In [3], two new kinds of topologies called the open-point topology and bi-point-open on C(X), set all real-valued continuous functions a Tychonoff space X, have been introduced. this article, we study separability P(X), maps [0; 1] into Hausdorff with topologies. Our result also demonstrates, claim made in that both domain as well codomain play significant roles construction

A hesitant fuzzy set (HFS) and a cubic (CS) are two independent approaches to deal with hesitancy vagueness simultaneously. An HFS assigns an essential grade each object in the universe, whereas CS deals uncertain information terms of sets as well interval-valued sets. (CHFS) is new computational intelligence approach that combines HFS. The primary objective this paper define topological struct...

Topology optimization is a method to find the best distribution of material in a given design domain. The use of topology optimization for structural design often leads to slender structures which are sensitive to geometric imperfections such as the misplacement or misalignment of material. A robust approach to topology optimization is therefore presented which takes into account these geometri...

In this article we derive the expression of renormalized energies for unit-valued harmonic maps defined on a smooth bounded domain in R 2 whose boundary has several connected components. The notion was introduced by Bethuel–Brezis–Hélein order to describe position limiting Ginzburg–Landau vortices simply domains. We show here, how non-trivial topology modifies energies. treat case Dirichlet con...

let g = (v,e) be a locally finite graph, i.e. a graph in which every vertex has finitely many adjacent vertices. in this paper, we associate a topology to g, called graphic topology of g and we show that it is an alexandroff topology, i.e. a topology in which intersec- tion of every family of open sets is open. then we investigate some properties of this topology. our motivation is to give an e...

This paper presents a geometric discretization of elasticity when the ambient space is Euclidean. This theory is built on ideas from algebraic topology, exterior calculus, and the recent developments of discrete exterior calculus. We first review some geometric ideas in continuum mechanics and show how constitutive equations of linearized elasticity, similar to those of electromagnetism, can be...

Let D be a Krull domain and Int(D) the ring of integer-valued polynomials on D. For any f ∈ Int(D), we explicitly construct a divisor homomorphism from [[f ]], the divisor-closed submonoid of Int(D) generated by f , to a finite sum of copies of (N0,+). This implies that [[f ]] is a Krull monoid. For V a discrete valuation domain, we give explicit divisor theories of various submonoids of Int(V ...

In this work, a recursive Levenberg-Marquardt (LM) learning algorithm in the complex domain is developed and applied to the learning of an adaptive control scheme composed by ComplexValued Recurrent Neural Networks (CVRNN). We simplified the derivation of the LM learning algorithm using a diagrammatic method to derive the adjoint CVRNN used to obtain the gradient terms. Furthermore, we apply th...

Latecki et al. introduced the notion of 2D and 3D wellcomposed images, i.e., a class of images free from the “connectivities paradox” of digital topology. Unfortunately natural and synthetic images are not a priori well-composed. In this paper we extend the notion of “digital well-composedness” to nD sets, integer-valued functions (graylevel images), and interval-valued maps. We also prove that...

Consider the B-valued probability space (A, E,B), where A is a tracial von Neumann algebra. We extend the theory of operator valued free probability to the algebra of affiliated operators Ã. For a random variable X ∈ Ã we study the Cauchy transform GX and show that the von Neumann algebra (B ∪ {X}) ′′ can be recovered from this function. In the case where B is finite dimensional, we show that, ...