Given (M,Ω) a calibrated Riemannian manifold with a parallel calibration of rank m, and M an immersed orientable submanifold with parallel mean curvature H we prove that if cos θ is bounded away from zero, where θ is the Ω-angle of M , and if M has zero Cheeger constant, then M is minimal. In the particular case M is complete with Ricc ≥ 0 we may replace the boundedness condition on cos θ by co...

Cheng Zhao∗, Yuejian Peng, Indiana State University In 1965, Motzkin and Straus establishes a remarkable connection between the maximum clique problem and the extrema of the Lagrangian of a graph. It is interesting to study a generalization of the Motzkin-Straus Theorem to hypergraphs. In this paper, we give some Motzkin-Straus type results.

Motivated by the Cauchy-Davenport theorem for sumsets, and its interpretation in terms of Cayley graphs, we prove the following main result: There is a universal constant � > 0 such that, if G is a connected, regular graph on n vertices, then either every pair of vertices can be connected by a path of length at most three, or the number of pairs of such vertices is at least 1 + � times the numb...

We prove a Bombieri-Vinogradov type result for linear exponential sums over primes. Then we apply it to show that, for any irrational α and some θ > 0, there are infinitely many primes p such that p+ 2 has at most two prime factors and ‖αp+ β‖ < p−θ.

Let {Xk , k ∈ Z} be a zero mean d-dimensional stationary process, and let Sn,d = (Sn,1, Sn,2, . . . , Sn,d ) T with Sn,h = 1 √ n n k=1 Xk,h , where Xk,h denotes the single components of {Xk , k ∈ Z}. Under a weak dependence condition, we show that the ellipsoid Xd = max1≤k≤d (2k) −1/2 |ST n,kΓ −1 k Sn,k − k| follows a Darling–Erdös type law as d → ∞, i.e., Xd converges to a Gumbel-type distrib...

An artin algebra A is said to be CM-finite if there are only finitely many, up to isomorphisms, indecomposable finitely generated Gorenstein-projective A-modules. We prove that for a Gorenstein artin algebra, it is CM-finite if and only if every its Gorenstein-projective module is a direct sum of finitely generated Gorenstein-projective modules. This is an analogue of Auslander’s theorem on alg...

The most commonly type 1 diabetes mellitus caused by destruction of b cell pancreatic leading to inadequate insulin production. Clinical and laboratory features at the times of diagnosis have been widely studied. We reviewed the clinical appearance of Type 1 Diabetes Mellitus in patients were diagnosed in the Pediatric Department of Saiful Anwar Hospital between 2005 and 2009. The study has bee...