See homogeneous in All languages combined, or Wiktionary
Download JSON data for homogeneous meaning in English (38.4kB)
{
"antonyms": [
{
"word": "heterogeneous"
},
{
"word": "inhomogeneous"
}
],
"derived": [
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "bihomogeneous"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "homogeneous broadening"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "homogeneous catalysis"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "homogeneous coordinate"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "homogeneous equilibrium"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "homogeneous function"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "homogeneous ideal"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "homogeneously"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "homogeneous mixture"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "homogeneousness"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "homogeneous number"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "homogeneous polynomial"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "homogeneous radiation"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "homogeneous society"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "homogeneous space"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "homogeneous system"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "homogeneous width"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "inhomogeneous"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "nonhomogeneous"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "prehomogeneous"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "subhomogeneous"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "superhomogeneous"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "ultrahomogeneous"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "unhomogeneous"
}
],
"etymology_templates": [
{
"args": {
"1": "en",
"2": "ML.",
"3": "homogeneus"
},
"expansion": "Medieval Latin homogeneus",
"name": "der"
},
{
"args": {
"1": "en",
"2": "grc",
"3": "ὁμογενής",
"4": "",
"5": "of the same race, family or kind"
},
"expansion": "Ancient Greek ὁμογενής (homogenḗs, “of the same race, family or kind”)",
"name": "der"
},
{
"args": {
"1": "grc",
"2": "ὁμός",
"3": "",
"4": "same"
},
"expansion": "ὁμός (homós, “same”)",
"name": "m"
},
{
"args": {
"1": "grc",
"2": "γένος",
"3": "",
"4": "kind"
},
"expansion": "γένος (génos, “kind”)",
"name": "m"
},
{
"args": {
"1": "en",
"2": "homo-",
"3": "",
"4": "same"
},
"expansion": "homo- (“same”)",
"name": "m"
},
{
"args": {
"1": "en",
"2": "-ous",
"pos": "adjectival suffix"
},
"expansion": "-ous (adjectival suffix)",
"name": "m"
}
],
"etymology_text": "From Medieval Latin homogeneus, from Ancient Greek ὁμογενής (homogenḗs, “of the same race, family or kind”), from ὁμός (homós, “same”) + γένος (génos, “kind”). Compare homo- (“same”) and -ous (adjectival suffix).",
"head_templates": [
{
"args": {
"1": "-"
},
"expansion": "homogeneous (not comparable)",
"name": "en-adj"
}
],
"hyponyms": [
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"source": "Thesaurus:homogeneous",
"word": "connatural"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"source": "Thesaurus:homogeneous",
"tags": [
"figuratively"
],
"word": "monolithic"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"source": "Thesaurus:homogeneous",
"word": "monotone"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"source": "Thesaurus:homogeneous",
"word": "steady"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"source": "Thesaurus:homogeneous",
"word": "unalloyed"
}
],
"lang": "English",
"lang_code": "en",
"pos": "adj",
"related": [
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "homogeneity"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "homogenesis"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "homogenise"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "homogenize"
},
{
"_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"word": "homogeny"
}
],
"senses": [
{
"glosses": [
"Of the same kind; alike, similar."
],
"id": "en-homogeneous-en-adj-rBYmedCj",
"links": [
[
"alike",
"alike"
],
[
"similar",
"similar"
]
],
"tags": [
"not-comparable"
],
"translations": [
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "af",
"lang": "Afrikaans",
"sense": "of the same kind; alike, similar",
"word": "homogeen"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "sq",
"lang": "Albanian",
"sense": "of the same kind; alike, similar",
"word": "homogjen"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "hy",
"lang": "Armenian",
"roman": "miatarr",
"sense": "of the same kind; alike, similar",
"word": "միատարր"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "hy",
"lang": "Armenian",
"roman": "hamaseṙ",
"sense": "of the same kind; alike, similar",
"word": "համասեռ"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "bg",
"lang": "Bulgarian",
"roman": "ednoroden",
"sense": "of the same kind; alike, similar",
"word": "еднороден"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "ca",
"lang": "Catalan",
"sense": "of the same kind; alike, similar",
"word": "homogeni"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "of the same kind; alike, similar",
"word": "同質"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "tóngzhí, tóngzhì",
"sense": "of the same kind; alike, similar",
"word": "同质"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "cs",
"lang": "Czech",
"sense": "of the same kind; alike, similar",
"word": "stejnorodý"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "cs",
"lang": "Czech",
"sense": "of the same kind; alike, similar",
"word": "homogenní"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "nl",
"lang": "Dutch",
"sense": "of the same kind; alike, similar",
"word": "homogeen"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "fi",
"lang": "Finnish",
"sense": "of the same kind; alike, similar",
"word": "samanlainen"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "fi",
