In this chapter, an innovative model for age replacement is proposed. The costs included in the age replacement model are not assumed to be constants. For effective optimization of statistical decisions for age replacement problems under parametric uncertainty, based on a past random sample of lifetimes, the pivotal quantity averaging (PQA) approach is suggested. The PQA approach represents a s...

An analytic proof of an evaluation theorem for the “convolution”type double L-values of non-principal characters is given. Along the way, Dirichlet character analogues of generalized single and double polylogarithms are defined. The monodromies of these functions play a pivotal role.

In the fundamental production inventory model, in order to solve the economic production quantity (EPQ) we always fix both the demand quantity and the production quantity per day. But, in the real situation, both of them probably will have little disturbances every day. Therefore, we should fuzzify both of them to solve the economic production quantity (q*) per cycle. Using α-cut for defuzzific...

In this paper, we show that the class of R-quadratic Finsler spaces is a proper subset of the class of generalized Douglas-Weyl spaces. Then we prove that all generalized Douglas-Weyl spaces with vanishing Landsberg curvature have vanishing the non-Riemannian quantity H, generalizing result previously only known in the case of R-quadratic metric. Also, this yields an extension of well-known Num...

The generalized entropic measure, which is optimized by a given arbitrary distribution under the constraints on normalization of the distribution and the finite ordinary expectation value of a physical random quantity, is considered and its Lesche stability property (that is different from thermodynamic stability) is examined. A general condition, under which the generalized entropy becomes sta...

A general variational principle of classical fields with a Lagrangian containing field quantity and its derivatives of up to the N-order is presented. Noether’s theorem is derived. The generalized Hamilton-Jacobi’s equation for the Hamilton’s principal functional is obtained. These results are surprisingly in great harmony with each other. They will be applied to general relativity in the subse...