Approximation by Gamma type operators

In this study, we introduce newly defined Gamma operators which preserve constants and e^2μ·, μ>0 functions. In accordance with this purpose, we focus on their approximation properties such as uniform convergence, rate of convergence, asymptotic formula, and saturation results. Superior properties of introduced operators have been tested both theoretically and numerically in certain senses to highlight the performance of the new constructions of Gamma operators.     

Optimal production in a competitive market under yield uncertainty

Motivated by the U.S. influenza vaccine market, we study the impact of random yield and production capacity on the number of firms, total supply, consumer surplus and social welfare in a market with identical suppliers. We formulate a two-stage game with endogenous entry, where each entering firm aims to maximize its profit under yield uncertainty subject to a production capacity constraint. We show that if firms produce full capacity in the equilibrium, then there are fewer firms in the equilibrium compared to the social optimum even for small levels of yield uncertainty. Furthermore, we prove that if firms do not produce full capacity in the equilibrium, they will not produce full capacity in the social optimum.     

Cutting plane algorithms for 0-1 programming based on cardinality cuts

We present new valid inequalities for 0-1 programming problems that work in similar ways to well known cover inequalities. Discussion and analysis of these cuts is followed by their revision and use in integer programming as a new generation of cuts that excludes not only portions of polyhedra containing noninteger points, also parts with some integer points that have been explored in search of an optimal solution. Our computational experimentations demonstrate that this new approach has significant potential for solving large scale integer programming problems.     

Labelling,Fractionation and Toxicity of Scorpion (Leiurus quinquestriatus H and E) Venom,using 125I, 131I and Gel-Filtration Technique

Labelling the venom of scorpion was achieved by means of a technique previously published by the author. The radioisotopes, used were both ¹²⁵I and ¹³¹I in a nascent form. Fractionation was done by the use of Sephadex G-100. Both the radioactivity and the extinction curves denoted the presence of three well defined peaks. The toxicity of the first fraction was found to be the most lethal. While the second peak was in the magnitude of 20 percent of the first, the third peak proved to be nontoxic to mice up to a concentration of 6 mg/kg body weight.     

γ-irradiation effect on the spectroscopic and electrical properties of K2SO4—Na2SO4 mixed system

Abstract

Measurements of electron paramagnetic resonance, infrared and electrical properties were carried out for the K₂SO₄—Na₂SO₄ mixed system before and after γ-irradiation. EPR measurements revealed the presence of a quartet of lines characterized by an isotropic g-value of 2.0034. These lines are mainly attributed to the formation of a SO^? ₃ center which results from the interaction of γ-rays with the sulfate ion. A decrease in the absorption intensity of the Infrared radiation was observed after γ-irradiation due to radiation damage in the sulfate group. The electrical conductivity, σ, was measured for the K₂SO₄—Na₂SO₄ system before and after γ-irradiation in the temperature range from 30 up to 430°C. A considerable decrease in the conductivity value accompanied by an increase in the activation energy was observed after γ-irradiation. The energy of formation of Frenkel defects was estimated to be 2.94eV. The current-voltage characteristics were measured at different temperatures in order to estimate the type of conduction in the samples. Isothermal annealing kinetics was investigated at different temperatures before and after γ-irradiation. The electrical conductivity decreases with increasing time of annealing and the annealing process is dominated by a unique rate process.     

Generating sets of finite singular transformation semigroups

J.M. Howie proved that $\operatorname {Sing}_{n}$ , the semigroup of all singular mappings of {1,…,n} into itself, is generated by its idempotents of defect 1 (in J. London Math. Soc. 41, 707–716, 1966). He also proved that if n≥3 then a minimal generating set for $\operatorname {Sing}_{n}$ contains n(n?1)/2 transformations of defect 1 (in Gomes and Howie, Math. Proc. Camb. Philos. Soc. 101. 395–403, 1987). In this paper we find necessary and sufficient conditions for any set for transformations of defect 1 in $\operatorname {Sing}_{n}$ to be a (minimal) generating set for $\operatorname {Sing}_{n}$ .     

Room temperature magnetocaloric effect in Pr1.75Sr1.25Mn2O7 double-layered perovskite manganite system

Abstract

In this work, we have studied on double-layered perovskite (Ruddlesden–Popper) manganite structure in Pr_1.75Sr_1.25Mn₂O₇ synthesised by sol–gel method. The crystal structure of the double-layered perovskite is found as tetragonal from the X-ray diffraction analysis with I4/mmm space group. A high Curie temperature, T_C = 305 K is observed from the temperature dependence of magnetisation measurement. The isothermal magnetisation curves showed that magnetic phase transition is second order due to the positive slope of the Arrott plots. Maximum magnetic entropy change (ΔS_M) and adiabatic temperature change (ΔT_ad) values are calculated as 3.99 J kg^?1 K^?1 and 2.1 K under external magnetic field of 70 kOe, respectively. Since our double-layered perovskite manganite sample has desired T_C value and relatively high ΔS_M, it can be a potential candidate as a magnetocaloric material for room temperature magnetic cooling systems.     

Dynamic phase transition and dynamic phase diagrams in the spin-5/2 Blume–Capel model under a time-dependent oscillating external field

We calculate the dynamic phase transition (DPT) temperatures and present the dynamic phase diagrams in the kinetic spin-5/2 Blume–Capel model under the presence of a time-dependent oscillating external magnetic field. First, we employ the Glauber transition rates to construct the mean-field dynamic equation. Then, we study the time variation of the average magnetization to find the phases in the system. We also investigate the behaviour of the dynamic magnetization to characterize the nature (continuous and discontinuous) of transition and to obtain the DPT points. We present the dynamic phase diagrams in two different planes. The phase diagrams include the ferromagnetic-5/2 (f_5/2), the ferromagnetic-1/2 (f_1/2) and paramagnetic (p) fundamental phases. In addition to these fundamental phases, we find 10 mixed phases, depending on the interaction parameters. The phase diagrams display many special points, such as a dynamic tricritical point, a double critical end point, a triple point and a quadruple point.     

Approximating the relationship among the degree of the reaction forces and the nodes on footprint during a stance phase

This study examined the foot biomechanics that are utilized when foot is in contact with the ground during a stance phase. The purpose of the study was to investigate the normalized ground reaction forces that impacted certain sections and points on the footprint, and to identify patterns in the degrees to which these forces occurred. Foot was modeled in such a manner that a vertex represented a bone and an edge represented a joint, and a graph that depicted the foot was created. Twelve nodes were marked on the footprint and these were linked together to create a gait path. By fusing the graph and the gait path and by manipulating the mathematical models, a profile for an ideal bipedal walking locomotion was developed. A male subject performed bipedal walking through a force plate system in order to obtain the profile that reflected actual bipedal walking. The actual and the proposed profiles were compared and there were significant similarities between the two profiles, with both exhibiting an double-bump pattern. It is therefore viable that the approximation techniques proposed in this work may provide an alternative means over the application of a force plate system to generate a profile for bipedal walking. However, the accuracy and reliability of the results yielded from this technique need further investigation.