The linear cosmological perturbation theory of an almost homogeneous and isotropic perfect fluid universe is reconsidered and formally simplified by introducing new covariant and gauge-invariant variables with physical interpretations on hypersurfaces of constant expansion, constant curvature or constant energy density. The existence of conserved perturbation quantities on scales larger than th...

The Hubble constant, which measures the expansion rate, together with the total energy density of the Universe, sets the size of the observable Universe, its age, and its radius of curvature. Excellent progress has been made recently toward the measurement of the Hubble constant: a number of different methods for measuring distances have been developed and refined, and a primary project of the ...

In our recent publications we have introduced the incomplete cosine expansion of the sinc function for efficient application in sampling [Abrarov & Quine, Appl. Math. Comput., 258 (2015) 425-435; Abrarov & Quine, J. Math. Research, 7 (2) (2015) 163-174]. Here we show that it can also be utilized as a flexible and efficient tool in mathematical analysis. In particular, an application of the inco...

We prove existence of an asymptotic expansion in the inverse dimension, to all orders, for the connective constant for self-avoiding walks on Z d . For the critical point, de ned to be the reciprocal of the connective constant, the coe cients of the expansion are computed through order d 6 , with a rigorous error bound of order d 7 . Our method for computing terms in the expansion also applies ...

With many years of construction and application of common concrete, researchers have always been searching for a better composition. One of the notable ideas for achieving such a composition is using recycled materials. One of the materials which is suitable for environment and constant development is damaged tires .For studying mechanical properties of concrete containing tire particles, a ser...

This article focuses on the analytical solution for uniform heating of a FGM hollow sphere made of two phase of different materials. It is assumed that the volume fraction of one phase is a function f1 = (rn−an)/(bn−an) varied in the radial direction. Based on the Voigt constant strain approximation, analytical solutions of stresses, displacements and the effective coefficient of thermal expans...

The dependence of critical exponents of statistical mechanical systems on the physical space dimension is one of the most fundamental features of critical phenomena [1]. Continuous change of the space dimension d has been the basic principle for constructing the famous Wilson-Fisher epsilon expansion [2] with ε = 4−d. However, the Renormalization Group (RG) [3], which provides the fundamental t...

We give an introduction to the lace expansion for self-avoiding walks, with emphasis on self-avoiding polygons, and with a focus on combinatorial rather than analytical aspects. We derive the lace expansion for self-avoiding walks, and show that this is equivalent to taking the reciprocal of the self-avoiding walk generating function. We list some of the rigorous results for self-avoiding walks...

When reasoning about parallel programs we would like to combine fixed-point laws for unrolling recursion with expansion laws for parallel composition. Algebraic manipulation using this combination is dangerous, because of the need to stay faithful to the assumption that parallel processes are executed fairly. We give an example of a finite-state parallel system in which the combination of fixed...

A binary system composed of nematogenic solvent (MBBA) and non-nematogenic solute (biphenyl) is investigated for its phase behavior and the dependence of the order parameter on temperature and composition over its entire nematic region. The nematic to isotropic transition temperature is predicted to be a linear function of solute concentration, whereby the dilation effect is shown to be moderat...