Analytical solutions of precise equations that describe the rf-coupling of two cavities through a co-axial cylindrical hole are given for various limited cases. For their derivation we have used the method of solution of an infinite set of linear algebraic equations, based on its transformation into dual integral equations.

We present a Lie algebraic framework for vortex sheets as singular 2-forms with support of codimension 1, i.e. singular elements of a completion of the dual to the Lie algebra of divergence-free vector fields. This framework allows one to define the Poisson and symplectic structures on the space of vortex sheets, which interpolate between the corresponding structures on filaments and smooth vor...

The Cuntz algebra carries in a natural way the structure of a module algebra over the quantized universal enveloping algebra Uq(g), and the structure of a co-module algebra over the quantum group Gq associated with Uq(g). These two algebraic structures are dual to each other via the duality between Gq and Uq(g).

For proving linear independence of real numbers, Hermite [18] considered simultaneous approximation to these numbers by algebraic numbers. The point of view introduced by Siegel in 1929 [34] is dual (duality in the sense of convex bodies): he considers simultaneous approximation by means of independent linear forms. We define the height of a linear form L = a0X0 + · · · + amXm with complex coef...

We investigate the geometry of the support of small weight codewords of dual algebraic geometric codes on smooth complete intersections by applying the powerful tools recently developed by Alain Couvreur. In particular, by restricting ourselves to the case of Hermitian codes, we recover and extend previous results obtained by the second named author joint with Marco Pellegrini and Massimiliano ...

The conception of multi-alphabetical genetics is considered. Matrix forms of the representation of the multi-level system of molecular-genetic alphabets have discovered algebraic properties of this system. These properties are connected with well-known notions of dyadic groups and dyadic-shift matrices. Matrix genetics shows relations of the genetic alphabets with some types of hypercomplex num...

A conformal partition function Pm n (s), which arose in the theory of Diophantine equations supplemented with additional restrictions, is concerned with self-dual symmetric polynomials – reciprocal R {m} Sn and skew-reciprocal S {m} Sn algebraic polynomials based on the polynomial invariants of the symmetric group Sn. These polynomials form an infinite commutative semigroup. Real solutions λn(x...

We introduce and study a transfer map between ideals of the universal enveloping algebras of two members of a reductive dual pair of Lie algebras. Its definition is motivated by the approach to the real Howe duality through the theory of Capelli identities. We prove that this map provides a lower bound on the annihilators of theta lifts of representations with a fixed annihilator ideal. We also...

Canonical extensions of lattice ordered algebras provide an algebraic formulation of what is otherwise treated via topological duality or relational methods. They were firstly introduced by Jónsson and Tarski for Boolean algebras with operators (see [8] and [9]) and generalized for distributive lattices with different operations in [5], [4] and [3]. If A = (A, {fi, i ∈ I}) is a distributive lat...

It is well known that a convolutional code is essentially a linear system defined over a finite field. In this paper we elaborate on this connection. We define a convolutional code as the dual of a complete linear behavior in the sense of Willems (1979). Using ideas from systems theory, we describe a set of generalized first-order descriptions for convolutional codes. As an application of these...