This paper explicitly computes the transition densities of a spectrally negative stable process with index greater than one, reflected at its infimum. First we derive the forward equation using the theory of sun-dual semigroups. The resulting forward equation is a boundary value problem on the positive half-line that involves a negative Riemann-Liouville fractional derivative in space, and a fr...

This paper studies the self-dual Einstein-Dirac theory. A generalization is obtained of the Jacobson-Smolin proof of the equivalence between the self-dual and Palatini purely gravitational actions. Hence one proves equivalence of self-dual EinsteinDirac theory to the Einstein-Cartan-Sciama-Kibble-Dirac theory. The Bianchi symmetry of the curvature, core of the proof, now contains a non-vanishin...

The present investigation deals with study of thermoelastic damping and frequency shift of Kirchhoff plate resonators by using generalized thermoelasticity theory of dual-phase-lag model. The basic equations of motion and heat conduction equation are written with the help of Kirchhoff-Love plate theory and dual phase lag model. The analytical expressions for thermoelastic damping and frequency ...

We apply algebraic and vertex operator techniques to solve two dimensional reduced vacuum Einstein's equations. This leads to explicit expressions for the coefficients of metrics solutions of the vacuum equations as ratios of determinants. No quadratures are left. These formulas rely on the identification of dual pairs of vertex operators corresponding to dual metrics related by the Kramer-Neug...

The structural equations for the Killing-Yano tensors of order two was investigated.The physical signification of the tensors Lαβγ and Mαβδγ was obtained using the dual transformation. The structural equations in the dual space was investigated. Permanent address:Institute for Space Sciences,P.O.BOX, MG-36, R 76900 MagureleBucharest, Romania e-mail:[email protected]

We present a powerful method to generate various equations which possess the Lax representations on noncommutative (1+1) and (1+2)-dimensional spaces. The generated equations contain noncommutative integrable equations obtained by using the bicomplex method and by reductions of the noncommutative (anti-)self-dual Yang-Mills equation. This suggests that the noncommutative Lax equations would be ...

In this paper we derive new farfield boundary conditions for the timedependent Navier–Stokes and Euler equations in two space dimensions. The new boundary conditions are derived by simultaneously considering well-posedess of both the primal and dual problems. We moreover require that the boundary conditions for the primal and dual Navier–Stokes equations converge to well-posed boundary conditio...

The rigorous Method of Regularization is applied to the problem of electromagnetic scattering of plane waves by a finite array of partiallyshielded circular cylinders. A set of ill-posed dual series equations is resulted from imposing the mixed boundary conditions on the surface of each of the cylinders. Each of the M sets of dual series equations are treated separately using the Method of Regu...