Zahid Raza

Cylindrically symmetric solutions in f(R,T) gravity

The main purpose of this paper is to investigate the exact solutions of cylindrically symmetric spacetime in the context of f(R,T) gravity (Harko et al. in Phys. Rev. D 84:024020, 2011), where f(R,T) is an arbitrary function of Ricci scalar R and trace of the energy momentum tensor T. We explore the exact solutions for two different classes of f(R,T) models. The first class f(R,T)=R+2f(T) yields a solution which corresponds to an exterior metric of cosmic string while the second class f(R,T)=f1(R)+f2(T) provides an additional solution representing a non-null electromagnetic field. The energy densities and corresponding functions for f(R,T) models are evaluated in each case.

Admissible local systems for a class of line arrangements

A rank one local system λ on a smooth complex algebraic variety M is admissible if roughly speaking the dimension of the cohomology groups H m (M, L) can be computed directly from the cohomology algebra H(M,C). We say that a line arrangement A is of type C k for some k > 0 if k is the minimal number of lines in A containing all the points of multiplicity at least 3. We show that if A is a line arrangement in the classes C k for k < 2, then any rank one local system L on the line arrangement complement M is admissible. Partial results are obtained for the class C 3 .

Gravitational Dust Collapse in f (R) Gravity

This paper is devoted to investigate gravitational collapse of dust in metric f(R) gravity. We take FRW metric for the interior region while the Schwarzchild spacetime is considered for the exterior region of a star. The junction conditions have been derived to match interior and exterior spacetimes. The assumption of constant scalar curvature is used to find a solution of field equations. Gravitational mass is found by using the junction conditions. It is concluded that the constant curvature term f(R0) plays the role of the cosmological constant involved in the field equations of general relativity.

FURTHER INEQUALITIES BETWEEN VERTEX-DEGREE-BASED TOPOLOGICAL INDICES

Topological indices play an important role in mathematical chemistry especially in the quantitative structure–property relationship and quantitative structure–activity relationship studies. Recent research indicates that the augmented Zagreb index (AZI) possess the best correlating ability among several topological indices to predict the certain physico-chemical properties of particular types of molecules. In the present work, several novel bounds (lower and upper) for the AZI in terms of first geometric–arithmetic index, Randić index, atom-bond connectivity index, sum-connectivity index, modified second Zagreb index and harmonic index are established. Moreover, the geometric–arithmetic index and modified second Zagreb index are also among the well known topological indices. Various relations between these two topological indices and some of the aforementioned indices are also derived.

Quasi-linear Quotients and Shellability of Pure Simplicial Complexes

For a square-free monomial ideal I ⊂ S = k[x 1, x 2,…, x n ], we introduce the notion of quasi-linear quotients. By using the quasi-linear quotients, we give a new algebraic criterion for the shellability of a pure simplicial complex Δ over [n]. Also, we provide a new criterion for the Cohen–Macaulayness of the face ring of a pure simplicial complex Δ. Moreover, we show that the face ring of the spanning simplicial complex (defined in [2]) of an r-cyclic graph is Cohen–Macaulay.

Spanning Simplicial Complexes of Uni-Cyclic Graphs

In this paper, we introduce the concept of the spanning simplicial complex Δs(G) associated to a simple finite connected graph G. We characterize all spanning trees of the uni-cyclic graph Un,m. In particular, we give a formula for computing the Hilbert series and h-vector of the Stanley-Reisner ring k[Δs(Un,m)]. Finally, we prove that the spanning simplicial complex Δs(Un,m) is shifted and hence is shellable.

Dust Static Cylindrically Symmetric Solutions in f(R) Gravity

This paper is devoted to investigate non-vacuum solutions of cylindrically symmetric spacetime in the context of metric f(R) gravity. We take dust matter to find energy density of the universe. In particular, we find two exact solutions, which correspond to two f(R) models in each case. The first solution provides constant curvature while the second solution corresponds to non-constant curvature. The functions of the Ricci scalar and energy densities are evaluated in each case.

Bond incident degree (BID) indices of polyomino chains

This work is devoted to establish a general expression for calculating the bond incident degree (BID) indices of polyomino chains and to characterize the extremal polyomino chains with respect to several well known BID indices. From the derived results, all the results of the papers (An and Xiong, 2016, Deng etźal., 2014, Yarahmadi etźal., 2012) and some results of the papers (Rada, 2014, Ali etźal., 2015) are obtained as corollaries.

Bounds for the general sum-connectivity index of composite graphs

The general sum-connectivity index is a molecular descriptor defined as χα(X)=∑xy∈E(X)(dX(x)+dX(y))α

ON THE UNITARY UNITS OF THE GROUP ALGEBRA &#x1d53d;2mM16

\chi_{\alpha}(X)=\sum_{xy\in E(X)}(d_{X}(x)+d_{X}(y))^{\alpha}