Meta-heuristic approaches with memory and evolution for a multi-product production/distribution system design problem

We consider a multi-product two-stage production/distribution system design problem (PDSD) where a fixed number of capacitated distribution centers are to be located with respect to capacitated suppliers (plants) and retail locations (customers) while minimizing the total costs in the system. We present a mixed-integer problem formulation that facilitates the development of efficient heuristic procedures. We provide meta-heuristic procedures, including a population-based scatter search with path relinking and trajectory-based local and tabu search, for the solution of the problem. We also develop efficient construction heuristics and transshipment heuristics that are incorporated into the heuristic procedures for the solution of subproblems. We present extensive computational results that show the high performance of the solution approaches. We obtain smaller than 1.0% average optimality gaps with acceptable runtimes, even for relatively large problems. The computational results also demonstrate the effectiveness of the construction and transshipment heuristics that impact the solution quality and overall runtimes.     

Dynamic Phase Transitions and Compensation Temperatures in a Mixed Spin-3/2 and Spin-5/2 Ising System

We examine the dynamic phase transitions and the dynamic compensation temperatures, within a mean-field approach, in the mixed spin-3/2 and spin-5/2 Ising system with a crystal-field interaction under a time-varying magnetic field on a hexagonal lattice by using Glauber-type stochastic dynamics. The model system consists of two interpenetrating sublattices with σ=3/2 and S=5/2. The Hamiltonian model includes intersublattice, intrasublattice, and crystal-field interactions. The intersublattice interaction is considered antiferromagnetic and to be a simple but interesting model of a ferrimagnetic system. We employ the Glauber transition rates to construct the mean-field dynamic equations, and we solve these equations in order to find the phases in the system. We also investigate the thermal behavior of the dynamic sublattice magnetizations and the dynamic total magnetization to obtain the dynamic phase transition points and compensation temperatures as well as to characterize the nature (continuous and discontinuous) of transitions. We also calculate the dynamic phase diagrams including the compensation temperatures in five different planes. According to the values of Hamiltonian parameters, five different fundamental phases, three different mixed phases, and six different types of compensation behaviors in the Néel classification nomenclature exist in the system.     

Mixed-Spin Ising Model in an Oscillating Magnetic Field and Compensation Temperature

Godoy et al. (Phys. Rev. B 69, 054428, 2004) presented a study of the magnetic properties of a mixed spin (1/2,1), Ising ferrimagnetic model on a hexagonal lattice without an oscillating magnetic field. They employed dynamic mean-field calculations and Monte Carlo simulations to find the compensation point of the model and to present the phase diagrams. It has been found that the N-type compensation temperature appears only when the intrasublattice interaction between spins in the σ sublattice is ferromagnetic. Moreover, the system only undergoes a second-order phase transition. In this work, we extend the study a dynamic compensation temperature of a mixed spin-1/2 and spin-1 Ising ferrimagnetic system on a hexagonal lattice in the presence of oscillating magnetic field within the framework of dynamic mean-field calculations. We find that the system displays the N-type compensation temperature. We also calculate dynamic phase diagrams in which contain the paramagnetic, ferrimagnetic, nonmagnetic fundamental phases and two different mixed phases, depending on the interaction parameters and oscillating magnetic field. The system also exhibits tricritical and reentrant behaviors.     

On dual of square free modules

A module M is said to be square free if whenever its submodule is isomorphic to N² = N⊕N for some module N, then N = 0. Dually, a module M is said to be d-square free (dual square free) if whenever its factor module is isomorphic to N² for some module N, then N = 0. In this paper, we give some fundamental properties of d-square free modules and study rings whose d-square free modules are closed under submodules or essential extensions.     

Characterizing student mathematics teachers’ levels of understanding in spherical geometry

This article presents an exploratory study aimed at the identification of students’ levels of understanding in spherical geometry as van Hiele did for Euclidean geometry. To do this, we developed and implemented a spherical geometry course for student mathematics teachers. Six structured, task-based interviews were held with eight student mathematics teachers at particular times through the course to determine the spherical geometry learning levels. After identifying the properties of spherical geometry levels, we developed Understandings in Spherical Geometry Test to test whether or not the levels form hierarchy, and 58 student mathematics teachers took the test. The outcomes seemed to support our theoretical perspective that there are some understanding levels in spherical geometry that progress through a hierarchical order as van Hiele levels in Euclidean geometry.     

On Fully Idempotent Modules

A submodule N of a module M is idempotent if N = Hom(M, N)N. The module M is fully idempotent if every submodule of M is idempotent. We prove that over a commutative ring, cyclic idempotent submodules of any module are direct summands. Counterexamples are given to show that this result is not true in general. It is shown that over commutative Noetherian rings, the fully idempotent modules are precisely the semisimple modules. We also show that the commutative rings over which every module is fully idempotent are exactly the semisimple rings. Idempotent submodules of free modules are characterized.     

