Explicit solutions to phase change problems

Explicit Solutions for Queueing Problems

Explicit Solutions in a Smooth Change Problem

A setting of the change-point estimation problem with a “smooth” change is investigated. A special class of such models, where the change is defined as a gradual shift in the parameter, is considered. We show that these models can be analyzed via explicitly given procedures. It is demonstrated that M -estimators can consistently estimate the change in the parameter structure as well as the addi...

Explicit solutions to some optimal variance stopping problems

The stopping problem with variance as the optimality criterion is introduced. Due to the variance criterion, smooth fit cannot be applied directly. The problem is solved by embedding it into tractable auxiliary optimal stopping problems, where smooth fit is used to obtain explicit, optimal solutions. Optimal strategies are presented in closed form for several examples. A characteristic feature ...

Algebraically Solvable Problems: Describing Polynomials as Equivalent to Explicit Solutions

The main result of this paper is a coefficient formula that sharpens and generalizes Alon and Tarsi’s Combinatorial Nullstellensatz. On its own, it is a result about polynomials, providing some information about the polynomial map P |X1×···×Xn when only incomplete information about the polynomial P (X1, . . . , Xn) is given. In a very general working frame, the grid points x ∈ X1 × · · · × Xn w...

Analytical Solutions to 3-D Bioheat Transfer Problems with or without Phase Change

Theoretical analysis on the bioheat transfer process has been an extremely important issue in a wide variety of bioengineering situations such as cancer hyperthermia, burn injury evaluation, brain hypothermia, disease diagnostics, thermal comfort analysis, cryosurgery and cryopreservation etc. In this chapter, the theoretical strategies towards exactly solving the three-dimensional (3-D) biohea...