Related papers: New discovery of a conversion of generalized singu…
In this paper, some new results on the distribution of the generalized singular value decomposition (GSVD) are presented.
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
In this work, we introduce a new generalized integral transform involving many potentially known or new transforms as special cases. Basic properties of the new integral transform, that investigated in this work, include the existence…
In this note, we prove a quantization formula for singular reductions. The main result is obtained as a simple application of an extended quantization formula proved in [TZ2].
In this paper, we derive new model formulations for computing generalized singular values of a Grassman matrix pair. These new formulations make use of truncated filter matrices to locate the $i$-th generalized singular value of a Grassman…
We state and prove a general summation identity. The identity is then applied to derive various summation formulas involving the generalized harmonic numbers and related quantities. Interesting results, mostly new, are obtained for both…
A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…
We present a new alternating convolution formula for the super Catalan numbers which arises as a generalization of two known binomial identities. We prove a generalization of this formula by using auxiliary sums, recurrence relations, and…
In this paper, the exact values of the structured singular values of some generalized stochastic complex matrices is explicit in term of the constant row (column) sum.
In this paper, we propose new generalizations of amicable numbers. We also give examples and prove properties of these new concepts.
In this paper, we introduce a novel identity for generalized Euler polynomials, leading to further generalizations for several relations involving classical Euler numbers, Euler polynomials, Genocchi polynomials, and Genocchi numbers.
We prove a new linear relation for multiple zeta values. This is a natural generalization of the restricted sum formula proved by Eie, Liaw and Ong. We also present an analogous result for finite multiple zeta values.
In this study, multivalued generalizations of certain classes of single-valued transformations defined on metric spaces are obtained. Building upon recently introduced concepts such as mappings contracting perimeters of triangles, new…
We propose a new integral based on Taylor measures, study its properties extensively, and we illustrate that it includes many concepts from mathematics as special cases. In particular, the new integral emerges as a generalization of the…
We prove some new results related to Tanaka's formula.
Recent results on finite open group transformations are reviewed.
Using Singular Rescaling We Prove Some Bifurcation Results. This note Presents short proofs for some Bifurcation results which had been appeared with other authors.
Combining the derivative operator with Chu-Vandermonde convolution, we establish a class of summation formulas on generalized harmonic numbers.
We discuss several existing proofs of the value of a quartic integral and present a new proof that evolved from rational Landen transformations.
This research extends quantum singular value transformation (QSVT) for general bounded operators embedded in unitary operators on possibly infinite-dimensional Hilbert spaces. Through in-depth mathematical exploration, we have achieved a…