Growth rate for beta-expansions

Let β > 1 and let m > β be an integer. Each x ? I_b:=[0,\fracm-1b-1]{x\in I_\beta:=[0,\frac{m-1}{\beta-1}]} can be represented in the form

Growth rate of the functions in Bergman type spaces

For 0<p,α<∞, let ‖f‖_p,α be the L^p-norm with respect the weighted measure . We define the weighted Bergman space A_α^p(D) consisting of holomorphic functions f with ‖f‖_p,α<∞. For any σ>0, let A^−σ(D) be the space consisting of holomorphic functions f in D with . If D has C² boundary, then we have the embedding A_α^p(D)⊂A^−(n+α)/p(D). We show that the condition of C²-smoothness of the boundary of D is necessary by giving a counter-example of a convex domain with C^1,λ-smooth boundary for 0<λ<1 which does not satisfy the embedding.     

Growth rate of the Schrödinger group on Zhidkov spaces

We give an upper bound on the growth rate of the Schrödinger group on Zhidkov spaces. In dimension 1, we prove that this bound is sharp. To cite this article: C. Gallo, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Growth rate of the state vector in a generalized linear stochastic system with a symmetric matrix

The mean growth rate of the state vector is evaluated for a generalized linear stochastic second-order system with a symmetric matrix. Diagonal entries of the matrix are assumed to be independent and exponentially distributed with different means, while the off-diagonal entries are equal to zero. Bibliography: 7 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 341, 2007, pp. 134–141.     

Convergence rate for consensus with delays

We study the problem of reaching a consensus in the values of a distributed system of agents with time-varying connectivity in the presence of delays. We consider a widely studied consensus algorithm, in which at each time step, every agent forms a weighted average of its own value with values received from the neighboring agents. We study an asynchronous operation of this algorithm using delayed agent values. Our focus is on establishing convergence rate results for this algorithm. In particular, we first show convergence to consensus under a bounded delay condition and some connectivity and intercommunication conditions imposed on the multi-agent system. We then provide a bound on the time required to reach the consensus. Our bound is given as an explicit function of the system parameters including the delay bound and the bound on agents’ intercommunication intervals.     

Error estimates for low rate codes

Summary Gallager [1] and Gallager, Shannon, Berlekamp [2] establish exponentially decreasing upper and lower bounds, respectively, on the error of the best codes for fixed code rates R smaller than the capacity for the standard channels (stationary finite alphabet channels without memory). These bounds happen to coincide up to the first order for rates near to the capacity.The authors of [2] regret that their proof of the lower bound cannot be extended to infinite alphabet channels or nonstationary channels because of the use of fixed composition codes (while the proofs of the upper estimate can be easily transferred to those channels).Changing parts of the proof in [2], we automatically obtain estimates of the same type as in [2] for the latter channels.Furthermore, as a matter of minor importance, we show that the order of coincidence of upper and lower bound for the high rates R can be rigorously improved.I would like to thank Johan H. B. Kemperman for a very stimulating discussion and for pointing out a gap in my original proof.     

Growth Sequences for Circle Diffeomorphisms

We obtain results on the growth sequences of the differential for iterations of circle diffeomorphisms without periodic points. Received: June 2005 Revision: December 2005 Accepted: February 2006     

A rate of convergence for asymptotic contractions

In [P. Gerhardy, A quantitative version of Kirk's fixed point theorem for asymptotic contractions, J. Math. Anal. Appl. 316 (2006) 339-345], P. Gerhardy gives a quantitative version of Kirk's fixed point theorem for asymptotic contractions. This involves modifying the definition of an asymptotic contraction, subsuming the old definition under the new one, and giving a bound, expressed in the relevant moduli and a bound on the Picard iteration sequence, on how far one must go in the iteration sequence to at least once get close to the fixed point. However, since the convergence to the fixed point needs not be monotone, this theorem does not provide a full rate of convergence. We here give an explicit rate of convergence for the iteration sequence, expressed in the relevant moduli and a bound on the sequence. We furthermore give a characterization of asymptotic contractions on bounded, complete metric spaces, showing that they are exactly the mappings for which every Picard iteration sequence converges to the same point with a rate of convergence which is uniform in the starting point.     

The rate of convergence for subexponential distributions

A distribution functionF on the nonnegative real line is called subexponential if

Blow-up rate for a nonlinear diffusion equation

In this work we study the blow-up rate for a nonlinear diffusion equation with an inner source and a nonlinear boundary flux, which is equivalent to a porous medium equation with convection. Depending upon the sign of a parameter included, the source can be positive or negative (absorption). By the scaling method, we obtain that the blow-up rate is independent of a negative source, while for the situation with a positive source, the blow-up rate is determined by the interaction between the inner source and the boundary flux. Comparing with the previous results for the porous medium model without convection, we observe that the gradient term included here does not affect the blow-up rates of solutions.     

Growth diagrams for the Schubert multiplication

We present a partial generalization of the classical Littlewood-Richardson rule (in its version based on Schützenberger's jeu de taquin) to Schubert calculus on flag varieties. More precisely, we describe certain structure constants expressing the product of a Schubert and a Schur polynomial. We use a generalization of Fomin's growth diagrams (for chains in Young's lattice of partitions) to chains of permutations in the so-called k-Bruhat order. Our work is based on the recent thesis of Beligan, in which he generalizes the classical plactic structure on words to chains in certain intervals in k-Bruhat order. Potential applications of our work include the generalization of the S₃-symmetric Littlewood-Richardson rule due to Thomas and Yong, which is based on Fomin's growth diagrams.     

Growth tightness for word hyperbolic groups

We show that non-elementary word hyperbolic groups are growth tight. This means that, given such a group G and a finite set A of its generators, for any infinite normal subgroup N of G, the exponential growth rate of G/N with respect to the natural image of A is strictly less than the exponential growth rate of G with respect to A. Received: 20 September 2001; in final form: 24 January 2002/ Published online: 5 September 2002 The work has been supported by the Swiss National Science Foundation. The second author has been supported also by INTAS, grant No. 97–1259     

Logarithmic Growth for Matrix Martingale Transforms

An example is given of an operator weight W that satisfies thedyadic operator Hunt–Muckenhoupt–Wheeden condition for which there exists a dyadic martingale transform on L² (W) that is unbounded. The constructionrelates weighted boundedness to the boundedness of dyadic vectorHankel operators.     

能源对中国经济增长制约作用的实证研究

本文从理论和实证角度研究了中国GDP和能源消费的动态关系,通过对GDP与能源消费格兰杰因果关系的检验,发现两者之间存在着单向因果关系,经济增长导致能源消费的增加;通过对GDP与能源消费的协整检验和建立误差修正模型发现:中国GDP与能源消费之间存在着协整关系,误差修正模型显示了两者之间的长期均衡机制,长短期能源弹性系数说明,从长期来看,能源并不会成为经济增长的“瓶颈”,但必须注意能源对经济发展方式的影响,制定中长期规划来引导经济结构和能源产业的结构调整。