math updates on arXiv.orgMathematics (math) updates on the arXiv.org e-print archiveJet and prolongation spaces. (arXiv:0806.4196v1 math.LO)- (Found June 29, 2008 ) The notion of prolongation of an algebraic variety is developed in an abstract setting that generalises the difference and (Hasse) differential contexts. An interpolating map that compares the prolongation spaces with algebraic jet spaces is introduced and studied.http://arxiv.org/abs/0806.4196 Convex functions on Grassmannian manifolds and Lawson-Osserman problem. (arXiv:0806.4247v1 math.DG)- (Found June 29, 2008 ) We derive estimates of the Hessian of two smooth functions defined on Grassmannian manifold. Based on it, we can derive curvature estimates for minimal submanifolds in Euclidean space via Gauss map. In this way, the result for Bernstein type theorem done by Jost and the first author could be improved.http://arxiv.org/abs/0806.4247 Entropy of meromorphic maps and dynamics of birational maps. (arXiv:0806.4284v1 math.DS)- (Found June 29, 2008 ) We study the dynamics of meromorphic maps for a compact Kaehler manifold X. More precisely, we give a simple criterion that allows us to produce a measure of maximal entropy. We can apply this result to bound the Lyapunov exponents. Then, we study the particular case of a family of generic birational maps of Pk for which we construct the Green currents and the equilibrium measure. We use for that the theory of super-potentials. We show that the measure is mixing and gives no mass to pluripolar.http://arxiv.org/abs/0806.4284 Dynamic programming for infinite horizon boundary control problems of PDE's with age structure. (arXiv:0806.4278v1 math.OC)- (Found June 29, 2008 ) We develop the dynamic programming approach for a family of infinite horizon boundary control problems with linear state equation and convex cost. We prove that the value function of the problem is the unique regular solution of the associated stationary Hamilton--Jacobi--Bellman equation and use this to prove existence and uniqueness of feedback controls. The idea of studying this kind of problem comes from economic applications, in particular from models of optimal investment with vintage...http://arxiv.org/abs/0806.4278 Complex Spaces and Nonstandard Schemes. (arXiv:0806.4271v1 math.AG)- (Found June 29, 2008 ) We apply methods of nonstandard mathematics in order to regard analytic geometry in a very different way. For example, complex spaces are seen to be the "standard part" of certain algebraic nonstandard schemes. We construct a category of such schemes, sitting in between usual algebraic schemes (over the complex numbers) and that of complex spaces. We clarify the structure of prime ideals in a Stein algebra, coming from nonstandard points and show in particular that ANY maximal and minimal prime.http://arxiv.org/abs/0806.4271 On the Birch and Swinnerton-Dyer conjecture for elliptic curves over ring class fields. (arXiv:0806.4267v1 math.NT)- (Found June 29, 2008 ) Let E be a rational elliptic curve of conductor N without complex multiplication and let K be an imaginary quadratic field of discriminant D prime to N. Assume that the number of primes dividing N and inert in K is odd, and let H be the ring class field of K of conductor c prime to ND with Galois group G over K. Fix a complex character chi of G. Our main result is that if the special value of the chi-twisted L-function of EK is non-zero then the tensor product (with respect to chi) of the...http://arxiv.org/abs/0806.4267 Online network coding for optimal throughput and delay -- the two-receiver case. (arXiv:0806.4264v1 cs.IT)- (Found June 29, 2008 ) For a packet erasure broadcast channel with two receivers, a new coding algorithm is proposed that makes use of feedback to achieve asymptotically optimal queue size at the sender and decoding delay at the receivers, without compromising on throughput. Our coding module is compatible with the drop-when-seen queuing algorithm proposed in earlier work -- Sundararajan et al. (ISIT 2008). Hence, it guarantees that the physical queue size at the sender tracks the backlog in degrees of freedom. In...http://arxiv.org/abs/0806.4264 The notion of $psi$-weak dependence and its applications to bootstrapping time series. (arXiv:0806.4263v1 math.PR)- (Found June 29, 2008 ) We give an introduction to a notion of weak dependence which is more general than mixing and allows to treat for example processes driven by discrete innovations as they appear with time series bootstrap. As a typical example, we analyze autoregressive processes and their bootstrap analogues in detail and show how weak dependence can be easily derived from a contraction property of the process. Furthermore, we provide an overview of classes of processes possessing the property of weak...http://arxiv.org/abs/0806.4263 A strong antidiamond principle compatible with CH. (arXiv:0806.4220v1 math.LO)- (Found June 29, 2008 ) A strong antidiamond principle (c) is shown to be consistent with CH. This principle can be stated as a "P-ideal dichotomy": every P-ideal on omega-1 (i.e. an ideal that is sigma-directed under inclusion modulo finite) either has a closed unbounded subset of omega-1 locally inside of it, or else has a stationary subset of omega-1 orthogonal to it. We rely on Shelah's theory of parameterized properness for NNR iterations, and make a contribution to the theory with a method of constructing the...http://arxiv.org/abs/0806.4220 Scalar Quantization for Audio Data Coding. (arXiv:0806.4293v1 cs.MM)- (Found June 29, 2008 ) This paper is concerned with scalar quantization of transform coefficients in an audio codec. The generalized Gaussian distribution (GGD) is used as an approximation of one-dimensional probability density function for transform coefficients obtained by modulated lapped transform (MLT) or modified cosine transform (MDCT) filterbank. The rationale of the model is provided in comparison with theoretically achievable rate-distortion function. The rate-distortion function computed for the random...http://arxiv.org/abs/0806.4293 |