Motivated by the work of Alzer and Richards \cite{ar}, here authors study the monotonicity and convexity properties of the function $$\Delta_{p,q} (r) = \frac{{E_{p,q}(r) - \left( {r'} \right)^p K_{p,q}(r) }}{{r^p }} - \frac{{E'_{p,q}(r) - r^p K'_{p,q}(r) }}{{\left( {r'} \right)^p }},$$ where $K_{p,q}$ and $E_{p,q}$ denote the complete $(p,q)$- elliptic integrals of the first and the second kind, respectively.

Barkat Ali Bhayo Li Yin

It is shown that, under certain conditions, the existence of a Killing spinor on a bosonic background of a supergravity theory implies that the Einstein equations are also satisfied. As an application of the theorem, we obtain a new black fivebrane solution of D=11 supergravity, which has $K3\times R$ topology and preserves 1/4'th supersymmetries of the theory.

Ali Kaya

The idea of applying the gauge principle to formulate the general theory of relativity started with Utiyama in 1956. I review various applications of the gauge principle applied to different aspects of the gravitational interactions.

Ali H. Chamseddine

We prove that the criterion for Markov equivalence provided by Zhao et al. (2005) may involve a set of features of a graph that is exponential in the number of vertices.

R. A. Ali T. Richardson P. Spirtes

Tangent Spaces of V^r_d(L), Specific subschemes of C_d arising from various line bundles on C, are described. Then we proceed to prove Martense Theorem for these schemes, by which we determine curves C, which for some very ample line bundle L on C and some integers r and d with d\leq h^{0}(L)-2, the subscheme V^r_d(L) might attain its maximum dimension.

Ali Bajravani

We prove a conjecture of Miller and Reiner on the existence of Smith normal form for the $DU$-operators for a certain class of $r$-differential posets.

Syed Waqar Ali Shah

We determine non hyper elliptic curves of genus $g(C)\geq 9$, such that for some very ample line bundle on them and for some integers d and r with some prescribed assumptions, the dimension of secant loci, attains one less than its maximum value. Then we proceed to generalize and extend a problem of M. Coppens to Secant Loci.

Ali Bajravani

We introduce partial $r$-Bell polynomials in three combinatorial Hopf algebras. We prove a factorization formula for the generating functions which is a consequence of the Zassenhauss formula.

Ali Chouria Jean-Gabriel Luque

We use quotients of span categories to introduce the language of a topos. We also study the logical relations and the quotients of span categories derived from them. As an application we show that the category of Boolean toposes is a reflective subcategory of the category of toposes, when the morphisms are logical functors.

M. Golshani A. R Shir Ali Nasab

We establish sharp pointwise estimates for the ground states of some singular fractional Schr\"odinger operators on relatively compact Euclidean subsets. The considered operators are of the type $(-\Delta)^{\alpha/2}|_\Om-c|x|^{-\alpha}$, where $(-\Delta)^{\alpha/2}|_\Om$ is the fraction-Laplacien on an open subset $\Om$ in $\R$ with zero exterior condition and $0<c\leq(\frac{d-\alpha}{2})^2$. The intrinsic ultracontractivity property for such operators is discussed as well and a sharp large time asymptotic for their heat kernels is derived.

Ali Beldi Nedra Belhajrhouma Ali BenAmor