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.
Direct contact membrane distillation is an effective method for production of fresh water from saline water. In this study two samples were used as feed solutions; the first one was RO waste from Al-Hilla Coca-Cola Factory (TDS= 2382 mg/l) and the other was Haji Ali drainage water (TDS= 4127 mg/l). Polytetrafluoroethylene (PTFE) hydrophobic membrane supported with polypropylene (PP) was used as flat sheet form with plate and frame cell. Results proved that membrane distillation is an effective technique to produce fresh water with high quality from brine with low salinity content. With membrane area of 8x8 cm2, the volume of treated water decreased from 34.97 ml at first half hour to 33.02 ml after 180 min of
... Show MoreIn this study, a system of nonthermal plasma that was operated under atmospheric pressure and was powered by argon gas was employed. The particular plasma properties are affected by changes in the Ar gas flow ranges from 0.5 to 2.5 l/min, product by stream of the plasma jet that is utilized. By using the aforementioned method generated from AC and DC. After placing Ar gas as the cathode, which represents the negative pole, flows toward the anode, which is represented by a tiny metal plate of Zn measuring 6 × 1 cm2 in size, with a submerged part of 4 cm2 long, with both types of current employed having a high voltage of 13.5 kV and the frequency of AC was 30 kHz, we measured these variable parameters. It has been shown that when argon f
... Show MoreThe need for an efficient method to find the furthermost appropriate document corresponding to a particular search query has become crucial due to the exponential development in the number of papers that are now readily available to us on the web. The vector space model (VSM) a perfect model used in “information retrieval”, represents these words as a vector in space and gives them weights via a popular weighting method known as term frequency inverse document frequency (TF-IDF). In this research, work has been proposed to retrieve the most relevant document focused on representing documents and queries as vectors comprising average term term frequency inverse sentence frequency (TF-ISF) weights instead of representing them as v
... Show MoreThe estimation of the stressÙ€ strength reliability of Invers Kumaraswamy distribution will be introduced in this paper based on the maximum likelihood, moment and shrinkage methods. The mean squared error has been used to compare among proposed estimators. Also a Monte Carlo simulation study is conducted to investigate the performance of the proposed methods in this paper.
Improving the accuracy of load-deformation behavior, failure mode, and ultimate load capacity for reinforced concrete members subjected to in-plane loadings such as corbels, wall to foundation connections and panels need shear strength behavior to be included. Shear design in reinforced concrete structures depends on crack width, crack slippage and roughness of the surface of cracks.
This paper illustrates results of an experimental investigation conducted to investigate the direct shear strength of fiber normal strength concrete (NSC) and reactive powder concrete (RPC). The tests were performed along a pre-selected shear plane in concrete members named push-off specimens. The effectiveness of concrete compressiv
... Show MoreElectrochemical decolorization of direct black textile dye was studied in the presence of sodiumhydroxide (NaCl). Electrochemical cell occupy about 1 liter of working electrolyte supplied with graphiteelectrodes for both anode and cathode was constructed for this purpose. Decolorization percent, treatment time, power consumption, and pH were studied as a function of the applied voltage and salt concentration. Results show that decolorization increase with increasing salt concentration and applied voltage. Best decolorization of 86% can be achieved after 17 min at 7 volt and 5 g/l salt concentration. Further decolorization can be achieved but this will be accompanied with a sharp increase in power consumption. No significant decrease
... Show MoreIn this paper we have presented a comparison between two novel integral transformations that are of great importance in the solution of differential equations. These two transformations are the complex Sadik transform and the KAJ transform. An uncompressed forced oscillator, which is an important application, served as the basis for comparison. The application was solved and exact solutions were obtained. Therefore, in this paper, the exact solution was found based on two different integral transforms: the first integral transform complex Sadik and the second integral transform KAJ. And these exact solutions obtained from these two integral transforms were new methods with simple algebraic calculations and applied to different problems.
... Show MoreThis paper is devoted to compare the performance of non-Bayesian estimators represented by the Maximum likelihood estimator of the scale parameter and reliability function of inverse Rayleigh distribution with Bayesian estimators obtained under two types of loss function specifically; the linear, exponential (LINEX) loss function and Entropy loss function, taking into consideration the informative and non-informative priors. The performance of such estimators assessed on the basis of mean square error (MSE) criterion. The Monte Carlo simulation experiments are conducted in order to obtain the required results.