"lang": "Finnish",
"sense": "of the same kind; alike, similar",
"word": "homogeeninen"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "fr",
"lang": "French",
"sense": "of the same kind; alike, similar",
"word": "homogène"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "gl",
"lang": "Galician",
"sense": "of the same kind; alike, similar",
"word": "homoxéneo"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "de",
"lang": "German",
"sense": "of the same kind; alike, similar",
"word": "homogen"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "de",
"lang": "German",
"sense": "of the same kind; alike, similar",
"word": "gleichartig"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "el",
"lang": "Greek",
"roman": "omogenís",
"sense": "of the same kind; alike, similar",
"word": "ομογενής"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "el",
"lang": "Greek",
"roman": "omoiogenís",
"sense": "of the same kind; alike, similar",
"word": "ομοιογενής"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "hu",
"lang": "Hungarian",
"sense": "of the same kind; alike, similar",
"word": "homogén"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "is",
"lang": "Icelandic",
"sense": "of the same kind; alike, similar",
"word": "einsleitur"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "is",
"lang": "Icelandic",
"sense": "of the same kind; alike, similar",
"word": "einleitur"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "is",
"lang": "Icelandic",
"sense": "of the same kind; alike, similar",
"word": "eingerður"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "is",
"lang": "Icelandic",
"sense": "of the same kind; alike, similar",
"word": "samkynja"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "is",
"lang": "Icelandic",
"sense": "of the same kind; alike, similar",
"word": "samleitur"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "ga",
"lang": "Irish",
"sense": "of the same kind; alike, similar",
"word": "aonchineálach"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "it",
"lang": "Italian",
"sense": "of the same kind; alike, similar",
"word": "omogeneo"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"alt": "きんしつ",
"code": "ja",
"lang": "Japanese",
"roman": "kinshitsu",
"sense": "of the same kind; alike, similar",
"word": "均質"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"alt": "どうしつ",
"code": "ja",
"lang": "Japanese",
"roman": "dōshitsu",
"sense": "of the same kind; alike, similar",
"word": "同質"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "kk",
"lang": "Kazakh",
"roman": "gomogendık",
"sense": "of the same kind; alike, similar",
"word": "гомогендік"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "kk",
"lang": "Kazakh",
"roman": "bırtektı",
"sense": "of the same kind; alike, similar",
"word": "біртекті"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "mk",
"lang": "Macedonian",
"roman": "ednoobrazen",
"sense": "of the same kind; alike, similar",
"word": "еднообразен"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "mk",
"lang": "Macedonian",
"roman": "ednoroden",
"sense": "of the same kind; alike, similar",
"word": "еднороден"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "mk",
"lang": "Macedonian",
"roman": "homogen",
"sense": "of the same kind; alike, similar",
"word": "хомоген"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "gv",
"lang": "Manx",
"sense": "of the same kind; alike, similar",
"word": "cocheintagh"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "nb",
"lang": "Norwegian Bokmål",
"sense": "of the same kind; alike, similar",
"word": "homogen"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "nn",
"lang": "Norwegian Nynorsk",
"sense": "of the same kind; alike, similar",
"word": "homogen"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "pl",
"lang": "Polish",
"sense": "of the same kind; alike, similar",
"word": "jednorodny"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "pl",
"lang": "Polish",
"sense": "of the same kind; alike, similar",
"word": "jednolity"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "pt",
"lang": "Portuguese",
"sense": "of the same kind; alike, similar",
"word": "homogêneo"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "pt",
"lang": "Portuguese",
"sense": "of the same kind; alike, similar",
"word": "homogéneo"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "ro",
"lang": "Romanian",
"sense": "of the same kind; alike, similar",
"word": "omogen"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "ru",
"lang": "Russian",
"roman": "odnoródnyj",
"sense": "of the same kind; alike, similar",
"word": "одноро́дный"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "ru",
"lang": "Russian",
"roman": "gomogénnyj",
"sense": "of the same kind; alike, similar",
"word": "гомоге́нный"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "ru",
"lang": "Russian",
"roman": "jedinoobráznyj",
"sense": "of the same kind; alike, similar",
"word": "единообра́зный"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "es",
"lang": "Spanish",
"sense": "of the same kind; alike, similar",
"word": "homogéneo"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "sv",
"lang": "Swedish",
"sense": "of the same kind; alike, similar",
"word": "homogen"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "sv",
"lang": "Swedish",
"sense": "of the same kind; alike, similar",
"word": "enhetlig"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "tl",
"lang": "Tagalog",
"sense": "of the same kind; alike, similar",
"word": "tulad-uriin"
},
{
"_dis1": "30 8 9 6 6 6 6 1 5 2 2 2 2 9 2 3 1",
"code": "te",
"lang": "Telugu",
"roman": "sajāti",
"sense": "of the same kind; alike, similar",
"word": "సజాతి"
}
]
},
{
"categories": [],
"examples": [
{
"ref": "1946, Bertrand Russell, History of Western Philosophy, I.25",
"text": "Their citizens were not of homogeneous origin, but were from all parts of Greece.",
"type": "quotation"
}
],
"glosses": [
"Having the same composition throughout; of uniform make-up."
