On the limiting behavior of weighted partial sums for<Emphasis Type="Italic">B</Emphasis> valued martingale difference sequences

Let {X_n, n≥1} be a martingale difference sequence and {a _nk , 1⩽k⩽n,n⩾1} an array of constant real numbers. The limiting behavior of weighted partial sums ∑ _k=1 ⁿ a _nk X _k is investigated and some new results are obtained. Foundation item: Supported by the National Natural Sciene Foundation of China (No. 10071058 and No. 10071019) Biography: Gan Shi-xin (1939-), male, Prof lessor, research direction: martingale theory, probability limiting theory and Banach space geometry theory.     

A Note on the Multifractal Decomposition of Directed Graph Self Similar Sets

We investigated the directed graph self similar sets under some weak overlapping condition. We get the multifractal decomposition formulas for these sets, i. e.,dim Ku^a DimKu^a =f(a), where fis the multifractal spectral function of the directed graph self similar measure. Especially, the results improve that of Edgar and Mauldin to the case which allows certain overlapping.     

Convergence in the<Emphasis Type="Italic">r</Emphasis>-th mean and the Marcinkiewicz type weak law of large numbers for weighted sums of<Emphasis Type="Italic">L</Emphasis><Subscript>q</Subscript>-mixingale arrays

L _r convergence and convergence in probability for weighted sums ofL _q-mixingale arrays have been discussed and the Marcinkiewicz type weak law of large numbers forL _q-mixingale arrays has been obtained. Foundation item: Supported by the National Natural Science Foundation of China (10071058) Biography: Gan Shi-xin (1939-), male, Professor, research direction; martingale theory, probability limiting theory and Banach space geometry theory.     

Characterization of type<Emphasis Type="Italic">p</Emphasis> Banach spaces by the weak law of large numbers

For weighted sums of the form where {a _nj , 1 ⩽j⩽k _n ↑∞,n⩾1} is a real constant array and {X _aj , 1≤j≤k _{n, n}≥1} is a rowwise independent, zero mean, random element array in a real separable Banach space of typep, we establishL ^r convergence theorem and a general weak law of large numbers respectively, conversely, we characterize Banach spaces of typep in terms of convergence inr-th mean and probability for such weighted sums. Foundation item: Supported by the National Natural Science Foundation of China (No. 10071058) Biography: Gan Shi-xin (1939-), male, Professor, research direction: martingale theory, probability limiting theory and Banach space geometry theory.     

Vector-valued dirichlet-type functions on the unit ball of C n

The vector-valued Dirichlet-type spaces on the unit ball of C ⁿ is introduced. We discuss the pointwise multipliers of Dirichlet-type spaces. Sufficient conditions of the pointwise multipliers of are given. Finally, Rademacherp-type space is characterized by vector-valued sequence spaces. Foundation item: Supported by the National Natural Science Foundation of China (10371093) Biography: LI Ying-kui (1975-), male, Ph. D candidate, research direction: Banach space geometry and martingale theory.     

On <Emphasis Type="Italic">k</Emphasis>-error linear complexity of some explicit nonlinear pseudorandom sequences

Combining with the research on the linear complexity of explicit nonlinear generators of pseudorandom sequences, we study the stability on linear complexity of two classes of explicit inversive generators and two classes of explicit nonlinear generators. We present some lower bounds in theory on the k-error linear complexity of these explicit generatol＇s, which further improve the cryptographic properties of the corresponding number generators and provide very useful information when they are applied to cryptography.     

Strong Law of Large Numbers and Complete Convergence for Sequences of φ-Mixing Random Var, ables

We give some theorems of strong law of large numbers and complete convergence for sequences of φ-mixing random variables. In particular, Wittmann＇s strong law of large numbers and Teicher＇s strong law of large nnumbers for independent random variables are generalized to the case of φ -minxing random variables.     

A Biplurisubharmonic Characterization of AUMD Spaces

0 IntroductionTsTphaece bsas ihca vpirnogpe rttihees o Uf MthDe f u(n udnacmoenndtiatilo cnlaalss mofar Btianngaaclehdifferences) property were established by Burkholder[1 ,2].Later , Garling[3]introducedthe AUMDpropertyfor complexBanach spaces .Piasecki[4]obtained some geometric conditionsfor the AUMDspaces by using skew-plurisubharmonic func-tions recently.In this paper we use biplurisubharmonic func-tions to characterize the AUMDproperty of a complex Banachspace.The main method com…     

Almost sure convergence and complete convergence for the weighted sums of martingale differences

Let {(D _n, FFF_n),n/->1} be a sequence of martingale differences and {a _ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums are discussed. We also discuss complete convergence for the moving average processes underB-valued martingale differences assumption. Foundation item: Supported by the National Natural Science Foundation of China and the Doctoral Programme Foundation of China Biography: DENG Ai-jiao (1974-), female, Ph.D. candidate. Research interest is in stochastic processes and random fractal.     

