srinivas, S. Kumar, B. K. Kureel, R. P. Malik, “2D Non-Abelian Theory: Some Novel Features”, in arXiv:

(mathematics) That produces anticommutation


aposyndetic

The families of nondegenerate colocally connected or aposyndetic continua in Iⁿ and of at least two-dimensional or decomposable Kelley continua are F#95;#123;#92;sigma#92;delta#125;-absorbers in the hyperspace C(Iⁿ) for n#92;ge 3.

2016, Paweł Krupski, Alicja Samulewicz, “More absorbers in hyperspaces”, in arXiv:

(topology) Having the property that for all points x distinct from a specified point p, there is a compact connected neighborhood of p that does not include x.


coflow

Furthermore, we give an O(#92;logn#47;#92;log#92;logn)-approximation polynomial time algorithm for scheduling circuit-based coflows where flow paths are not given (here n is the number of network edges). We note that our task-based coflow scheduling problem is equivalent to the fully-flexible order scheduling problem on unrelated parallel machines for which no O(1)-factor approximation algorithm was known prior to this work. We obtain our results by developing a general framework for coflow schedules, based on interval-indexed linear programs, which may extend to other coflow models and objective functions and may also yield improved approximation bounds for specific network scenarios..

2016, Hamidreza Jahanjou, Erez Kantor, Rajmohan Rajaraman, “Asymptotically Optimal Approximation Algorithms for Coflow Scheduling”, in arXiv:

(graph theory) Any of a series of flows that have a common source and destination


digirth

We prove a relaxed version of this conjecture: every planar digraph of digirth at least four is 2-colourable..

2016, Zhentao Li, Bojan Mohar, “Planar digraphs of digirth four are 2-colourable”, in arXiv:


hyperelliptical

The focus of this paper is to extend the previous DM unit in order to create an hyperelliptical shaped decision region and to perform feature selection.

1994 May, F. Mana, D. Albesano, R. Gemello, “Integrating Distance Measure and Inner Product Neurons”, in ICANN ’94: Proceedings of the International Conference on Artificial Nerual Networks:

We present the analytical solutions of the geodesic equations in terms of Weierstrass elliptic and Kleinian sigma hyperelliptical functions.

2016, Sobhan Kazempour, Reza Saffari, Saheb Soroushfar, “Analytical solutions of the geodesic equation in the (rotating) black string-(anti-) de sitter spacetime”, in arXiv:

(mathematics) Alternative form of hyperelliptic


hyperfibonacci

We also prove further identities involving both hyperfibonacci and hyperlucas sequences, in full generality..

2016, Ligia Loretta Cristea, Ivica Martinjak, Igor Urbiha, “Hyperfibonacci Sequences and Polytopic Numbers”, in arXiv:

(mathematics) Pertaining to a generalization of the Fibonacci sequence that derives each term as the sum of the previous r terms for any r ≥ 1.


hypersemigroup

An hypersemigroup H is left (resp. right) quasi-regular if and only if, for any fuzzy subset f of S we have f#92;preceq 1#92;circf#92;circ 1#92;circf (resp. f#92;preceqf#92;circ 1#92;circf#92;circ 1) and it is semisimple if and only if, for any fuzzy subset f of S we have f#92;preceq 1#92;circf#92;circ 1#92;circf#92;circ 1.

2016, Niovi Kehayopulu, “A characterization of regular, intra-regular, left quasi-regular and semisimple hypersemigroups in terms of fuzzy sets”, in arXiv:

(mathematics) A nonempty set for which the set of all subsets forms a semiring.


semisimplicial

We show that if a semisimplicial set map F: C -> D respects identity maps up to homotopy, then there exists an honest functor F': C -> D which is homotopic to F..

2016, Hiro Lee Tanaka, “Functors (between oo-categories) that aren't strictly unital”, in arXiv:


suborbifold

We also investigate the property of saturation in this context, and give an example of a suborbifold with the canonical orbifold substructure that is not saturated..

2016, Joseph E. Borzellino, Victor Brunsden, “On the Inheritance of Orbifold Substructures”, in arXiv:

(mathematics) A submanifold of a space that is not smooth at every point, although it remains well-defined within the space.


binoid

This implies that the corresponding Hilbert-Kunz multiplicity for the binoid algebras does not depend on the characteristic..

2016, Bayarjargal Batsukh, “Hilbert-Kunz theory for binoids”, in arXiv:


fiberedness

In particular, we discuss fibering and genus detecting problems of oriented links, and give some finiteness theorems which characterize fiberedness and the genus of an alternating link.

2016, Takayuki Morifuji, Anh T. Tran, “Twisted Alexander polynomials and character varieties of links”, in arXiv:

(mathematics) The condition of being fibered


polyton

We call these sets the matching polyton and the fractional vertex cover polyton. We also study properties of matching polytons and fractional vertex cover polytons along convergent sequences of graphons..

2016, Martin Dolezal, Jan Hladky, “Matching polytons”, in arXiv:

(mathematics) An ordered set of singletons


subdisk

We show that if a reduction of K along D yields an (n-1)-bridge position, then K bounds a disk that contains D as a subdisk and intersects S in n arcs..

2016, Jung Hoon Lee, “Reduction of bridge positions along a bridge disk”, in arXiv:


subuppersemilattice

First, given any finite subuppersemilattice U ot 3[0,0'] with top element 0' and an isomorphism type V of a poset extending U consistently with its structure as an usl such that V and U have the same top element and V is an end extension of ...

1988, Manuel Lerman, Richard A. Shore-, “Decidability and invariant classes for degree structures”, in Transactions of the American Mathematical Society, volume 310, number 2:

This is achieved by using Kumabe-Slaman forcing - along with other known results - to show that given finite uppersemilattices #92;mathcal#123;M#125; and #92;mathcal#123;N#125;, where #92;mathcal#123;M#125; is a subuppersemilattice of #92;mathcal#123;N#125;, then for both degree structures, every embedding of #92;mathcal#123;M#125; into the structure extends to one of #92;mathcal#123;N#125; iff #92;mathcal#123;N#125; is an end-extension of #92;mathcal#123;M#125;..

2016, James Barnes, “On the decidability of the Σ₂ theories of the arithmetic and hyperarithmetic degrees as uppersemilattices”, in arXiv:

(mathematics) A sub-semilattice of an uppersemilattice.


uppersemilattice

This is achieved by using Kumabe-Slaman forcing - along with other known results - to show that given finite uppersemilattices #92;mathcal#123;M#125; and #92;mathcal#123;N#125;, where #92;mathcal#123;M#125; is a subuppersemilattice of #92;mathcal#123;N#125;, then for both degree structures, every embedding of #92;mathcal#123;M#125; into the structure extends to one of #92;mathcal#123;N#125; iff #92;mathcal#123;N#125; is an end-extension of #92;mathcal#123;M#125;.

