We give some new results on sparse signal recovery in the presence of noise, for weighted spaces. Traditionally, were used dictionaries that have the norm equal to 1, but, for random dictionaries this condition is rarely satised. Moreover, we give better estimations then the ones given recently by Cai, Wang and Xu.

Continuing the work K. C. Das, I. Gutman, B. Furtula, On second geometric-arithmetic index of graphs, Iran. J. Math Chem., 1(2) (2010) 17-28, in this paper we present lower and upper bounds on the third geometric-arithmetic index GA3 and characterize the extremal graphs. Moreover, we give Nordhaus-Gaddum-type result for GA3.

We consider the class of polynomial differential equation x&= , 2(,)(,)(,)nnmnmPxyPxyPxy++++2(,)(,)(,)nnmnmyQxyQxyQxy++&=++. For where and are homogeneous polynomials of degree i. Inside this class of polynomial differential equation we consider a subclass of Darboux integrable systems. Moreover, under additional conditions we proved such Darboux integrable systems can have at most 1 limit cycle.

we derive the formulas of the maximal andminimal ranks of four real matrices $x_{1},x_{2},x_{3}$ and $x_{4}$in common solution $x=x_{1}+x_{2}i+x_{3}j+x_{4}k$ to quaternionmatrix equations $a_{1}x=c_{1},xb_{2}=c_{2},a_{3}xb_{3}=c_{3}$. asapplications, we establish necessary and sufficient conditions forthe existence of the common real and complex solutions to the matrixequations. we give the exp...

This paper reports on the minimization of the average waiting time of the customers in the M/G/1 queue with vacation. Explicit formula for the unknown service parameter of a particular customer has been obtained by considering the exhaustive service discipline in the case of multi-user with unlimited service system. Moreover, results in case of partially gated and gated service disciplines unde...

The whole plant of Biophytum petersianum was extracted with a mixture of water – alcohol (1:1) to evaluate its relaxant effect on aorta rings. In isolated Wistar rat tissue, the hydro-ethanolic extract (0.1; 0.25 and 0.5 mg/ml) non-competitively antagonized calcium chloride and high-K + - induced aorta contractions in a concentration-dependent manner. Moreover, the inhibition of noradr...

let $g$ be a $p$-group of nilpotency class $k$ with finite exponent $exp(g)$ and let $m=lfloorlog_pk floor$. we show that $exp(m^{(c)}(g))$ divides $exp(g)p^{m(k-1)}$, for all $cgeq1$, where $m^{(c)}(g)$ denotes the c-nilpotent multiplier of $g$. this implies that $exp( m(g))$ divides $exp(g)$, for all finite $p$-groups of class at most $p-1$. moreover, we show that our result is an improvement...

The purpose of the present study was to investigate the limits of irrigationwater salinity and soil water content for growth inhibition of vetiver. Moreover,different models were studied to describe the root water uptake and plant topgrowth under salinity and water stresses in a pot experiment. Irrigation treatmentsconsisted of three irrigation intervals (3, 6 and 9-day). The salinity levels of...

In this paper, we consider the projective special linear group $PSL_2(59)$ and construct some 1-designs by applying the Key-Moori method on $PSL_2(59)$. Moreover, we obtain parameters of these designs and their automorphism groups. It is shown that $PSL_2(59)$ and $PSL_2(59):2$ appear as the automorphism group of the constructed designs.