Degenerate parabolic partial differential equations (PDEs) with vanishing or unbounded leading coefficient make the PDE non-uniformly parabolic, and new theories need to be developed in the context of practical applications of such rather unstudied mathematical models arising in porous media, population dynamics, financial mathematics, etc. With this new challenge in mind, this paper considers investigating newly formulated direct and inverse problems associated with non-uniform parabolic PDEs where the leading space- and time-dependent coefficient is allowed to vanish on a non-empty, but zero measure, kernel set. In the context of inverse analysis, we consider the linear but ill-posed identification of a space-dependent source from a time-integral observation of the weighted main dependent variable. For both, this inverse source problem as well as its corresponding direct formulation, we rigorously investigate the question of well-posedness. We also give examples of inverse problems for which sufficient conditions guaranteeing the unique solvability are fulfilled, and present the results of numerical simulations. It is hoped that the analysis initiated in this study will open up new avenues for research in the field of direct and inverse problems for degenerate parabolic equations with applications.
Cryptosporidiosis is mainly cause a persistent diarrhea in immune compromised patients, BALB/c mice have been suppressed by dexamethasone, tissue Th1, Th2 and Th17 cytokines concentrations in the ileum were significantly diminished in both infected and immunosuppressed mice. Level of IFN-g, TNF-a, IL-12, IL-6, IL-17A was increased in level, IL-4 didn’t increases, in both ileal and spleen tissue. Levels of above cytokines were examined in spleen in order to follow the proliferation of CD4+ T-cell during C. parvum infection.
Dielectric measurements were carried on pure and doping potassium sulfate with copper and iron ions samples at 1wt.% and 3wt.% for both of copper and iron. The dielectric constant (ε') decreases exponentially from 2.8 to 1.5 as frequency increase for both dopant which is attributed to the space charge and structural distortion. The dielectric loss (ε") for Cu dopant decrease gradually with frequency. The same behavior for 1%Fe dopant while its 3%Fe doping started from 0.27 then decrease exponential. Band gaps for all samples almost constant around 6 eV.
Abstract
The curriculum is the major effective tool in achieving the goals of
education and society.
Many countries that want to reach the forefront of developed countries
through their curriculum have realized this fact. School text book, the
application assessment for knowing the rang of success or fail of this text
book in achieving the general aims. therefore this study aims at assessing the
principals and techniques of geography text book for fourth secondary class of
literary studying from the teachers point of view according to the fields of the
book, style of material, technical arrangement of the material, ethnical
arrangement the language of the book, style of the material, technical
arrang
Nowadays, a strong relationship between the agriculture sectors and digital technologies is really interesting. The article describes how recent intelligent technologies can improve agricultural fields. Mobile applications are software programs created on smartphones, tablets, and computers. Agricultural fields mainly represent the pillar of the economy and the business sector that fulfills the world's food requirements. The United States has a valuable rank in potato production, which depends on this production economically.
Nevertheless, so many insects affect potato yield production quantitatively and qualitatively. So, a smartphone App was created to help potato growers diagnose insects that directly attack potato cro
... Show MoreFace recognition system is the most widely used application in the field of security and especially in border control. This system may be exposed to direct or indirect attacks through the use of face morphing attacks (FMAs). Face morphing attacks is the process of producing a passport photo resulting from a mixture of two images, one of which is for an ordinary person and the other is a judicially required. In this case, a face recognition system may allow travel of persons not permitted to travel through face morphing image in a Machine-Readable Electronic Travel Document (eMRTD) or electronic passport at Automatic Border Control (ABC) gates. In creating an electronic passport, most countries rely on applicant to submit ima
... Show MoreThe gas material balance equation (MBE) has been widely used as a practical as well as a simple tool to estimate gas initially in place (GIIP), and the ultimate recovery (UR) factor of a gas reservoir. The classical form of the gas material balance equation is developed by considering the reservoir as a simple tank model, in which the relationship between the pressure/gas compressibility factor (p/z) and cumulative gas production (Gp) is generally appeared to be linear. This linear plot is usually extrapolated to estimate GIIP at zero pressure, and UR factor for a given abandonment pressure. While this assumption is reasonable to some extent for conventional reservoirs, this may incur