math updates on arXiv.orgMathematics (math) updates on the arXiv.org e-print archiveOn the Representation Theory of an Algebra of Braids and Ties. (arXiv:0801.3633v2 math.RT UPDATED)- (Found June 29, 2008 ) We consider the algebra $cal E_n(u)$ introduced by F. Aicardi and J. Juyumaya as an abstraction of the Yokonuma-Hecke algebra. We construct a tensor space representation for $cal E_n(u)$ and show that this is faithful. We use it to give a basis for $cal E_n(u)$ and to classify its irreducible representations.http://arxiv.org/abs/0801.3633 The canonical volume of threefolds of general type with $chi<1$. (arXiv:0704.1702v3 math.AG UPDATED)- June 29, 2008 We prove that the canonical volume $K3geq 130$ for all projective 3-folds of general type with $chi(mathcalO)leq 0$. This bound is sharp.http://arxiv.org/abs/0704.1702 Sums and Differences of Three k-th Powers. (arXiv:0806.4330v1 math.NT)- (Found June 29, 2008 ) Let k>2 be a fixed integer exponent and let theta > 910. We show that a positive integer N can be represented as a non-trivial sum or difference of 3 k-th powers, using integers of size at most B, in O(BthetaN110) ways, providing that N << B313. The significance of this is that we may take theta strictly less than 1. We also prove the estimate O(B10k), (subject to N << B) which is better for large k. The results extend to representations by an arbitrary fixed...http://arxiv.org/abs/0806.4330 Heat-flow monotonicity related to the Hausdorff--Young inequality. (arXiv:0806.4329v1 math.CA)- (Found June 29, 2008 ) It is known that if $q$ is an even integer then the $Lq(mathbbRd)$ norm of the Fourier transform of a superposition of translates of a fixed gaussian is monotone increasing as their centres "simultaneously slide" to the origin. We provide explicit examples to show that this monotonicity property fails dramatically if $q > 2$ is not an even integer. These results are equivalent, upon rescaling, to similar statements involving solutions to heat equations. Such considerations are natural given..http://arxiv.org/abs/0806.4329 The Charney-Davis conjecture for certain subdivisions of spheres. (arXiv:0806.4213v1 math.CO)- (Found June 29, 2008 ) Notions of sesquiconstructible complexes and odd iterated stellar subdivisions are introduced, and some of their basic properties are verified. The Charney-Davis conjecture is then proven for odd iterated stellar subdivisions of sesquiconstructible balls and spheres.http://arxiv.org/abs/0806.4213 More Constructions for Tur'an's (3, 4)-Conjecture. (arXiv:0806.4208v1 math.CO)- (Found June 29, 2008 ) For Tur'an's (3, 4)-conjecture, in the case of n = 3k+1 vertices, (.5)6k-1 non-isomorphic complexes are constructed that attain the conjecture. In the case of n = 3k+2 vertices, 6k-1 non-isomorphic complexes are constructed that attain the conjecture.http://arxiv.org/abs/0806.4208 Compact composition operators on $H2$ and Hardy-Orlicz spaces. (arXiv:0806.4206v1 math.FA)- (Found June 29, 2008 ) We compare the compactness of composition operators on $H2$ and on Orlicz-Hardy spaces $HPsi$. We show in particular that exists an Orlicz function $Psi$ such that $H3+eps subseteq HPsi subseteq H3$ for every $eps >0$, and a composition operator $C_phi$ which is compact on $H3$ and on $H3+eps$, but not compact on $HPsi$.http://arxiv.org/abs/0806.4206 A criterion of weak compactness for operators on subspaces of Orlicz spaces. (arXiv:0806.4204v1 math.FA)- (Found June 29, 2008 ) To appear in J. Funct. Spaces and Appl.http://arxiv.org/abs/0806.4204 Some examples of compact composition operators on $H2$. (arXiv:0806.4203v1 math.FA)- (Found June 29, 2008 ) To appear in J. Functional Analysishttp://arxiv.org/abs/0806.4203 The Secrecy Rate Region of the Broadcast Channel. (arXiv:0806.4200v1 cs.IT)- (Found June 29, 2008 ) In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers, while a wire-tapper also receives the transmitted signal. This model is motivated by wireless communications, where individual secure messages are broadcast over open media and can be received by any illegitimate receiver. The secrecy level is measured by equivocation rate at the eavesdropper. We first study the general (non-degraded) broadcast channel with...http://arxiv.org/abs/0806.4200 |