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.
The dramatic decrease in the cost of genome sequencing over the last two decades has led to an abundance of genomic data. This data has been used in research related to the discovery of genetic diseases and the production of medicines. At the same time, the huge space for storing the genome (2–3 GB) has led to it being considered one of the most important sources of big data, which has prompted research centers concerned with genetic research to take advantage of the cloud and its services in storing and managing this data. The cloud is a shared storage environment, which makes data stored in it vulnerable to unwanted tampering or disclosure. This leads to serious concerns about securing such data from tampering and unauthoriz
... Show MoreThe curing process of epoxy resin was investigated with some additives and fillers such as nano fumed silica with primary particle diameter of 56–58 nanometers, fine ferric oxide with an average particle diameter of 0.4 micrometer, fine calcium carbonate with an average particle diameter of 0.58 micrometer, and plasticizer, a new composite resin has been obtained. Based on present experimental results, the new composite resin shows high impact strength and hardness as well as the ability of the composite withstand to degradation from water way in. Additionally, curing time of composite was reduced to the minimum set time than epoxy resin at different temperature. This new composite resin was used appropriately for coating to protect su
... Show MoreParental socialization trends impacting seriously on the growth of individual
personality and psychological health trends ,love, acceptance and on confidence help
children to grow as a person who loves other accept others and trust and negative parental
attitudes such as excess portents us or negligence . and the focusing and demonstrate a
negative impact on the growth of excess an mental health and family play a significant role in
a childes life we can see how many manifestation of compatibility or incompatibility thatappear on individual behaviors and achieve their success or failure in life be returned to the
of human relations that prevailed between the family members of children in various stages of
his life fi
In this paper, we introduce a new class of Weighted Rayleigh Distribution based on two parameters, one is the scale parameter and the other is the shape parameter introduced in Rayleigh distribution. The main properties of this class are derived and investigated . The moment method and least square method are used to obtain estimators of parameters of this distribution. The probability density function, survival function, cumulative distribution and hazard function are derived and found. Real data sets are collected to investigate two methods that depend on in this study. A comparison is made between two methods of estimation and clarifies that MLE method is better than the OLS method by using the mea
... Show MoreIn this paper the manufacture of an alkaline fuel cell electrodes made upfrom a Nano mesh (Pt:NiO) catalyst has been studying , made from a Nano mesh (Pt:NiO ) catalyst. The general morphology of the samples is were imaged by using with the an Atomic Force Microscope (AFM) to determine the roughness of the prepared surface, it constructed from nanostructure with dimensions in order of 35 nm. The Structural characteristics were studied through the analysis of X-ray diffraction (XRD) of the prepared nanomaterial for determining the yielding phase;1. 72 volt was also obtained at 0.02 A/cm2 current density for an alkaline fuel cell.
The Environmental Data Acquisition Telemetry System is a versatile, flexible and economical means to accumulate data from multiple sensors at remote locations over an extended period of time; the data is normally transferred to the final destination and saved for further analysis.
This paper introduces the design and implementation of a simplified, economical and practical telemetry system to collect and transfer the environmental parameters (humidity, temperature, pressure etc.) from a remote location (Rural Area) to the processing and displaying unit.
To get a flexible and practical system, three data transfer methods (three systems) were proposed (including the design and implementation) for rural area services, the fi
... Show MoreBased on a finite element analysis using Matlab coding, eigenvalue problem has been formulated and solved for the buckling analysis of non-prismatic columns. Different numbers of elements per column length have been used to assess the rate of convergence for the model. Then the proposed model has been used to determine the critical buckling load factor () for the idealized supported columns based on the comparison of their buckling loads with the corresponding hinge supported columns . Finally in this study the critical buckling factor () under end force (P) increases by about 3.71% with the tapered ratio increment of 10% for different end supported columns and the relationship between normalized critical load and slenderness ratio was g
... Show MoreThis paper describes the use of microcomputer as a laboratory instrument system. The system is focused on three weather variables measurement, are temperature, wind speed, and wind direction. This instrument is a type of data acquisition system; in this paper we deal with the design and implementation of data acquisition system based on personal computer (Pentium) using Industry Standard Architecture (ISA)bus. The design of this system involves mainly a hardware implementation, and the software programs that are used for testing, measuring and control. The system can be used to display the required information that can be transferred and processed from the external field to the system. A visual basic language with Microsoft foundation cl
... Show MoreResearch included the preparation of medicinal substances ( propyl thiouracil). Which is the rule thiourea and related compounds a fundamental rule in preparation fall within the range of drugs of anti-thyroid activity (Antithyroid Drug ) , this drug prevents the thyroid hormone production against excessive activity of the thyroid gland .That the formation of iodine is important for their impact on hormone secretion thyroid , the two types, thyroxin or T4 is the main hormone ,Triiodothyronine or T3, and these hormones released by hormone regulator called (TSH) . Article attend thiourea treatment with an alcohol- soluble sodium and added to the interaction rule b- oxo ester after adjusting the PH=4 output ( propylthiouracil ) the
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