This paper concentrates on the propagation of waves in a layer of binary mixture of elastic solids subjected to stress free boundaries. Secular equations for the layer corresponding to symmetric and antisymmetric wave modes are derived in completely separate terms. The amplitudes of displacement components and specific loss for both symmetric and antisymmetric modes are obtained. The effect of ...

We investigate Hamiltonian systems with two degrees of freedom by using renormalization group method. We show that the original Hamiltonian systems and the renormalization group equations are integrable if the renormalization group equations are Hamiltonian systems up to the second leading order of small parameter. To understand temporal evolutions of Hamiltonian systems, one useful method is t...

The relationship between modernity and religiosity has been in the center of many scholarly debates. Among others, Charles Taylor presents in his works a general picture of the elements that shape the secular age. He starts with the question why people used to be faithful, while they are not easily so in our age. To answer, he explores the past five centuries in the West and coins some terms to...

Bernard S. Jackson has rightly warned that while it is tempting to analyze Jewish law in terms of secular theories of jurisprudence, the success of such a project is not guaranteed. For while there are correspondences between Jewish law and positivism, Jewish law and natural law theory, Jewish law and social contract theory – there is no systematic correspondence and indeed, there are points of...

We pose and solve a parameter estimation problem in the presence of bounded data uncertainties. The problem involves a minimization step and admits a closed form solution in terms of the positive root of a secular equation.

In the present paper is concerned with study of thermoelastic interaction in an infinite KelvinVoigt type viscoelastic, thermally conducting solid bordered with viscous liquid half-spaces/layers of varying temperature. Complex secular equations in closed and isolated mathematical conditions for Rayleigh wave propagation in completely separate terms are derived. The results for coupled and uncou...

A simplified molecular orbital (MO) formalism based on density functional theory is developed. Starting from the same energy expression as Kohn-Sham theory the electronic density is expanded in terms of atomic mono-center densities. Application of the variational principle leads to a secular matrix with a particularly transparent structure which allows the definition of a resonance integral tak...

For a class of multidimensional linear perturbation problems of considerable significance in applications, the Poincarc-Lighthill technique is shown to give first-order expansion terms which grow unbounded relative to the leading term (secular behavior), while the method of linear time scales leads to well-behaved expansion terms. A solvable example is introduced for comparison with the exact s...

We study the Schrr odinger equation of a class of two-level systems under the action of a periodic time-dependent external eld in the situation where the energy diierence 2 between the free energy levels is suuciently small with respect to the strength of the external interaction. Under suitable conditions we show that this equation has a solution in terms of converging power series expansions ...

We study the Schrödinger equation of a class of two-level systems under the action of a periodic time-dependent external field in the situation where the energy difference 2 between the free energy levels is sufficiently small with respect to the strength of the external interaction. Under suitable conditions we show that this equation has a solution in terms of converging power series expansio...