We now return to the one basic design paradigm we skipped in our discussion of approximation algorithms for NP-hard optimization problems, namely divide-and-conquer (DC), and apply it to problems on graphs. The basic idea is as follows: Find a balanced cut of small capacity, i.e., a cut in which both sides contain roughly the same number of vertices and such that few edges cross the cut. Ignore...

Many polynomially solvable combinatorial optimization problems (COP) become NP hard when we require solutions to satisfy an additional cardinality constraint. This family of problems has been considered only recently. We study a new problem of this family: the k-cardinality minimum cut problem. Given an undirected edge-weighted graph the k-cardinality minimum cut problem is to nd a partition of...

trypsin is a serine protease found in the digestive system of many vertebrates, where it hydrolyses proteins. trypsin has been used widely in various biotechnological processes. in this study trypsin was purified using two precipitation cut, 35% and 75% as saturation percent of ammonium sulfate solutions, tca precipitation (2.5% w/v), ph precipitation and finally affinity chromatography. this m...

In this work a solution using evolutionary algorithms with penalty function for the non-guillotine cutting problem is presented. In this particular problem, the rectangular pieces have to be cut from an unique large object, being the goal to maximize the total value of cut pieces. Some chromosomes can hold pieces to be cut, but some pieces cannot be arranged into the object, generating infeasib...

We study the existence of global-in-time weak solutions to a coupled microscopicmacroscopic bead-spring model with microscopic cut-off, which arises from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The model consists of the unsteady incompressible Navier–Stokes equations in a bounded domain Ω ⊂ Rd, d = 2 or 3, for the velocity and the pressure...

introduction: nowadays, due to mechanization of life, consumers need of food which they spent little time for preparation, so fresh cut industry is growing rapidly in the world. these products had strong growth since 1940, and in 2013, most sales of fresh cut fruit related to apples, against 21.8 percent. minimal processing operations include grading, washing, sorting, slicing, chopping and the...