The faithful quasi-dual H and strict quasi-dual H ′ of an infinite braided Hopf algebra H are introduced and it is proved that every strict quasi-dual H ′ is an HHopf module. The connection between the integrals and the maximal rational Hsubmodule H of H is found. That is, H ∼= ∫ l H ⊗H is proved. The existence and uniqueness of integrals for braided Hopf algebras in the Yetter-Drinfeld categor...

The automorphism group of a binary doubly-even self-dual code is always contained in the alternating group. On the other hand, given a permutation group G of degree n there exists a doubly-even self-dual G-invariant code if and only if n is a multiple of 8, every simple self-dual F2G-module occurs with even multiplicity in F n 2 , and G is contained in the alternating group.

A triangular matrix ring Λ is defined by a triplet (R, S, M) where R and S are rings and RMS is an S-R-bimodule. In the main theorem of this paper we show that if TS is a tilting S-module, then under certain homological conditions on the S-module MS , one can extend TS to a tilting complex over Λ inducing a derived equivalence between Λ and another triangular matrix ring specified by (S′, R, M ...

We recently succeeded in producing nanostructures made of RNA-protein (RNP) complexes. We show that RNA and the ribosomal protein L7Ae can form a triangular-like nanostructure that consists of three L7Ae proteins, which form the apices of the triangle, bound to one RNA scaffold. This shape is created through a 60° kink introduced into the RNA structure on L7Ae binding. By varying the size of th...

We introduce a spanning set of BLM type, {A(j, r)}A,j, for affine quantum Schur algebras S△(n, r) and construct a linearly independent set {A(j)}A,j for an associated algebra K̂△(n). We then establish explicitly some multiplication formulas of simple generators E △ h,h+1(0) by an arbitrary element A(j) in K̂△(n) via the corresponding formulas in S△(n, r), and compare these formulas with the multi...

This paper investigates the design, measurement and characteristics of a probe-fed dual patch equilateral triangular antenna. A lossless foam material is sandwiched between the two patches to provide a mechanically stable and uniform height. It is shown that the separation height between the two patches plays a significant role in improving the impedance bandwidth of the antenna. A bandwidth of...

We show that the characters of all highest weight modules over an affine Lie algebra with the highest weight away from the critical hyperplane are meromorphic functions in the positive half of the Cartan subalgebra, their singularities being at most simple poles at zeros of real roots. We obtain some information about these singularities. 0. Introduction 0.0.1. Let g be a simple finite-dimensio...

Graphs composed of node and link are the most common way of representing street networks for any analysis beyond pure visual representation. The intuitive primal approach to convert a physical street network into an abstract mathematical graph is mapping street intersections as nodes while mapping street segments between intersections as links connecting nodes in the graph. Correspondingly, a d...

The existence and construction of self-dual codes in a permutation module of a finite group for the semisimple case are described from two aspects, one is from the point of view of the composition factors which are self-dual modules, the other one is from the point of view of the Galois group of the coefficient field.

For a module V over a finite semisimple algebra A we give the total number of self-dual codes in V . This enables us to obtain a mass formula for self-dual codes in permutation representations of finite groups over finite fields of coprime characteristic.