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On Hecke-type double-sums and general string functions for the affine Lie algebra A1⁽¹⁾

RAMANUJAN JOURNAL 2024年第3期63卷 553-582页

作者： Mortenson, Eric T. St Petersburg State Univ Dept Math & Comp Sci St Petersburg 199178 Russia

We demonstrate how formulas that express Hecke-type double-sums in terms of theta functions and Appell-Lerch functions-the building blocks of Ramanujan's mock theta functions-can be used to give general string fun... 详细信息

关键词： Hecke-type double-sums Appell functions Theta functions string functions Affine Lie algebras

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On string functions and double-sum formulas

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RESEARCH IN THE MATHEMATICAL SCIENCES 2023年第2期10卷 1-23页

作者： Mortenson, Eric T. Postnova, Olga Solovyev, Dmitry St Petersburg State Univ Dept Math & Comp Sci St Petersburg 199034 Russia St Petersburg Dept Steklov Inst Math Euler Int Math Inst Lab Math Problems Phys Fontanka River Emb 27 St Petersburg 191023 Russia St Petersburg State Univ Dept Phys Ulyanovkaya Str 1 St Petersburg Russia

string functions are important building blocks of characters of integrable highest modules over affine Kac-Moody algebras. Kac and Peterson computed string functions for affine Lie algebras of type A((1)) (1) in terms of Dedekind eta functions. We obtain new symmetries for string functions by exploiting their natural setting of Hecke-type double-sums, where special double-sums are expressed in terms of Appell-Lerch functions and theta functions, where we point out that Appell-Lerch functions are the building blocks of Ramanujan's classical mock theta functions. We then demonstrate the utility of the new symmetries by giving new proofs of classical string function identities.

关键词： Hecke-type double-sums Mock theta functions Theta functions string functions Affine Lie algebras

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q-Identities for parafermion theories

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JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 2024年第50期57卷 505201-505201页

作者： Bouwknegt, Peter Chern, Shane Han, Bolin Australian Natl Univ Math Sci Inst Canberra ACT 2601 Australia Univ Wien Fak Math Oskar Morgenstern Pl 1 A-1090 Vienna Austria Dalhousie Univ Dept Math & Stat Halifax NS B3H 4R2 Canada

In this paper, we will prove a series ofq-identities suggested by the realisationof certain conformal field theories involving the so-called 'coupled free fermi-ons.' We will considerq-series arising from coupled free fermions constructedby the parafermion coset construction as well as from scaled root lattices, andsome interesting relations between the two.

关键词： conformal field theories parafermion theories Kac-Moody algebras root lattices universal chiral partition functions string functions generalised Rogers-Ramanujan identities

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Zx Format09A

引用

2017年

Zx Format09A by published by

关键词： basic chapter emulator format09a functions games games designer platform games retro sinclair solar crisis spectrum spectrum games spectrum software spectrum storage string functions version white cross white noise years ago zxf

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A Characterization of Barycentrically Preassociative functions

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RESULTS IN MATHEMATICS 2016年第1-2期69卷 245-256页

作者： Marichal, Jean-Luc Teheux, Bruno Univ Luxembourg FSTC Math Res Unit 6 Rue Coudenhove Kalergi L-1359 Luxembourg Luxembourg

We provide a characterization of the variadic functions which are barycentrically preassociative as compositions of length-preserving associative string functions with one-to-one unary maps. We also discuss some conse... 详细信息

关键词： Associativity barycentric associativity barycentric preassociativity string functions functional equation axiomatization

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Mit :: Cadr :: Chinual 5Thed Jan83 :: Chinualjan83 09 strings

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2016年

Mit :: Cadr :: Chinual 5Thed Jan83 :: Chinualjan83 09 strings by published by

关键词： 5thed array basic string char string character characters chinual chinualjan83 defaults jan83 lisp lisp machine machine manual returns search starts special form string string functions string operations string returns string searching stringl strings substring

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Get Personal with Your Ti-99/4A

引用

2016年

作者： william a manning

Get Personal with Your Ti-99/4A by Manning, William A; Ingalsbe, Lon; published by Beaverton, or. : Dilithium Press

关键词： basic basic (computer program language) basic program basic programs call clear call sound computer data input loop structures personal press enter print program programs rem example string string functions texas instruments ti 99 4a (computer) ti-99 4a top card

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Input - Vol 2 No 19 (1997)(Marshall Cavendish)(Gb)

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2016年

Input - Vol 2 No 19 (1997)(Marshall Cavendish)(Gb) by published by

关键词： (1997)(marshall acorn acorn program ball carry flag cavendish)(gb) computer cursor diagonally opposite function goto initial speed input marshall cavendish player pontoon print print paper program randomize usr space bar string function string functions

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Prime :: Pdr :: Pdr3058 Basic Vm Pgmguide Apr79

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2016年

Prime :: Pdr :: Pdr3058 Basic Vm Pgmguide Apr79 by published by

关键词： apr79 basic command data data file define file direct access file file handling files mat print mat read matrix midas file numeric pdr3058 pgmguide prime print program program control record size statement string string functions

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Speaking Stata: On structure and shape: the case of multiple responses

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STATA JOURNAL 2003年第1期3卷 81-99页

作者： Cox, Nicholas J. Kohler, Ulrich Univ Durham Durham England Social Sci Res Ctr Berlin Germany

A frequent problem in data management is that datasets may not arrive in the best structure for many analyses, so that it may be necessary to restructure the data in some way. The particular case of multiple response data is discussed at length, with special attention to different possible structures;the generation of new variables holding the data in different form;valuable inbuilt string and egen functions;using foreach and forvalues to loop over lists;and the use of the reshape command. Tabulations and graphics for such data are also reviewed briefly.

关键词： pr0008 composite variables concatenation egen foreach forvalues graphics indicator variables multiple responses reshape split string functions tabulations

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