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We show the existence of many infinite classes of permutations over finite fields and bent functions by extending the notion of linear translators, introduced by Kyureghyan [12]. We call these translators Frobenius translators since the…
We investigate three combinatorial problems considered by Erd\"os, Rivat, Sark\"ozy and Sch\"on regarding divisibility properties of sum sets and sets of shifted products of integers in the context of function fields. Our results in this…
We discuss non-Hermitian field theories where the spectrum of the Hamiltonian involves only real energies. We make three observations. (i) The theories obtained from supersymmetric theories by nonanticommutative deformations belong in many…
We study new consistent scalar-tensor theories of gravity recently introduced by Langlois and Noui with potentially interesting cosmological applications. We derive the conditions for the existence of a primary constraint that prevents the…
We generalize the Stueckelberg formalism in the (1/2,1/2) representation of the Lorentz Group. Some relations to other modern-physics models are found.
The problem of neutral fermions subject to an inversely linear potential is revisited. It is shown that an infinite set of bound-state solutions can be found on the condition that the fermion is embedded in an additional uniform background…
I review a number of the open questions about neutrino properties, critique recent hints of neutrino mass, and discuss one recently proposed neutrino mass matrix to illustrate the direction in which we may be headed. I also present one…
We give a brief overview of recent developments in Sturm-Liouville theory concerning operators of transmutation (transformation) and spectral parameter power series (SPPS) and propose a new method for numerical solution of corresponding…
Field equations in four order derivatives with respect to time and space coordinates based on modified classic relativistic energy of the fractal theory of time and space are received. It is shown appearing of new spin characteristics and…
The non-trivial zeros of the Riemann zeta function and the prime numbers can be plotted by a modified von Mangoldt function. The series of non-trivial zeta zeros and prime numbers can be given explicitly by superposition of harmonic waves.…
This article provides a thorough investigation into Gilbert's Conjecture, pertaining to Hardy spaces in the upper half-space valued in Clifford modules. We explore the conjecture proposed by Gilbert in 1991, which seeks to extend the…
A complete discussion of the constraints on the Michel parameters and the ambiguities of their interpretation is presented. Estimators of new physics, optimized for a very wide class of hypotheses and models, are proposed.
We solve some famous conjectures on the distribution of primes. These conjectures are to be listed as Legendre's, Andrica's, Oppermann's, Brocard's, Cram\'{e}r's, Shanks', and five Smarandache's conjectures. We make use of both…
In this survey article we give a brief history of symbolic powers and its connection with the interesting problem of set-theoretic complete intersection. We also state a few problems and conjectures. Recently, in connection to symbolic…
In this paper, we generalize the weighted Fourier transform with respect to a function, originally proposed for the one-dimensional case in \cite{Dorrego}, to the $n$-dimensional Euclidean space $\mathbb{R}^{n}$. We develop a comprehensive…
In this note, we highlight the impact of the paper G. H. Hardy, A theorem concerning Fourier transforms, J. Lond. Math. Soc. (1) 8 (1933), 227--231 in the community of harmonic analysis in the last 90 years, reviewing, on the one hand, the…
An open problem concerning Riemann sums, posed by O. Furdui, is considered.
The usual fluid equations describing the large-scale evolution of mass density in the universe can be written as local in the density, velocity divergence, and velocity potential fields. As a result, the perturbative expansion in small…
We prove a conjecture of Frenkel, Gaitsgory, Kazhdan and Vilonen, related to Fourier coefficients of spherical perverse sheaves on the affine Grassmannian associated to a a split reductive group. Our proof is an extension of the proof given…
Mathematicians had little idea whether the easy-to-state union-closed conjecture was true or false even after $40$ years. However, last winter saw a surge of interest in the conjecture and its variants, initiated by the contribution of a…