The aim of this paper is to introduce some generalizations for closed sets in generalized topology and minimal structure spaces. We investigate some properties of these sets on these spaces. Moreover, we give the concept of T0-GTMS spaces, T1/2-GTMS spaces and R0-GTMS spaces, and the various relationships between them.

1. Let X be a locally compact Hausdorff space, C(X)ß the locally convex topological vector space obtained from all bounded complex continuous functions on X by employing the strict topology [2]. The present note is devoted to a version of Bishop's generalized StoneWeierstrass theorem [l] applicable to certain subspaces of C(X)ß-, essentially it is a footnote to an earlier paper [4], in which a ...

This survey article reflects the topological and inverse behaviour of generalized semi-infinite optimization problems P(f, h, g, u, v), and presents the analytical methods. These differentiable problems admit an infinite set Y (x) of inequality constraints y which depends on the state x. We extend investigations from Weber [77] based on research of Guddat, Jongen, Rückmann, Twilt and others. Un...

modeling and simulation of processing plants are widely used in industry. construction of a mathematical model for a plant is a time-consuming and error-prone task. in light of extensive advancements in computer science (both hardware and software), computers are becoming a necessary instrument in industrial activities. many software tools for modeling, simulation and optimization of processing...

We introduce a novel mid-structure called the generalized swept mid-structure (GSM) of a closed polygonal shape, and a framework to compute it. The GSM contains both curve and surface elements and has consistent sheet-by-sheet topology, versus triangle-by-triangle topology produced by other mid-structure methods. To obtain this structure, a harmonic function, defined on the volume that is enclo...

We consider a phase field model for the formulation and solution of topology optimization problems in the minimum compliance case. In this model, the optimal topology is obtained as the steady state of the phase transition described by the generalized Cahn–Hilliard equation which naturally embeds the volume constraint on the amount of material available for distribution in the design domain. We...

Network structure is a product of both its topology and interactions between its nodes. We explore this claim using the paradigm of distributed synchronization in a network of coupled oscillators. As the network evolves to a global steady state, nodes synchronize in stages, revealing the network's underlying community structure. Traditional models of synchronization assume that interactions bet...

Deformable models” refers to a class of physics-based modeling methods with an extensive track record in computer vision, medical imaging, computer graphics, geometric design, and related areas. Unlike the Eulerian (fluid) formulations associated with level set methods, deformable models are characterized by Lagrangian (solid) formulations, three variants of which are reviewed herein.

The logical theory of branching space-times (Belnap, Synthese 1992), which provides a relativistic framework for studying objective indeterminism, remains mostly disconnected from the discussion of space-time theories in the philosophy of physics. Earman has criticized the branching approach and suggested “pruning some branches from branching space-time” (2008). This paper identifies the differ...