On cuts and matchings in planar graphs

We study the max cut problem in graphs not contractible toK ₅, and optimum perfect matchings in planar graphs. We prove that both problems can be formulated as polynomial size linear programs.Supported by the joint project Combinatorial Optimization of the Natural Sciences and Engineering Research Council of Canada and the German Research Association (Deutsche Forschungsgemeinschaft, SFB 303).     

Signature classes of transportation polytopes

Signature algorithms solve certain classes of transportation problems in a number of steps bounded by the diameter of the dual polyhedron. The class of problems to which signature algorithms may be applied—the signature classes of the title—are characterized, and the monotonic Hirsch conjecture is shown to hold for them. In addition, certain more precise results are given for different cases. Finally, it is explained why a supposed proof of the Hirsch conjecture for all transportation polytopes is incomplete and apparently irremedial.Dedicated with affection to Philip Wolfe on the occasion of his 65th birthday.     

Minimization of a quasi-concave function over an efficient set

We introduce a projective approach for studying symmetric travelling salesman polytopes (STSPs). Thesymmetric travelling salesman polytope STSP(V) (resp.,Hamiltonian path polytope HP(V)) is the convex hull of incidence vectors of all Hamiltonian cycles (resp., paths) on the complete undirected graph with node setV. For any nodeh V, HP(V) is aprojection of STSP(V {h}). We show that HP(V) and STSP(V {h}) are isomorphic, and HP(V) is of full dimension minus one. By this projective approach, we obtain generalclique-lifting results, all based on simple conditions, for deriving large new classes of STSP facets. These results apply to all known non-trivial STSP facets, and generalize clique-lifting results of Maurras (1975), Grötschel and Padberg (1979) and Naddef and Rinaldi (1988).This research is supported in part by a grant from the Natural Sciences and Engineering Research Council of Canada to the first author.     

Null controllability of a pseudo-parabolic equation with moving control

In this paper, we study the internal controllability of the pseudo-parabolic equation on the one-dimensional torus. Our control function is acting on a moving small interval with a constant velocity. With this moving distributed control, we obtain the system is null controllable for given data with certain regularity.     

Generalized Taylor-Aris moment analysis of the transport of sorbing solutes through porous media with spatially-periodic retardation factor

Taylor-Aris dispersion theory, as generalized by Brenner, is employed to investigate the macroscopic behavior of sorbing solute transport in a three-dimensional, hydraulically homogeneous porous medium under steady, unidirectional flow. The porous medium is considered to possess spatially periodic geochemical characteristics in all three directions, where the spatial periods define a rectangular parallelepiped or a unit-element. The spatially-variable geochemical parameters of the solid matrix are incorporated into the transport equation by a spatially-periodic distribution coefficient and consequently a spatially-periodic retardation factor. Expressions for the effective or large-time coefficients governing the macroscopic solute transport are derived for solute sorbing according to a linear equilibrium isotherm as well as for the case of a first-order kinetic sorption relationship. The results indicate that for the case of a chemical equilibrium sorption isotherm the longitudinal macrodispersion incorporates a second term that accounts for the eflect of averaging the distribution coefficient over the volume of a unit element. Furthermore, for the case of a kinetic sorption relation, the longitudinal macrodispersion expression includes a third term that accounts for the effect of the first-order sorption rate. Therefore, increased solute spreading is expected if the local chemical equilibrium assumption is not valid. The derived expressions of the apparent parameters governing the macroscopic solute transport under local equilibrium conditions agreed reasonably with the results of numerical computations using particle tracking techniques.     

Thermodynamic Properties and Molecular Dipole Moments of Antimony Compounds from Quantum Chemical Evaluations

By the PM3 method, standard values of entropy, heats and Gibbs energies of formation and dipole moments of the molecules have been computed for a series of inorganic and organic antimony compounds. Linear dependences P exper = bP theor (where P is any of the mentioned properties) have been stated, allowing a priori evaluation of thermodynamic characteristics and molecular dipole moments of Sb-containing substances. It has been concluded that triphenylstibinedichloride in benzene solution, as well as triphenylstibinehydroxychloride in dioxane medium, exist in the form of trigonal bipyramid with two axial chlorine and oxygen atoms.     

Extremal properties of strong quadrature weights and maximal mass results for truncated strong moment problems

A bisequence of complex numbers {μ_n}_−∞^∞ determines a strong moment functional satisfying L[xⁿ] = μ_n. If is positive-definite on a bounded interval (a,b) R{0}, then has an integral representation , n=0, ±1, ±2,…, and quadrature rules {w_ni,x_ni} exist such that μ_k = ∑_i=i^n_ns_ni^kw_ni. This paper is concerned with establishing certain extremal properties of the weights w_ni and using these properties to obtain maximal mass results satisfied by distributions ψ(x) representing when only a finite bisequence of moments {μ_k}_k=−nⁿ⁻¹ is given.     

基于高储能密度电容退化数据的可靠性评估

 根据强激光能源模块高储能密度电容器在工作过程中,受到连续冲击而使退化失效具有累积效应的特点,提出了利用产品运行过程中性能参数退化的信息,用复合Poisson过程对退化轨道建模并进行可靠性评估的方法。给出了模型参数的矩估计和电容器的平均退化量、可靠度、平均寿命等可靠性指标评估的Bootstrap仿真过程。并通过实例说明了该评估方法在工程中的应用。基于电容退化信息的可靠性评估方法,可以在极少甚至没有寿命数据的情况下给出客观可信的评估结果,在理论和应用上都具有重要的价值。     

Tangentially positive isometric actions and conjugate points

Let be a complete Riemannian manifold with no conjugate points and a principal -bundle, where is a Lie group acting by isometries and the smooth quotient with the Riemannian submersion metric.

We obtain a characterization of conjugate point-free quotients in terms of symplectic reduction and a canonical pseudo-Riemannian metric on the tangent bundle , from which we then derive necessary conditions, involving and , for the quotient metric to be conjugate point-free, particularly for a reducible Riemannian manifold.

Let , with the Lie Algebra of , be the moment map of the tangential -action on and let be the canonical pseudo-Riemannian metric on defined by the symplectic form and the map , . First we prove a theorem, stating that if is not positive definite on the action vector fields for the tangential action along then acquires conjugate points. (We proved the converse result in 2005.) Then, we characterize self-parallel vector fields on in terms of the positivity of the -length of their tangential lifts along certain canonical subsets of . We use this to derive some necessary conditions, on and , for actions to be tangentially positive on relevant subsets of , which we then apply to isometric actions on complete conjugate point-free reducible Riemannian manifolds when one of the irreducible factors satisfies certain curvature conditions.