],
"id": "en-homogeneous-en-adj-6oN~FP6g",
"links": [
[
"composition",
"composition"
],
[
"uniform",
"uniform"
]
],
"tags": [
"not-comparable"
],
"translations": [
{
"_dis1": "8 22 10 7 7 7 7 1 5 3 3 2 2 10 3 3 1",
"code": "hy",
"lang": "Armenian",
"roman": "hamaseṙ",
"sense": "having the same composition throughout",
"word": "համասեռ"
},
{
"_dis1": "8 22 10 7 7 7 7 1 5 3 3 2 2 10 3 3 1",
"code": "bg",
"lang": "Bulgarian",
"roman": "ednoroden",
"sense": "having the same composition throughout",
"word": "еднороден"
},
{
"_dis1": "8 22 10 7 7 7 7 1 5 3 3 2 2 10 3 3 1",
"code": "bg",
"lang": "Bulgarian",
"roman": "homogenen",
"sense": "having the same composition throughout",
"word": "хомогенен"
},
{
"_dis1": "8 22 10 7 7 7 7 1 5 3 3 2 2 10 3 3 1",
"code": "ca",
"lang": "Catalan",
"sense": "having the same composition throughout",
"word": "homogeni"
},
{
"_dis1": "8 22 10 7 7 7 7 1 5 3 3 2 2 10 3 3 1",
"code": "fi",
"lang": "Finnish",
"sense": "having the same composition throughout",
"word": "tasa-aineinen"
},
{
"_dis1": "8 22 10 7 7 7 7 1 5 3 3 2 2 10 3 3 1",
"code": "fi",
"lang": "Finnish",
"sense": "having the same composition throughout",
"word": "homogeeninen"
},
{
"_dis1": "8 22 10 7 7 7 7 1 5 3 3 2 2 10 3 3 1",
"code": "fr",
"lang": "French",
"sense": "having the same composition throughout",
"word": "homogène"
},
{
"_dis1": "8 22 10 7 7 7 7 1 5 3 3 2 2 10 3 3 1",
"code": "it",
"lang": "Italian",
"sense": "having the same composition throughout",
"word": "omogeneo"
},
{
"_dis1": "8 22 10 7 7 7 7 1 5 3 3 2 2 10 3 3 1",
"code": "mk",
"lang": "Macedonian",
"roman": "ednoroden",
"sense": "having the same composition throughout",
"word": "еднороден"
},
{
"_dis1": "8 22 10 7 7 7 7 1 5 3 3 2 2 10 3 3 1",
"code": "mk",
"lang": "Macedonian",
"roman": "ednoobrazen",
"sense": "having the same composition throughout",
"word": "еднообразен"
},
{
"_dis1": "8 22 10 7 7 7 7 1 5 3 3 2 2 10 3 3 1",
"code": "mk",
"lang": "Macedonian",
"roman": "homogen",
"sense": "having the same composition throughout",
"word": "хомоген"
},
{
"_dis1": "8 22 10 7 7 7 7 1 5 3 3 2 2 10 3 3 1",
"code": "mi",
"lang": "Maori",
"sense": "having the same composition throughout",
"word": "kanorite"
},
{
"_dis1": "8 22 10 7 7 7 7 1 5 3 3 2 2 10 3 3 1",
"code": "pt",
"lang": "Portuguese",
"sense": "having the same composition throughout",
"word": "homogêneo"
},
{
"_dis1": "8 22 10 7 7 7 7 1 5 3 3 2 2 10 3 3 1",
"code": "es",
"lang": "Spanish",
"sense": "having the same composition throughout",
"word": "homogéneo"
},
{
"_dis1": "8 22 10 7 7 7 7 1 5 3 3 2 2 10 3 3 1",
"code": "sv",
"lang": "Swedish",
"sense": "having the same composition throughout",
"word": "homogen"
},
{
"_dis1": "8 22 10 7 7 7 7 1 5 3 3 2 2 10 3 3 1",
"code": "tl",
"lang": "Tagalog",
"sense": "having the same composition throughout",
"word": "tulad-uriin"
}
]
},
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Chemistry",
"orig": "en:Chemistry",
"parents": [
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"_dis": "5 6 8 4 6 6 6 1 7 7 7 6 6 7 7 7 2",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "5 6 9 4 6 6 6 2 7 7 7 7 7 7 7 7 2",
"kind": "other",
"name": "English entries with language name categories using raw markup",
"parents": [
"Entries with language name categories using raw markup",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "4 4 10 5 9 8 5 3 6 8 4 6 5 6 6 8 3",
"kind": "other",
"name": "English terms prefixed with homo-",
"parents": [],
"source": "w+disamb"
}
],
"glosses": [
"In the same state of matter."
