В статье рассматриваются однородные функции, имеющие вид $\theta \left(\tau \right)\left|t\right|^{\alpha },$ гдепорядок однородности $\alpha >-n$, а \left(\tau\right)$ - функция на единичной сфере $S^{n-1}=\left\{t{\in}R^n, \left|t\right|=1\right\}$. При вычислении преобразования Лапласа этих функций с носителем востром конусе необходимо получить их явное представление. Это достигается сумм...

Abstract We provide two characterizations, one axiomatic and the other neuro-computational, of dependence choice probabilities on deadlines, within widely used softmax representation $$\begin{align*} p_{t}\left( a,A\right) =\dfrac{e^{\frac{u\left( a\right) }{\lambda\left( t\right) }+\alpha\left( }}{\sum_{b\in A}e^{\frac{u\left( b\right) }}, \end{align*}$$ where $p_{t}\left( $ is probability tha...

In this paper, we investigate the homogeneous and isotropic flat FLRW Universe in logarithmic form of $f\left( Q\right) $ gravity, where $% Q is non-metricity scalar, specifically, =\alpha +\beta \log \left( $, $\alpha $\beta are free model parameters. study, consider a parametrization Hubble parameter as $H\left( z\right) =\eta \left[ (z+1)^{-\gamma }+1\right] $\gamma $\eta model/free paramete...

In this paper, we propose a new method to obtain the eigenvalues and fuzzy triangular eigenvectors of matrix $$\left( {\tilde{A}} \right)$$ , where elements are given. For purpose, solve 1-cut eigenvectors. Considering interval system $$\left[ \right]_{\alpha } \left[ {\tilde{X}} = {\tilde{\lambda }} 0 \le \alpha 1$$ as α-cut $$\tilde{A}\tilde{X} \tilde{\lambda }\tilde{X}$$ determine left right...

Let $A(G)$ be the adjacency matrix and $D(G)$ diagonal of vertex degrees a simple connected graph $G$. Nikiforov defined $A_{\alpha}(G)$ convex combinations as $A_{\alpha}(G)=\alpha D(G)+(1-\alpha)A(G)$, for $0\leq \alpha\leq 1$. If $ \rho_{1}\geq \rho_{2}\geq \dots \geq \rho_{n}$ are eigenvalues (which we call $\alpha$-adjacency $G$), \alpha $-adjacency energy $G$ is $E^{A_{\alpha}}(G)=\sum_{i...

We study structural, integral, differential, variational, and fractal properties of a function f whose argument $$ x={\Delta }_{\alpha_1{\alpha}_2\dots {\alpha}_n\dots}^{Q_s^{\ast }} is represented by polybasic s-symbol {Q}_s^{\ast } -representation (1 < s ∈ N) its corresponding value expressed as follows: f\left(x={\Delta }}\right)={a}^{\alpha_1{u}_1+{\alpha}_2{u}_2+\dots +{\alpha}_n{u}_n+\dot...

For $\alpha > 0$ we consider the operator $K_\alpha \colon \ell^2 \to \ell^2$ corresponding to matrix \[\left(\frac{(nm)^{-\frac{1}{2}+\alpha}}{[\max(n,m)]^{2\alpha}}\right)_{n,m=1}^\infty.\] By interpreting $K_\alpha$ as inverse of an unbounded Jacobi matrix, show that absolutely continuous spectrum coincides with $[0, 2/\alpha]$ (multiplicity one), and there is no singular spectrum. There a f...

We construct the existence theory for generalized fractional Bessel differential equations and find solutions in form of or logarithmic power series. figure out cases when series solution is unique, non-unique, does not exist. The uniqueness theorem space Cp proved corresponding initial value problem. are concerned with following homogeneous equation $$\sum\limits_{i = 1}^m {{d_i}{x^{{\alpha _i...

Let G G be a finite group admitting coprime automorphism alttext="alpha"> α encoding="application/x-tex">\al...

In this paper we consider the approximate Jordan maps and boundedness of these maps. Also we investigate the stability of approximate Jordan maps and prove some stability properties for approximate Jordan maps. Keywords—Approximate Jordan map; Stability.