Related papers: Shift equivalence in the generalized factor order
We consider the Principle of Equivalence along with Weyl theorem to discuss the interpretation of gravity as a geometric effect; we study what are the restrictions on the connections that must be required for this geometrization to occur in…
The generalized weighted mean operator $\mathbf{M}^{g}_{w}$ is given by $$[\mathbf{M}^{g}_{w}f](x)= g^{-1}\left(\frac{1}{W(x)}\int_{0}^{x}w(t)g(f(t))\,\mathrm{d}t\right),$$ with $$W(x)=\int_{0}^{x} w(s)\,\mathrm{d}s, \quad \textrm{for} x…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
We construct a generalized dynamics for particles moving in a symmetric space-time, i.e. a space-time admitting one or more Killing vectors. The generalization implies that the effective mass of particles becomes dynamical. We apply this…
New sufficient conditions for representation of a function of several variables as an absolutely convergent Fourier integral are obtained in the paper.
A generalized numerical semigroup is a submonoid of $\mathbb{N}^d$ with finite complement in it. In this work we study some properties of three different classes of generalized numerical semigroups. In particular, we prove that the first…
This note concerns exponential sheaves and the "universal" Fourier transform on them. Fourier invertibility and the subsequent Fourier miracle is demonstrated. Further, t-structures and realizations are constructed and shown to have…
This paper presents a new formula for the q-shift operator, building on the techniques by Liu and Sears. This formula provides fresh proof of the Carlitz formula and extends it naturally. As applications, we derive an equivalent form of the…
We introduce a geometric generalization of Hall's marriage theorem. For any family $F = \{X_1, \dots, X_m\}$ of finite sets in $\mathbb{R}^d$, we give conditions under which it is possible to choose a point $x_i\in X_i$ for every $1\leq i…
A complete characterization of the similarity between two operator-valued multishifts with invertible operator weights is obtained purely in terms of operator weights. This generalizes several existing results of the unitary equivalence of…
Given a functor $T:C \to D$ carrying a class of morphisms $S\subset C$ into a class $S'\subset D$, we give sufficient conditions in order that $T$ induces an equivalence on the localised categories. These conditions are in the spirit of…
This paper introduces Generalized Fourier transform (GFT) that is an extension or the generalization of the Fourier transform (FT). The Unilateral Laplace transform (LT) is observed to be the special case of GFT. GFT, as proposed in this…
A simple proof is provided to show that any bounded normal operator on a real Hilbert space is orthogonally equivalent to its transpose(adjoint). A structure theorem for invertible skew-symmetric operators, which is analogous to the finite…
In [2] we introduced a new notion of Wilf equivalence of integer partitions and proved that rook equivalence implies Wilf equivalence. In the present paper we prove the converse and thereby establish a new criterion for rook equivalence. We…
A general canonical transformation of mechanical operators of position and momentum is considered. It is shown that it automatically generates a parameter s which leads to a generalized (or s-parameterized) Wigner function. This allows one…
A natural occurrence of shift equivalence in a purely algebraic setting constitutes the subject matter of the following short exposition.
We describe a sufficient condition for the localization functor to be a categorical equivalence. Using this result we explain how to simplify the test for projectivity. This leads to a description of the strictly simple algebras which are…
We present generalisations of Wilson's theorem for double factorials, hyperfactorials, subfactorials and superfactorials.
Closed-form expressions for the distributions of the order statistics on the spacings between order statistics for the uniform distribution are obtained. This generalizes a result by Fisher concerning tests of significance in the harmonic…
In the context of formal deformation quantization, we provide an elementary argument showing that any universal quantization formula necessarily involves graphs with wheels.