],
"id": "en-homogeneous-en-adj-1v2Brlrf",
"links": [
[
"chemistry",
"chemistry"
],
[
"state of matter",
"state of matter"
]
],
"raw_glosses": [
"(chemistry) In the same state of matter."
],
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}
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"text": "The polynomial x²+5xy+y² is homogeneous of degree 2, because x², xy, and y² are all degree 2 monomials"
}
],
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"Of polynomials, functions, equations, systems of equations, or linear maps:",
"Such that all its nonzero terms have the same degree."
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"(of a linear differential equation) Having its degree-zero term equal to zero; admitting the trivial solution."
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"Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)"
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[
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"(ring theory, of an element of a graded ring) Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)"
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"glosses": [
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"Which respects the grading of its domain and codomain. Formally: Satisfying f(V_j)⊆W_i+j for fixed i (called the degree or grade of f), V_j the jth component of the grading of f 's domain, W_k the kth component of the grading of f 's codomain, and + representing the monoid operation in I."
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"In abstract algebra and geometry:",
"(of a linear map f between vector spaces graded by a commutative monoid I) Which respects the grading of its domain and codomain. Formally: Satisfying f(V_j)⊆W_i+j for fixed i (called the degree or grade of f), V_j the jth component of the grading of f 's domain, W_k the kth component of the grading of f 's codomain, and + representing the monoid operation in I."
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"glosses": [
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"Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful)."
],
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[
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[
"automorphism",
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[
"faithful",
"faithful"
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],
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"glosses": [
"In abstract algebra and geometry:",
"Of or relating to homogeneous coordinates."
],
"id": "en-homogeneous-en-adj-U6d14Ipd",
"links": [
[
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"abstract algebra#English"
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[
"geometry",
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[
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"geometry"
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[
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"homogeneous coordinate"
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],
"raw_glosses": [
"In abstract algebra and geometry:",
"(geometry) Of or relating to homogeneous coordinates."
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"tags": [
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],
"topics": [
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},
{
"categories": [
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"kind": "topical",
"langcode": "en",
"name": "Probability theory",
"orig": "en:Probability theory",
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"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
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{
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"_dis": "3 4 7 3 8 8 8 1 5 5 5 7 7 7 7 10 3",
"kind": "topical",
"langcode": "en",
"name": "Systems theory",
"orig": "en:Systems theory",
"parents": [
"Sciences",
"Systems",
"All topics",
"Interdisciplinary fields",
"Society",
"Fundamental"
],
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}
],
"glosses": [
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"(probability theory, Fourier analysis, of a distribution S on Euclidean n-space (or on ℝⁿmathbf 0)) Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m.",
"Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m."
],
"id": "en-homogeneous-en-adj-YpyqyBwO",
"links": [
[
"probability theory",
"probability theory"
],
[
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"Fourier analysis"
],
[
"distribution",
"distribution"
],
[
"Euclidean",
"Euclidean"
],
[
"test function",
"test function"
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],
"qualifier": "Fourier analysis",
"raw_glosses": [
"In miscellaneous other senses:",
"(probability theory, Fourier analysis, of a distribution S on Euclidean n-space (or on ℝⁿmathbf 0)) Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m."
],
"raw_tags": [
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"tags": [
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"topics": [
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"sciences"
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{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Set theory",
"orig": "en:Set theory",
"parents": [
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"Formal sciences",
"Sciences",
"All topics",
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"Holding between a set and itself; being an endorelation."
