We present fermionic quasi-particle sum representations for some of the characters (or branching functions) of the characters are written as the partition function of a set of rank G types of massless quasi-particles in certain charge sectors, with nontrivial lower bounds on the one-particle momenta. We discuss the non-uniqueness of the representation for the identity character of the critical ...

We report on a quasi-planar quantum-dot-based single-photon source that shows an unprecedented high extraction efficiency of 42% without complex photonic resonator geometries or post-growth nanofabrication. This very high efficiency originates from the coupling of the photons emitted by a quantum dot to a Gaussian shaped nanohill defect that naturally arises during epitaxial growth in a self-al...

Let G be the discrete group of orientation preserving diffeomorphisms of the circle, and let H be the subgroup of diffeomorphisms which are the identity in a neighborhood of a given point. It is proved that there is a short exact sequence in the integral homology of groups O-Hz(H)Hz(G) SZ-0. The epimorphism E can be identified with the Euler class for transversally foliated circle bundles. The ...

We show that the epimorphism problem is solvable for targets are virtually cyclic or a product of an Abelian group and finite group.

In this paper we study the problem of deciding the existence of a subgraph epimorphism between two graphs. Our interest in this variant of graph matching problem stems from the study of model reductions in systems biology, where large systems of biochemical reactions can be naturally represented by bipartite digraphs of species and reactions. In this setting, model reduction can be formalized a...

A Lie version of Turaev’s G-Frobenius algebras from 2-dimensional homotopy quantum field theory is proposed. The foundation for this Lie version is a structure we call a g-quasi-Frobenius Lie algebra for g a finite dimensional Lie algebra. The latter consists of a quasi-Frobenius Lie algebra (q, β) together with a left g-module structure which acts on q via derivations and for which β is g-inva...

Let R be a ring. A right R-module is said to C-flat if the kernel of any epimorphism B → C-pure in B, i.e. induced map Hom(C,B) Hom(C,A) surjective for cyclic C. Projective modules are and weakly-flat neat-flat. In this article, it discussed connections between C-flat, weakly-flat, neat-flat singly flat modules. It shown that coincide with singly-projective over arbitrary rings. Next, several c...

A lattice L is projective in a variety V of lattices if whenever f : K L is an epimorphism, there is a homomorphism g : L→ K such that f(g(a)) = a for all a ∈ L. Note g is one-to-one and ρ = gf : K→ K is a retraction of K; that is, ρ is an endomorphism of K and ρ2 = ρ. The sublattice ρ(K) = g(L) of K is isomorphic to L. The image g(L) is a retract of K. In a slight abuse of terminology, we will...

In this paper we obtain a number of [70,35,12] singly even self-dual codes as a quasi-cyclic codes with m=2 (tailbitting convolutional codes). One of them is the first known code with parameters Beta=140 Gamma=0. All codes are not pure double circulant i.e. could not be represented in systematic form. Keywords—convolutional encoding, quasi-cyclic codes weight enumeratorg, double circulant