This paper is mainly devoted to the study and applications of Hölder metric subreg-ularity (or metric q-subregularity of order q ∈ (0, 1]) for general set-valued mappings between infinite-dimensional spaces. Employing advanced techniques of variational analysis and generalized differentiation, we derive neighborhood and pointbased sufficient conditions as well as necessary conditions for q-metr...

Automatic feature learning algorithms are at the forefront of modern day machine learning research. We present a novel algorithm, supervised Q-walk, which applies Q-learning to generate random walks on graphs such that the walks prove to be useful for learning node features suitable for tackling with the node classification problem. We present another novel algorithm, k-hops neighborhood based ...

A geodesic metric space X is called hyperbolic if there exists δ ≥ 0 such that every geodesic triangle ∆ in X is δ-slim, i.e., each side of ∆ is contained in a closed δ-neighborhood of the two other sides. Let G be a group generated by a finite set A and let Γ(G,A) be the corresponding Cayley graph. The group G is said to be word hyperbolic if Γ(G,A) is a hyperbolic metric space. A subset Q of ...

neighborhood attachment is closely related to concrete and abstract conceptions that set the scene for a variety of interactions among the residents. it is on the basis of social-physical location which happens over time. neighborhood attachment also enhances the possibility of residents’ social participation in urban neighborhoods and has a bilateral relationship with residents’ satisfaction. ...

Define a k to be the smallest positive multiple of k such that the sum of its digits in base q is equal to k. The asymptotic behavior, lower and upper bound estimates of a k are investigated. A characterization of the minimality condition is also considered. A positive integer n is a Niven number (or a Harshad number) if it is divisible by the sum of its (decimal) digits. For instance, 2007 is ...

We prove that every continuous value on a space of vector measure market games Q, containing the space of nonatomic measures NA, has the conic property, i.e., if a game v ∈ Q coincides with a nonatomic measure ν on a conical diagonal neighborhood then φ(v) = ν. We deduce that every continuous value on the linear spaceM, spanned by all vector measure market games, is determined by its values on ...

We construct normal numbers in base q by concatenating q-adic expansions of prime powers αp θ with α > 0 and θ > 1.

Mathematical models of complex objects in the form interval difference equations are built on basis obtained experimental data within limits inductive approach. At same time, interpretation physical properties object base such model is enough. A method transformation a mathematical differential was proposed article. The based formulas for representing values function at node grid Taylor series ...

as N → ∞, where the supremum is taken over all blocks d1 . . . dl ∈ {0, 1, . . . , q − 1} . We want to look at numbers whose digits are generated by the integer part of entire functions. Let f be any function and [f(n)]q denote the base q expansion of the integer part of f(n), then define θq = θq(f) = 0.[f(1)]q[f(2)]q[f(3)]q[f(4)]q[f(5)]q[f(6)]q . . . , τq = τq(f) = 0.[f(2)]q[f(3)]q[f(5)]q[f(7)...