Abstract In the study of cyclicity a function f in reproducing kernel Hilbert spaces an important role is played by sequences polynomials $$\{p_n\}_{n\in \mathbb {N}}$$ {pn}n∈<...

Abstract A repdigit is a positive integer that has only one distinct digit in its decimal expansion, i.e., number of the form $$a(10^m-1)/9$$ a ( 10 m - 1 ) / 9<...

In this study a spatio-temporal approach for the solution of time-dependent Boltzmann (transport) equation is derived. Finding exact using general case generally an open problem and approximate methods are usually used. One most common spherical harmonics method (the $P_N$ approximation), when transport replaced with closed set equations moments density, some closure assumption. Unfortunately, ...

Let $\sigma=(\sigma_{1},\sigma_{2},\dots,\sigma_{n})\in \mathbb{S}^{n-1}$ and $d\sigma$ denote the normalised Lebesgue measure on $\mathbb{S}^{n-1},~n\geq 2$. For functions $f_1, f_2,\dots,f_n$ defined $\R$ consider multilinear operator given by $$T(f_{1},f_{2},\dots,f_{n})(x)=\int_{\mathbb{S}^{n-1}}\prod^{n}_{j=1}f_{j}(x-\sigma_j)d\sigma, ~x\in \R.$$ In this paper we obtain necessary sufficien...

Let \(G=(V,E)\) be a finite graph. We consider the existence of solutions to generalized Chern–Simons–Higgs equation $$\begin{aligned} \Delta u=-\lambda e^{g(u)}\left( e^{g(u)}-1\right) ^2+4\pi \sum \limits _{j=1}^{N}\delta _{p_j} \end{aligned}$$on G, where \(\lambda \) is positive constant; g(u) inverse function \(u=f(\upsilon )=1+\upsilon -e^{\upsilon }\) on \((-\infty , 0]\); N integer; \(p_...

Abstract In this chapter, we discuss the higher order differentiability properties of Σ g when lies in $$\mathcal {C}^r\cap \mathcal {D}^p\cap {K}^{\max \{p,r\}}$$ C r ∩ D p K max</mm...

Abstract In this note, we study discrete time majority dynamics over an inhomogeneous random graph G obtained by including each edge e in the complete $$K_n$$ K n independently with probability $$p_n(e)$$ p ( e</mml:m...