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Comparing Solutions to the Nonlinear Dissipative Wave Equation

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Journal of Applied Mathematics and Physics 2022年第4期10卷 1281-1296页

作者： Zaki Mrzog Alaofi Talaat Sayed el-Danaf Silvestru Sever Dragomir Department of Mathematics College of Science and Arts King Khalid University Muhayil Asir KSA Mathematics College of Engineering & Science Victoria University Melbourne Australia Department of Mathematics Faculty of Sciences and Arts Taibah University Medina KSA

In previous decades, many of the practical problems arising in scientific fields such as physics, engineering, and mathematics have been related to nonlinear fractional partial differential equations. One of these nonlinear partial differential equations, the dissipative wave equation, has been found to have a plethora of useful applications in different fields. A special class of solutions has been studied for the dissipative wave equation including exact solutions and approximate solutions. The aim of this article is to compare the non-polynomial spline method and the cubic B-spline method with the solution of a nonlinear dissipative wave equation. We will conduct a comparison of the stability of the two methods using the Von Neumann stability analysis. In addition, a numerical example will be presented to illustrate the accuracy of these methods.

关键词： Dissipative Wave Equation Cubic B-Spline Non-Polynomial Spline Truncation Error Von Neumann Stability

heterospecific interactions and the proliferation of sexually dimorphic traits

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Current Zoology 2012年第3期58卷 453-462页

作者： Karin S. PFENNIG Allen h. hURLBERT Department of Biology University of North Carolina Chapel Hill Chapel Hill NC 27599-3280

Sexual selection is expected to promote speciation by fostering the evolution of sexual traits that minimize reproductive interactions among existing or incipient species. In species that compete for access to, or attention of, females, sexual selec- tion fosters more elaborate traits in males compared to females. If these traits also minimize reproductive interactions with het- erospecifics, then species with enhanced risk of interactions between species might display greater numbers of these sexually di- morphic characters. We tested this prediction in eight families of North American birds. In particular, we evaluated whether the number of sexually dimorphic traits was positively associated with species richness at a given site or with degree of sympatry with congeners. We found no strong evidence of enhanced sexual dimorphism with increasing confamilial species richness at a given site. We also found no overall relationship between the number of sexually dimorphic traits and overlap with congeners across these eight families. however, we found patterns consistent with our prediction within Anatidae （ducks, geese and swans） and, to a lesser degree, Parulidae （New World warblers）. Our results suggest that sexually selected plumage traits in these groups potentially play a role in reproductive isolation [Current Zoology 58 （3）： 453--462, 2012].

关键词： Speciation Reproductive character displacement Sexual selection species recognition Reinforcement

CONVERGENCE OF ThE LAX-FRIEDRIChS SChEME AND STABILITY FOR CONSERVATION LAWS WITh A DISCONTINUOUS SPACE-TIME DEPENDENT FLUX

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Chinese Annals of Mathematics,Series B 2004年第3期25卷 287-318页

作者： K.h.KARLSEN J.D.TOWERS DepartmentofMathematics UniversityofBergenJohs.Brunsgt.12N-5008BergenNorway MiraCostaCollege 3333ManchesterAvenueCardiff-by-the-SeaCA92007-1516USA

The authors give the first convergence proof for the Lax-Friedrichs finite differencescheme for non-convex genuinely nonlinear scalar conservation laws of the formu_t + f(k(x, t), u)_x = 0,where the coefficient k(x, t) is allowed to be discontinuous along curves in the (x, t)plane. In contrast to most of the existing literature on problems with discontinuouscoefficients, here the convergence proof is not based on the singular mapping approach,but rather on the div-curl lemma (but not the Young measure) and a Lax type en-tropy estimate that is robust with respect to the regularity of k(x, t). Following [14],the authors propose a definition of entropy solution that extends the classical Kruzkovdefinition to the situation where k(x, t) is piecewise Lipschitz continuous in the (x, t)plane, and prove the stability (uniqueness) of such entropy solutions, provided that theflux function satisfies a so-called crossng condition, and that strong traces of the solu-tion exist along the curves where k(x, t) is discontinuous. It is shown that a convergentsubsequence of approximations produced by the Lax-Friedrichs scheme converges tosuch an entropy solution, implying that the entire computed sequence converges.

