Some q-supercongruences from Watson’s $$_8\phi _7$$ Transformation Formula

2020 ◽  
Vol 75 (2) ◽  
Author(s):  
Xiaoxia Wang ◽  
Mingbing Yue
Keyword(s):  
Transformation Formula

scholarly journals The intersection between dual potential and sl(2) algebraic spectral problems

2020 ◽  
Vol 35 (32) ◽  
pp. 2050208
Author(s):  
William H. Pannell
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Transformation Formula ◽  
Algebraic Construction ◽  
Spectral Problems ◽  
Partner Potential

The relation between certain Hamiltonians, known as dual, or partner Hamiltonians, under the transformation [Formula: see text] has long been used as a method of simplifying spectral problems in quantum mechanics. This paper seeks to examine this further by expressing such Hamiltonians in terms of the generators of sl(2) algebra, which provides another method of solving spectral problems. It appears that doing so greatly restricts the set of allowable potentials, with the only nontrivial potentials allowed being the Coulomb [Formula: see text] potential and the harmonic oscillator [Formula: see text] potential, for both of which the sl(2) expression is already known. It also appears that, by utilizing both the partner potential transformation and the formalism of the Lie-algebraic construction of quantum mechanics, it may be possible to construct part of a Hamiltonian’s spectrum from the quasi-solvability of its partner Hamiltonian.

Dedekind sums and the transformation formula in function fields

2016 ◽  
Vol 12 (08) ◽  
pp. 2061-2072 ◽  
Author(s):  
Yoshinori Hamahata
Keyword(s):  
Function Fields ◽  
Transformation Formula ◽  
Dedekind Sums ◽  
Dedekind Sum ◽  
Sum Formula

Dedekind used the classical Dedekind sum [Formula: see text] to describe the transformation of [Formula: see text] under the substitution [Formula: see text]. In this paper, we use the Dedekind sum [Formula: see text] in function fields to describe the transformation of a certain series under the substitution [Formula: see text].

scholarly journals A post-structuralist revised Weil–Lévi-Strauss transformation formula for conceptual value-fields

2018 ◽  
Vol 46 (2/3) ◽  
pp. 255-281 ◽  
Author(s):  
James B. Harrod
Keyword(s):  
Logic Model ◽  
Comparative Religion ◽  
Cultural Value ◽  
Transformation Formula ◽  
General Transformation ◽  
Cultural Space ◽  
Literature And Philosophy

The structuralist André-Weil–Claude-Lévi-Strauss transformation formula (CF), initially applied to kinship systems, mythology, ritual, artistic design and architecture, was rightfully criticized for its rationalism and tendency to reduce complex transformations to analogical structures. I present a revised non-mathematical revision of the CF, a general transformation formula (rCF) applicable to networks of complementary semantic binaries in conceptual value-fields of culture, including comparative religion and mythology, ritual, art, literature and philosophy. The rCF is a rule-guided formula for combinatorial conceptualizing in non-representational, presentational mythopoetics and other cultural symbolizations. I consider poststructuralist category-theoretic and algebraic mathematical interpretations of the CF as themselves only mathematical analogies, which serve to stimulate further revision of the logic model of the rCF. The rCF can be used in hypothesis-making to advance understanding of the evolution and prehistory of human symbolic behaviour in cultural space, philosophical ontologies and categories, definitions and concepts in art, religion, psychotherapy, and other cultural-value forms.

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