In this paper, we investigate the quintessence model with a minimally coupled scalar field in the context of recent supernovae observations. By choosing a particular form of the deceleration parameter q , which gives an early deceleration and late time acceleration for dust dominated model, we show that this sign flip in q can be obtained by a simple trigonometric potential. The early matter do...

This report considers low resolution scalar quantization. Specifically, it considers entropyconstrained scalar quantization for memoryless Gaussian and Laplacian sources with both squared and absolute error distortion measures. The slope of the operational rate-distortion functions of scalar quantization for these sources and distortion measures is found. It is shown that in three of the four c...

We consider a model of inhomogeneous universe with the presence of a massless scalar field, where the inhomogeneity is assumed to consist of many black holes. Such model can be constructed by following Lindquist and Wheeler, which has already been investigated without the presence of scalar field to show that an averaged scale factor coincides with that of Friedmann model. In this paper we cons...

In 1953 Peter Roquette gave an arithmetic proof of the Riemann hypothesis for algebraic function fields over a finite constants field, which was proved by André Weil in 1940. The construction of Weil’s scalar product is essential in Roquette’s theory. In this paper a scalar product for algebraic function fields over a number field is constructed which is the analogue of Weil’s scalar product.

Gyroscopic systems in classical and quantum field theory are characterized by the presence of at least two scalar degrees freedom terms that mix fields their time derivatives quadratic Lagrangian. In Minkowski spacetime, they naturally appear a coupling among with time-dependent vacuum expectation values space-dependent values, breaking spontaneously Lorentz symmetry; this is case for supersoli...

In this paper, by modifying Cheng-Yau$'$s technique to complete hypersurfaces in $S^{n+1}(1)$, we prove a rigidity theorem under the hypothesis of the mean curvature and the normalized scalar curvature being linearly related which improve the result of [H. Li, Hypersurfaces with constant scalar curvature in space forms, {em Math. Ann.} {305} (1996), 665--672].  

The five integrable vortex equations, recently studied by Manton, are generalized to include magnetic impurities of the Tong–Wong type. Under certain conditions, these generalizations remain integrable. We further set up a gauge theory with product group, two complex scalar fields and general charge matrix. second species vortices, when frozen, interpreted as impurity for all equations. then gi...

1 Three Axioms for a Determinant Function Let d be a scalar-valued function on the space Mn×n of all n×n matrices. Let A1, A2, . . . , An be the n rows of an n×n matrix A. We will denote the value d(A) of A under the function d as d(A) = d(A1, A2, . . . , An), indicating that d is a scalar-valued function of n n-dimensional row vectors A1, A2, . . . , An. The scalar-valued function d is called ...