(mathematics) The upper subset of a semilattice


BOCS

(mathematics) Abbreviation of bimodules over categories.


biprojective

For a Clifford semigroup S, we show that `1(S) is approximately left character biprojective if and only if `1(S) is pseudo-amenable.

2016, Amir Sahami, “On approximately left phi-biprojective banach algebras”, in arXiv:

(mathematics) Acting as both a projective left and right module, such that the left and right multiplications are compatible.


bistatistics

This conjecture has been proved by Aas in 2014, and the generating function of the corresponding bistatistics is the double Eulerian polynomial.

2016, Jean-Luc Baril, Vincent Vajnovszki, “A permutation code preserving a double Eulerian bistatistic”, in arXiv:

(mathematics) Pairs of statistics on the same set.


minorization

minorization (countable and uncountable, plural minorizations)

Then, using minorization maximization (MM) algorithm based on an affine approximation, we obtain a solution for the reformulated problem.

2016, Jinwoo Kim, Wan Choi, Hyuncheol Park, “Beamforming for Full-Duplex Multiuser MIMO Systems”, in arXiv:

(mathematics) The action of forming a lower bound


preasymptotic

We prove that for compactly perturbed elliptic problems, where the corresponding bilinear form satisfies a Garding inequality, adaptive mesh-refinement is capable of overcoming the preasymptotic behavior and eventually leads to convergence with optimal algebraic rates.

2016, Alex Bespalov, Alexander Haberl, Dirk Praetorius, “Adaptive FEM with coarse initial mesh guarantees optimal convergence rates for compactly perturbed elliptic problems”, in arXiv:

(mathematics) Prior to becoming asymptotic


subexcedant

In this paper we define a permutation code (that is, a bijection between permutations and subexcedant sequences) and show the more general result that two 5-tuples of set-valued statistics on the set of permutations and on the set of subexcedant sequences, respectively, are equidistributed.

(mathematics) (of a sequence of nonnegative integers) such that the value of each term is less than the position of that term in the sequence (e.g. the first term is less than 1, the second term is less than 2, etc.)


translocal

At the end of the paper we briefly mention the possibility that our network carries a translocal far-order which leads to the concept of wormhole spaces and a scale dependent dimension if the coarse graining procedure is no longer local..

2016, Saeed Rastgoo, Manfred Requardt, “Emergent Space-Time via a Geometric Renormalization Method”, in arXiv:

(mathematics) Between points in a space.


codifferential

In the language of differential geometry, the incompressible inviscid Euler equations can be written in vorticity-vector potential form as #92;begin#123;matrix#125;#92;partial#95;t#92;omega#43;#123;#92;mathcalL#125;#95;u#92;omegaamp;#61;0#92;#92;uamp;#61;#92;delta#92;tilde#92;eta#123;-1#125;#92;Delta#123;-1#125;#92;omega#92;end#123;matrix#125; where #92;omega is the vorticity 2-form, #123;#92;mathcalL#125;#95;u denotes the Lie derivative with respect to the velocity field u, #92;Delta is the Hodge Laplacian, #92;delta is the codifferential (the negative of the divergence operator), and #92;tilde#92;eta#123;-1#125; is the canonical map from 2-forms to 2-vector fields induced by the Euclidean metric #92;eta.

2016, Terence Tao, “Finite time blowup for Lagrangian modifications of the three-dimensional Euler equation”, in arXiv:

(mathematics) The projected differential of an extensor field.

One important concept is the introduction of codifferential operator

2015, 1:19:34 from the start, in 2 Tangent Space, Differential Forms, Metric (Mathematics for Theoretical Physicists - Hirosi Ooguri), spoken by Hiroshi Ooguri (Hiroshi Ooguri), K Raviteja (YouTube):

differential geometry
differential geometry

(differential geometry) the formal adjoint of the exterior derivative; a differential-geometric version of the divergence operator; the exterior derivative sandwiched between two Hodge star operators with some additional factor(s) that take(s) care of the sign; the Hermitian conjugate of the exterior derivative under the inner product for k-form fields over some manifold M: (α,β)=∫_Mα∧⋆β, so that (α,dβ)=(δα,β).


protomodular

This leads to a basic theory involving what we call unital and strongly unital objects, subtractive objects, Mal'tsev objects and protomodular objects.

2016, Andrea Montoli, Diana Rodelo, Tim Van der Linden, “Two characterisations of groups amongst monoids”, in arXiv:


subgridding

As an example of application, we derive a new subgridding method with material traverse, arbitrary grid refinement, and guaranteed stability.

2016, Fadime Bekmambetova, Xinyue Zhang, Piero Triverio, “A Dissipative Systems Theory for FDTD with Application to Stability Analysis and Subgridding”, in arXiv:


biproportional

Given a rectangular non-negative matrix X#95;0 and two positive marginals a and b, the algorithm generates a sequence of matrices (X#95;n) starting at X#95;0, supposed to converge to a biproportional fitting, that is, to a matrix Y whose marginals are a and b and of the form Y#61;D#95;1X#95;0D#95;2, for some diagonal matrices D#95;1 and D#95;2 with positive diagonal entries. When a biproportional fitting does exist, it is unique and the sequence (X#95;n) converges to it at an at least geometric rate.

2016, Jean Brossard, Christophe Leuridan, “Iterated proportional fitting procedure and infinite products of stochastic matrices”, in arXiv:

(mathematics) Providing two-way proportionality.


negabent

In addition, a conjecture on negabent monomials whose exponents are of Niho type is given..

2016, Gaofei Wu, Nian Li, Yuqing Zhang, Xuefeng Liu, “Several Classes of Negabent Functions over Finite Fields”, in arXiv:


Earth day

(science fiction) A day in Earth time; the period it takes planet Earth to revolve once; a period of 24 hours.


opmonoidal

(mathematics) Having a natural family of distributive morphisms and an identity morphism that are coherent.


cocontinuous

(mathematics, of a functor) Commutative with small colimits; right-exact and transforming small direct sums into small direct sums.


Goodstein sequence

Goodstein sequence (plural Goodstein sequences)

Named after Reuben Goodstein (1912–1985), English mathematician.

(mathematics) A sequence of natural numbers generated from an initial value m, starting with that value, and proceeding by performing certain operations on it. Although such sequences rapidly produce very large numbers, they always terminate at zero.


dominable

en-adj

dominable (comparative more dominable, superlative most dominable)

more dominable (comparative)
most dominable (superlative)

An important tool for the study of laterally complete Riesz spaces is the notion of the dominable set, which is introduced next.

