四阶椭圆方程的弱解(英文)

本文研究了一个四阶椭圆方程解的存在性问题.利用山路定理和喷泉定理,结合变分方法,获得了该问题弱解的几个存在性定理,推广了现有的一些结果.     

Motion of a vortex filament with axial flow in the half space

We consider a nonlinear third order dispersive equation which models the motion of a vortex filament immersed in an incompressible and inviscid fluid occupying the three dimensional half space. We prove the unique solvability of initial–boundary value problems as an attempt to analyze the motion of a tornado.     

A discrete artificial bee colony algorithm for the multi-objective flexible job-shop scheduling problem with maintenance activities

This paper presents a novel discrete artificial bee colony (DABC) algorithm for solving the multi-objective flexible job shop scheduling problem with maintenance activities. Performance criteria considered are the maximum completion time so called makespan, the total workload of machines and the workload of the critical machine. Unlike the original ABC algorithm, the proposed DABC algorithm presents a unique solution representation where a food source is represented by two discrete vectors and tabu search (TS) is applied to each food source to generate neighboring food sources for the employed bees, onlooker bees, and scout bees. An efficient initialization scheme is introduced to construct the initial population with a certain level of quality and diversity. A self-adaptive strategy is adopted to enable the DABC algorithm with learning ability for producing neighboring solutions in different promising regions whereas an external Pareto archive set is designed to record the non-dominated solutions found so far. Furthermore, a novel decoding method is also presented to tackle maintenance activities in schedules generated. The proposed DABC algorithm is tested on a set of the well-known benchmark instances from the existing literature. Through a detailed analysis of experimental results, the highly effective and efficient performance of the proposed DABC algorithm is shown against the best performing algorithms from the literature.     

The inverse solution of the atomic mixing equations by an operator-splitting method

The quantification problem of recovering the original material distribution from secondary ion mass spectrometry (SIMS) data is considered in this paper. It is an inverse problem, is ill-posed and hence it requires a special technique for its solution. The quantification problem is essentially an inverse diffusion or (classically) a backward heat conduction problem. In this paper an operator-splitting method (that is proposed in a previous paper by the first author for the solution of inverse diffusion problems) is developed for the solution of the problem of recovering the original structure from the SIMS data. A detailed development of the quantification method is given and it is applied to typical data to demonstrate its effectiveness.     

An accurate application of the integral method applied to the diffusion of oxygen in absorbing tissue

Accurate integral methods are applied to a one dimensional moving boundary problem describing the diffusion of oxygen in absorbing tissue. These methods have been well studied for classic Stefan problems but this situation is unusual because there is no condition which contains the velocity of the moving boundary explicitly. This paper begins by giving a short time solution and then discusses some of the previous integral methods found in the literature. The main drawbacks of these solutions are that they cannot be solved from $t=0$ and also cannot determine the end behaviour. This is due to the non-uniform initial profile which integral methods typically fail to capture. The use of a novel transformation removes this non-uniformity and, on applying optimal integral methods to the resulting system, leads to simple and yet very accurate approximate solutions that overcome the deficiencies of previous methods.     

Smallest Vertex‐Transitive Graphs of Given Degree and Diameter

For every d and k, we determine the smallest order of a vertex‐transitive graph of degree d and diameter k, and in each such case we show that this order is achieved by a Cayley graph.     

Unitary Graphs

Unitary graphs are arc‐transitive graphs with vertices the flags of Hermitian unitals and edges defined by certain elements of the underlying finite fields. They played a significant role in a recent classification of a class of arc‐transitive graphs that admit an automorphism group acting imprimitively on the vertices. In this article, we prove that all unitary graphs are connected of diameter two and girth three. Based on this, we obtain, for any prime power , a lower bound of order on the maximum number of vertices in an arc‐transitive graph of degree and diameter two.     

Two Questions of Erdős on Hypergraphs above the Turán Threshold

For ordinary graphs it is known that any graph G with more edges than the Turán number of must contain several copies of , and a copy of , the complete graph on vertices with one missing edge. Erd?s asked if the same result is true for , the complete 3‐uniform hypergraph on s vertices. In this note, we show that for small values of n, the number of vertices in G, the answer is negative for . For the second property, that of containing a , we show that for the answer is negative for all large n as well, by proving that the Turán density of is greater than that of .     

Requiem for the Miller–Tucker–Zemlin subtour elimination constraints?

The Miller–Tucker–Zemlin (MTZ) Subtour Elimination Constraints (SECs) and the improved version by Desrochers and Laporte (DL) have been and are still in regular use to model a variety of routing problems. This paper presents a systematic way of deriving inequalities that are more complicated than the MTZ and DL inequalities and that, in a certain way, “generalize” the underlying idea of the original inequalities. We present a polyhedral approach that studies and analyses the convex hull of feasible sets for small dimensions. This approach allows us to generate generalizations of the MTZ and DL inequalities, which are “good” in the sense that they define facets of these small polyhedra. It is well known that DL inequalities imply a subset of Dantzig–Fulkerson–Johnson (DFJ) SECs for two-node subsets. Through the approach presented, we describe a generalization of these inequalities which imply DFJ SECs for three-node subsets and show that generalizations for larger subsets are unlikely to exist. Our study presents a similar analysis with generalizations of MTZ inequalities and their relation with the lifted circuit inequalities for three node subsets.