],
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[
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[
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{
"ipa": "/ˌhəʊ.mə(ʊ)ˈdʒiː.nɪəs/",
"tags": [
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{
"ipa": "/ˌhoʊ.moʊˈd͡ʒiː.njəs/",
"tags": [
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{
"ipa": "/ˌhoʊ.məˈd͡ʒiː.njəs/",
"tags": [
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},
{
"ipa": "/ˌhoʊ.moʊˈd͡ʒɛ.njəs/",
"tags": [
"US"
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},
{
"ipa": "/həˈmɑ.d͡ʒə.nəs/",
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"alt": "may be considered incorrect; see usage note at §§ Usage notes",
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"source": "Thesaurus:homogeneous",
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"source": "Thesaurus:homogeneous",
"word": "onefold"
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{
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"source": "Thesaurus:homogeneous",
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"word": "uniform"
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"source": "Thesaurus:homogeneous",
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{
"word": "inhomogeneous"
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"English terms with audio links",
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"word": "bihomogeneous"
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{
"word": "homogeneous broadening"
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{
"word": "homogeneous catalysis"
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{
"word": "homogeneous coordinate"
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{
"word": "homogeneous equilibrium"
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{
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{
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{
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{
"word": "homogeneous mixture"
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{
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{
"word": "homogeneous number"
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{
"word": "homogeneous polynomial"
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{
"word": "homogeneous radiation"
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{
"word": "homogeneous society"
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{
"word": "homogeneous space"
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{
"word": "homogeneous system"
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{
"word": "homogeneous width"
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{
"args": {
"1": "en",
"2": "grc",
"3": "ὁμογενής",
"4": "",
"5": "of the same race, family or kind"
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{
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{
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{
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"2": "-ous",
"pos": "adjectival suffix"
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"name": "m"
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"etymology_text": "From Medieval Latin homogeneus, from Ancient Greek ὁμογενής (homogenḗs, “of the same race, family or kind”), from ὁμός (homós, “same”) + γένος (génos, “kind”). Compare homo- (“same”) and -ous (adjectival suffix).",
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"word": "connatural"
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{
"source": "Thesaurus:homogeneous",
"tags": [
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"word": "monolithic"
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{
"source": "Thesaurus:homogeneous",
"word": "monotone"
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{
"source": "Thesaurus:homogeneous",
"word": "steady"
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{
"source": "Thesaurus:homogeneous",
"word": "unalloyed"
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"lang": "English",
"lang_code": "en",
"pos": "adj",
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{
"word": "homogenesis"
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{
"word": "homogenise"
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{
"word": "homogenize"
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{
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"categories": [
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"Quotation templates to be cleaned"
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"ref": "1946, Bertrand Russell, History of Western Philosophy, I.25",
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"text": "The polynomial x²+5xy+y² is homogeneous of degree 2, because x², xy, and y² are all degree 2 monomials"
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"(linear algebra, by specialization, of a system of linear equations) Such that all the constant terms are zero."
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"Such that if each of f 's inputs are multiplied by the same scalar, f 's output is multiplied by the same scalar to some fixed power (called the degree of homogeneity or degree of f). (Formally and more generally, of a partial function f between vector spaces whose domain is a linear cone) Satisfying the equality f(s mathbf x)=sᵏᶠ("
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"(mathematical analysis, generalizing the case of polynomial functions, of a function f) Such that if each of f 's inputs are multiplied by the same scalar, f 's output is multiplied by the same scalar to some fixed power (called the degree of homogeneity or degree of f). (Formally and more generally, of a partial function f between vector spaces whose domain is a linear cone) Satisfying the equality f(s mathbf x)=sᵏᶠ("
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"glosses": [
"The function f(x,y)#x3D;x²#x2B;x²ʸ#x2B;y² is not homogeneous on all of #x5C;mathbb#x7B;R#x7D;² because f(2,2)#x3D;16#x5C;neq 2ᵏ#x2A;3#x3D;2ᵏf(1,1) for any k, but f is homogeneous on the subspace of #x5C;mathbb#x7B;R#x7D;² spanned by (1,0) because f(#x5C;alphax,#x5C;alphay)#x3D;#x5C;alphax²#x3D;#x5C;alpha²f(x,y) for all (x,y)#x5C;in#x5C;operatorname#x7B;Span#x7D;#x5C;#x7B;(1,0)#x5C;#x7D;."
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{
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"In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):",
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"(of a first-order differential equation) Capable of being written in the form f(x,y) mathop dy=g(x,y) mathop dx where f and g are homogeneous functions of the same degree as each other."
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"(of a general differential equation) Homogeneous as a function of the dependent variable and its derivatives."
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"tags": [
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"categories": [
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"glosses": [
"In abstract algebra and geometry:",
"Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)"
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"links": [
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[
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"qualifier": "ring theory",
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"(ring theory, of an element of a graded ring) Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)"
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{
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"In abstract algebra and geometry:",
"Which respects the grading of its domain and codomain. Formally: Satisfying f(V_j)⊆W_i+j for fixed i (called the degree or grade of f), V_j the jth component of the grading of f 's domain, W_k the kth component of the grading of f 's codomain, and + representing the monoid operation in I."
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"links": [
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[
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"(of a linear map f between vector spaces graded by a commutative monoid I) Which respects the grading of its domain and codomain. Formally: Satisfying f(V_j)⊆W_i+j for fixed i (called the degree or grade of f), V_j the jth component of the grading of f 's domain, W_k the kth component of the grading of f 's codomain, and + representing the monoid operation in I."
