Related papers: On the generalized numerical criterion
Thanks to recent advances in parametric geometry of numbers, we know that the spectrum of any set of $m$ exponents of Diophantine approximation to points in $\mathbb{R}^n$ (in a general abstract setting) is a compact connected subset of…
In this paper, a detrimental mathematical mistake is pointed out in the proof of \textit{Theorem 1} presented in the paper\textit{ [Generalization of the gradient method with fractional order gradient direction, J. Franklin Inst., 357…
We obtain generalisations of some inequalities for positive unital linear maps on matrix algebra. This also provides several positive semidefinite matrices and we get some old and new inequalities involving the eigenvalues of a Hermitian…
Negative probability has found diverse applications in theoretical physics. Thus, construction of sound and rigorous mathematical foundations for negative probability is important for physics. There are different axiomatizations of…
Recently Rather et al. \cite{NT} considered the generalized derivative and the generalized polar derivative and studied the relative position of zeros of generalized derivative and generalized polar derivative with respect to the zeros of…
A number has the "collective" property if the number is the greatest lower bound of a bounded, strictly decreasing sequence on the real line. We prove that numbers with the collective property constitute an empty set.
The Kaplansky unit conjecture for group rings is false in characteristic zero.
We show that, under reasonable assumptions, two negative roots can be eliminated from the characteristic equation of a polynomial-like iterative equation. This result gives a new case where we may lower the order of such an equation.
Count data take on non-negative integer values and are challenging to properly analyze using standard linear-Gaussian methods such as linear regression and principal components analysis. Generalized linear models enable direct modeling of…
In this paper we obtain some slight correction and generalization of the results of Ryabtseva on the generalized resolvents for isometric operators with a gap in their spectrum. Also, analogs of some McKelvey's results and a short proof of…
We introduce the notion of the generalized-analytical function of the poly-number variable, which is a non-trivial generalization of the notion of analytical function of the complex variable and, therefore, may turn out to be fundamental in…
Some of the multiplicity-freeness results in ``Modular Gelfand pairs and multiplicity-free representations'' are stated in overly broad generality. We provide counterexamples and partial corrections.
We give a generalization of Collatz conjecture or 3n+1 problem on 2-adic completion of Q. A isometric of $Q_2$ provides information on the average behavior of the firsts terms of the sequence according to the class of $u_0$ modulo $2^m$. A…
A simple proof of the convergence of the variational regularization, with the regularization parameter, chosen by the discrepancy principle, is given for linear operators under suitable assumptions. It is shown that the discrepancy…
We consider statistical procedures for hypothesis testing of real valued functionals of matched pairs with missing values. In order to improve the accuracy of existing methods, we propose a novel multiplication combination procedure.…
We study a broad class of numerical problems that can be defined as the solution of a system of (nonlinear) equations for a subset of the dependent variables. Given a system of the form $F(x,y,z) = c$ with multivariate input $x$ and…
In this paper, we give explicit evaluation for some infinite series involving generalized (alternating) harmonic numbers. In addition, some formulas for generalized (alternating) harmonic numbers will also be derived.
We prove the existence of common fixed points for two weakly compatible mappings satisfying a 'generalized condition (B)'. This result generalizes some theorems of Al-Thagafi and Shahzad \cite{AlThagafi2006} and Babu, Sandhya and Kameswari…
In this note we give a short, direct proof of the well known Combinatorial Nullstellensatz.
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…