Diffusion-weighted imaging features of brain in obesity

PURPOSE: Obesity is characterized by an altered distribution of body fluid. However, distribution of fluid (extracellular/intracellular) in brain tissues has not been studied in obese subjects yet. The purpose of this study was to detect possible brain diffusion changes especially in satiety and hunger related centers in obese subjects by diffusion weighted imaging (DWI). METHODS: Conventional MRI and DWI of the brain was obtained from 81 obese patients (obese=68, morbid obese=13) and 29 age-matched, nonobese. The apparent diffusion coefficient (ADC) values were calculated in hypothalamus; amygdala; hippocampal gyrus; thalamus; insula; cingulate gyrus; orbitofrontal, dorsomedial and dorsolateral frontal, middle temporal and occipital cortex; cerebellum; midbrain and corpus striatum. RESULTS: The ADC values of hypothalamus, hippocampal gyrus, amygdala, insula, cerebellum and midbrain were significantly increased in patients (n:81) when compared to nonobese subjects. The ADC values of thalamus, hippocampal gyrus, amygdala, orbitofrontal, occipital, dorsolateral and middle temporal cortex, insula and midbrain were significantly increased in morbid obese when compared to nonobese subjects. The ADC values of orbitofrontal and occipital cortex were significantly higher in morbid obese than the values in the obese. The body mass index positively correlated with ADC values of amygdala, insula, orbitofrontal and middle temporal cortex. CONCLUSION: We observed increased ADC values of distinct locations related to satiety and hunger that suggest altered fluid distribution and/or vasogenic edema in obese subjects. Awareness of this abnormalities in brain tissue composition/function in obesity may contribute to better understanding of the underlying mechanisms.     

Synthesis and EPR studies of porphyrazines with bulky substituents

Magnesium porphyrazinate substituted with eight 4-tert-butylphenylthio-groups on the peripheral positions has been synthesized by cyclotetramerization of 1,2-bis(4-tert-butylphenylthio)maleonitrile in the presence of magnesium butanolate. The metal-free derivative was obtained by its treatment with trifluoroacetic acid and further reaction of this product with copper(II) acetate, zinc(II) acetate and cobalt(II) acetate led to the metal porphyrazinates (M = Cu, Zn, Co). These new compounds have been characterized by elemental analysis, together with FT-IR, ¹H NMR, UV–Vis spectral data. By using EPR technique, room temperature paramagnetic properties of Cu(II) doped porphyrazine sample as powder and solution forms were measured. The first-derivative EPR signals taken from as powder and solution forms shows that the sample is axially symmetric. The trend g_∥ > g_⊥ > 2 indicates that the unpaired electron is located mainly in the _dx2-y2${\mathrm{d}}_{x^2-y^2}$ orbital (²B₁ as ground state).     

Label-free detection of proteins from dried-suspended droplets using surface enhanced Raman scattering

A simple sample preparation method to obtain rich and reproducible surface-enhanced Raman scattering (SERS) spectra from proteins regardless of their surface properties and dimensions for label-free detection and identification is reported. The method uses colloidal silver nanoparticles (AgNPs) as substrates and is based on suspending the droplet of a mixture containing AgNPs and proteins from a hydrophobic surface. Drying the droplet at this suspended configuration allows the accumulation and packing of AgNPs and protein molecules in the middle of the droplet area rather than getting jammed at the edges of drying droplets as the solvent evaporates. A detection limit of down to 0.05 μg mL(-1) for some of the model proteins used in this study is obtained with this simple approach. The advantage of this method is its simplicity and improved sensitivity over other approaches reported in the literature.     

Analysis of the effects of the global financial crisis on the Turkish economy, using hierarchical methods

We have analyzed the topology of 50 important Turkish companies for the period 2006-2010 using the concept of hierarchical methods (the minimal spanning tree (MST) and hierarchical tree (HT)). We investigated the statistical reliability of links between companies in the MST by using the bootstrap technique. We also used the average linkage cluster analysis (ALCA) technique to observe the cluster structures much better. The MST and HT are known as useful tools to perceive and detect global structure, taxonomy, and hierarchy in financial data. We obtained four clusters of companies according to their proximity. We also observed that the Banks and Holdings cluster always forms in the centre of the MSTs for the periods 2006-2007, 2008, and 2009-2010. The clusters match nicely with their common production activities or their strong interrelationship. The effects of the Automobile sector increased after the global financial crisis due to the temporary incentives provided by the Turkish government. We find that Turkish companies were not very affected by the global financial crisis.