The order of the stress singularity of a magnetoelectroelastic bonded antiplane wedge is analyzed by complex potential function and eigenfunction expansion method. Contrary to the familiar problem of elastic anisotropic bonded wedges which always produce real values for the order of singularity, the results of the magnetoelectroelastic bonded wedges may be real or complex. Numerical results are...

The J-matrix method is extended to difference and q-difference operators and is applied to several explicit differential, difference, q-difference and second order Askey– Wilson type operators. The spectrum and the spectral measures are discussed in each case and the corresponding eigenfunction expansion is written down explicitly in most cases. In some cases we encounter new orthogonal polynom...

Using traditional methods, especially that of eigenfunction expansions combined with the penalty method, sharp conditions are given for the existence of solutions to a general weakly elliptic linear N N second order systems subjected to obstacle type constraints. The result applies to systems with deening coeecient matrices A and B having complex eigenvalues as well as to the case of singular s...

The rnapshot method is used to analyze a large eddy simulation of axisymmetric jet flow. An ensemble of realizations is collected using a sampling condition that corresponds to the passage of a large scale vortex at a position six diameters downstream from the nozzle. The analysis is performed separately on a variable composed of the primitive flow quantities and the mass fraction of the materi...

We first show that the quasiclassical limit of the squared eigenfunction symmetry constraint of the Sato operator for the mKP hierarchy leads to a reduction of the Sato function for the dispersionless mKP hierarchy. The constrained dispersionless mKP hierarchy (cdmKPH) is obtained and it is shown that the (2+1)-dimensional dispersionless mKP hierarchy is decomposed to two (1+1)-dimensional hier...

An exact analytical solution is obtained for the problem of three-dimensional transient heat conduction in the multilayered sphere. The sphere has multiple layers in the radial direction and, in each layer, time-dependent and spatially nonuniform volumetric internal heat sources are considered. To obtain the temperature distribution, the eigenfunction expansion method is used. An arbitrary comb...

This paper develops an eigenfunction expansion approach to pricing options on scalar diffusion processes. All derivative securities are unbundled into portfolios of primitive securities termed eigensecurities. Eigensecurities are eigenvectors of the pricing operator (present value operator). Pricing is then immediate by the linearity property of the pricing operator and the eigenvector property...

Soliton equations are infinite-dimensional integrable systems described by nonlinear evolution equations. As one of the soliton equations, long wave equation takes on profound significance of theory and reality. By using the method of nonlinearization, the relation between long wave equation and second-order eigenvalue problem is generated. Based on the nonlinearized Lax pairs, Euler-Lagrange f...

Let u be an eigenfunction of the Laplacian on a compact manifold with boundary, with Dirichlet or Neumann boundary conditions, and let −λ2 be the corresponding eigenvalue. We consider the problem of estimating maxM u in terms of λ, for large λ, assuming ∫ M u 2 = 1. We prove that maxM u ≤ CMλ (n−1)/2, which is optimal for some M . Our proof simplifies some of the arguments used before for such ...

The characterization or subsequent use of a propagating optical quantum state requires the knowledge of its precise temporal mode. Defining this mode structure very often relies on a detailed a priori knowledge of the used resources, when available, and can additionally call for an involved theoretical modeling. In contrast, here we report on a practical method enabling us to infer the optimal ...