Background This study establishes a mathematically consistent and computational framework for the simultaneous identification of two time-dependent coefficients in a one-dimensional second-order parabolic partial differential equation. The considered problem is governed by nonlocal initial, boundary, and integral overdetermination conditions. Methods The direct problem is solved using the Crank-Nicolson finite difference method (FDM), which ensures unconditional stability and second-order accuracy in both spatial and temporal discretizations. The corresponding inverse problem is reformulated as a nonlinear regularized least-squares optimization problem and efficiently solved used the MATLAB subroutine
Silymarin, a flavolignans from seeds of ‘milk thistle’ “Silybum marianum†has been widely used from ancient times because of its excellent hepatoprotective action. It has been used clinically to treat liver disorders including acute and chronic viral hepatitis, toxin/drug-induced hepatitis and cirrhosis and alcoholic liver disease. The efficacy and dose-response effect of silymarin (125, 250 and 500 mg/kg) were assessed using egg albumin-induced paw edema in rats as a model of acute inflammation. In this model, 56 rats were used and allocated into 7 subgroups each containing 8 rats. All treatments were given intraperitonealy 30 minutes before induction of inflammation by egg albumin and then the increase
... Show MoreWe investigate mathematical models of the Hepatitis B and C viruses in the study, considering vaccination effects into account. By utilising fractional and ordinary differential equations, we prove the existence of equilibrium and the well-posedness of the solution. We prove worldwide stability with respect to the fundamental reproduction number. Our numerical techniques highlight the biological relevance and highlight the effect of fractional derivatives on temporal behaviour. We illustrate the relationships among susceptible, immunised, and infected populations in our epidemiological model. Using comprehensive numerical simulations, we analyse the effects of fractional derivatives and highlight solution behaviours. Subsequent investigatio
... Show MoreIn solar-thermal adsorption/desorption processes, it is not always possible to preserve equal operating times for the adsorption/desorption modes due to the fluctuating supply nature of the source which largely affects the system’s operating conditions. This paper seeks to examine the impact of adopting unequal adsorption/desorption times on the entire cooling performance of solar adsorption systems. A cooling system with silica gel–water as adsorbent-adsorbate pair has been built and tested under the climatic condition of Iraq. A mathematical model has been established to predict the system performance, and the results are successfully validated via the experimental findings. The results show that, the system can be operational
... Show MoreIn this paper, we introduce a DCT based steganographic method for gray scale images. The embedding approach is designed to reach efficient tradeoff among the three conflicting goals; maximizing the amount of hidden message, minimizing distortion between the cover image and stego-image,and maximizing the robustness of embedding. The main idea of the method is to create a safe embedding area in the middle and high frequency region of the DCT domain using a magnitude modulation technique. The magnitude modulation is applied using uniform quantization with magnitude Adder/Subtractor modules. The conducted test results indicated that the proposed method satisfy high capacity, high preservation of perceptual and statistical properties of the steg
... Show MoreSurface drip irrigation is one of the most conservative irrigation techniques that help control providing water directly on the soil through the emitters. It can supply fertilizer and providing water directly to plant roots by drippers. One of the essential needs for trickle irrigation nowadays is to obtain more knowledge about the moisture pattern under the trickling source for various types of soil with various discharge levels with trickle irrigation. Simulation numerical using HYDRUS-2D software, version 2.04 was used to estimate an equation for the wetted area from a single surface drip irrigation in unsaturated soil is taking into account water uptake by roots. In this paper, using two soil types were used, namely
... Show MoreNatural frequency under initial stresses for simply supported cross-ply composite laminated plates (E glass- fiber) are obtained using Refind theory (RPT). This theory accounts for parabolic distribution of the transverse shear strain through the plate thickness and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. The governing equations for Eigen value problem under initial stress are derived using Hamilton’s principle and solved using Navier solution for simply supported cross-ply symmetric and antisymmetric laminated plates. The effect of many design factors such as modulus ratio, thickness ratio and number of laminates on the Natural frequency and buckling stresses
... Show MoreIn this paper, the dynamic behaviour of the stage-structure prey-predator fractional-order derivative system is considered and discussed. In this model, the Crowley–Martin functional response describes the interaction between mature preys with a predator. e existence, uniqueness, non-negativity, and the boundedness of solutions are proved. All possible equilibrium points of this system are investigated. e sucient conditions of local stability of equilibrium points for the considered system are determined. Finally, numerical simulation results are carried out to conrm the theoretical results.
Current numerical research was devoted to investigating the effect of castellated steel beams without and with strengthening. The composite concrete asymmetrical double hot rolled steel channels bolted back to back to obtain a built-up I-shape form are used in this study. The top half part of the steel is smaller than the bottom half part, and the two parts were connected by bolting and welding. The ABAQUS/2019 program employed the same length and conditions of loading for four models: The first model is the reference without castellated and strengthening; the second model was castellated without strengthened; the third model was castellated and strengthened with reactive powder concrete encased in the
... Show MoreThe aim of this paper is to examine cases of deletion not dependent on linguistic context. Perlmutter (1971) claims that any sentence other than an imperative1 in which there is an S that does not contain a subject in the surface structure is ungrammatical. Dillon (1978) counts elliptical sentences such as ^ Beg your pardon2 as grammatically incomplete (and hence as strictly ungrammatical). Such statements are, however, not without problems for reasons that will be given below.