1978, Charalambos D. Aliprantis, Owen Burkinshaw, Locally solid Riesz spaces, →ISBN, page 170:

(mathematics) Order bounded in the universal completion.


hyperhomology

(mathematics) A generalization of homology of an object to complexes.


self-commutator

(mathematics) Given a bounded linear operator B and its adjoint B*, the self-commutator is B*B - BB*.


scr.

Abbreviation of scruple (“unit of measure”).


Suzhou numeral

A calque of Chinese 蘇州碼子 /苏州码子 (Sūzhōu mǎzi), from their use at the formerly important market town of Suzhou in Jiangsu Province. Mistakenly entered into Unicode as "Hangzhou numerals", which Unicode's policy precludes changing.

calque

A system of Chinese numerals based on Southern Song rod numerals.


overfunctor

(category theory) A morphism of an overcategory.


overcategory

(category theory) Any functor into a specified base category.


ladderize

en-verb

ladderize (third-person singular simple present ladderizes, present participle ladderizing, simple past and past participle ladderized)

ladderizes (present singular third-person)
ladderizing (participle present)
ladderized (participle past)
ladderized (past)

(mathematics) to sort the nodes of a tree graph on one level by the count of their subnodes (on all levels under the node)


functionhood

He did not distill the essential idea of functionhood: that to each x in the domain there corresponds a unique y in the range.

1999, William Dunham, Euler: The Master of Us All, The Mathematical Association of America, published 1999, page 17:

(mathematics, logic, grammar) The state or quality of being a function.


DCNN

convolutional neural network
convolutional neural network#English

(machine learning) Initialism of deep convolutional neural network.


subcross

(mathematics) The cross product of two cross products.


subcross

subcross (third-person singular simple present subcrosses, present participle subcrossing, simple past and past participle subcrossed)

subcrosses (present singular third-person)
subcrossing (participle present)
subcrossed (participle past)
subcrossed (past)

In this paper we define the notions of normal subcrossed module and quotient crossed module within groups with operations; and using the equivalence of crossed modules over groups with operations and internal groupoids we prove how normality and quotient concepts are related in these two categories.

2016, Tunçar Şahan, Osman Mucuk, “Normality and quotient in crossed modules, cat¹-groups and internal groupoids within groups with operations”, in arXiv:


alpha level

(statistics) The significance level of a statistical test.


trust anchor

(cryptography) An authoritative entity that is assumed to be trustable.


adelically

en-adv

adelically (comparative more adelically, superlative most adelically)

more adelically (comparative)
most adelically (superlative)

Indeed in this paper we work completely adelically, which allow us to work over any field.

2017, David Loeffler, Elliptic Curves, Modular Forms and Iwasawa Theory:


plug and chug

(mathematics, colloquial) A technique in which values are entered to get a numerical answer without any problem-solving skills being necessary.


SHA

Secure Hash Algorithm
w:Secure Hash Algorithms

(cryptography) Acronym of Secure Hash Algorithm.


bilogarithmic

(mathematics, especially of a graph) Based on two logarithms; logarithmic in two directions


Harnack's curve theorem

(mathematics) In real algebraic geometry, a theorem that describes the possible numbers of connected components that an algebraic curve can have, in terms of the degree of the curve.


Tarski-Seidenberg theorem

the Tarski-Seidenberg theorem (canonical)

Named after Alfred Tarski and Abraham Seidenberg.

(mathematics) A theorem stating that a set in (n + 1)-dimensional space defined by polynomial equations and inequalities can be projected down onto n-dimensional space, and the resulting set is still definable in terms of polynomial identities and inequalities.


constant problem

(mathematics) The problem of deciding whether a given expression is equal to zero.


kilogram-force

(obsolete) A unit of force equal to the weight, on earth (subject to standard gravity at 9.80665 m/s²), of a mass of one kilogram; equal to 9.80665 newtons. Symbol kgf or kg_f.


Ricci flow

(differential geometry) A process that deforms the metric of a Riemannian manifold in a way formally analogous to the diffusion of heat, smoothing out irregularities in the metric.


extra large

en-noun

extra large (countable and uncountable, plural extra larges)

(uncountable) One of several sizes to which an item may be manufactured.

(countable) An item labelled or denoted as being that size.

(countable) One who fits an item of that size.


extra large

(especially clothing) That is extra large (the manufactured size).


artificial stupidity

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

From the analogy with artificial intelligence.

artificial intelligence
artificial intelligence

Artificial intelligence
artificial intelligence#English

(humorous, artificial intelligence, computing, science fiction) Artificial intelligence that is not well developed.


artificial incompetence

artificial stupidity
artificial stupidity#English


artificially intelligent

en-adj

artificially intelligent (comparative more artificially intelligent, superlative most artificially intelligent)

more artificially intelligent (comparative)
most artificially intelligent (superlative)

artificial intelligence
artificial intelligence#English

(artificial intelligence, computing, science fiction) Possessing artificial intelligence.


artificially intelligently

en-adv

artificially intelligently (comparative more artificially intelligently, superlative most artificially intelligently)

more artificially intelligently (comparative)
most artificially intelligently (superlative)

(very rare, artificial intelligence, computing) By means of or through artificial intelligence.


Jacobian conjecture

en-noun

Jacobian conjecture (plural Jacobian conjectures)

(mathematics) A famous problem on polynomials in several variables.


Dixmier conjecture

(algebra) The conjecture that any endomorphism of a Weyl algebra is an automorphism.


ACW

(mathematics, electronics) Abbreviation of anticlockwise.


machine-translate

en-verb

machine-translate (third-person singular simple present machine-translates, present participle machine-translating, simple past and past participle machine-translated)

machine-translates (present singular third-person)
machine-translating (participle present)
machine-translated (participle past)
machine-translated (past)

Back-formation from machine translation.

(transitive) To translate using machine translation.


Floer homology

(mathematics) A tool for studying symplectic geometry and low-dimensional topology. It is a novel invariant that arises as an infinite-dimensional analog of finite-dimensional Morse homology.


quasi-transitive

(graph theory, of a graph) Such that its vertex set can be partitioned into finitely many sets, so that there exists an automorphism mapping a vertex to another vertex if and only if the two vertices belong to the same set in that partition.


semi-transitive

(graph theory, of a graph) Such that there exists a finite vertex set so that for any vertex there exists another vertex in that finite set and an injective homomorphism of the graph that maps the second vertex to the first vertex.


census-designated place

en-noun

census-designated place (plural census-designated places)

(US, demography) A place containing a concentration of population, defined by the United States Census Bureau for statistical purposes only; it is not a municipality, but either a subset of one or spanning into several.


artificial superintelligence

artificial superintelligence (plural artificial superintelligences)

Coordinate term: AGI

(artificial intelligence, science fiction) Artificial intelligence that is far greater than any human intelligence.


initial value problem

initial value problem (plural initial value problems)

ordinary differential equation
ordinary differential equation

(calculus) The problem of solving an ordinary differential equation together with an initial condition (a set of specified values for the unknown function or its derivatives at some point).


plesiohedron

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

The plesiohedra include such well-known shapes as the cube, hexagonal prism, rhombic dodecahedron, and truncated octahedron.

