Quintessence with Hybrid Potential

I present the numerical solution of equations of the evolution of a universe containing background fluids (radiation, dark matter and baryonic matter), plus a scalar matter field with a hybrid potential that is a combination of exponential potential and power-law potential. The plot of the evolution of density parameters is compatible with our universe; and today's values of density parameters of dark energy, dark matter, baryonic matter, and Hubble parameter, and the age and size of our universe, found from this model, are very close to (and some times the same as) measured values.Comment: 10 pages, 4 figures include

Study of the antibacterial activity of total extract and Petroleum ether, chloroform, ethyl acetate and aqueous fractions of aerial parts of heliotropium bacciferum against staphylococcus aureus, Bacillus cereus, Pseudomonas aeruginosa, E.coli, Salmonella enteritidis

Heliotropium bacciferum is One of the plants belonging to the family Boraginaceae , which is Restricted distribution in the south of Iran. It is used for Hypotension, fever, stomach ulcers in traditional medicine. In this study, the antibacterial effects of extracts and fractions of chloroform, ethyl acetate and aqueous, aerial parts of Heliotropium bacciferum Forssk was evaluated against five bacterial strains. The methanol extract were prepared using the percolation method. Fractions of chloroform, Petroleum ether, ethyl acetate, methanol and aqueous respectively by Liquid - Liquid fractionation of the total extract were prepared. The antibacterial activity against two Gram positive bacteria, three Gram negative bacterial using Minimum inhibitory concentration in microplate and well plate method. Results showed that H. bacciferum extracts exhibited a significant activity against strains Staphylococcus aureus, Bacillus cereus,Pseudomonas aeruginosa, E.coli, Salmonella enteritidis. MIC and well plate is between 7.6-125 μg/ml. The results of this study indicate that extracts of the plant H.bacciferum has a antimicrobial effect against strains are listed And among the extracts, aqueous part is that most antibacterial effect of the other fraction and then methanolic extract has the greatest effect

Quintessence Ghost Dark Energy Model

A so called "ghost dark energy" was recently proposed to explain the present acceleration of the universe expansion. The energy density of ghost dark energy, which originates from Veneziano ghost of QCD, is proportional to the Hubble parameter, $\rho_D=\alpha H$, where $\alpha$ is a constant which is related to the QCD mass scale. In this paper, we establish the correspondence between ghost dark energy and quintessence scalar field energy density. This connection allows us to reconstruct the potential and the dynamics of the quintessence scalar field according to the evolution of ghost energy density.Comment: 8 pages, 7 figures, version to appear in Europhys. Let

The Cognitive Compressive Sensing Problem

In the Cognitive Compressive Sensing (CCS) problem, a Cognitive Receiver (CR) seeks to optimize the reward obtained by sensing an underlying $N$ dimensional random vector, by collecting at most $K$ arbitrary projections of it. The $N$ components of the latent vector represent sub-channels states, that change dynamically from "busy" to "idle" and vice versa, as a Markov chain that is biased towards producing sparse vectors. To identify the optimal strategy we formulate the Multi-Armed Bandit Compressive Sensing (MAB-CS) problem, generalizing the popular Cognitive Spectrum Sensing model, in which the CR can sense $K$ out of the $N$ sub-channels, as well as the typical static setting of Compressive Sensing, in which the CR observes $K$ linear combinations of the $N$ dimensional sparse vector. The CR opportunistic choice of the sensing matrix should balance the desire of revealing the state of as many dimensions of the latent vector as possible, while not exceeding the limits beyond which the vector support is no longer uniquely identifiable.Comment: 8 pages, 2 figure

Graded Betti numbers of powers of ideals

Using the concept of vector partition functions, we investigate the asymptotic behavior of graded Betti numbers of powers of homogeneous ideals in a polynomial ring over a field. Our main results state that if the polynomial ring is equipped with a positive \ZZ-grading, then the Betti numbers of powers of ideals are encoded by finitely many polynomials. More precisely, in the case of \ZZ-grading, \ZZ^2 can be splitted into a finite number of regions such that each region corresponds to a polynomial that depending to the degree $(\mu, t)$, \dim_k \left(\tor_i^S(I^t, k)_{\mu} \right) is equal to one of these polynomials in $(\mu, t)$. This refines, in a graded situation, the result of Kodiyalam on Betti numbers of powers of ideals. Our main statement treats the case of a power products of homogeneous ideals in a \ZZ^d-graded algebra, for a positive grading.Comment: 20 page