In this paper, a displacement-constrained volume-minimizing topology optimization model is present for two-dimensional continuum problems. The new model is a generalization of the displacement-constrained volume-minimizing model developed by Yi and Sui [1] in which the displacement is constrained in the loading point. In the original model the displacement constraint was formulated as an equali...

In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...  

The linear multiobjective transportation problem is a special type of vector minimum problem in which constraints are all equality type and the objectives are conicting in nature. This paper presents an application of fuzzy goal programming to the linear multiobjective transportation problem. In this paper, we use a special type of nonlinear (hyperbolic and exponential) membership functions to ...

An algorithm is presented for determining whether or not two instances of formulas are equal based on previous equality and inequality declarations. The equality determination algorithm is shown to be linear along with a completeness proof.

An algorithm for minimizing a sum of Euclidean Norms subject to linear equality constraints is described. The algorithm is based on a recently developed Newton barrier method for the unconstrained minimization of a sum of Euclidean norms (MSN). The linear equality constraints are handled using an exact L 1 penalty function which is made smooth in the same way as the Euclidean norms. It is shown...

With the help of elementary results and techniques from Real Analysis and Optimization at the undergraduate level, we study least squares solutions of linear inequality systems. We prove existence of solutions in various ways, provide a characterization of solutions in terms of nonlinear systems, and illustrate the applicability of results as a mathematical tool for checking the consistency of ...

We introduce equality up-to constraints over nite trees and investigate their expressiveness. Equality up-to constraints subsume equality constraints, subtree constraints, and one-step rewriting constraints. We establish a close correspondence between equality up-to constraints over nite trees and context uniication. Context uniication subsumes string uniication and is subsumed by linear second...

Extracting equilibrium information from nonequilibrium measurements is a challenge task of great importance in understanding the thermodynamic properties physical, chemical, and biological systems. The discovery Jarzynski equality illumines way to estimate free energy difference work performed driving processes. However, nonlinear (exponential) relation causes poor convergence equality. Here, w...