Vector And Tensor Analysis By Nawazish Ali Shah Pdf Free 165 NEW! ✋🏿
Vector And Tensor Analysis By Nawazish Ali Shah Pdf Free 165
In this paper, we propose a new model of the trajectory description for a time series using autoregressive vector autoregression models. The proposed approach eliminates redundancies due to the use of orthogonal bases through the matrix algebra methods. The final trajectories in the spaces of $L^1$ function or continuous functions are determined by their characteristics. In the case of the $L^1$ functions, we have: the regularity character of the functions, their trend, and their stationarity, while in the case of the continuous function, we have: the number of extrema, the extremities, their derivatives at the extremity, trends of the extremities and derivatives, and stationarity.
The aim of this work is to present the issue of the boundary value problem for a system of two ordinary differential equations with the input-output variables and two auxiliary functions of a single argument. The variables of the problem are known functions of the time t and the general solution of the initial value problem is representable as a double integral. Under certain conditions we establish the equivalence of two methods for its solution. We find the second-order differential equation which represents the time-parameter dependence of the general solution of the problem. The main result of this work is the necessary condition which has to be fulfilled by the integral constant to ensure the uniqueness of the general solution.
In this work, we study the existence and uniqueness analysis of the solutions of the initial-boundary value problem and the existence of the solutions of a system of a first-order systems of ordinary differential equations of the second order with the input-output variables and two auxiliary functions of a single argument.