幂次为3 和4 的整数变量非线性型的整数部分

本文利用Davenport-Heilbronn 方法证明了对于自然数x_j, 表达式
λ₁x₁³+λ₂x₂³+λ₃x₃³+λ₄x₄⁴+λ₅x₅⁴+λ₆x₆⁴
的整数部分在给定条件下可表示无穷多素数, 深化了Brüdern 等人的广义Riemann 假设下等幂次的结果.     

Extended integer rank reduction formulas and Smith normal form

We present an integer rank reduction formula for transforming the rows and columns of an integer matrix A. By repeatedly applying the formula to reduce rank, an extended integer rank reducing process is derived. The process provides a general finite iterative approach for constructing factorizations of A and A ^T under a common framework of a general decomposition V ^T AP?=?Ω. Then, we develop the integer Wedderburn rank reduction formula and its integer biconjugation process. Both the integer biconjugation process associated with the Wedderburn rank reduction process and the scaled extended integer Abaffy–Broyden–Spedicato (ABS) class of algorithms are shown to be in the integer rank reducing process. We also show that the integer biconjugation process can be derived from the scaled integer ABS class of algorithms applied to A or A ^T . Finally, we show that the integer biconjuagation process is a special case of our proposed ABS class of algorithms for computing the Smith normal form.     

An optimality criterion for a limited capacity queueing system

A single server, limited capacity queueing system with Poisson arrivals and exponential service is studied. The joint probability distribution of the number of times the system reaches its capacity in time interval (0t] and the number of customers in the system at time i has been obtained. From, the joint probability, the probability that the system has reached its capacity m times in time interval (0t] has been determined and the expectation and variance have been found explicitly. A criterion for the system to be optimum is established and is illustrated numerically.     

The locomotive fleet fueling problem

This paper considers the problem of how to determine an optimal fueling schedule and contracting policy with fuel suppliers so as to minimize the total cost of the fueling operation. The problem is formulated as a mixed integer program and the formulation is enhanced by valid inequalities and domination rules. The enhanced model allows us to obtain near optimal solutions for large scale instances.     

Mixed integer goal programming models for the flexible job-shop scheduling problems with separable and non-separable sequence dependent setup times

The optimization problem addressed in this paper is an advanced form of the flexible job shop scheduling problem (FJSP) which also covers process plan flexibility and separable/non-separable sequence dependent setup times in addition to routing flexibility. Upon transforming the problem into an equivalent network problem, two mixed integer goal programming models are formulated. In the first model (Model A) the sequence dependent setup times are non-separable. In the second one (Model B) they are separable. Model B is obtained from Model A with a minor modification. The formulation of the models is described on a small sized numerical example and the solutions are interpreted. Finally, computational results are obtained on test problems.     

Monodisperse porous polymer particles with polyionic ligands for ion exchange separation of proteins

A new “grafting to” strategy was proposed for the preparation of polymer based ion exchange supports carrying polymeric ligands in the form of weak or strong ion exchangers. Monodisperse porous poly(glycidyl methacrylate-co-ethylene dimethacrylate), poly(GMA-co-EDM) particles 5.9 μm in size were synthesized by “modified seeded polymerization”. Poly(2,3-dihydroxypropyl methacrylate-co-ethylene dimethacrylate), poly(DHPM-co-EDM) particles were then obtained by the acidic hydrolysis of poly(GMA-co-EDM) particles. The hydroxyl functionalized beads were treated with 3-(trimethoxysilyl)propyl methacrylate to have covalently linked methacrylate groups on the particle surface. The selected monomers carrying weak or strong ionizable groups (2-acrylamido-2-methyl-1-propane sulfonic acid, AMPS; 2-dimethylaminoethylmethacrylate, DMAEM and N-[3-(dimethylamino)propyl] methacrylamide, DMAPM) were subsequently grafted onto the particles via immobilized methacrylate groups. The final polymer based materials with polyionic ligands were tried as chromatographic packing in the separation of proteins by ion exchange chromatography. The proteins were successfully separated both in the anion and cation exchange mode with higher column yields with respect to the previously proposed materials. The plate heights obtained for poly(AMPS) and poly(DMAEM) grafted poly(DHPM-co-EDM) particles by using proteins as the analytes were 80 and 200 μm, respectively. Additionally, the plate height exhibited no significant increase with the increasing linear flow rate in the range of 1–20 cm/min. The most important property of the proposed strategy is to be applicable for the synthesis of any type of ion exchanger both in the strong and weak form.     

Spin-Hall Effect with Quantum Group Symmetries

We construct a model of spin-Hall effect on a noncommutative four sphere S ⁴ _Θ with isospin degrees of freedom, coming from a noncommutative instanton, and invariance under a quantum group SO _θ. The corresponding representation theory allows to explicitly diagonalize the Hamiltonian and construct the ground state; there are both integer and fractional excitations. Similar models exist on higher dimensional spheres S _Θ ^N and projective spaces . Dedicated to Rafael Sorkin with friendship and respect.     

On the gap between the quadratic integer programming problem and its semidefinite relaxation

Consider the semidefinite relaxation (SDR) of the quadratic integer program (QIP): where Q is a given symmetric matrix and D is diagonal. We consider the SDR gap We establish the uniqueness of the SDR solution and prove that if and only if γ_r:=n⁻¹max{x^TVV^Tx:x ∈ {-1, 1}ⁿ}=1 where V is an orthogonal matrix whose columns span the (r–dimensional) null space of D−Q and where D is the unique SDR solution. We also give a test for establishing whether that involves 2^r−1 function evaluations. In the case that γ_r<1 we derive an upper bound on γ which is tighter than Thus we show that `breaching' the SDR gap for the QIP problem is as difficult as the solution of a QIP with the rank of the cost function matrix equal to the dimension of the null space of D−Q. This reduced rank QIP problem has been recently shown to be solvable in polynomial time for fixed r.     

Asymptotic Determination of the Last Packing Number of Quadruples

A 3-(n,4,1) packing design consists of an n-element set X and a collection of 4-element subsets of X, called blocks, such that every 3-element subset of X is contained in at most one block. The packing number of quadruples d(3,4,n) denotes the number of blocks in a maximum 3-(n,4,1) packing design, which is also the maximum number A(n,4,4) of codewords in a code of length n, constant weight 4, and minimum Hamming distance 4. In this paper the last packing number A(n,4,4) for n≡ 5(mod 6) is shown to be equal to Johnson bound with 21 undecided values n=6k+5, k∈{m: m is odd , 3≤ m≤ 35, m≠ 17,21}∪ {45,47,75,77,79,159}. AMS Classification:05B40, 94B25