We investigate the Hasse principles for isotropy and isometry of quadratic forms over finitely generated field extensions with respect to various sets discrete valuations. Over purely transcendental fields that satisfy property $\mathscr{A}_i(2)$ some $i$, we find numerous counterexamples principle a relatively small set For $K$ transcendence degree $r$ an algebraically closed characteristic $\...

The Bergman tau functions are applied to the study of Picard group moduli spaces quadratic differentials with at most $n$ simple poles on genus $g$ complex algebraic curves. This generalizes our previous results holomorphic differentials.

In this paper, we will study a partial sum modulus distribution for specific natural number set using dynamically sliding window. Then construct cubic equation from and formula to calculate zero. go through some applications of Cubic the basic algebraic concepts explain numbers.
 
 First part in interduce sums numbers dynamic window as parameter explore distribution. As simpler way st...

In this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual Interior Point Method (IPM) based on a new kernel function with a trigonometric barrier term. Iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. Although our proposed kernel function is neither a Self-Regular (SR) fun...

Corrections to solar system gravity are derived for f(G) gravity theories, in which a function of the Gauss-Bonnet curvature term is added to the gravitational action. Their effects on Newton’s law, as felt by the planets, and on the frequency shift of signals from the Cassini spacecraft, are both determined. Despite the fact that the Gauss-Bonnet term is quadratic in curvature, the resulting c...

In the talk I first explained how we came up with this conjecture in an attempt to prove a conjecture on a refined enumeration of vertically symmetric alternating sign matrices. An alternating sign matrix is a quadratic 0, 1,−1 matrix such that the non-zero entries alternate and sum up to 1 in each row and column. Next we give an example of such an object  0 0 1 0 0 1 0 −1 0 1 0 0 1 0 0 0...

The Orlik-Solomon algebra A of a matroid is isomorphic to the quotient of an exterior algebra E by a defining ideal I . We find an explicit presentation of the annihilator ideal of I or, equivalently, the E-module dual to A. As an application of that we provide a necessary, combinatorial condition for the algebra A to be quadratic. We show that this is stronger than matroid being line-closed th...