In this research, our aim is to study the optimal control problem (OCP) for triple nonlinear elliptic boundary value problem (TNLEBVP). The Mint-Browder theorem is used to prove the existence and uniqueness theorem of the solution of the state vector for fixed control vector. The existence theorem for the triple continuous classical optimal control vector (TCCOCV) related to the TNLEBVP is also proved. After studying the existence of a unique solution for the triple adjoint equations (TAEqs) related to the triple of the state equations, we derive The Fréchet derivative (FD) of the cost function using Hamiltonian function. Then the theorems of necessity conditions and the sufficient condition for optimality of

Due to its importance in physics and applied mathematics, the non-linear Sturm-Liouville problems
witnessed massive attention since 1960. A powerful Mathematical technique called the Newton-Kantorovich
method is applied in this work to one of the non-linear Sturm-Liouville problems. To the best of the authors’
knowledge, this technique of Newton-Kantorovich has never been applied before to solve the non-linear
Sturm-Liouville problems under consideration. Accordingly, the purpose of this work is to show that this
important specific kind of non-linear Sturm-Liouville differential equations problems can be solved by
applying the well-known Newton-Kantorovich method. Also, to show the efficiency of appl

This paper focuses on developing a self-starting numerical approach that can be used for direct integration of higher-order initial value problems of Ordinary Differential Equations. The method is derived from power series approximation with the resulting equations discretized at the selected grid and off-grid points. The method is applied in a block-by-block approach as a numerical integrator of higher-order initial value problems. The basic properties of the block method are investigated to authenticate its performance and then implemented with some tested experiments to validate the accuracy and convergence of the method.

Scheduling problems have been treated as single criterion problems until recently. Many of these problems are computationally hard to solve three as single criterion problems. However, there is a need to consider multiple criteria in a real life scheduling problem in general. In this paper, we study the problem of scheduling jobs on a single machine to minimize total tardiness subject to maximum earliness or tardiness for each job. And we give algorithm (ETST) to solve the first problem (p1) and algorithm (TEST) to solve the second problem (p2) to find an efficient solution.  

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In this paper, first we   refom1Ulated   the finite   element  model

(FEM)   into   a   neural   network   structure   using   a   simple   two   - dimensional problem. The structure of this neural network is described

, followed  by its   application   to   solving  the forward    and  inverse problems. This model is then extended to the general case and the advantages and  di sadvantages  of  this  approach  are  descri bed  along with an analysis  of  the sensi tivity   of

The organization and coordination of any communication is based on the system of turn-taking which refers to the process by which a participant in a conversation takes the role of speaker. The progression of any conversation is achieved by the change of roles between speaker and hearer which, in its turn, represents the heart of the turn-taking system. The turn-taking system is not a random process but it is a highly organized process governed by a set of rules. Thus, this system has certain features and rules which exist in any English communicative process. These rules, if applied by speakers, help to achieve successful exchange of turns in any conversation. This paper attempts to present full exposition of the concepts of conversation