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"raw_tags": [
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"tags": [
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},
{
"categories": [
"en:Geometry"
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"glosses": [
"In abstract algebra and geometry:",
"Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful)."
],
"links": [
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[
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[
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[
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[
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[
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[
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[
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[
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[
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"faithful"
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"raw_glosses": [
"In abstract algebra and geometry:",
"(geometry, of a space equipped with a group action) Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful)."
],
"raw_tags": [
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"tags": [
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"topics": [
"geometry",
"mathematics",
"sciences"
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},
{
"categories": [
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"glosses": [
"In abstract algebra and geometry:",
"Of or relating to homogeneous coordinates."
],
"links": [
[
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"abstract algebra#English"
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[
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"geometry#English"
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[
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"geometry"
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[
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"raw_glosses": [
"In abstract algebra and geometry:",
"(geometry) Of or relating to homogeneous coordinates."
],
"tags": [
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],
"topics": [
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"mathematics",
"sciences"
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},
{
"categories": [
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],
"glosses": [
"In miscellaneous other senses:",
"(probability theory, Fourier analysis, of a distribution S on Euclidean n-space (or on ℝⁿmathbf 0)) Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m.",
"Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m."
],
"links": [
[
"probability theory",
"probability theory"
],
[
"Fourier analysis",
"Fourier analysis"
],
[
"distribution",
"distribution"
],
[
"Euclidean",
"Euclidean"
],
[
"test function",
"test function"
]
],
"qualifier": "Fourier analysis",
"raw_glosses": [
"In miscellaneous other senses:",
"(probability theory, Fourier analysis, of a distribution S on Euclidean n-space (or on ℝⁿmathbf 0)) Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m."
],
"raw_tags": [
"of a distribution S on Euclidean n-space (or on ℝⁿmathbf 0)"
],
"tags": [
"not-comparable"
],
"topics": [
"mathematics",
"probability-theory",
"sciences"
]
},
{
"categories": [
"en:Set theory"
],
"glosses": [
"In miscellaneous other senses:",
"Holding between a set and itself; being an endorelation."
],
"links": [
[
"set theory",
"set theory"
],
[
"order theory",
"order theory"
],
[
"relation",
"relation"
],
[
"set",
"set"
],
[
"endorelation",
"endorelation"
]
],
"raw_glosses": [
"In miscellaneous other senses:",
"(set theory, order theory, of a relation) Holding between a set and itself; being an endorelation."
],
"raw_tags": [
"of a relation"
],
"tags": [
"not-comparable"
],
"topics": [
"mathematics",
"order-theory",
"sciences",
"set-theory"
]
}
],
"sounds": [
{
"ipa": "/ˌhɒ.mə(ʊ)ˈdʒiː.nɪəs/",
"tags": [
"UK"
]
},
{
"ipa": "/ˌhəʊ.mə(ʊ)ˈdʒiː.nɪəs/",
"tags": [
"UK"
]
},
{
"ipa": "/ˌhoʊ.moʊˈd͡ʒiː.njəs/",
"tags": [
"US"
]
},
{
"ipa": "/ˌhoʊ.məˈd͡ʒiː.njəs/",
"tags": [
"US"
]
},
{
"ipa": "/ˌhoʊ.moʊˈd͡ʒɛ.njəs/",
"tags": [
"US"
]
},
{
"ipa": "/həˈmɑ.d͡ʒə.nəs/",
"tags": [
"US"
]
},
{
"audio": "En-uk-homogeneous.ogg",
"mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/4/41/En-uk-homogeneous.ogg/En-uk-homogeneous.ogg.mp3",
"ogg_url": "https://upload.wikimedia.org/wikipedia/commons/4/41/En-uk-homogeneous.ogg",
"tags": [
"UK"
],
"text": "Audio (UK)"
}
],
"synonyms": [
{
"alt": "may be considered incorrect; see usage note at §§ Usage notes",