(geometry) A special kind of space-filling polyhedron, defined as the Voronoi cell of a symmetric Delone set. Three-dimensional Euclidean space can be completely filled by copies of any one of these shapes, with no overlaps.


Delone set

(mathematics) In the theory of metric spaces, a well-spaced set of points that is both uniformly discrete and relatively dense.


rep-tile

Coined as a pun on reptile by US mathematician Solomon W. Golomb. See repeat and tile.

(geometry) A shape that can be dissected into a number of smaller copies of the same shape.


metrization

(mathematics) The process or result of metrizing a topological space.

metrisering

the process or result of metrizing a space


SRW

simple random walk
simple random walk#English

(mathematics, probability) Initialism of simple random walk.


locally finite

(mathematics, of a graph) For which every vertex has finite degree.


gyrobifastigium

gyrobifastigium (plural gyrobifastigia or gyrobifastigiums)

gyrobifastigia (plural)
gyrobifastigiums (plural)

To elucidate this complex correlation, we carried out detailed Monte Carlo simulations of six convex space-filling polyhedrons, namely, truncated octahedrons, rhombic dodecahedrons, hexagonal prisms, cubes, gyrobifastigiums and triangular prisms.

2011 February, Umang Agarwal, Fernando A Escobedo, “Mesophase behaviour of polyhedral particles”, in Nature materials, volume 10:

They observed hard triangular prisms and hard gyrobifastigia to directly transform into their space-filling crystal, while hard truncated octahedra, rhombic.

2012, Amir Haji Akbari Balou, Thermodynamics of the Hard Tetrahedron System (PhD Dissertation in Chemical Engineering, University of Michigan):

But there are solids constructed from two or more regular prisms that also pack space. An interesting example (with an equally interesting name) is the gyrobifastigium, constructed from two regular triangular prisms. See Figure 1.2.14 for a picture of a gyrobifastigium, and a pattern (called a net) for constructing one.

2015, Claudi Alsina, Roger B. Nelsen, A Mathematical Space Odyssey: Solid Geometry in the 21st Century, →ISBN:

A polyhedral solid formed by joining two face-regular triangular prisms along corresponding square faces, giving a quarter-turn to one prism. It is noted for being one of the few regular polyhedra that packs in three dimensions.

異相双三角柱

いそうそうさんかくちゅう


DEX

DEX (countable and uncountable, plural DEXes or DEXs)

Examining the history of how DEXs have evolved can help elucidate where DEXs are headed and how they will compete with centralized exchanges.

2024 April 10, Alex Wearn, “CEXs vs. DEXs: The Future Battle Lines”, in CoinDesk:

The Solana blockchain alone did more volume than Ethereum, Base and BSC's cumulative DEX activity of $37.9 billion, of which Ethereum accounted for $14.3 billion while the rest did over $11 billion each.

2024 November 19, Omkar Godbole, “SOL Looks Set to Outperform BTC as Solana-Based DEXs Register Record $41B in Trading Volume: Godbole”, in CoinDesk:

(cryptocurrencies) Abbreviation of decentralized exchange.


sq yd

Abbreviation of square yard, a unit of area.


Weyl algebra

Named after Hermann Weyl, who introduced them to study the Heisenberg uncertainty principle in quantum mechanics.

differential operator
differential operator

(algebra) The ring of differential operators with polynomial coefficients (in one variable), namely expressions of the form f_m(X)∂_Xᵐ+f_m-1(X)∂_Xᵐ⁻¹+⋯+f_1(X)∂_X+f_0(X).


principal root

The square roots of 4 are 2 and −2; the principal square root of 4 is 2.

The 3rd roots of −8 are 1 + i√3, −2 and 1 − i√3; the principal 3rd root of −8 is 1 + i√3 and the real root is −2.

The 4th roots of 16 are 2, −2, 2i and −2i; the principal 4th root of 16 is 2.

(mathematics) A complex number which, when raised to the power of n, yields the radicand of its nth degree radical, and which has the greatest real part among all such numbers, and positive imaginary part in case of equality of the real parts.


abracadabrangle

A representation of the word "abracadabra" in the visual form of a triangle, used as an amulet or charm.


domain of convergence

domain of convergence (plural domains of convergence)

(mathematics) The process of approaching some limiting value.


Borel

(mathematical analysis, of a set) being a member of a Borel σ-algebra; being a Borel set

(mathematical analysis, of a function) Borel measurable


Rademacher distribution

probability distribution
probability distribution

(probability theory, statistics) A discrete probability distribution where a random variate has a 50% chance of being +1 and a 50% chance of being -1.


Young symmetrizer

Young symmetrizer (plural Young symmetrizers)

Named after British mathematician Alfred Young.

(mathematics) An element of the group algebra of the symmetric group, constructed in such a way that, for the homomorphism from the group algebra to the endomorphisms of a vector space V^(⊗n) obtained from the action of S_n on V^(⊗n) by permutation of indices, the image of the endomorphism determined by that element corresponds to an irreducible representation of the symmetric group over the complex numbers.


Nyquist

(mathematics, engineering) The Nyquist frequency of a system.


octacube

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


nodeset

(computing, graph theory) A set of nodes.


symptosis

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

(geometry) The meeting of polars of the same point with reference to different loci.


paracontrolled distribution

paracontrolled distribution (plural paracontrolled distributions)

(mathematics) A distribution d ∈ C^α is called paracontrolled by u ∈ C^α if there exists d′ ∈ Cᵝ such that d − d′ ≺ u ∈ C^(α+β).


impredicativity

(mathematics, logic) A self-referencing definition.


Morin surface

(topology) A halfway model of the sphere eversion, featuring fourfold rotational symmetry.


halfway model

(topology) An immersion of the sphere S² in R ³, which is the halfway point of a sphere eversion.


Willmore energy

Willmore energy (plural Willmore energies)

Named after the English geometer Thomas Willmore.

(differential geometry) A quantitative measure of how much a given surface deviates from a round sphere.


Eulerian trail

(graph theory) a trail that contains each edge exactly once.


