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We study 1-parameter families of Morse functions for manifolds with boundary. We list all degeneracies that may occur in generic 1-parameter families.
In this paper we established new integral inequalities which are more general results for coordinated convex functions on the coordinates by using some classical inequalities.
Finite trigonometric sums appear in various branches of Physics, Mathematics and their applications. For p; q to coprime positive integers and r we consider the finite trigonometric sums involving the product of three trigonometric…
Discrete trigonometric transformations, such as the discrete Fourier and cosine/sine transforms, are important in a variety of applications due to their useful properties. For example, one well-known property is the convolution theorem for…
In the Schroedinger picture, we find explicit solutions for two models of degenerate parametric oscillators in the case of multiparameter squeezed input photons. The corresponding photon statistics and Wigner's function are also derived in…
In this work, generalized hypergeometric functions for bicomplex argument is introduced and its convergence criteria is derived. Furthermore, integral representation of this function has been established. Moreover, quadratic transformation,…
The main purpose of this paper is to study formal deformations of evolution algebras, determining their existence and classifying them up to equivalence. In addition, we examine degenerations in this setting and provide Hasse diagrams that…
The Sinc approximation is known to be a highly efficient approximation formula for rapidly decreasing functions. For unilateral rapidly decreasing functions, which rapidly decrease as $x\to\infty$ but does not as $x\to-\infty$, an…
Generalizations of some known results on the best, best linear and best one-sided approxima- tions by trigonometric polynomials of the classes of 2\pi - periodic functions presented in the form of convolutions to the case of set-valued…
Recently, Bovadzhiev studied a power series whose coefficients are binomial expressions and extended some known formulas involving classical special functions and polynomials. The aim of this paper is to adopt his ideas to express several…
Some divergent trigonometric integrals have appeared in standard tables for many years, listed as converging. We give a simple proof that these integrals diverge and trace their history. The original error was made when a (startlingly)…
A generating function for reciprocal binomial coefficients is written down, integral representations of this function are obtained, generating functions for sums of reciprocal binomial coefficients are derived, new identities are obtained,…
It is shown how to calculate asymptotics of integrals over the positive semi-axis of two functions related to the Degenerate Third Painlev\'e Equation (dP3). As an example, the corresponding results for the meromorphic solution of the dP3…
In this paper, we study some combinations of the degenerate and incomplete Stirling numbers of the second kind. We use a combinatorial approach and provide some asymptotic results.
This brief survey deals with multi-dimensional Diophantine approximations in sense of linear form and with simultaneous Diophantine approximations. We discuss the phenomenon of degenerate dimension of linear subspaces generated by the best…
Different types of sinc integrals are investigated when the standard sine function is replaced by the generalised $\sin_{p,q}$ in two parameters. A striking generalisation of the improper Dirichlet integral is achieved. A second surprising…
Let $f(\mathbf z)$ be an analytic function defined in the neighborhood of the origin of $\mathbb C^n$ which have some Newton degenerate faces. We generalize the Varchenko formula for the zeta function of the Milnor fibration of a Newton…
We use the orbifold approach to study theta functions in intrinsic mirror symmetry. We introduce a new type of orbifold invariants for snc pairs, called mid-age invariants, and use these invariants to define orbifold invariants associated…
An analysis of the zeta and gamma function is presented, using elementary functions like [] and {}, a general formula for the angle of zeta(1/2 + i*n) is found and the same for the gamma function.
A few formulas and theorems for statistical structures are proved. They deal with various curvatures as well as with metric properties of the cubic form or its covariant derivative. Some of them generalize formulas and theorems known in the…