"word": "homogenous"
},
{
"source": "Thesaurus:homogeneous",
"word": "homogeneous"
},
{
"source": "Thesaurus:homogeneous",
"word": "invariable"
},
{
"source": "Thesaurus:homogeneous",
"tags": [
"idiomatic"
],
"word": "of a piece"
},
{
"source": "Thesaurus:homogeneous",
"word": "onefold"
},
{
"source": "Thesaurus:homogeneous",
"tags": [
"dialectal"
],
"word": "samely"
},
{
"source": "Thesaurus:homogeneous",
"word": "uniform"
},
{
"source": "Thesaurus:homogeneous",
"tags": [
"obsolete"
],
"word": "uniformal"
},
{
"source": "Thesaurus:homogeneous",
"word": "unmixed"
},
{
"source": "Thesaurus:homogeneous",
"word": "unvaried"
},
{
"source": "Thesaurus:homogeneous",
"word": "unvarying"
}
],
"translations": [
{
"code": "af",
"lang": "Afrikaans",
"sense": "of the same kind; alike, similar",
"word": "homogeen"
},
{
"code": "sq",
"lang": "Albanian",
"sense": "of the same kind; alike, similar",
"word": "homogjen"
},
{
"code": "hy",
"lang": "Armenian",
"roman": "miatarr",
"sense": "of the same kind; alike, similar",
"word": "միատարր"
},
{
"code": "hy",
"lang": "Armenian",
"roman": "hamaseṙ",
"sense": "of the same kind; alike, similar",
"word": "համասեռ"
},
{
"code": "bg",
"lang": "Bulgarian",
"roman": "ednoroden",
"sense": "of the same kind; alike, similar",
"word": "еднороден"
},
{
"code": "ca",
"lang": "Catalan",
"sense": "of the same kind; alike, similar",
"word": "homogeni"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "of the same kind; alike, similar",
"word": "同質"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "tóngzhí, tóngzhì",
"sense": "of the same kind; alike, similar",
"word": "同质"
},
{
"code": "cs",
"lang": "Czech",
"sense": "of the same kind; alike, similar",
"word": "stejnorodý"
},
{
"code": "cs",
"lang": "Czech",
"sense": "of the same kind; alike, similar",
"word": "homogenní"
},
{
"code": "nl",
"lang": "Dutch",
"sense": "of the same kind; alike, similar",
"word": "homogeen"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "of the same kind; alike, similar",
"word": "samanlainen"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "of the same kind; alike, similar",
"word": "homogeeninen"
},
{
"code": "fr",
"lang": "French",
"sense": "of the same kind; alike, similar",
"word": "homogène"
},
{
"code": "gl",
"lang": "Galician",
"sense": "of the same kind; alike, similar",
"word": "homoxéneo"
},
{
"code": "de",
"lang": "German",
"sense": "of the same kind; alike, similar",
"word": "homogen"
},
{
"code": "de",
"lang": "German",
"sense": "of the same kind; alike, similar",
"word": "gleichartig"
},
{
"code": "el",
"lang": "Greek",
"roman": "omogenís",
"sense": "of the same kind; alike, similar",
"word": "ομογενής"
},
{
"code": "el",
"lang": "Greek",
"roman": "omoiogenís",
"sense": "of the same kind; alike, similar",
"word": "ομοιογενής"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "of the same kind; alike, similar",
"word": "homogén"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "of the same kind; alike, similar",
"word": "einsleitur"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "of the same kind; alike, similar",
"word": "einleitur"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "of the same kind; alike, similar",
"word": "eingerður"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "of the same kind; alike, similar",
"word": "samkynja"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "of the same kind; alike, similar",
"word": "samleitur"
},
{
"code": "ga",
"lang": "Irish",
"sense": "of the same kind; alike, similar",
"word": "aonchineálach"
},
{
"code": "it",
"lang": "Italian",
"sense": "of the same kind; alike, similar",
"word": "omogeneo"
},
{
"alt": "きんしつ",
"code": "ja",
"lang": "Japanese",
"roman": "kinshitsu",
"sense": "of the same kind; alike, similar",
"word": "均質"
},
{
"alt": "どうしつ",
"code": "ja",
"lang": "Japanese",
"roman": "dōshitsu",
"sense": "of the same kind; alike, similar",
"word": "同質"
},
{
"code": "kk",
"lang": "Kazakh",
"roman": "gomogendık",
"sense": "of the same kind; alike, similar",
"word": "гомогендік"
},
{
"code": "kk",
"lang": "Kazakh",
"roman": "bırtektı",
"sense": "of the same kind; alike, similar",
"word": "біртекті"
},
{
"code": "mk",
"lang": "Macedonian",
"roman": "ednoobrazen",
"sense": "of the same kind; alike, similar",
"word": "еднообразен"
},
{
"code": "mk",
"lang": "Macedonian",
"roman": "ednoroden",
"sense": "of the same kind; alike, similar",
"word": "еднороден"
},
{
"code": "mk",
"lang": "Macedonian",
"roman": "homogen",
"sense": "of the same kind; alike, similar",
"word": "хомоген"
},
{
"code": "gv",
"lang": "Manx",
"sense": "of the same kind; alike, similar",