Pisot-Vijayaraghavan number

Pisot-Vijayaraghavan number (plural Pisot-Vijayaraghavan numbers)

They became widely known after the publication of Charles Pisot's dissertation in 1938. Tirukkannapuram Vijayaraghavan continued their study in the 1940s.

(mathematics) A real algebraic integer greater than 1 all of whose Galois conjugates are less than 1 in absolute value.


crowdsale

The most proven use case for smart contracts so far is custom tokens and crowdsales.

2018, Kedar Iyer, Building Games with Ethereum Smart Contracts:

The sale documents said that once the Ethereum blockchain launched and the premined ether was issued, miners would generate new ether initially at an annual rate of 26% of the amount of ether issued in the crowdsale – the issuance rate isn’t fixed and is capped at 18 million ETH minted per year.

2020 November 7, Camila Russo, “Sale of the Century: The Inside Story of Ethereum's 2014 Premine”, in CoinDesk, archived from the original on 2024-06-17:

(Internet) An online event where participants can purchase tokens in a cryptocurrency.


Levi graph

Named for F. W. Levi, who wrote about them in 1942.

(mathematics) A bipartite graph associated with an incidence structure.


cold storage

(cryptocurrencies) A place where private keys are stored away from the Internet to prevent them from being stolen.


yugada

From Spanish yugada, from yugo (“yoke”) + -ada (“-ful”), from Latin iugum. Compare Latin iugerum (“juger”).

(historical) A traditional Spanish unit of land area, equivalent to about 32.2 ha.


outlyingness

(statistics, of a data point, etc.) The measure, degree or quality of being an outlier.


MSE

MSE (countable and uncountable, plural MSEs)

(statistics) Initialism of mean squared error.


MSD

MSD (countable and uncountable, plural MSDs)

mean squared deviation
w:mean squared deviation

(statistics) Initialism of mean squared deviation.

mean squared displacement
w:mean squared displacement

(statistics) Initialism of mean squared displacement.


cold boot attack

cold boot attack (plural cold boot attacks)

(cryptography) A type of sidechannel attack in which somebody with physical access to a computer is able to retrieve encryption keys from a running operating system after a reboot. It relies on the fact that the contents of memory can still be read for a short period after power is cut off.


smart contract

Coined by American computer scientist Nick Szabo in 1996.

coin

These are only a few examples of ways you can secure your smart contracts. The best thing to do to create a secure smart contract is to find an external auditor.

2019, Kevin Solorio, Randall Kanna, David H. Hoover, Hands-On Smart Contract Development with Solidity and Ethereum, O'Reilly Media, →ISBN, page 240:

Technically speaking a smart contract is a self-enforcing agreement between parties, mutually unknown and otherwise anonymous counterparts, which is capable of executing the rules automatically in satisfying certain conditions.

2020, Miadreza Shafie-khah, Blockchain-Based Smart Grids, Elsevier, →ISBN, page 112:

(technology, cryptocurrencies) A software protocol that is capable of automatically enforcing terms agreed upon in a contract.


Ethereum

List of fictional elements, materials, isotopes and subatomic particles

Coined by Russian-Canadian programmer Vitalik Buterin after browsing a list of fictional elements on Wikipedia; based on ether.

All Ethereum clients provide a set of JSON-RPC methods for external DApps to interact with the Ethereum blockchain network.

2019, Xun (Brian) Wu, Zhihong Zou, Dongying Song, “Ethereum Architecture and Ecosystem”, in Learn Ethereum […] , Packt Publishing Ltd, →ISBN, page 74:

An open source, blockchain-based cryptocurrency network, that features smart contracts.


interprime

(mathematics) The mean of two consecutive odd primes


compressed sensing

(statistics, signal processing) A signal processing technique for efficiently acquiring and reconstructing a signal, by finding solutions to underdetermined linear systems.


centerpoint

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

(statistics, geometry) A generalization of the median to data in higher-dimensional Euclidean space.


emirp

The sequence of emirps begins: 13, 17, 31, 37, 71, 73, 79, 97, 107, ...

The first few emirps in base 12 (using the convention T for ten and E for eleven) are: 15, 51, 57, 5E, 75, E5, 107, ...

Therefore we do not yet know whether the general emirps go on forever or whether they too eventually end with a largest emirp of all.

1986, Malcolm E. Lines, A Number for your Thoughts, Taylor & Francis, page 39:

(number theory) A prime number that becomes a different prime when its decimal digits (or digits in some specified other base) are reversed.


PEDMAS

order of operations
order of operations#English

please excuse my dear Aunt Sally#English

(mathematics, mnemonic) An acronym used to help people remember the order of operations, in the PEDMAS order (cf. "please excuse my dear Aunt Sally").


self-signed

(computing, cryptography) Of a security certificate: signed by the same entity whose identity it certifies; signed with its own private key.


self-signing

(computing, cryptography) The use of self-signed security certificates.


ochava

From Spanish ochava (“⅛ Spanish ounce”), from Latin octāvus (“one-eighth”). Doublet of octave, octavo, and oitava.

(historical) A traditional Spanish unit of mass, equivalent to about 3.6 g.


pseudologarithmic

A scale marked in this way will be termed an 'ideal' pseudologarithmic scale, departures from a true logarithmic relationship occurring only because of the presence in the grid current of a constant component, I₀, in addition to the ion current I.

1970, Electronic Engineering (volume 42, part 1, page 84)

(mathematics) Apparently, but not actually, logarithmic


Cremona-Richmond configuration

It was studied by Cremona (1877) and Richmond (1900).

(geometry) A configuration of 15 lines and 15 points, having three points on each line and three lines through each point, and containing no triangles.


Heegner point

Named after Kurt Heegner, German mathematician.

(geometry) A point on a modular curve that is the image of a quadratic imaginary point of the upper half-plane.


Seeds

Life-like cellular automaton
Life-like cellular automaton

(cellular automata) A Life-like cellular automaton with the rule B2/S.


cryptoworm

(cryptography, computer security) A form of malware that spreads in the form of a worm and encrypts victims' data.


Stark-Heegner theorem

Named after Kurt Heegner and Harold Stark, who contributed to the earliest proof.

(number theory) A theorem that states precisely which quadratic imaginary number fields admit unique factorization in their ring of integers.


pre-mine

(ecology) Before the opening of a mine in a region.


pre-mine

en-verb

pre-mine (third-person singular simple present pre-mines, present participle pre-mining, simple past and past participle pre-mined)

pre-mines (present singular third-person)
pre-mining (participle present)
pre-mined (participle past)
pre-mined (past)

To mine units of a cryptocurrency before its official launch.


scamcoin

(informal, derogatory) Any cryptocurrency designed primarily to benefit its creators.


