One-dimensional chemotaxis kinetic model

In this paper, we study a variation of the equations of a chemotaxis kinetic model and investigate it in one dimension. In fact, we use fractional diffusion for the chemoattractant in the Othmar–Dunbar–Alt system (Othmer in J Math Biol 26(3):263–298, 1988). This version was exhibited in Calvez in Amer Math Soc, pp 45–62, 2007 for the macroscopic well-known Keller–Segel model in all space dimensions. These two macroscopic and kinetic models are related as mentioned in Bournaveas, Ann Inst H Poincaré Anal Non Linéaire, 26(5):1871–1895, 2009, Chalub, Math Models Methods Appl Sci, 16(7 suppl):1173–1197, 2006, Chalub, Monatsh Math, 142(1–2):123–141, 2004, Chalub, Port Math (NS), 63(2):227–250, 2006. The model we study here behaves in a similar way to the original model in two dimensions with the spherical symmetry assumption on the initial data which is described in Bournaveas, Ann Inst H Poincaré Anal Non Linéaire, 26(5):1871–1895, 2009. We prove the existence and uniqueness of solutions for this model, as well as a convergence result for a family of numerical schemes. The advantage of this model is that numerical simulations can be easily done especially to track the blow-up phenomenon.     

Wavelets generated by the Rudin-Shapiro polynomials

In this paper, we consider the well-known Rudin-Shapiro polynomials as a class of constant multiples of low-pass filters to construct a sequence of compactly supported wavelets.     

An efficient heuristic algorithm for the capacitated p-\! median problem

The capacitated $p$ -median problem (CPMP) is one of the well-known facility-location problems. The objective of the problem is to minimize total cost of locating a set of capacitated service points and allocating a set of demand points to the located service points, while the total allocated demand for each service point is not be greater than its capacity limit. This paper presents an efficient heuristic algorithm based on the local branching and relaxation induced neighborhood search methods for the CPMP. The proposed algorithm is a heuristic technique that utilizes a general mixed integer programming solver to explore neighborhoods. The parameters of the proposed algorithm are tuned by design of experiments. The proposed method is tested on a large set of benchmark instances. The results show that the method outperforms the best method found in the literature.     

Direct limits of Cohen–Macaulay rings

Let A be a direct limit of a direct system of Cohen–Macaulay rings. In this paper, we describe the Cohen–Macaulay property of A. Our results indicate that A is not necessarily Cohen–Macaulay. We show A is Cohen–Macaulay under various assumptions. As an application, we study Cohen–Macaulayness of non-affine normal semigroup rings.     

An improved method for ranking alternatives in multiple criteria decision analysis

Scoring rules are an important disputable subject in data envelopment analysis (DEA). Various organizations use voting systems whose main object is to rank alternatives. In these methods, the ranks of alternatives are obtained by their associated weights. The method for determining the ranks of alternatives by their weights is an important issue. This problem has been the subject at hand of some authors. We suggest a three-stage method for the ranking of alternatives. In the first stage, the rank position of each alternative is computed based on the best and worst weights in the optimistic and pessimistic cases, respectively. The vector of weights obtained in the first stage is not a singleton. Hence, to deal with this problem, a secondary goal is used in the second stage. In the third stage of our method, the ranks of the alternatives approach the optimistic or pessimistic case. It is mentionable that the model proposed in the third stage is a multi-criteria decision making (MCDM) model and there are several methods for solving it; we use the weighted sum method in this paper. The model is solved by mixed integer programming. Also, we obtain an interval for the rank of each alternative. We present two models on the basis of the average of ranks in the optimistic and pessimistic cases. The aim of these models is to compute the rank by common weights.     

Analytical Study on the Rate of Sound Transmission Loss in Single Row Honeycomb Sandwich Panel Using a Numerical Method

Honeycomb structures have recently, replaced with conventional homogeneous materials. Given the fact that sandwich panels containing a honeycomb core are able to adjust geometric parameters, including internal angles, they are suitable for acoustic control applications. The main objective of this study was to obtain a transmission loss curve in a specific honeycomb frequency range along with same overall dimensions and weight. In this study, a finite element model (FEM) in ABAQUS software was used to simulate honeycomb panels, evaluate resonant frequencies, and for acoustic analysis. This model was used to obtain acoustic pressure and then to calculate the sound transmission loss (STL) in MATLAB software. Vibration and acoustic analysis of panels were performed in the frequency range of 1 to 1000 Hz. The models analyzed in this design includes 14-single row-honeycomb designs with angles of −45°, −30°, −15°, 0°, +15°, +30°, +45°. The results showed that a-single row and −45°cell angle honeycomb panel in the frequency range of 1 to 1000 Hz had the highest STL as well as the highest number of frequency modes (90 mods). Furthermore, the panel had the highest STL regarding the area under the STL curve (dB∙Hz). The panels containing more frequency mods, have a higher transmission loss. Moreover, the sound transmission loss is more sensitive to the cell angle variable (θ). In other studies, the STL was more sensitive to the number of honeycomb cells in the horizontal and vertical directions, as well as the angle of cells.     

A product of varieties in relation to Baer invariants

The concept of the Baer invariant is useful in classifying groups into isologism classes. In this paper two sequences of varieties {^rV_n}n∈N₀ and {^lV_n}n∈N₀, are considered from a given variety V. The structure of Baer invariants of some groups with respect to these varieties, are determined for some specific V.