关键词： Conservation law Discontinuous coefficient Nonconvex flux LaxFriedrichs difference scheme Convergence Compensated compactness Entropy condition Uniqueness

Air Cooling of Mini-Channel heat Sink in electronic Devices

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Journal of electronics Cooling and Thermal Control 2013年第2期3卷 49-57页

作者： Mousa M. Mohamed Mostafa A. Abd el-Baky Mechanical Power Engineering Department Faculty of Engineering Minufiya University Shebin El-Kom Egypt

heat transfer experiments were conducted to investigate the thermal performance of air cooling through mini-channel heat sink with various configurations. Two types of channels have been used, one has a rectangular cross section area of 5 × 18 mm2 and the other is triangular with dimension of 5 × 9 mm2. Four channels of each configuration have been etched on copper block of 40 mm width,30 mm height, and 200 mm length. The measurements were performed in steady state with air flow rates of 0.002 - 0.005 m3/s, heating powers of 80 - 200 W and channel base temperatures of 48°C, 51°C, 55°C and 60°C. The results showed that the heat transfer to air stream is increased with increasing both of air mass flow rate and channel base temperature. The rectangular channels have better thermal performance than trian- gular ones at the same conditions. Analytical fin approach of 1-D and 2-D model were used to predict the heat transfer rate and outlet air temperature from channels heat sink. Theoretical results have been compared with experimental data. The predicted values for outlet air temperatures using the two models agree well with a deviation less than ±10%. But for the heat transfer data, the deviation is about +30% to –60% for 1-D model, and –5% to –80% for 2-D model. The global Nusselt number of the present experimental data is empirically correlated as with accuracy of ±20% for and compared with other literature correlations.

关键词： Mini-Channel heat Sink Channel Air Cooling electronic Cooling Fin Approach

Trauma patterns in patients attending the Emergency Department of Jazan General hospital, Saudi Arabia

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World Journal of Emergency Medicine 2015年第1期6卷 48-53页

作者： Emad hokkam Abdelaziz Gonna Ossama Zakaria Amany el-shemally Department of Surgery Faculty of Medicine Jazan University Department of Surgery Faculty of Medicine Suez Canal University Department of Surgery Jazan General Hospital Department of Surgery Faculty of Medicine King Faisal University

BACKGROUND: Modern civilization and the sharp rise in living standards have led to dramatic changes in trauma pattern in Saudi Arabia. This study aimed to describe the different patterns of injuries of patients attending the Emergency Department of Jazan General hospital(JGh) in the southwest corner of Saudi ***: A total number of 1 050 patients were enrolled in the study. A pre-organized data sheet was prepared for each patient attended the Emergency Department of JGh from February 2012 to January 2013. It contains data about socio-demographics, trauma data, clinical evaluation results, investigations as well as treatment ***: The mean age of the patients was 25.3±16.8 years. Most(45.1%) of the patients were at age of 18–30 years. Males(64.3%) were affected by trauma more common than females. More than half(60.6%) of the patients were from urban areas. The commonest kind of injury was minor injury(60%), followed by blunt trauma(30.9%) and then penetrating trauma(9.1%). The mean time from the incident to arrival at hospital was 41.3±79.8 minutes. The majority(48.2%) of the patients were discharged after management of trivial trauma, whereas 2.3% were admitted to ICU, 7.7% transferred to inpatient wards, and 17.7% observed and subsequently discharged. The mortality rate of the patients was 2.6%.CONCLUSION: Trauma is a major health problem, especially in the young population in Saudi Arabia. Blunt trauma is more frequent than penetrating trauma, with road traffic accidents accounting for the majority.

关键词： Trauma Injury Emergency Saudi Arabia

Monotonicity and Best Approximation in Banach Lattices

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Acta Mathematica Sinica,English Series 2009年第5期25卷 785-794页

作者： Shu Tao ChEN Xin hE h. hUDZIK Department of Mathematics Harbin Normal University Harbin 150080 P. R. China Faculty of Mathematics and Computer Science Adam Mickiewicz University Umultowska 87 61-614 Poznan Poland

hudzik and Kurc discussed some best approximation problems in Banach lattices by means of monotonicities. This paper deals with more general best approximation problems in Banach lattices. Existence, uniqueness, stabi... 详细信息

关键词： Banach lattice uniform monotonicity strict monotonicity upper (lower) locally uniform monotonicity best approximation