Bitcoin faucet

(Internet) A website or app that gives out tiny amounts of bitcoin.


paper wallet

(cryptocurrencies) A collection of pieces of paper written or printed with credentials needed to spend one’s cryptocoins.


cryptocoin

Other risks related to the cryptocoin exchanges are related to operations and governance, which are too often informal and key-person dependent.

2020, Peet van Biljon, Alexandra Lajoux, Making Money […] , Walter de Gruyter GmbH & Co KG, →ISBN:


ICO

We have finished the coin website and are ready to launch the ICO offering. We are currently in the Phase 1 portion of the offering which is by far the best. We need your help in building a great community and we want to say Thank you with our ICO Phase one offering.

2014 February 27, Sparta, “Posted on Cryptocointalk.com”, in SpartaCoin, archived from the original on 2014-03-17:

The hype around blockchain technology is turning ICOs into the next digital gold rush: According to the research firm Smith and Crown, ICOs raised $27.6 million in the first two weeks of May alone.

2017 May 31, David Z. Morris, “The Rise of Cryptocurrency Ponzi Schemes”, in The Atlantic:

initial coin offering
initial coin offering#English

(cryptocurrencies) Initialism of initial coin offering.


initial coin offering

en-noun

initial coin offering (plural initial coin offerings)

The idea of an appcoin is not without its critics, however, as the topic broaches the sensitive topic of how assets are pre-allocated by cryptocurrency projects. In the altcoin world, where the development team commonly keeps a certain share of the initial coin offering, this process is known as premining.

2014 August 2, Daniel Cawrey, “The Promise and Pitfalls of Crypto Crowdfunding”, in CoinDesk, archived from the original on 2014-08-05:

A type of funding using cryptocurrencies.


orthopedal

On the other hand, the sides of the orthopedal Δ are equal to a cos A, etc. Hence, calling R, P, S, J circumradius, inradius, perimeter and area of ABC, an original Δ ; and r, p. s. j. those of DEF its orthopedal Δ, we have this neat reciprocation : Δ ABC = PS = Rs;

1936, Norman Alliston, Mathematical snack bar: a collection of notes and results, page 11:

The incentre of the orthopedal triangle is the orthocentre of the parent triangle.

1952, Marshall Henry Haddock, The Basis of Mine Surveying, page 26:

(mathematics) Orthogonal to the foot of a geometric figure.


qirat

From Arabic قِيرَاط (qīrāṭ). Doublet of carat.

bor

Arabic قِيرَاط (qīrāṭ)

A unit of weight, one twentieth of a mithqal.


Euler-Mascheroni constant

Named after mathematicians Leonhard Euler (1707—1783) and Lorenzo Mascheroni (1750—1800).
The origin of the notation γ is unclear: it may have been first used by either Euler or Mascheroni. It possibly reflects the constant's connection to the gamma function.

The run for #92;gamma, the Euler-Mascheroni constant, for instance, yielded 583 approximations with six decimals or more!

1988, Mathematics Magazine, Volume 61, Mathematical Association of America, page 82:

In the previous section we mentioned that we do no know, for instance, whether the Euler–Mascheroni constant or the numbers #92;zeta#95;#123;2k#43;1#125; for k#92;ge 2 are rational.

2003, János Surányi, Paul Erdős, translated by Barry Guiduli, Topics in the Theory of Numbers, Springer, page 100:

The Euler–Mascheroni constant, #92;gamma, considered to be the third important mathematical constant next to #92;pi and e, has appeared in a variety of mathematical formulae involving series, products and integrals[…].

2013, Ovidiu Furdui, Limits, Series, and Fractional Part Integrals: Problems in Mathematical Analysis, Springer, page 252:

(mathematics) A constant, denoted γ and recurring in analysis and number theory, that is defined as the limiting difference between the harmonic series and the natural logarithm and has the approximate value 0.57721566.

Euler-Mascheroni constant
Leonhard Euler
Lorenzo Mascheroni


preradical

(mathematics) A subfunctor of the identity functor in the category of left modules over a ring with identity.


Eulerian circuit

en-noun

Eulerian circuit (plural Eulerian circuits)

(graph theory) A Eulerian trail that begins and ends at the same node.


switch engine

2. Is it possible to make the switch engine leave debris other than the normal 8 blocks/288 generations?

1990 May 17, David Moews, “Life questions”, in comp.theory.cell-automata (Usenet):

He did this by placing a large number of switch engines together so as to eliminate all debris. His original ship required 13 switch engines, but his smaller one given here only uses 10 of them.

1992 August 13, David Bell, “Spaceships in Conway's Life (Part 1)”, in comp.theory.cell-automata (Usenet):

The average random Life pattern settles down instead of exploding (if you ignore output gliders and spaceships). There are exceptional quadratic-growth cases, mostly involving switch engines, but most random patterns affect only their immediate area.

2007 May 12, Dave Greene, “Wanted: 2D CA, "as complex" but "denser" than Life”, in comp.theory.cell-automata (Usenet):

(cellular automata) A particular methuselah in Conway's Game of Life that temporarily exhibits glide reflection symmetry while leaving debris behind, allowing for the construction of spaceships, puffers, and rakes.


octarius

Olivae oleum, L. Olea Europæa, E. Olive oil. An octarius of which acts as a gentle laxative.

1814, W. Peck, Veterinary Medicine, and Therapeutics: Containing the Effects of Medicines on various Animals; the Symptoms, Causes, and Treatment of Diseases, with a Select Collection of Formulaes, London, page 40:

(historical) the pint (eighth of a gallon) in the apothecaries' system


octavius

From New Latin octāvius, a misspelling or alteration of octārius.

apothecaries' system
w:apothecaries' system

(historical) Alternative form of octarius (the pint (eighth of a gallon) in the apothecaries' system)


CFA

confirmatory factor analysis
w:confirmatory factor analysis

(statistics) Initialism of confirmatory factor analysis.


Clifford module

Clifford module (plural Clifford modules)

(mathematics) A representation of a Clifford algebra.


Rice distribution

Rice distribution (plural Rice distributions)

(statistics) The probability distribution of the magnitude of a circular bivariate normal random variable with potentially non-zero mean.


plantkin

Some people were definitely fucking around: One blog, run by a "social justice warrior plantkin" who obsessively demands that their followers check their species privilege, was clearly a hoax.

2016 August 4, Callie Beusman, “'I Look at a Cloud and I See It as Me': The People Who Identify As Objects”, in Broadly:

As a demisexual plantkin I can't stand how white privileged transgendered people are acting as if they're the vanguard of the trans movement.

