The dynamics of Lennard-Jones fluid is studied through extended mode coupling theory (MCT) with the inclusion of the slow mode of defect density. Inclusion of defect density facilitates the liquid like state for temperatures much lower than predicted from ideal MCT. From the present model the temperature dependence of the power law exponent is obtained at a constant pressure. We have also compu...

where Aj(z) (j = 0, 1, . . . , k) are meromorphic functions with finite order. Under some conditions on the coefficients, we show that all meromorphic solutions f 6≡ 0 of the above equations have an infinite order and infinite lower order. Furthermore, we give some estimates of their hyper-order, exponent and hyper-exponent of convergence of distinct zeros. We improve the results due to Kwon; C...

We show that, for any transcendental real number ξ, the uniform exponent of simultaneous approximation of the triple (ξ, ξ, ξ) by rational numbers with the same denominator is at most (1 + 2γ − √ 1 + 4γ)/2 ∼= 0.4245 where γ = (1 + √ 5)/2 stands for the golden ratio. As a consequence, we get a lower bound on the exponent of approximation of such a number ξ by algebraic integers of degree at most 4.

We apply the Hurst exponent idea for investigation of DJIA index time-series data. The behavior of the local Hurst exponent prior to drastic changes in financial series signal is analyzed. The optimal length of the time-window over which this exponent can be calculated in order to make some meaningful predictions is discussed. Our prediction hypothesis is verified with examples of '29 and '87 c...

Given a corrupted word w = (w1, . . . , wn) from a Reed-Solomon code of distance d, there are many ways to efficiently find and correct its errors. But what if we are instead given (g1 , . . . , gn) where g generates some large cyclic group — can the errors still be corrected efficiently? This problem is called error correction in the exponent, and though it arises naturally in many areas of cr...

The capacity and error exponent of the direct detection optical channel are considered. The channel input in a T-second interval is a waveform A(r), 0 5 t I T, which satisfies 0 I A(t) I A, and (l/r)],,%(t) dt I aA, 0 < IT 11. The channel output is a Poisson process with intensity parameter X(t) + he. ‘The quantities A and CIA represent the peak and average power, respectively, of the optical s...

‎by considering a degenerate $p(x)-$laplacian equation‎, ‎a generalized compact embedding in weighted variable‎ ‎exponent sobolev space is presented‎. ‎multiplicity of positive solutions are discussed by applying fibering map approach for the‎ ‎corresponding nehari manifold‎.

In the present paper we study the weak lower semicontinuity of the functional