A semianalytic partition of unity finite element method (PUFEM) is presented to solve the transient FokkerPlanck equation (FPE) for high-dimensional nonlinear dynamical systems. Meshless spatial discretization of the PUFEM is employed to develop linear ordinary differential equations for the time varying coefficients of the local shape functions. A similarity transformation to the modal coordin...

‎let $l$ be a lie algebra‎, ‎$mathrm{der}(l)$ be the set of all derivations of $l$ and $mathrm{der}_c(l)$ denote the set of all derivations $alphainmathrm{der}(l)$ for which $alpha(x)in [x,l]:={[x,y]vert yin l}$ for all $xin l$‎. ‎we obtain an upper bound for dimension of $mathrm{der}_c(l)$ of the finite dimensional nilpotent lie algebra $l$ over algebraically closed fields‎. ‎also‎, ‎we classi...

This paper considers the Economic Lot Scheduling Problem, that is, the problem of scheduling several products on a single facility so as to minimize holding and setup costs. Combination of frequency and timing as well as production quantity make this problem Np-hard. A heuristic is developed to obtain a good solution to ELSP. The proposed heuristic makes use of the Simulated Annealing Technique...

In this paper, we intend to define and study concepts of weight and weighted spaces of holomorphic (analytic) functions on the upper half plane. We study two special classes of these spaces of holomorphic functions on the upper half plane. Firstly, we prove these spaces of holomorphic functions on the upper half plane endowed with weighted norm supremum are Banach spaces. Then, we investigate t...

‎Let $L$ be a Lie algebra‎, ‎$mathrm{Der}(L)$ be the set of all derivations of $L$ and $mathrm{Der}_c(L)$ denote the set of all derivations $alphainmathrm{Der}(L)$ for which $alpha(x)in [x,L]:={[x,y]vert yin L}$ for all $xin L$‎. ‎We obtain an upper bound for dimension of $mathrm{Der}_c(L)$ of the finite dimensional nilpotent Lie algebra $L$ over algebraically closed fields‎. ‎Also‎, ‎we classi...

We demonstrate the possibility of achieving the maximum possible singlet fraction using a entangled mixed two-qubit state as a resource. For this, we establish a tight upper bound on singlet fraction and show that the maximal singlet fraction obtained in [6] does not attain the obtained upper bound on the singlet fraction. Interestingly, we found that the required upper bound can in fact be ach...

(i) We prove that the maximum number of geometric permutations, induced by line transversals to a collection of n pairwise disjoint balls in IR d , is (n d?1). This improves substantially the general upper bound of O(n 2d?2) given in 11]. (ii) We show that the maximum number of geometric permutations of a suuciently large collection of pairwise disjoint unit discs in the plane is 2, improving a...

In this paper, an upper bound approach is used to analyze the extrusion process of bimetallic rods through arbitrarily curved dies. Based on a spherical velocity field, internal, shearing and frictional power terms are calculated. The developed upper bound solution is used for calculating the extrusion force for two types of die shapes: a conical die as a linear die profile and a streamlined di...

Vertex colorings of the square of an outerplanar graph have received a lot of attention recently. In this article we prove that the chromatic number of the square of an outerplanar graph of maximum degree ∆ = 6 is 7. The optimal upper bound for the chromatic number of the square of an outerplanar graph of maximum degree ∆ 6= 6 is known. Hence, this mentioned chromatic number of 7 is the last an...

The Maximum Entropy Principle (MEP) maximises the entropy provided that the effort remains constant. The Principle of Least Effort (PLE) minimises the effort provided that the entropy remains constant. The paper investigates the relation between these two principles. In some kinds of effort functions, called admissible, it is shown that these two principles are equivalent. The results are illus...