2015 September 4, Michelle Steiner, “Caitlyn Jenner on Ellen: Marriage equality views have evolved since transitioning”, in Entertainment Weekly:

No, sorry, but Jared is plantkin, though he's still searching to narrow it down.

2017, Bryant A. Loney, Take Me to the Cat, →ISBN, page 190:

A type of otherkin that identifies as a plant.


Langlands

(mathematics, used attributively) Canadian mathematician Robert Langlands.


Zhegalkin polynomial

Zhegalkin polynomial (plural Zhegalkin polynomials)

Named after the Russian mathematician Ivan Ivanovich Zhegalkin (1869–1947), who introduced them in 1927.

(logic, algebra) A Boolean-valued polynomial formed as a XOR-sum (or "ring sum") of conjunctions.

Ivan Ivanovich Zhegalkin
Zhegalkin polynomial


taxidistance

taxidistance (countable and uncountable, plural taxidistances)

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

Taxidistance is greater than Euclidean Distance.

1970 March, F Papy, G Papy, “Taximetry”, in International Journal of Mathematical Education in Science, volume 1, number 4:

Although she was still ready to support her previous result — that her diamond represented all the points at the same taxidistance from the center point — she also began to realize that this figure did not satisfy many of the other properties of circles.

1992, Raffaella Borasi, Learning mathematics through inquiry, page 86:

Help the students understand that there are multiple pathways between two points which have the minimum taxidistance.

1997, HRW geometry: explore, communicate, apply. Teaching transparencies directory, →ISBN:

taxicab distance
taxicab distance#English

(geometry) Alternative form of taxicab distance


taxi distance

taxi distance (countable and uncountable, plural taxi distances)

What is the taxi distance from A to P? Mark all the points you can find at a taxi distance 4 from A. Connect these points to form a square. This figure is a taxi circle.

2000, Alfred S. Posamentier, Making Geometry Come Alive: Student Activities and Teacher Notes, →ISBN:

To find the taxi distance between your home and your school, use the Ruler Postulate to find the horizontal and vertical distances.

2007, Orlando A. Oronce, Marilyn O. Mendoza, E-math: Geometry, →ISBN, page 423:

The taxi distance from P to Q is 7.

2012, EF Krause, Taxicab geometry: An adventure in non-Euclidean geometry:


Butterworth filter

Butterworth filter (plural Butterworth filters)

First described in 1930 by the British engineer and physicist Stephen Butterworth.

(signal processing) A kind of filter designed to have as flat a frequency response as possible in the passband.


trimean

(statistics) A measure of a probability distribution's location defined as a weighted average of the distribution's median and its two quartiles.


ring sum normal form

"Ring sum" refers to a XOR-sum of monomials, where XOR is the additive operator of a Boolean ring.

(algebra, logic) The form of a Boolean formula expressed using only the operators and constants of a Boolean ring (XOR, AND, 0, 1), some variables and possibly also coefficients, and without using any parentheses.


algebraic normal form

"Algebraic" would refer to the fact that a two-element Galois field, 𝔽₂ adjoined with some variables forms a polynomial algebra, 𝔽₂[x_1,...,x_n].

It is well known that every (n,1)-function f can be written uniquely as a multilinear polynomial over #92;mathbb#123;F#125;#95;2
#92;qquad#92;qquad#92;qquad#92;qquad#92;qquadf(x#95;1,...,x#95;n)#61;#92;sum#95;#123;X#92;subseteq#91;n#93;#125;#92;alpha#95;X#92;prod#95;#123;i#92;inX#125;x#95;i.
This polynomial is called the Zhegalkin polynomial or the algebraic normal form (ANF) of f.

2015 September 22, Magnus Gausdal Find, Joan Boyar, “Multiplicative Complexity of Vector Valued Boolean Functions”, in arxiv.org, retrieved 2017-08-10:

ring sum normal form
ring sum normal form


Boolean derivative

Boolean derivative (plural Boolean derivatives)

Named after George Boole (1815–1864), an English mathematician, educator, philosopher and logician.

(algebra) With respect to a Boolean variable x_i: The XOR-sum of the positive and negative Shannon cofactors of the given derived function with respect to x_i. In symbols: ∂f/∂x_i(⃑x)=f_x_i(⃑x)⊕f_̄x_i(⃑x).


Threefish

From three + fish, modelled on the earlier Twofish.

(cryptography) A symmetric-key tweakable block cipher involving the Skein hash function.


zero mode

(mathematics) An eigenvector that has a vanishingly small eigenvalue


semialgebra

(mathematics) A class that is closed under intersection and semiclosed under set difference


degree sequence

degree sequence (plural degree sequences)

(mathematics) A monotonic nonincreasing sequence of the vertex degrees of the vertices of a graph


anabelioid

(mathematics) An anabelian category or similar structure


subshot

We propose a novel supervised learning technique for summarizing videos by automatically selecting keyframes or key subshots.

2016, Ke Zhang, Wei-Lun Chao, Fei Sha, Kristen Grauman, “Video Summarization with Long Short-term Memory”, in arXiv:

(signal processing) A portion of a shot, in video material.


closed interval

closed interval (plural closed intervals)

(mathematics) an interval in the real number line which contains its supremum and infimum.


superdisk

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

(geometry) A closed curve, of form y = (1-xⁿ)^(1/n) (where n > 2), having properties intermediate between those of a circle and a square


halfsphere

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


comdag

Blend of combined + DAG (“directed acyclic graph”).

blend

(graph theory) A directed acyclic combined graph.


Hadamard transform

en-noun

Hadamard transform (plural Hadamard transforms)

Named for the French mathematician Jacques Hadamard.

(signal processing) A generalized Fourier transform that performs an orthogonal, symmetric, involutive, linear operation on 2ᵐ real numbers (or complex numbers, although the Hadamard matrices themselves are purely real).


X-shaped

x-förmig

shaped like the 24th letter of the alphabet

A-shaped - B-shaped - C-shaped - D-shaped - E-shaped - F-shaped - G-shaped - H-shaped - I-shaped - J-shaped - K-shaped - L-shaped - M-shaped - N-shaped - O-shaped - P-shaped - Q-shaped - R-shaped - S-shaped - T-shaped - U-shaped - V-shaped - W-shaped - X-shaped - Y-shaped - Z-shaped


Y-shaped

An immunoglobulin is a large, Y-shaped protein.

The constellation Virgo is a Y-shaped group, of which α, the star at the foot, is the well-known Spica, a star of the first magnitude.

1920, Edward Carpenter, Pagan and Christian Creeds, New York: Harcourt, Brace and Co., published 1921:


Z-shaped

Shaped like the letter "Z" or its mirror image.


zweibein

Equivalent to German zwei (“two”) + Beine (“legs”).

