Integer programming formulations of vehicle routing problems

Various mathematical formulations are available for situations represented by vehicle routing problems. The assignment-based integer programming formulations of these problems are more common and easy to understand. Such formulations are discussed in this paper and a much simpler formulation for the vechicle routing problem is presented for the case, when all the vehicles have the same load capacity and maximum allowable cost per route.     

Combinatorial synthesis and characterization of a ternary epitaxial film of Co and Mn doped Ge (0 0 1)

We report combinatorial molecular beam epitaxy synthesis and properties of a ternary epitaxial film of Co and Mn co-doped Ge grown on Ge (0 0 1) substrate. Structural effects were examined in situ by reflection high-energy electron diffraction and ex situ by microbeam X-ray diffraction techniques, and magnetic properties were probed by using magnetooptic Kerr effect. Ternary epitaxial phase diagrams have been studied for total doping concentrations up to 30 at.%, where regions of coherent epitaxy and rough disordered growth and those of near room temperature ferromagnetic ordering have been identified.     

Hudson模型适用性及储层微观建模应用*

为明确裂缝间相互作用对各向异性的影响，本文以Hudson模型为例分析了裂缝密度、裂缝倾角对地震波波场、弹性常数和Thomsen系数的影响规律，然后采用“基质-骨架-流体”组合化的方法进行了裂缝储层微观尺度的建模，并与实际测井资料进行了对比。结果表明该模型适用条件为低裂缝密度储层，二阶模型适用的裂缝密度范围比一阶模型大，但在裂缝密度过大时，二阶模型会出现不收敛的现象，模型便不再适用。裂缝储层纵横波速度随裂缝倾角增大而增大，纵波速度对裂缝倾角更为敏感。另外，在与实际测井曲线对比时，在高裂缝密度地层二阶模型的应用效果明显优于一阶模型，说明了在高裂缝密度储层考虑裂缝间的相互作用的必要性。     

Linear recurrence relations in the algebra of matrices and applications

We study here some linear recurrence relations in the algebra of square matrices. With the aid of the Cayley–Hamilton Theorem, we derive some explicit formulas for Aⁿ (nr) and e^tA for every r×r matrix A, in terms of the coefficients of its characteristic polynomial and matrices A^j, where 0jr−1.     

A Combinatorial Approach to Piecewise Linear Time Series Analysis

Over recent years, several nonlinear time series models have been proposed in the literature. One model that has found a large number of successful applications is the threshold autoregressive model (TAR). The TAR model is a piecewise linear process whose central idea is to change the parameters of a linear autoregressive model according to the value of an observable variable, called the threshold variable. If this variable is a lagged value of the time series, the model is called a self-exciting threshold autoregressive (SETAR) model. In this article, we propose a heuristic to estimate a more general SETAR model, where the thresholds are multivariate. We formulate the task of finding multivariate thresholds as a combinatorial optimization problem. We develop an algorithm based on a greedy randomized adaptive search procedure (GRASP) to solve the problem. GRASP is an iterative randomized sampling technique that has been shown to quickly produce good quality solutions for a wide variety of optimization problems. The proposed model performs well on both simulated and real data.     

A convenient semicarbazide resin for the solid-phase synthesis of peptide ketones and aldehydes

Use of a semicarbazide resin for the solid-phase preparation of peptide ketones and aldehyde led to optimal results in terms of both purity of the final product and overall yield. This resin was prepared without complication by activation of the commercial available aminomethyl polystyrene with CDI at room temperature, followed by treatment with tert-butyl carbazate. Furthermore, the TNBSA colorimetric assay has been adapted for checking the incorporation of the carbonyl moiety onto hydrazine-based resins.     

Equalizer technology followed by DIGE‐based proteomics for detection of cellular proteins in artificial peritoneal dialysis effluents

Peritoneal dialysis effluent (PDE) represents a rich pool of potential biomarkers for monitoring disease and therapy. Until now, proteomic studies have been hindered by the plasma‐like composition of the PDE. Beads covered with a peptide library are a promising approach to remove high abundant proteins and concentrate the sample in one step. In this study, a novel approach for proteomic biomarker identification in PDEs consisting of a depletion and concentration step followed by 2D gel based protein quantification was established. To prove this experimental concept a model system of artificial PDEs was established by spiking unused peritoneal dialysis (PD) fluids with cellular proteins reflecting control conditions or cell stress. Using this procedure, we were able to reduce the amount of high abundant plasma proteins and concentrate low abundant proteins while preserving changes in abundance of proteins with cellular origin. The alterations in abundance of the investigated marker for cell stress, the heat shock proteins, showed similar abundance profiles in the artificial PDE as in pure cell culture samples. Our results demonstrate the efficacy of this system in detecting subtle changes in cellular protein expression triggered by unphysiological stress stimuli typical in PD, which could serve as biomarkers. Further studies using patients’ PDE will be necessary to prove the concept in clinical PD and to assess whether this technique is also informative regarding enriching low abundant plasma derived protein biomarker in the PDE.     

Minmax regret approach and optimality evaluation in combinatorial optimization problems with interval and fuzzy weights

This paper deals with a general combinatorial optimization problem in which closed intervals and fuzzy intervals model uncertain element weights. The notion of a deviation interval is introduced, which allows us to characterize the optimality and the robustness of solutions and elements. The problem of computing deviation intervals is addressed and some new complexity results in this field are provided. Possibility theory is then applied to generalize a deviation interval and a solution concept to fuzzy ones.     

Highly efficient synthesis of triazolo[1,2-a]indazole-triones and novel spiro triazolo[1,2-a]indazole-tetraones under solvent-free conditions

A new, convenient, and high yielding procedure for the synthesis of triazolo[1,2-a]indazole-triones by the condensation reaction between dimedone, aryl aldehydes, and ueazoles in the presence of a catalytic amount of sulfonated polyethylene glycol (PEG-SO₃H) as a highly stable and reusable eco-friendly degradable polymeric catalyst is described under solvent-free conditions. This procedure has also been applied successfully for the synthesis of novel spiro triazolo[1,2-a]indazole-tetraones.