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On string functions and double-sum formulas

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

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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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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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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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Speaking Stata: On numbers and strings

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STATA JOURNAL 2002年第3期2卷 314-329页

作者： Cox, Nicholas J. Univ Durham Durham England

The great divide among data types in Stata is between numeric and string variables. Most of the time, which kind you want to use for particular variables is clear and unproblematic, but surprisingly often, users face difficulties in making the right decision or need to convert variables from one kind to another. The main problems that may arise and their possible solutions are surveyed with reference both to official Stata and to user-written programs.

关键词： pr0006 binary variables categorical variables Data Editor dates decode destring encode identifiers missing values numeric variables spreadsheets string functions string variables tostring value labels

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Turn BASIC into PASCAL

Microprocessing and Microprogramming

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Microprocessing and Microprogramming 1981年第4期7卷 260-265页

作者： Worland, Peter Gustavus Adolphus College St. Peter MN 56082 United States

Unlike PASCAL, most versions of BASIC, and especially those available on microcomputers, lack adequate control structures for the practice of structured programming. However, BASIC remains one of the most frequently learned 'first' programming languages, thereby resulting in a large number of programmers accustomed to poor programming techniques. This paper presents the author's approach to solving this problem. It describes a preprocessor, written in various micro-computer BASIC dialects, which accepts 'structured BASIC' code as input and produces an equivalent BASIC program that will run on the host machine. Limitations and possible extensions are described. The paper is tutorial in nature, in that some illustrations are given on how BASIC string functions may be used conveniently to implement such a preprocessor. © 1981.

关键词： BASIC high-level languages PASCAL pre-processor string functions structured programming

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