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.
This study was aimed to synthesis Ag2O nanoparticles (N.P.s) utilizing the Ginger plant (Zingiber officinale) extract. As catalysts for pyran derivatives formation employing a three-component coupling reaction among aromatic and aliphatic aldehydes, malononitrile, and dimedone. The nanoparticles exhibit robust catalytic activity with high productivity. Results revealed that Ag2O NPs improved various vital features, like higher yields, reaction time, simple chemical separation, catalytic economic efficiency, and quick process. This study aimed to cyclize heterocyclic compounds to provide new hetero compounds applying nano-oxides obtained from natural (unmanufactured) sources and used in several medical, pharmaceutical, and industrial
... Show MoreThis paper suggests a novel optimal inverse Radial Basis Function (RBF) neural network model for the control of Twin Rotor Aerodynamic Systems (TRAS), such as Multi-Input–Multi-Output (MIMO) systems with high nonlinearity and coupling effects between channels. After analyzing and linearizing the dynamic model, TRAS is decoupled into two Single Input Single Output (SISO) systems, thereby creating vertical (pitch model) and horizontal (yaw model) systems. The relationship between the output angle of each subsystem and the input voltage is modeled using the inverse RBF neural network. The weights, biases, centers and widths of the Gaussian function are unknown parameters of the proposed inverse neural model, and they are obtained usi
... Show MoreThis study deals with 3rd-order difference equations with alternating coefficients (NDEAC) with a focus on studying the oscillatory properties of their solutions. An additional sufficient condition can be derived to ensure continuity for the oscillatory solution in equations. An applied example is presented to illustrate the theoretical result obtained.
The 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 MoreIn this paper, some necessary and sufficient conditions are obtained to ensure the oscillatory of all solutions of the first order impulsive neutral differential equations. Also, some results in the references have been improved and generalized. New lemmas are established to demonstrate the oscillation property. Special impulsive conditions associated with neutral differential equation are submitted. Some examples are given to illustrate the obtained results.
In this paper, the proposed phase fitted and amplification fitted of the Runge-Kutta-Fehlberg method were derived on the basis of existing method of 4(5) order to solve ordinary differential equations with oscillatory solutions. The recent method has null phase-lag and zero dissipation properties. The phase-lag or dispersion error is the angle between the real solution and the approximate solution. While the dissipation is the distance of the numerical solution from the basic periodic solution. Many of problems are tested over a long interval, and the numerical results have shown that the present method is more precise than the 4(5) Runge-Kutta-Fehlberg method.