This paper aims to retrieve the initial value for a non-local fractional Sobolev–Galpern problem. The given data are subject to noise by the discrete random model. We show that the solution to the problem is ill-posed in the sense of Hadamard. In this paper, we applied the Fourier truncation method to construct the regularized solution. We estimate the convergence between the...
Given a connected graph G, the total mutual-visibility number of G, denoted $$\mu _t(G)$$ , is the cardinality of a largest set $$S\subseteq V(G)$$ such that for every pair of vertices $$x,y\in V(G)$$ there is a shortest x, y-path whose interior vertices are not contained in S. Several combinatorial properties, including bounds and closed formulae, for $$\mu _t(G)$$ are given in...
In this paper, we locally classify the surfaces immersed into the non-flat (Riemannian or Lorentzian) 3-space forms satisfying the condition $$\Box \vec {\textbf{H}}=\lambda \vec {\textbf{H}}$$ for a real number $$\lambda $$ , where $$\vec {\textbf{H}}$$ is the mean curvature vector field and $$\Box $$ denotes the Cheng–Yau operator of the surface. We obtain the classification...
In this paper, by using linking methods, we obtain the existence of the nontrivial standing wave solutions for the discrete nonlinear Schrödinger equations with resonance and unbounded potentials. In order to prove the existence of standing wave solutions, we give resonant condition to find a bounded critical sequence, and we show that such a sequence guarantees the existence of...
A metric continuum X is indecomposable if it cannot be put as the union of two of its proper subcontinua. A subset R of X is said to be continuumwise connected provided that for each pair of points $$p,q\in R$$ , there exists a subcontinuum M of X such that $$\{p,q\}\subset M\subset R$$ . Let $$X^{2}$$ denote the Cartesian square of X and $$\Delta $$ the diagonal of $$X^{2...
We give necessary and sufficient conditions for the divisibility of two finite geometric series $$ G_n(x) = 1 + x + x ^ 2 + \cdots + x^{n-1} $$ over a field of characteristic zero.
The aim of this paper is to prove the theorem which generates many examples of functions belonging to a geometrically defined class of uniformly starlike functions introduced by Goodman in 1991. Only a very few explicit uniformly starlike functions were known until now. Next we obtain inclusion relations between some subclasses of convex functions and the class of uniformly...
The aim of this work is to first build the underlying theory behind fractional Brownian motion and applying fractional Brownian motion to financial market. By incorporating the Hurst parameter into geometric Brownian motion in order to characterize the long memory among disjoint increments, geometric fractional Brownian motion model is constructed to model S &P 500 stock price...
Let R be a ring and $$N \ge 2$$ . First, we prove that any deconstructible class of modules $${\mathcal {F}}$$ over R induces two coreflective subcategories of the homotopy category $$\textbf{K}_N(\mathrm {Mod-}{R})$$ of (unbounded) N-complexes of right R-modules: the one whose objects are all N-complexes with components in $${\mathcal {F}}$$ , $$\textbf{K}_N({\mathcal {F...
The relation between a considered family of analytic functions and the class $${\mathcal {P}}$$ of functions with a positive real part is one of the main tools used in solving various extremal problems, among others coefficient problems. Another approach can be useful in solving such tasks. This approach is to exploit the correspondence between a considered family and the family...
Let $$M_s^2$$ be an orientable surface immersed in the De Sitter space $$\mathbb {S}_1^3\subset \mathbb {R}^4_1$$ or anti de Sitter space $$\mathbb {H}_1^3\subset \mathbb {R}^4_2$$ . In the case that $$M_s^2$$ is of $$L_1$$ -2-type we prove that the following conditions are equivalent to each other: $$M_s^2$$ has a constant principal curvature; $$M_s^2$$ has constant mean...
