A new class of solutions of Einstein field equations has been investigated for inhomogeneous cylindrically symmetric space-time with string source. To get the deterministic solution, it has been assumed that the expansion (θ) in the model is proportional to the eigen value σ 1 of the shear tensor σ j . Certain physical and geometric properties of the models are also discussed.

A new class of cylindrically symmetric inhomogeneous string cosmological models is investigated. To get the deterministic solution, it has been assumed that the expansion (θ) in the model is proportional to the eigen value σ 1 of the shear tensor σ i j . The physical and geometric aspects of the model are also discussed.

We map the Eigen model of biological evolution [Naturwissenschaften 58, 465 (1971)] into a quantum spin model with non-Hermitian Hamiltonian. Based on such a connection, we derive exact relaxation periods for the Eigen model to approach static energy landscape from various initial conditions. We also study a simple case of dynamic fitness function.

We show that functions which are invariant for suitable product semigroups (one of which is a quasi-Poisson semigroup on a general state space) decompose into a singular eigen-function and a mixture of products of minimal eigen-functions. Mathematics Subject Classifications (2000): 31C20, 35C15, 47G20, 60J45, 46A55.

An approximation-free, numerically efficient algorithm is presented for the Hamiltonian eigen-states of Stark-Hydrogen problem describing a quantum particle exposed to central Coulomb force and homogeneous external field. As an example application in state-expansion with continuous energy, we calculate time-dependent wavefunction electron tunneling from hydrogen atom suddenly electric

Abstract We study the meromorphy of various Euler products degree two attached to holomorphic Hecke eigen cusp forms for elliptic modular group, including Ramanujan’s $\Delta $-function.

A mixed method by combining a Eigen algorithm and improved pade approximations is proposed for reducing the order of the large-scale dynamic systems. The most dominant Eigen value of both original and reduced order systems remain same in this method. The proposed method guarantees stability of the reduced model if the original high-order system is stable and is comparable in quality with the ot...

The study of sound attenuation in an elliptical chamber involves the solution of the Helmholtz equation in elliptic coordinate systems. The Eigen solutions for such problems involve the Mathieu and the modified Mathieu functions. The computation of such functions poses considerable challenge. An alternative method to solve such problems had been proposed in this paper. The elliptical cross-sect...