Systematic study of kinematic and dynamic moments of inertia of superdeformed bands with NpNn scheme

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Chinese Physics C 2017年第8期41卷 101-107页

作者： honey Sharma Neha Sharma h.M.Mittal Dr.B.R.Ambedkar National Institute of Technology Jalandhar144011India CT Institute of Engineering Management and Technology Jalandhar144020India

The systematics of kinematic moment of inertia J and dynamic moment of inertia J of superdeformed（SD） bands in A -130, 150, 190 mass regions have been studied. We have obtained the values of J^（1） and J^（2）for all the SD bands observed in the A-130, 150, 190 mass regions by using the experimental intraband E2 transition energies. The result of this work includes the variation of J with the product of valence proton and neutron numbers（NpNn）. The phenomenon of band mixing has been observed in the A -130, 150 mass regions and band crossing has been observed in the A-190 mass region. The systematics also includes the variation of J with the product of valence proton and neutron numbers（NpNn）. Evidence of staggering behaviour has been observed in all three A-130, 150 and 190 mass regions. We present for the first time the variation of J^（1）and J^（2）of SD bands in the A-130, 150, 190 mass regions with NpNn.

关键词： kinematic moment of inertia j dynamic moment of inertia j NpYn scheme

Effect of Soil Water Repellency on Energy Partitioning Between Soil and Atmosphere:A Conceptual Approach

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Pedosphere 2014年第4期24卷 498-507页

作者： h.SChONSKY A.PETERS G.WESSOLEK Department of Soil Conservation Institute of EcologyTechnical University of BerlinD-10587 Berlin(Germany)

Water repellency(WR) is a phenomenon known from many soils around the world and can occur in arid as well as in humid climates;few studies,however,have examined the effect of soil WR on the soil-plant-atmosphere energy *** aim of our study was to estimate the effects of soil WR on the calculated soil-atmosphere energy balance,using a solely model-based *** made out evapotranspiration to have the largest influence on the energy balance;therefore the effect of WR on actual evapotranspiration was *** achieve this we used climate data and measured soil hydraulic properties of a potentially water-repellent sandy soil from a site near Berlin,Germany.A numerical 1D soil water balance model in which WR was incorporated in a straightforward way was applied,using the effective cross section *** were carried out with vegetated soil and bare *** simulation results showed a reduction in evapotranspiration of 30-300 mm year^(-1)(9%-76%) at different degrees of WR compared to completely wettable soil,depending on the severity degree of soil *** energy that is not being transported away by water vapor(i.e.,due to reduced evapotranspiration) had to be transformed into other parts of the energy balance and thus would influence the local climate.

关键词： climate effective cross section evapotranspiration soil-atmosphere energy balance soil hydraulic property water balance

The Effect of Spherical Surface on Noise Suppression of a Supersonic Jet

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Journal of Thermal Science 2003年第2期12卷 144-150,113页

作者： Md.TawhidulIslamKhan KunisatoSeto ZhixiangXu h.Ohta Graduate School Saga UniversitySaga 840-8502JapanDepartment of Mechanical EngineeringSaga UniversitySaga 840-8502JapanDepartment of Mechanical EngineeringSaga UniversitySaga 840-8502JapanDepartment of Mechanical EngineeringNational Fishery UniversityShimonosekiJapan

Experiments were carried out to eliminate the screech tone generated from a supersonic jet. Compressed air was passed through a circular convergent nozzle preceded by a straight tube of same diameter. In order to reduce the jet screech a spherical reflector was used and placed at the nozzle exit. The placement of the spherical reflector at the nozzle exit controlled the location of the image source as well as minimized the sound pressure at the nozzle exit. The weak sound pressure did not excite the unstable disturbance at the exit. Thus the loop of the feedback mechanism could not be accomplished and the jet screech was eliminated. The technique of screech reduction with a flat plate was also examined and compared with the present method. A good and effective performance in canceling the screech component by the new method was found by the investigation. Experimental results indicate that the new system suppresses not only the screech tones but also the broadband noise components and reduces the overall noise of the jet flow. The spherical reflector was found very effective in reducing overall sound pressure level in the upstream region of the nozzle compared to a flat plate. The proposed spherical reflector can, accordingly, protect the upstream noise propagation.

关键词： under-expanded supersonic jet jet screech spherical reflector noise reduction.