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Piecewise Approximate Analytical Solutions of High-Order Singular Perturbation Problems with a Discontinuous Source Term

A reliable algorithm is presented to develop piecewise approximate analytical solutions of third- and fourth-order convection diffusion singular perturbation problems with a discontinuous source term. The algorithm is based on an asymptotic expansion approximation and Differential Transform Method (DTM). First, the original problem is transformed into a weakly coupled system of ODEs and a zero-order asymptotic expansion of the solution is constructed. Then a piecewise smooth solution of the terminal value reduced system is obtained by using DTM and imposing the continuity and smoothness conditions. The error estimate of the method is presented. The results show that the method is a reliable and convenient asymptotic semianalytical numerical method for treating high-order singular perturbation problems with a discontinuous source term

Epidemic malaria and warmer temperatures in recent decades in an East African highland

Climate change impacts on malaria are typically assessed with scenarios for the long-term future. Here we focus instead on the recent past (1970–2003) to address whether warmer temperatures have already increased the incidence of malaria in a highland region of East Africa. Our analyses rely on a new coupled mosquito–human model of malaria, which we use to compare projected disease levels with and without the observed temperature trend. Predicted malaria cases exhibit a highly nonlinear response to warming, with a significant increase from the 1970s to the 1990s, although typical epidemic sizes are below those observed. These findings suggest that climate change has already played an important role in the exacerbation of malaria in this region. As the observed changes in malaria are even larger than those predicted by our model, other factors previously suggested to explain all of the increase in malaria may be enhancing the impact of climate change

Mathematical Modeling of Heat-Transfer for a Moving Sheet in a Moving Fluid

A mathematical model was developed for determining the heat transfer between a moving sheet that passes through a moving fluid environment to simulate the fabrication process of sheet and fiber-like materials. Similarity transformations were introduced to reduce the governing equations to two nonlinear ordinary differential equations. For high values Prandtl number, the energy equation became much stiffer or singularly perturbed and the standard numerical methods failed to handle it. An innovative procedure combining shooting and singular perturbation technique was developed. The results show that the heat transfer depends on the relative velocity between the moving fluid and the moving sheet to a certain value after that value the relative velocity has no effect. If blowing effect is found the thermal layer becomes thinner and temperature profiles are backed together

Re-Evaluating the Classical Falling Body Problem

This paper re-analyzes the falling body problem in three dimensions, taking into account the effect of the Earth’s rotation (ER). Accordingly, the analytic solution of the three-dimensional model is obtained. Since the ER is quite slow, the three coupled differential equations of motion are usually approximated by neglecting all high order terms. Furthermore, the theoretical aspects describing the nature of the falling point in the rotating frame and the original inertial frame are proved. The theoretical and numerical results are illustrated and discussed.The authors would like to thank the referees for their valuable comments and suggestions, which helped to improve the manuscript. Moreover, the first author thanks Prince Sattam bin Abdulaziz University and Deanship of Scientific Research at Prince Sattam bin Abdulaziz University for their continuous support and encouragement.info:eu-repo/semantics/publishedVersio

Effect of storage temperature on the keeping quality of commercially pasteurized milk

Pour étudier l'effet de la température sur la durée de conservation du lait pasteurisé, du lait fraîchemf:'nt pasteurisé et non homogénéisé provenant de deux laiteries industrielles, a été conservé à 7 et à 25°C. L'évolution du pH, des caractéristiques sensorielles, et de la flore totale du lait a été étudiée durant la période de conservation. L'altération du lait dont le taux microbien initial était de 10 3 UFC/ml a été observée entre le 5 ème et 6ème jour de conservation à 7°C. A 25°C, cette durée n'a été que de 20 à 24 heures. Au début de l'altération, le taux microbien a dépassé 10 7 UFC/ml. Les deux laits ont montré les mêmes signes d'altération à savoir la putréfaction, l'amertume, le caractère fruité, et la rancidité à 7°C; tandis qu'à 25°C, les défauts détectés étaient l'acidité, le surissement, et la rancidité. Les échantillons de lait ont montré également le signe de coagulation après ébullition, 2 heures avant l'altération à 25°C alors qu'à 7°C la coagulation du lait a eu lieu le même jour du début de l'altération. To study the effect of temperature on the shelf-life, freshly pasteurized and unhomogenized whole milk from two dairy plants was stored at 7 and 25°C. Microbial, sensory, and pH changes were monitored during storage. Milk of 1000 CFU/ml, as initial microbial count, showed evidence of spoilage between 5th and 6th day of storage at 7°C. When stored at 25°C, the shelf-life was only 20 to 24 hours. The microbial count at the time of spoilage exceeded 10000000 CFU/ml. Both brands ofmilk showed similar spoilage characteristics of putrid, bitter, fruity and rancid at 7°C and acid, sour, and rancid defects at 25°C. Milk samples showed clotting on boiling 2 hours before evidence of spoilage at 25°C and simultaneously with spoilage at 7°C

Segregation and charge-density-wave order in the spinless Falicov-Kimball model

The spinless Falicov-Kimball model is solved exactly in the limit of infinite-dimensions on both the hypercubic and Bethe lattices. The competition between segregation, which is present for large U, and charge-density-wave order, which is prevalent at moderate U, is examined in detail. We find a rich phase diagram which displays both of these phases. The model also shows nonanalytic behavior in the charge-density-wave transition temperature when U is large enough to generate a correlation-induced gap in the single-particle density of states.Comment: 10 pages, 10 figure

Systematic studies of binding energy dependence of neutron - proton momentum correlation function

Hanbury Brown-Twiss (HBT) results of the neutron-proton correlation function have been systematically investigated for a series nuclear reactions with light projectiles with help of Isospin-Dependent Quantum Molecular Dynamics model. The relationship between the binding energy per nucleon of the projectiles and the strength of the neutron-proton HBT at small relative momentum has been obtained. Results show that neutron-proton HBT results are sensitive to the binding energy per nucleon.Comment: 10 pages, 5 figures; accepted by Journal of Physics G: Nuclear and Particle Physic

Phase separation and the segregation principle in the infinite-U spinless Falicov-Kimball model

The simplest statistical-mechanical model of crystalline formation (or alloy formation) that includes electronic degrees of freedom is solved exactly in the limit of large spatial dimensions and infinite interaction strength. The solutions contain both second-order phase transitions and first-order phase transitions (that involve phase-separation or segregation) which are likely to illustrate the basic physics behind the static charge-stripe ordering in cuprate systems. In addition, we find the spinodal-decomposition temperature satisfies an approximate scaling law.Comment: 19 pages and 10 figure

The practices of apartheid as a war crime: a critical analysis

The human suffering caused by the political ideology of apartheid in South Africa during the Apartheid era (1948-1994) prompted worldwide condemnation and a variety of diplomatic and legal responses. Amongst these responses was the attempt to have apartheid recognised both as a crime against humanity in the 1973 Apartheid Convention as well as a war crime in Article 85(4)(c) of Additional Protocol I. This article examines the origins, nature and current status of the practices of apartheid as a war crime and its possible application to the Israeli-Palestinian conflict