A One-Dimensional Binary Integer Programming Problem (1DB-IPP) is concerned with selecting a subset from a set of k items in budget constraint to optimize an objective function. In this problem a dominant solution is defined as a feasible selection to which no further item could be added in budget constraint. This paper presents a simple algorithm for Enumeration of Dominant Solutions (EDS) and...

Let O = {O1, . . . , Om} be a set of m convex polygons in R 2 with a total of n vertices, and let B be another convex k-gon. A placement of B, any congruent copy of B (without reflection), is called free if B does not intersect the interior of any polygon in O at this placement. A placement z of B is called critical if B forms three “distinct” contacts with O at z. Let φ(B,O) be the number of f...

to calculation non-bonded interaction of the [cocl6]3- complex embedded in nano ring, we focus on the single wall boron-nitride b18n18 nano ring. thus, the geometry of b18n18 nano ring has been optimized by b3lyp method with epr-ii (electron paramagnetic resonance) basis set and geometry of the [cocl6]3- complex has been optimized at b3lyp method with aldrich’s vtz basis set and stuttgart rsc 1...

We prove the following theorem, which is an analog for discrete set functions of a geometric result of Lovász and Simonovits. Given two real-valued set functions f1, f2 defined on the subsets of a finite set S, satisfying ∑ X⊆S fi(X) 0 for i ∈ {1, 2}, there exists a positive multiplicative set function over S and two subsetsA,B ⊆ S such that for i ∈ {1, 2} (A)fi(A)+ (B)fi(B)+ (A∪B)fi(A∪ B) + (A...

The traditional set stability of Boolean networks (BNs) refers to whether all the states can converge a given state subset. Different from existing results, investigated in this paper is initial destination set. This studies and stabilization avoiding undesirable sets BNs control (BCNs), respectively. First, by virtue semi-tensor product (STP) matrices, dynamics are established. Then, reachabil...

For given integers a, b and j ≥ 1 we determine the set R a,b of integers n for which an − bn is divisible by nj . For j = 1, 2, this set is usually infinite; we determine explicitly the exceptional cases for which a, b the set R a,b (j = 1, 2) is finite. For j = 2, we use Zsigmondy’s Theorem for this. For j ≥ 3 and gcd(a, b) = 1, R a,b is probably always finite; this seems difficult to prove, h...