Expressed in terms of zweibein and spin-connection, non-einsteinian gravity in d = 2 resembles a gauge theory with noncompact group and with nonpolynomial self-interactions.

1992 August 31, Wolfgang Kummer, Dominik J. Schwarz, “Renormalization of R² gravity with dynamical torsion in d = 2”, in Nuclear Physics B, volume 382, number 1, →DOI, pages 171–186:


pronumeral

/pɹəʊˈnjuːməɹəl/

From pro- + numeral, modelled on pronoun.

Pronumerals are symbols, usually letters, used in place of numbers in an expression.

2006, Lyn Baker, “Algebraic Techniques”, in Year 9 Mathematics: Stage 5.3, page 15:

(Australia, mathematics) variable (symbol)


irregular prism

irregular prism (plural irregular prisms)

A right prism, having regular polygons for its terminating planes, is said to be regular ; an irregular prism is one in which the ends are irregular polygons.

1867, William Chambers, Robert Chambers, Chambers's Information for the People, page 652:

If the base be an irregular polygon of any number of sides, the prism is then called an irregular prism.

1806, Peter Jonas, The Genuine Art of Gauging Made Easy and Familiar, page 138:

(geometry) a prism whose cross section is an irregular polygon

If the base be a triangle, it is called a triangular prism; if a square, a square prism; if a pentagon, a pentagonal prism; and' if the base is any irregular figure, it is called an irregular prism : ...

1850, John Radford Young, An introductory treatise on mensuration, in theory and practice, page 115:

Irregular prisms have a cross-section with no well known shape. Some of the steel sections used in the construction industry belong to this category.

2016, Kusum Wadhwa, Anju Loomba, Saraswati Mathematics, Saraswati House Pvt Ltd, →ISBN, page 234:

(geometry) a solid that is like a prism but whose cross section is not (necessarily) a polygon


exponential decay

exponential decay (countable and uncountable, plural exponential decays)

The service value of the capital stock, i.e. the product of its price and quantity component, is decomposed into a depreciation component and an interest component, similar to the decomposition which holds under exponential decay.

2017, E. Biørn, Taxation, Technology, and the User Cost of Capital, →ISBN, page 239:

A decrease where the rate of decrease is proportional to the amount remaining.


extreme point

For convex cones, the concept of an extreme point is not of much use, since the origin would be the only candidate for an extreme point.

1970, R. Tyrrell Rockafellar -, Convex Analysis, →ISBN, page 162:

(mathematics) A point in a convex set which does not lie in any open line segment joining two points in the set.

At first glance, degeneracy, a concept based on properties of extreme point solutions, does not seem to be as serious a problem for IPMs as it is for simplex methods.

2001, Encyclopedia of Optimization, →ISBN, page 288:

(mathematics) The maximum or minimum of a function.

Since the extreme points are sorted in an ascending order, and it is known that there is no more event other than the event at the current leftmost extreme point, and therefore we traverse from the root of the tree to the bottom while we re-evaluating the new interval values of each node and testing the inclusion of the extreme point in the interval.

2004, Antonio Laganà, Marina L. Gavrilova, Vipin Kumar, Computational Science and Its Applications, →ISBN:

(mathematics) A leaf vertex of a tree data structure.


MML

minimum message length
w:minimum message length

(information theory) Initialism of minimum message length.


studentization

From student (“pseuodnym of William Sealy Gossett”) + -ization.

suffix

(statistics, originally) The use of Student's t-test.

(statistics, generally) The determination or use of a sampling distribution that is independent of nuisance parameters of the population distribution, which are not directly relevant to the estimates or tests of significance of primary interest.


nuisance parameter

en-noun

nuisance parameter (plural nuisance parameters)

(statistics) A parameter of the distribution of a population that is not directly relevant to solving the significance test or estimate problem under consideration.


GPT

/ˈd͡ʒiːˈpiːˈtiː/

We will use a 345M parameter GPT-2 transformer in TensorFlow from OpenAI's repository. We must get our hands dirty to understand GPT models.

2022, Denis Rothman, Antonio Gulli, Transformers for Natural Language Processing […] , Packt Publishing Ltd, →ISBN, page 168:

(machine learning) Initialism of generative pretrained transformer.


SYZ conjecture

From the initials of Strominger, Yau, and Zaslow, who proposed it.

(mathematics, physics) An attempt to understand the mirror symmetry conjecture, an issue in theoretical physics and mathematics.


ropani

(Nepal) A unit of area equal to 5476 square feet or roughly 0.126 acres.


eigenangle

(mathematics) An angle whose value is an eigenvalue


subarrangement

(mathematics) A subset of an arrangement


Wishart distribution

Wishart distribution (plural Wishart distributions)

Named in honour of Scottish mathematician John Wishart, who formulated the distribution in 1928.

The novelty of this work lies in its incorporation of a general conjugate prior distribution for the covariance matrix, namely a generalized inverted Wishart distribution (GIW). As its name suggests, this distribution, discovered by Brown et al. (1994b) generalizes the well-known inverted Wishart distribution.

2006, Nhu D. Le, James V. Zidek, Statistical Analysis of Environmental Space-Time Processes, Springer, page 142:

The basic properties of Wishart distributions are studied in Section 7.3.

2008, Martin Bilodeau, David Brenner, Theory of Multivariate Statistics, Springer, page 85:

Recall from Appendix B that the Wishart distribution W#95;d(#92;Sigma,n) is characterized by a positive definite matrix #92;Sigma and the degrees of freedom n.

2015, Sudharman K. Jayaweera, Signal Processing for Cognitive Radios, Wiley, page 459:

chi-square distribution
chi-square distribution

(statistics) A generalisation of the chi-square distribution to an arbitrary (integer) number of dimensions, or of the gamma distribution to a non-integer number of degrees of freedom.


artab

From Coptic ⲁⲣⲧⲁⲃ (artab), via Old Persian from Akkadian 𒅈𒁕𒁉 (/ardabu/, “capacity measure of about 56 litres”). Also found in Ancient Greek ἀρτάβη (artábē).

der

(historical) A dry measure, in ancient Egypt and Persia.


trivial topology

en-noun

trivial topology (plural trivial topologies)

(topology) A topology consisting only of the empty set and the underlying set.


underlying set

(topology) A set of "points" upon which a topology is built, thereby yielding a topological space.

(algebra) A set upon which some operations are defined, thereby yielding an algebraic structure.


cofinite topology

cofinite topology (plural cofinite topologies)

(topology) A topology consisting of the empty set and all cofinite subsets of the underlying set.