where A and B are some explicit constants. This provides an asymptotic formula for M(p, q) − √ p/qM(−q, p) under the condition that p ≪ q2/3−ε. The error term above was improved by Young [6] so that the asymptotic formula holds for p ≪ q1−ε. In this paper, we consider the twisted moments of the families of L-functions arising from S∗ 2 (p) and S∗ 2 (q), the sets of primitive Hecke eigenforms of...

We study a special class of binary trees. Our results have implications on Maker/Breaker games and SAT: We disprove a conjecture of Beck on positional games and construct an unsatisfiable k-CNF formula with few occurrences per variable, thereby improving a previous result by Hoory and Szeider and showing that the bound obtained from the Lovász Local Lemma is tight up to a constant factor. A (k,...

We prove a sharp isoperimetric inequality for the second nonzero eigenvalue of Laplacian on S m S^m ...

We prove that any odd dimensional geometric graph G = (V,E) has zero curvature everywhere. To do so, we prove that for every injective function f on the vertex set V of a simple graph the index formula 1 2 [1 − χ(S(x))/2 − χ(Bf (x))] = (if (x) + i−f (x))/2 = jf (x) holds, where if (x) is a discrete analogue of the index of the gradient vector field ∇f and where Bf (x) is a graph defined by G an...

Let ω \omega be a weight on right cancellative semigroup alttext="upper S"> S encoding="application/x-tex">S</...

let $n$ be a submodule of a module $m$ and a minimal primary decomposition of $n$ is known‎. ‎a formula to compute baer&apos;s lower nilradical of $n$ is given‎. ‎the relations between classical prime submodules and their nilradicals are investigated‎. ‎some situations in which semiprime submodules can be written as finite intersection of classical prime submodule are stated‎.

We prove a new formula for the Hirzebruch-Milnor classes of global complete intersections with arbitrary singularities describing the difference between the Hirzebruch classes and the virtual ones. This generalizes a formula for the Chern-Milnor classes in the hypersurface case that was conjectured by S. Yokura and was proved by A. Parusinski and P. Pragacz. It also generalizes a formula of J. ...

This paper presents a compact diierential formula for the rst derivative of a unit quaternion curve deened on SO(3) or S 3. The formula provides a convenient way to compute the angular velocity of a rotating 3D solid. We demonstrate the eeectiveness of this formula by deriving the diierential properties of various unit quaternion curves 4, 5, 6, 7, 8] at the curve end points.

Breast-feeding is the best method of feeding infants. In some cases, formula milk can be a suitable alternative, so this study aimed to compare the safety and nutritional adequacy of commonly available formula milks in the Iraqi market. An observational study for the commonly available formula milks was conducted in the largest supermarkets of Baghdad, Iraq, during January-March 2015. The macro...

TA-3037A, a new inhibitor of glutathione S-transferase was discovered in the fermentation broth of Streptomyces sp. TA-3037. It was purified by chromatography followed by solvent extraction and then isolated as yellow needles. TA-3037A has the molecular formula of C16H11NO4. It was competitive with the substrate, and the inhibition constant (Ki) was 4.9 microM.