The purpose of this paper is to study laminar two-dimensional unsteady mixed convection boundary-layer flow of a viscous incompressible fluid past a symmetric wedge embedded in a porous medium in the presence of the first and second orders resistances.The governing boundary-layer equations along with the boundary conditions are first converted into dimensionless form by a non-similar transformation, and then resulting system of coupled non-linear partial differential equations were solved by perturbation solutions for small dimensionless time until the second order. Numerical solutions of the governing equations are obtained employing the implicit finite-difference scheme in combination with the quasi-linearization technique. The obtained results will be compared with earlier papers on special cases of the problem to examine validity of the method of solution.The effects of various parameters on the fluid velocity and fluid temperature as well as the wall heat transfer rate and skin-friction coefficient are presented graphically and in tabulated form.

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The aim of this paper is to calculate the analytical form of the equation of state for dilute relativistic plasma. We obtained the excess free energy and pressure in the form of a convergent series expansion in terms of the thermal parameter μ where μ = mc^2/KT, m is the mass of charge, c is the speed of light, K is the Boltzmann’s constant, and T is the absolute temperature. The results are discussed and compared with previous work of other authors.

The aim of this paper is to calculate the analytical form of the equation of state for dilute relativistic plasma. We obtained the excess free energy and pressure in the form of a convergent series expansion in terms of the thermal parameter μ where μ = mc^2/KT, m is the mass of charge, c is the speed of light, K is the Boltzmann’s constant, and T is the absolute temperature. The results are discussed and compared with previous work of other authors.

The aim of this paper is to calculate the analytical form of the equation of state for dilute relativistic plasma. We obtained the excess free energy and pressure in the form of a convergent series expansion in terms of the thermal parameter μ where μ = mc^2/KT, m is the mass of charge, c is the speed of light, K is the Boltzmann’s constant, and T is the absolute temperature. The results are discussed and compared with previous work of other authors.

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The main aim of this paper is to define a new family of special matrix functions, say, -Hypergeometric, -Bessel, -modified Bessel and -Tricomi matrix functions, where is a positive integer. The convergence properties of the -Hypergeometric matrix function are established and the matrix differential equation is constructed. The differential properties, integral representations, integrals and various particular cases on the $p$-Bessel matrix function have been obtained. The -modified Bessel matrix functions, and some properties of this function are investigated. Finally, the -Tricomi matrix function and several results of the function are defined and studied.

Abstract: Many analytic strategies have emerged to estimate plant responses to Fusarium wilt. The demand for fast and reliable method (diagnosis, prediction) to determine isolate strength accurately is not established yet. Early determination of pathogen strength helps in plant medication. The aim of this study was to develop a faster strategy and method for early determination of fungal isolates strength in correlation to plant response. Till now, the scientists have no consensus on the most correlated parameters that could express wilt precisely. In this study, 30 isolates of Fusarium oxysporum isolated from Lupinus termis L. were used to provide an explicit image about the real strength of Fusarium isolates and its impact on the plant. Wilting percentage ranged from 26.67% to 93.33% of the infected plants depending on isolate virulence. Some of cellular, morphological and physical measurements were conducted on 8 out of 30 isolates, including root (length, fresh weight (FW) and dry weight (DW)), nodules (water content (WC), FW, DW), stem (height, WC, FW, DW), total leaves/plant (WC, FW, DW) and the fourth leaf (WC, FW, DW, leaf area, epidermal cell area, epidermal cell number, succulence). Hierarchical clustering was used to determine the variance between the isolates. Detrended correspondence analysis (DCA) and canonical correspondence analysis (CCA) were used to determine the most important growth parameters that could express wilting accurately. The CCA results showed that most of the measured parameters on the fourth leaf, except for leaf epidermal cell number, were highly and positively correlated to wilt. That makes these specific parameters valuable and sensitive for any changes in isolates strength. Accordingly, a mathematical model was created to be helpful in the quick determination of isolate strength and precise medication.

Abstract: Many analytic strategies have emerged to estimate plant responses to Fusarium wilt. The demand for fast and reliable method (diagnosis, prediction) to determine isolate strength accurately is not established yet. Early determination of pathogen strength helps in plant medication. The aim of this study was to develop a faster strategy and method for early determination of fungal isolates strength in correlation to plant response. Till now, the scientists have no consensus on the most correlated parameters that could express wilt precisely. In this study, 30 isolates of Fusarium oxysporum isolated from Lupinus termis L. were used to provide an explicit image about the real strength of Fusarium isolates and its impact on the plant. Wilting percentage ranged from 26.67% to 93.33% of the infected plants depending on isolate virulence. Some of cellular, morphological and physical measurements were conducted on 8 out of 30 isolates, including root (length, fresh weight (FW) and dry weight (DW)), nodules (water content (WC), FW, DW), stem (height, WC, FW, DW), total leaves/plant (WC, FW, DW) and the fourth leaf (WC, FW, DW, leaf area, epidermal cell area, epidermal cell number, succulence). Hierarchical clustering was used to determine the variance between the isolates. Detrended correspondence analysis (DCA) and canonical correspondence analysis (CCA) were used to determine the most important growth parameters that could express wilting accurately. The CCA results showed that most of the measured parameters on the fourth leaf, except for leaf epidermal cell number, were highly and positively correlated to wilt. That makes these specific parameters valuable and sensitive for any changes in isolates strength. Accordingly, a mathematical model was created to be helpful in the quick determination of isolate strength and precise medication.