The method of intermediate problems of Weinstein and Aronszajn (cf. [19, 20]) provides a means of calculation for bounds to eigenvalues complementary to the Rayleigh{Ritz bounds. Convergence theorems for the method of intermediate problems in a generality that includes problems with essential spectra can be found in [5, 7{9, 12]. This paper supplements the general convergence theorems of [7, 9]...

We study the band structure of semiconductor nanowires with quantum dots embedded in them. The is calculated using Rayleigh–Ritz variational method. consider two different types, one type defined by electrostatic potentials applied to nanowire, while other adding materials offsets respect parameters nanowire. are particularly interested appearance discrete energy levels gap between conduction a...

Abstract The article deals with a continual segment of an inter-resonance vibration machine. In the form solid distributed parameters this combines two defining parameters, namely: inertial parameter reactive: masses and appropriate rigidity elastic coupling. These operation factors are revealed only in dynamic processes clearly not included segment. Analytical dependences developed for modelin...

An intra-cavity adaptive mirror is required to compensate for time-dependent phase aberrations to the laser beam, such as those caused by thermal lensing. A piezoelectric unimorph design can provide a small, low-cost deformable mirror for this application. The unimorph consists of a metallic disc, with a mirror finish, bonded to a piezoelectric disc. In adaptive optics the deformations that the...

A new geometric invariant is defined from "first principles" for a point ensemble, which can represent clusters, molecules, crystals, and biomolecules. The scattering of a point ensemble is defined in terms of the Euclidean distance matrix and a vector measuring the weighted departure of the points from the cluster centre. Using the Rayleigh-Ritz theorem this function is maximized obtaining the...

Recent work on mutation-selection models has revealed that, under specific assumptions on the fitness function and the mutation rates, asymptotic estimates for the leading eigenvalue of the mutation-reproduction matrix may be obtained through a lowdimensional variational principle in the limit N → ∞ (where N is the number of types). In order to generalize these results, we consider here a large...

A simple model presented here is to study the thermal effect on vibration of non-homogeneous orthotropic visco-elastic rectangular plate of parabolically varying thickness having clamped boundary conditions on all the four edges. For non-homogeneity of the plate material, density is assumed to vary linearly in one direction. Using the separation of variables method, the governing differential e...