We study bounded actions of groups and semigroups G on exact sequences of Banach spaces from the point of view of (generalized) quasilinear maps, characterize the actions on the twisted sum space by commutator estimates and introduce the associated notions of G-centralizer and G-equivariant map. We will show that when (A) G is an amenable group and (U) the target space is...
A connected graph of order n admitting a semiregular automorphism of order n/k is called a k-multicirculant. Highly symmetric multicirculants of small valency have been extensively studied, and several classification results exist for cubic vertex- and arc-transitive multicirculants. In this paper, we study the broader class of cubic vertex-transitive graphs of order n admitting...
We construct and study sequences of linear operators of Bernstein-type acting on bivariate functions defined on the unit disk. To this end, we study Bernstein-type operators under a domain transformation, we analyze the bivariate Bernstein–Stancu operators, and we introduce Bernstein-type operators on disk quadrants by means of continuously differentiable transformations of the...
A set of edges $$X\subseteq E(G)$$ of a graph G is an edge general position set if no three edges from X lie on a common shortest path in G. The cardinality of a largest edge general position set of G is the edge general position number of G. In this paper, edge general position sets are investigated in partial cubes. In particular, it is proved that the union of two largest...
Given any finite subset A of order n of a distributive lattice and $$k\in \{1,\ldots ,n\}$$ , there is a natural extension of the median operation to n variables which generalizes the notion of the kth smallest element of A. By applying each of these operations to A, a totally ordered set to(A) is obtained. We refer to to(A) as the total orderization of A. After developing a...
A wide range of parameters of domination in graphs can be defined and studied through a common approach that was recently introduced in [ https://doi.org/10.26493/1855-3974.2318.fb9 ] under the name of w-domination, where $$w=(w_0,w_1, \dots ,w_l)$$ is a vector of non-negative integers such that $$ w_0\ge 1$$ . Given a graph G, a function $$f: V(G)\longrightarrow \{0,1,\dots ,l...
In this paper, we introduce a generalized core inverse (called the C-S inverse) and give some properties and characterizations of the inverse. By applying the C-S inverse, we introduce a binary relation (denoted “ $${\mathop \le \limits ^{\textcircled {S}}}$$ ”) and a partial order (called the C-S partial order and denoted “ $${\mathop \le \limits ^{\textcircled {{c\!s...
We study various structures of general Volterra-type integral and weighted composition operators acting between two Fock-type spaces $$\mathcal {F}_{\varphi }^p$$ and $$\mathcal {F}_{\varphi }^q,$$ where $$\varphi $$ is a radial function growing faster than the function $$z\rightarrow |z|^2/2$$ . The main results show that the unboundedness of the Laplacian of $$\varphi...
A graph G is $$\alpha $$ -excellent if every vertex of G is contained in some maximum independent set of G. In this paper, we characterize $$\alpha $$ -excellent bipartite graphs, $$\alpha $$ -excellent unicyclic graphs, $$\alpha $$ -excellent simplicial graphs, $$\alpha $$ -excellent chordal graphs, $$\alpha $$ -excellent block graphs, and we show that every generalized Petersen...
Some examples of Appell–Dunkl sequences are shown using determined operators. Specifically, Appell–Dunkl sequences whose generating functions are of the form $$E_{\alpha }(xt)/(1\pm t^m)$$ , where the function $$E_{\alpha }(xt)$$ is given in terms of Bessel functions. Particular cases of these examples are also generated by means of the inverse of the Dunkl operator.
In this note, the Ulam stability of a general functional equation in several variables is investigated. It is shown that this equation is Ulam stable in m-Banach spaces. Since a particular case of the considered equation is, among others, a functional equation introduced by Ji et al. and Zhao et al. for a characterization of the so-called multi-quadratic mapping, a result on its...
The statistical inference of multi-component reliability stress–strength system with nonidentical-component strengths is considered for the modified Weibull extension distribution in the presence of progressive censoring samples. For this aim, we study the estimation of multi-component reliability parameter in classical and Bayesian inference. So we derive some point and interval...