A mixed graph is called second kind hermitian integral (or HS-integral) if the eigenvalues of its Hermitian-adjacency matrix are integers. Eisenstein (0, 1)-adjacency Let ? be an abelian group. We characterize set S for which a Cayley Cay(?,S) HS-integral. also show that and only it

We investigate a generalization of many functional equations. Namely, we consider the following equation ?S f(x + y t) d?(t) ?(y) = f(x) h(y), x, ? S, where (S,+) is an abelian semigroup, surjective endomorphism E linear space over field K {R, C} and ?,? are combinations Dirac measures. Under appropriate conditions on based Stetkar?s result [9], find characterize solutions previous equation.

A graph is called integral, if its adjacency eigenvalues are integers. In this paper we determine integral quartic Cayley graphs on finite abelian groups. As a side result we show that there are exactly 27 connected integral Cayley graphs up to 11 vertices.

We prove the integral Hodge conjecture for one-cycles on a principally polarized complex abelian variety whose minimal class is algebraic. In particular, Jacobian of smooth projective curve over numbers satisfies one-cycles. The main ingredient lift Fourier transform to Chow groups. Similarly, we Tate separable closure finitely generated field. Furthermore, varieties satisfying such are dense i...

We study the density of integral points on punctured abelian surfaces. Linear growth rates are observed experimentally.

We offer an elementary proof of Pontryagin duality theorem for compact and discrete abelian groups. To this end we make use of an elementary proof of Peter-Weyl theorem due to Prodanov that makes no recourse to Haar integral. As a long series of applications of this approach we obtain proofs of Bohr von Neumann’s theorem on almost periodic functions, Comfort-Ross’ theorem on the description of ...

We consider the Wess-Zumino-Witten theory to obtain the functional integral bosonization of the Thirring-Wess model with an arbitrary regularization parameter. Proceeding a systematic of decomposing the Bose field algebra into gauge-invariantand gauge-noninvariant field subalgebras, we obtain the local decoupled quantum action. The generalized operator solutions for the equations of motion are ...

It has been conjectured that the Abelian projection of QCD is responsible for the confinement of color. Using a gauge independent definition of the Abelian projection (which does not employ any gauge fixing) we prove the Abelian dominance. In specific we prove that the gauge field configuration which contributes to the Wilson loop integral is precisely the gauge covariant part of the restricted...

Using algebraic and topological K-theory together with complex C∗-algebras, we prove that every abelian group may be realized as the centre of a strongly torsion generated group whose integral homology is zero in dimension one and isomorphic to two arbitrarily prescribed abelian groups in dimensions two and three.