Vol 27, No 4 (2016)

We investigate the solutions of the nonlinear heat equation with a volume heat source and thermal conductivity dependent on a negative power of temperature. Properties of self-similar solutions are examined. Structures with contracting half-width evolve in the LS-regime with blowup. Self-similar analysis shows that the system attains a self-similar regime. The nonlinear heat equation is applied to model fast heating of the plasma in flares forming in a magnetic tube cross section, when heat is propagated by plasma ions across the magnetic field. Microflares are described by localized structures evolving in LS-regime with blowup. They may form thin hot filaments stretched in the direction of the magnetic field. The modeling results are consistent with experimental observations.

Differential electroprospecting methods provide an efficient technique to search for mineral deposits, but technical difficulties have so far prevented their widespread use. A stable method is available for numerical differentiation of functions defined by tabular data with errors. The method relies on integral splines. The present article applies the integral spline method to process electromagnetic sounding data. The efficiency of the numerical method is analyzed by modeling magnetotelluric fields in twodimensional nonhomogeneous media. The results show that numerical differentiation of profile curves can be efficiently applied for resolution enhancement in magnetotelluric sounding with the purpose of identifying structural features of the medium longitudinally to the Earth’s surface.

Field energy relationships are applied to avoid multiple evaluations of the absorption cross section in problems of fluorescence or optical antenna efficiency in the presence of plasmon structures. The results are of primary importance for averaging the fluorescence quantum yield over position or orientation of the molecule.

An upper bound on the value of a two-sided Margrabe option is obtained from the approximation of the immediate exercise set by polygonal sets using an integral formula. A lower bound is obtained by the Monte Carlo method using the decision rule that follows from this approximation.

In this article, a modification of Newton’s method with fifteenth-order convergence is presented. The modification of Newton’s method is based on the method of fifth-order convergence of Hu et al. First, we present theoretical preliminaries of the method. Second, we solve some nonlinear equations and then systems of nonlinear equations obtained by means of the finite element method. In contrast to the eleventh-order M. Raza method, the fifteenth-order method needs less function of evaluation per iteration, but the order of convergence increases by four units. Numerical examples are given to show the efficiency of the proposed method.

In this article we describe the construction of discrete functions such that some of their values specify (generate) arbitrary pairs of literals under two mutually exclusive assumptions: the function is equal to one of the variables or to its negation. We prove the existence of such functions with at least seven arguments and show that for sufficiently large n this function can be defined on O(n log₂n) tuples. We also consider the problem of simultaneous generation of k literals. We show that with k < n − log₂n+log₂(log₃ 4−1), functions generating arbitrary k literals exist, and if (n−log₂n−k) → ∞ as n → ∞ , then almost all functions generate arbitrary k literals.

In this paper, we introduce a new method to analyze the convergence of the standard finite element method for the noncoercive impulse control quasi-variational inequality (QVI). L^∞ convergence of the approximation is derived as a result of the geometrical convergence of a Bensoussan–Lions algorithm type and uniform error estimate between the continuous algorithm and its finite element counterpart. This approach is completely different from the one inroduced in [2] as it enables us to derive the error estimate through a computational iterative scheme.