Various industrial sectors require highly specialized and efficient materials for applications in fields such as the military, aeronautics, aerospace, and mechanical and civil engineering. Composite materials that meet the stringent requirements across these domains have become prominent, often serving as structural components and requiring precise mathematical modeling. Zigzag (ZZ) and Layerwise (LW) theories are commonly used for laminated-beam structural analysis. Although the LW theory provides superior accuracy, it suffers from an increase in unknowns as the number of layers grows. Conversely, the ZZ theory is less computationally intensive and less accurate. This study proposes an Exponential high-order zigzag function with a unified kinematic formulation to enhance the accuracy of the ZZ theory. The results were compared with those of existing models and demonstrated excellent agreement with the reference solutions, irrespective of the layer count or slenderness index, making it a more efficient choice for laminated-beam analysis.

In this article, a new censoring scheme is considered, namely, a middle part of a random sample is censored. A treatment for reconstructing the missing order statistics is investigated. The proposed procedure is studied in detail under Exponential distribution which is widely used as a constant failure model in reliability.Different approaches are used to obtain point and interval reconstructors and then they are compared. A numerical example is presented for illustrating all the proposed inferential procedures. Eventually, we present some remarks including how the results of the paper can be used when the parameters of the Exponential distribution are unknown.

The multidimensional Exponential Levy equations are used to describe many stochastic phenomena such as market fluctuations. Unfortunately in practice an exact solution does not exist for these equations. This motivates us to propose a numerical solution for n-dimensional Exponential Levy equations by block pulse functions. We compute the jump integral of each block pulse function and present a Poisson operational matrix. Then we reduce our equation to a linear lower triangular system by constant, Wiener and Poisson operational matrices. Finally using the forward substitution method, we obtain an approximate answer with the convergence rate of O(h). Moreover, we illustrate the accuracy of the proposed method with a 95% confidence interval by some numerical examples.

Fuzziness is ever presented in real life decision making problems. In this paper, we adapt the pessimistic approach to study a pair of linear primal-dual problem under intuitionistic fuzzy (I-fuzzy) environment and prove certain duality results. We generate the duality results using Exponential membership and non-membership functions to represent the decision maker's satisfaction and dissatisfaction level. Further, two numerical examples have been given. In each of these illustrations, varying the values of the shape variables in the Exponential membership functions, various nonlinear optimization problems have been constructed, analyzed and solved. The duality gaps for all these optimization problems have been computed and compared with the duality gap under the linear membership function. We found that these gaps for the I-fuzzy linear primal-dual pair under the Exponential membership functions are smaller as compared with the linear membership functions. The main advantage of using the Exponential membership function is that it has the exibility of altering the values of the shape parameters (as per the decision-maker's satisfaction). Finally, with the help of a suitable ranking defuzzification function, we have extended our approach to the I-fuzzy linear problem with fuzzy parameters and fuzzy constraints.

The present research aims to find a precise method for the wu-zhang system on scattered long waves, which can be a positive step for physical science in dealing with the structure of scattered waves and provide 3D diagrams for further studies of other sciences.