Efficient Approximation of the Capacitated Vehicle Routing Problem in a Metric Space of an Arbitrary Fixed Doubling Dimension

Doklady Mathematics - In this paper, for the first time, we provide a quasi-polynomial time approximation scheme for the well-known capacitated vehicle routing problem formulated in metric spaces...     

Comparison of dispersion models in the optical characterization of As–S chalcogenide thin films

In this paper, the optical analysis of the As–S thin films prepared under different conditions is performed using three dispersion models for amorphous materials typically employed in practice. The Tauc–Lorentz (TL) model, Urbach–Cody–Lorentz (UCL) model and our model based on the parameterization of the density of electronic states (PDOS model) are namely used to determine the optical parameters of these films. Within the structural model of the As–S films, the existence of the optical constants profiles and overlayers on to the upper boundaries of these films are included. Dispersion and structural models are employed within the analysis based on a combination of variable angle spectroscopic ellipsometry and transmission spectrophotometry in conjunction with multi-sample modification. It is demonstrated that the TL model is not suitable for the optical characterization of the As–S thin films because of the absence of the Urbach tail. Furthermore, it is shown that both the UCL and PDOS models are satisfactory ones for the optical characterization of these films. Moreover, it is also shown that, using the PDOS dispersion model, one can evaluate the material parameters of these As–S films that correspond to the electronic band structure.     

Existence of the uniformly minimum risk equivariant estimators of parameters in a class of normal linear models

In this paper, we study the existence of the uniformly minimum risk equivariant (UMRE) estimators of parameters in a class of normal linear models, which include the normal variance components model, the growth curve model, the extended growth curve model, and the seemingly unrelated regression equations model, and so on. The necessary and sufficient conditions are given for the existence of UMRE estimators of the estimable linear functions of regression coefficients, the covariance matrixV and (trV)^α, where α > 0 is known, in the models under an affine group of transformations for quadratic losses and matrix losses, respectively. Under the (extended) growth curve model and the seemingly unrelated regression equations model, the conclusions given in literature for estimating regression coefficients can be derived by applying the general results in this paper, and the sufficient conditions for non-existence of UMRE estimators ofV and tr(V) are expanded to be necessary and sufficient conditions. In addition, the necessary and sufficient conditions that there exist UMRE estimators of parameters in the variance components model are obtained for the first time.     

Local and Parallel Finite Element Algorithms for Eigenvalue Problems

Abstract Some new local and parallel finite element algorithms are proposed and analyzed in this paper foreigenvalue problems.With these algorithms, the solution of an eigenvalue problem on a fine grid is reduced tothe solution of an eigenvalue problem on a relatively coarse grid together with solutions of some linear algebraicsystems on fine grid by using some local and parallel procedure.A theoretical tool for analyzing these algorithmsis some local error estimate that is also obtained in this paper for finite element approximations of eigenvectorson general shape-regular grids.     

Letter to the Editor

Mathematical Notes -     

Total Variation and Multisymplectic Structure for CNLS System

The relation between the total variation of classical field theory and the multisymplectic structure is shown. Then the multisymplectic structure and the corresponding multisymplectic conservation of the coupled nonlinear Schrodinger system are obtained directly from the variational principle.     

Enriched workflow modelling and Stochastic Branch-and-Bound

Workflow systems provide means and techniques for modelling, designing, performing and controlling repetitive (business) processes. The quality of commercial workflow systems is usually determined to a large extent by their versatility and multi-purpose application. One of the current trends in improving workflow systems lies in enriching modelling methods and techniques in order to enlarge design alternatives.The need for such advanced methods is particularly apparent in those fields in which the process duration can be determined only vaguely, but whose completion schedules are at the same time strictly enforced by a highly competitive market by means of fines and penalties. The risk of an overrun has to be weighed against the expected costs and benefits of certain measures reducing turn-around time and their combinations. Because they can help to avoid such penalties—or, at least, keep any potential losses low by identifying critical subprocesses and evaluate appropriate measures—modelling and evaluation techniques are becoming essential features of workflow systems.Methodologically, we use Stochastic Branch-and-Bound as a technique for finding “optimal” bundles of measures. A numerical study shows the benefits of this meta-approach by means of five stepwise-developed decision scenarios requiring rich modelling. Petri nets as a modelling tool and Stochastic Branch-and-Bound as an optimization technique determine for multi-mode resource constrained workflows of varying complexity an optimal workforce strategy with respect to the number of workers and their qualification.     

自旋-轨道耦合系统中的自旋流定义

通常的自旋流定义在描述自旋-轨道耦合系统中的自旋输运是不完整的与非物理的。文章作者提出在这类系统中自旋流的恰当定义。新定义的自旋流克服了通常定义下的本质缺点，可通过实验直接观测。     

Well-Posedness by Perturbations of Variational Problems

In this paper, we consider the extension of the notion of well-posedness by perturbations, introduced by Zolezzi for optimization problems, to other related variational problems like inclusion problems and fixed-point problems. Then, we study the conditions under which there is equivalence of the well-posedness in the above sense between different problems. Relations with the so-called diagonal well-posedness are also given. Finally, an application to staircase iteration methods is presented.