Related papers: Generalized Watson Transforms II: The Complementar…
Ordinary and gl(n,R) generalized Toda systems as well as a related hierarchy are probed with respect to certain quantization characteristics. "Quantum" canonical and Poisson transformations are used to study quantizations of transformed…
We present generalisations of Wilson's theorem for double factorials, hyperfactorials, subfactorials and superfactorials.
We discuss the divergence structure of Wilson line operators with partially overlapping segments on the basis of the cyclic Wilson loop as an explicit example. The generalized exponentiation theorem is used to show the exponentiation and…
The general problem of the factorization of a basic hypergeometric series is presented and discussed. The case of the general $_2\psi_2$ series is examined in detail. Connections are found with the theory of basic hypergeometric series on…
This paper refers to the study of generalized Struve type function. Using generalized Galue type Struve function (GTSF) by Nisar et al. [13], we derive various integral transform, including Euler transform, Laplace transform, Whittakar…
We give a transform of convergent trigonometric series into equivalent convergent series and sufficient conditions for the transformed series to converge faster than the original one.
We introduce a geometric completion of the stack of maps from stable marked curves to the quotient stack [point/GL(1)], and use it to construct some gauge-theoretic analogues of the Gromov-Witten invariants. We also indicate the…
In this lecture note, we give a basic introduction to the rapidly developing concepts of generalized symmetries, from the perspectives of both high energy physics and condensed matter physics. In particular, we emphasize on the (invertible)…
We apply an integral formula obtained by the author for a general $G$--structure to the case of $G=G_2$. We derive an integral formula relating curvatures and some quadratic invariants of the endomorphism induced by the intrinsic torsion.…
We introduce a family of generalized Broughton polynomials and compute the characteristic varieties of complement of a curve arrangement defined by fibers of some generalized Broughton polynomials
In this note we consider representations of the group GL(n,F), where F is the field of real or complex numbers or, more generally, an arbitrary local field, in the space of equivariant line bundles over Grassmannians over the same field F.…
We treat the quaternionic Fourier transform (QFT) applied to quaternion fields and investigate QFT properties useful for applications. Different forms of the QFT lead us to different Plancherel theorems. We relate the QFT computation for…
The class of generalized shearlet dilation groups has recently been developed to allow the unified treatment of various shearlet groups and associated shearlet transforms that had previously been studied on a case-by-case basis. We consider…
We generalize the connection between 2t physics and noncommutative geometry. In particular, we apply our formalism to a target spacetime of signature (2+2). Specifically, we compute an algebra of a generalized SL(2, R)-Hamiltonian…
We present a general formalism for incorporating the string corrections in generalised geometry, which necessitates the extension of the generalised tangent bundle. Not only are such extensions obstructed, string symmetries and the…
We introduce a generalization of the Stirling numbers via symmetric functions involving two weight functions. The resulting extension unifies previously known Stirling-type sequences with known symmetric function forms, as well as other…
In the theories of generalized modified gravity, the acceleration equation is generally fourth order. So it is hard to analyze the evolution of the Universe. In this paper, we present a class of generalized modified gravity theories which…
A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…
We discuss certain representations of GL 2 Fq[T] in equal characteristic and associated vectorial modular forms
We study a family of integrals parameterised by $ N = 2,3,\dots $ generalising the Askey-Wilson integral $ N=2 $ which has arisen in the theory of $q$-analogs of monodromy preserving deformations of linear differential systems and in theory…