On some specific cases of quantum state in testing its separability

This paper shows a simple computational scheme for determining whether a particular quantum state in a specific form is separable across two given sets of qubits. That is, given a set of qubits partitioned into two, it answers the question: does the original state have a separable form as a tensor product of some two other states, which are set up of the two given subsets of qubits?

Disentangling Intertemporal Substitution and Risk Aversion Under the Expected Utility Theorem

This paper presents an axiomatic approach to separately control for the attitudes toward intertemporal substitution and risk aversion under the expected utility theorem. The standard time-separable form is recovered only if the functions dictating the two attitudes are identical. Risk aversion is defined on consumption amount rather than on utility (as in Kihlstrom and Mirman (1974 and 1981)). Moreover, the agent is allowed to trade his lottery outcome to optimize his consumption. As a result, this approach provides a straightforward extension of the familiar Arrow-Pratt results to multiple periods. These include categorizing, measuring, and comparing risk aversions.

The piston problem in hyperelasticity with the stored energy in separable form

The piston problem for a hyperelastic hyperbolic conservative model where the stored energy is given in separable form is studied. The eigenfields corresponding to the hyperbolic system are of three types: linearly degenerate fields (corresponding to the contact characteristics), the fields which are genuinely nonlinear in the sense of Lax (corresponding to longitudinal waves), and, finally, nonlinear fields which are not genuinely nonlinear (corresponding to transverse waves). Taking the initial state free of stresses, we presented possible auto-similar solutions to the piston problem. In particular, we have shown that the equations admit transverse shock waves having a remarkable property: the solid density is decreasing through such a shock, it is thus a ‘rarefaction’ shock.

Analysis of general creeping motion of a sphere inside a cylinder

In this paper, we develop an efficient procedure to solve for the Stokesian fields around a spherical particle in viscous fluid bounded by a cylindrical confinement. We use our method to comprehensively simulate the general creeping flow involving the particle-conduit system. The calculations are based on the expansion of a vector field in terms of basis functions with separable form. The separable form can be applied to obtain general reflection relations for a vector field at simple surfaces. Such reflection relations enable us to solve the flow equation with specified conditions at different disconnected bodies like the sphere and the cylinder. The main focus of this article is to provide a complete description of the dynamics of a spherical particle in a cylindrical vessel. For this purpose, we consider the motion of a sphere in both quiescent fluid and pressure-driven parabolic flow. Firstly, we determine the force and torque on a translating-rotating particle in quiescent fluid in terms of general friction coefficients. Then we assume an impending parabolic flow, and calculate the force and torque on a fixed sphere as well as the linear and angular velocities of a freely moving particle. The results are presented for different radial positions of the particle and different ratios between the sphere and the cylinder radius. Because of the generality of the procedure, there is no restriction in relative dimensions, particle positions and directions of motion. For the limiting cases of geometric parameters, our results agree with the ones obtained by past researchers using different asymptotic methods.

VACUUM BRANS–DICKE THEORY AND WORMHOLES

This paper deals with vacuum Brans–Dicke theory in an anisotropic Kantowski–Sachs model and Euclidean wormhole solutions have been obtained. The Wheeler–Dewitt (WD) equation has been solved using separable form of the wave function and these solutions have been examined whether wormhole boundary condition due to Hawking is satisfied or not.