"word": "cocheintagh"
},
{
"code": "nb",
"lang": "Norwegian Bokmål",
"sense": "of the same kind; alike, similar",
"word": "homogen"
},
{
"code": "nn",
"lang": "Norwegian Nynorsk",
"sense": "of the same kind; alike, similar",
"word": "homogen"
},
{
"code": "pl",
"lang": "Polish",
"sense": "of the same kind; alike, similar",
"word": "jednorodny"
},
{
"code": "pl",
"lang": "Polish",
"sense": "of the same kind; alike, similar",
"word": "jednolity"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "of the same kind; alike, similar",
"word": "homogêneo"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "of the same kind; alike, similar",
"word": "homogéneo"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "of the same kind; alike, similar",
"word": "omogen"
},
{
"code": "ru",
"lang": "Russian",
"roman": "odnoródnyj",
"sense": "of the same kind; alike, similar",
"word": "одноро́дный"
},
{
"code": "ru",
"lang": "Russian",
"roman": "gomogénnyj",
"sense": "of the same kind; alike, similar",
"word": "гомоге́нный"
},
{
"code": "ru",
"lang": "Russian",
"roman": "jedinoobráznyj",
"sense": "of the same kind; alike, similar",
"word": "единообра́зный"
},
{
"code": "es",
"lang": "Spanish",
"sense": "of the same kind; alike, similar",
"word": "homogéneo"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "of the same kind; alike, similar",
"word": "homogen"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "of the same kind; alike, similar",
"word": "enhetlig"
},
{
"code": "tl",
"lang": "Tagalog",
"sense": "of the same kind; alike, similar",
"word": "tulad-uriin"
},
{
"code": "te",
"lang": "Telugu",
"roman": "sajāti",
"sense": "of the same kind; alike, similar",
"word": "సజాతి"
},
{
"code": "hy",
"lang": "Armenian",
"roman": "hamaseṙ",
"sense": "having the same composition throughout",
"word": "համասեռ"
},
{
"code": "bg",
"lang": "Bulgarian",
"roman": "ednoroden",
"sense": "having the same composition throughout",
"word": "еднороден"
},
{
"code": "bg",
"lang": "Bulgarian",
"roman": "homogenen",
"sense": "having the same composition throughout",
"word": "хомогенен"
},
{
"code": "ca",
"lang": "Catalan",
"sense": "having the same composition throughout",
"word": "homogeni"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "having the same composition throughout",
"word": "tasa-aineinen"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "having the same composition throughout",
"word": "homogeeninen"
},
{
"code": "fr",
"lang": "French",
"sense": "having the same composition throughout",
"word": "homogène"
},
{
"code": "it",
"lang": "Italian",
"sense": "having the same composition throughout",
"word": "omogeneo"
},
{
"code": "mk",
"lang": "Macedonian",
"roman": "ednoroden",
"sense": "having the same composition throughout",
"word": "еднороден"
},
{
"code": "mk",
"lang": "Macedonian",
"roman": "ednoobrazen",
"sense": "having the same composition throughout",
"word": "еднообразен"
},
{
"code": "mk",
"lang": "Macedonian",
"roman": "homogen",
"sense": "having the same composition throughout",
"word": "хомоген"
},
{
"code": "mi",
"lang": "Maori",
"sense": "having the same composition throughout",
"word": "kanorite"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "having the same composition throughout",
"word": "homogêneo"
},
{
"code": "es",
"lang": "Spanish",
"sense": "having the same composition throughout",
"word": "homogéneo"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "having the same composition throughout",
"word": "homogen"
},
{
"code": "tl",
"lang": "Tagalog",
"sense": "having the same composition throughout",
"word": "tulad-uriin"
}
],
"word": "homogeneous"
}
{
"called_from": "page/1412",
"msg": "gloss may contain unhandled list items: The function f(x,y)#x3D;x²#x2B;x²ʸ#x2B;y² is not homogeneous on all of #x5C;mathbb#x7B;R#x7D;² because f(2,2)#x3D;16#x5C;neq 2ᵏ#x2A;3#x3D;2ᵏf(1,1) for any k, but f is homogeneous on the subspace of #x5C;mathbb#x7B;R#x7D;² spanned by (1,0) because f(#x5C;alphax,#x5C;alphay)#x3D;#x5C;alphax²#x3D;#x5C;alpha²f(x,y) for all (x,y)#x5C;in#x5C;operatorname#x7B;Span#x7D;#x5C;#x7B;(1,0)#x5C;#x7D;.",
"path": [
"homogeneous"
],
"section": "English",
"subsection": "adjective",
"title": "homogeneous",
"trace": ""
}
{
"called_from": "extractor.en.page.sense_template_fn/1415",
"msg": "Example template is used for gloss text",
"path": [
"homogeneous",
"ux"
],
"section": "English",
"subsection": "adjective",
"title": "homogeneous",
"trace": ""
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-01 from the enwiktionary dump dated 2024-04-21 using wiktextract (f4fd8c9 and c9440ce). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.