Stumpff functions are an infinite series that depends on the value of z. This value results from multiplying the reciprocal semi-major axis with a universal anomaly. The purpose from those functions is to calculate the variation of the universal parameter (variable) using Kepler's equation for different orbits. In this paper, each range for the reciprocal of the semi-major axis, universal anomaly, and z is calculated in order to study the behavior of Stumpff functions C(z) and S(z). The results showed that when z grew, Stumpff functions for hyperbola, parabola, and elliptical orbits were also growing. They intersected and had a tendency towards zero for both hyperbola and parabola orbits, but for elliptical orbits, Stumpff functions

This paper aims to study the quaternary classical continuous optimal control problem consisting of the quaternary nonlinear parabolic boundary value problem, the cost function, and the equality and inequality constraints on the state and the control. Under appropriate hypotheses, it is demonstrated that the quaternary classical continuous optimal control ruling by the quaternary nonlinear parabolic boundary value problem has a quaternary classical continuous optimal control vector that satisfies the equality constraint and inequality state and control constraint. Moreover, mathematical formulation of the quaternary adjoint equations related to the quaternary state equations is discovered, and then the weak form of the quaternary adjoint

Transient mixed convection heat transfer in a confined porous medium heated at periodic sinusoidal heat flux is investigated numerically in the present paper. The Poisson-type pressure equation, resulted from the substituting of the momentum Darcy equation in the continuity equation, was discretized by using finite volume technique. The energy equation was solved by a fully implicit control volume-based finite difference formulation for the diffusion terms with the use of the quadratic upstream interpolation for convective kinetics scheme to discretize the convective terms and the temperature values at the control volume faces. The numerical study covers a range of the hydrostatic  pressure sinusoidal  amplitude  range and

Transient mixed convection heat transfer in a confined porous medium heated at periodic sinusoidal heat flux is investigated numerically in the present paper. The Poisson-type pressure equation, resulted from the substituting of the momentum Darcy equation in the continuity equation, was discretized by using finite volume technique. The energy equation was solved by a fully implicit control volume-based finite difference formulation for the diffusion terms with the use of the quadratic upstream interpolation for convective kinetics scheme to discretize the convective terms and the temperature values at the control volume faces. The numerical study covers a range of the hydrostatic pressure head , , , , and ), sinusoidal amplitude range of

    This paper is devoted to the analysis of nonlinear singular boundary value problems for ordinary differential equations with a singularity of the different kind. We propose semi - analytic technique using two point osculatory interpolation to construct polynomial solution, and discussion behavior of the solution in the neighborhood of the singular points and its numerical approximation. Two examples are presented to demonstrate the applicability and efficiency of the methods. Finally, we discuss behavior of the solution in the neighborhood of the singularity point which appears to perform satisfactorily for singular problems.

    In this paper generalized spline method is used for solving linear system of fractional integro-differential equation approximately. The suggested method reduces the system to system of  linear algebraic equations. Different orders of fractional derivative for test example is given in this paper to show the accuracy and applicability of the presented method.

In high-dimensional semiparametric regression, balancing accuracy and interpretability often requires combining dimension reduction with variable selection. This study intro- duces two novel methods for dimension reduction in additive partial linear models: (i) minimum average variance estimation (MAVE) combined with the adaptive least abso- lute shrinkage and selection operator (MAVE-ALASSO) and (ii) MAVE with smoothly clipped absolute deviation (MAVE-SCAD). These methods leverage the flexibility of MAVE for sufficient dimension reduction while incorporating adaptive penalties to en- sure sparse and interpretable models. The performance of both methods is evaluated through simulations using the mean squared error and variable selection cri

      The aim of this research is to solve a real problem in the Department of Economy and Investment in the Martyrs establishment, which is the selection of the optimal project through specific criteria by experts in the same department using a combined mathematical model for the two methods of analytic hierarchy process and goal programming, where a mathematical model for goal programming was built that takes into consideration the priorities of the goal criteria by the decision-maker to reach the best solution that meets all the objectives, whose importance was determined by the hierarchical analysis process. The most important result of this research is the selection of the second pro