Lp径向Blaschke-Minkowski同态的Lp对偶几何表面积

2006年,Schuster提出了径向Blaschke-Minkowski同态的概念.随后,汪卫等人将其推广到L_p径向Blaschke-Minkowski同态.本文结合L_p对偶几何表面积,建立了L_p径向Blaschke-Minkowski同态的若干不等式,包括Brunn-Minkowski型不等式和单调不等式.并给出了L_p径向Blaschke-Minkowski同态的Busemann-Petty问题的肯定和否定形式.     

Solving multiobjective,multiconstraint knapsack problems using mathematical programming and evolutionary algorithms

In this paper, we solve instances of the multiobjective multiconstraint (or multidimensional) knapsack problem (MOMCKP) from the literature, with three objective functions and three constraints. We use exact as well as approximate algorithms. The exact algorithm is a properly modified version of the multicriteria branch and bound (MCBB) algorithm, which is further customized by suitable heuristics. Three branching heuristics and a more general purpose composite branching and construction heuristic are devised. Comparison is made to the published results from another exact algorithm, the adaptive ε-constraint method [Laumanns, M., Thiele, L., Zitzler, E., 2006. An efficient, adaptive parameter variation scheme for Metaheuristics based on the epsilon-constraint method. European Journal of Operational Research 169, 932–942], using the same data sets. Furthermore, the same problems are solved using standard multiobjective evolutionary algorithms (MOEA), namely, the SPEA2 and the NSGAII. The results from the exact case show that the branching heuristics greatly improve the performance of the MCBB algorithm, which becomes faster than the adaptive ε -constraint. Regarding the performance of the MOEA algorithms in the specific problems, SPEA2 outperforms NSGAII in the degree of approximation of the Pareto front, as measured by the coverage metric (especially for the largest instance).     

Scheduling elective surgery under uncertainty and downstream capacity constraints

The objective of this study is to generate an optimal surgery schedule of elective surgery patients with uncertain surgery operations, which includes uncertainty in surgery durations and the availability of downstream resources such as surgical intensive care unit (SICU) over multi-periods. The stochastic optimization is adapted and the sample average approximation (SAA) method is proposed for obtaining an optimal surgery schedule with respect to minimizing the total cost of patient costs and overtime costs. A computational experiment is presented to evaluate the performance of the proposed method.     

Time reversal for obstacle location in elastodynamics from acoustic recording

The Note is concerned with a feasibility study of time reversal in a non-homogeneous elastic medium, from data recorded in an acoustic medium. Our aim here is to determine the presence and some physical properties of elastic “inclusions” (unknown, not observable solid objects, characterized by their elastic properties) from partial observations of acoustic waves scattered by these inclusions. A finite element numerical method, based on a variational acousto-elastodynamics formulation, is derived and used to solve the forward, and then, the time-reversed problem. A criterion, derived from the reverse time migration framework, is introduced, to help construct images of the inclusions to be determined. Numerical illustrations on configurations that mimic the breast cancer configuration are proposed, and show that one can differentiate between two inclusions, even with different properties.     

Hjelmslev quadrilateral central configurations

A Hjelmslev quadrilateral is a quadrilateral with two right angles at opposite vertices. Using mutual distances as coordinates, we show that any four-body central configuration forming a Hjelmslev quadrilateral must be a right kite configuration.     

A nonlocal multi-point singular fractional integro-differential problem of Lane–Emden type

In this paper, using Riemann–Liouville integral and Caputo derivative, we study a nonlinear singular integro-differential equation of Lane–Emden type with nonlocal multi-point integral conditions. We prove the existence and uniqueness of solutions by application of Banach contraction principle. Also, we prove an existence result using Schaefer fixed point theorem. Then, we present some examples to show the applicability of the main results.     

Domain decomposition methods in a geometrical multiscale domain using finite volume schemes

The heat equation is solved by using a finite volume discretization in a domain that consists of a two-dimensional central node and several one-dimensional outgoing branches. Several interface connection options to match the submodels set on the node and on the branches, with or without continuity, are looked at. For each of them, a monolithic scheme is defined, and existence and uniqueness of the solution is proved. New schemes are deduced, which are obtained through domain decomposition methods in the form of interface systems, with one or two unknowns per interface. A comparative systematic study is carried out from an algebraic and numerical point of view according to the interface conditions: Dirichlet, Neumann, or Robin. An efficient diagonal preconditioning is proposed.     

Two-dimensional problem of two Coulomb centers at small intercenter distances

We use analytic methods to analyze the discrete spectrum for the problem (Z₁eZ₂)₂ in the united-atom limit (R ≪ 1) and obtain asymptotic expansions for the quantum defect and energy terms of the system (Z₁eZ₂)₂ at small intercenter distances R up to terms of the order O(R⁶). We investigate the effect of the dimensionality factor on the energy spectrum of the hydrogen molecular ion H ₂ ⁺ . __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 2, pp. 269–287, August, 2006.