A solution is presented to a doubly mixed boundary value problem of the torsion of an elastic layer, partially resting on a rigid circular base by a circular rigid punch attached to its surface. This problem is reduced to a system of dual integral equations using the Boussinesq stress functions and the Hankel integral transforms. With the help of the Gegenbauer expansion formula of the Bessel f...

We examine Killing spinor equations of the general IIB pp-wave backgrounds, which contain a scalar H(xm, x) in the metric and a self-dual four-form ξ(xm, x) in the self-dual five-form flux. We find that if the backgrounds admit at least one extra Killing spinor characterized by mutually commuting projection operators in addition to 16 standard Killing spinors, backgrounds must reduce to the for...

The time-dependent Ginzburg-Landau model which describes the phase transitions taking place in superconductors is a coupled system of nonlinear parabolic equations. It is discretized semi-implicitly in time and in space via continuous piecewise linear nite elements. A posteriori error estimates are derived for the L 1 L 2 norm by studying a dual problem of the linearization of the original syst...

We study the equations of motion of fermions in type IIB supergravity in the context of the gauge/gravity correspondence. The main motivation is the search for normalizable fermionic zero modes in such backgrounds, to be interpreted as composite massless fermions in the dual theory. We specialize to backgrounds characterized by a constant dilaton and a self-dual three-form. In the specific case...

The unsteady stagnation point flow and heat transfer over a stretching/shrinking sheet with suction/injection is studied. The governing partial differential equations are converted into nonlinear ordinary differential equations using a similarity transformation and solved numerically. Both stretching and shrinking cases are considered. Results for the skin friction coefficient, local Nusselt nu...

are based on the ansätze for the Yang–Mills field Aμ(x) suggested by Wu and Yang, Rosen, ’t Hooft, Corrigan and Fairlie, Wilczek, Witten (see [1] and references therein). There were further developments for the self-dual YMEs (which form the first-order system of nonlinear partial differential equations such that system (1) is its differential consequence). Let us mention the Atiyah–Hitchin–Dri...

This paper provides a new formulation of second order stochastic target problems introduced in [19] by modifying the reference probability so as to allow for different scales. This new ingredient enables us to prove a dual formulation of the target problem as the supremum of the solutions of standard backward stochastic differential equations. In particular, in the Markov case, the dual problem...

We give a characterization of all (quasi) aane frames in L 2 (R n) which have a (quasi) aane dual in terms of the two simple equations in the Fourier transform domain. In particular, if the dual frame is the same as the original system, i.e. it is a tight frame, we obtain the well known characterization of wavelets. Although these equations have already been proven under some special conditions...