The Hàjek-Rènyi inequlity for Banach space valued random variable sequences and its application

In this paper we prove the following Hàjek-Rènyi inequality: Let 0≤p≤1, then for any Banach spaceB, anyL ^p integrableB valued random variable sequence {D _n , n≥1}, any real number sequence {b _n , n≥1} with 0<b _n, ↑ ∞, any integern≥1, there exist a constantC=C _p>0 (only depending onp) such that

Strong stability of linear forms in φ -mixing random variables

In this paper some new results of strong stability of linear forms in φ-mixing random variables are given. It is mainly proved that for a sequence of φ-mixing random variables {x _n , n ⩾ 1} and two sequences of positive numbers {a _n , n ⩾ 1} and {b _n , n ⩾ 1} there exist d _n ∈ R, n = 1,2,L, such that a.s. under some suitable conditions. The results extend and improve the corresponding theorems for independent identically distributed random variables. Foundation item: Supported by the National Natural Science Foundation of China(10671149)     

Atomic Decompositions of Weak Hardy Spaces of B-Valued Martingales

The atomic decompositions of weak Hardy spaces of Banach-space-valued martingales are given. With the help of the atomic decompositions, some inequalities for B-valued martingales are established in the case 0〈r≤1. Here the results are connected closely with the p-uniform smoothness and q-uniform convexity of Banach spaces which the martingales take values in.     

A note on characteristic generators of a free cyclic code and its dual

Let C be a free cyclic code over Z _n ^α and dim _p C = k. In the paper, we prove that if the k characteristic generators of C are p-linearly independent then the corresponding nα − k characteristic generators of C ^⊥ are p-linearly independent. We then show that to any trellis that can be constructed from k p-linearly independent characteristic generators of C, there exists a trellis for C ^⊥ with the same state-complexity profile, which generalizes the conjecture of Koetter and Vardy to a free cyclic code over Z _n ^α. Foundation item: Supported by the National Natural Science Foundation of China(60673071)     

基于改进ADPP的多变量时间序列异常检测

针对多变量时间序列异常检测问题进行研究,提出基于改进ADPP的多变量时间序列异常检测算法IADPP.IADPP算法引入适用于多变量时间序列的张量相似性度量SSOTPCA,并以此相似性度量构造序列集的k-近邻图,在构造的k-近邻图上计算多变量时间序列的异常系数.研究结果表明,IADPP算法克服了原有ADPP算法不支持多变量时间序列和要求密度均匀的缺陷,取得了较好的检测结果.     

A laurent expansion and residue theorems of k -regular functions in clifford analysis

In this context, we mainly study the behavior in the neighborhood of finite singular points for k-regular functions in 1 R ₁ ⁿ with values in R _0,n . We get a Laurent expansion of them in an open set, prove its uniqueness, give the definitions of k-poles, isolated and essential singular points and removable singularity, discuss some properties, and further obtain the residue theorems.      

Statistical Characteristics of the Complexity for Prime-Periodic Sequences

Using the fact that the factorization of x^N-1 over GF(2) is especially explicit, we completely establish the distributions and the expected values of the linear complexity and the k-error linear complexity of the N-periodic sequences respectively, where N is an odd prime and 2 is a primitive root modulo N. The results show that there are a large percentage of sequences with both the linear complexity and the k-error linear complexity not less than N, quite close to their maximum possible values.     

Bridging of Calixarenes with N, N＇-Bis（Chloroacetyl） Propylenediamine

A new bridging reagent, N, N‘-bis (chloroacetyl) propylenediamine was used to explore the relativeactivity and bridging pattern of p-ten-bury lcalix [4] arene, p-tert-butylcalix [6] arene and butylcalix [8] arene. It wasfound that the bridging reaction is selectively, at least, preferably at 1, 3-position for p-tert-butylcalix [4] arene and p-tert-butylcalix [6] arene, 1,5-position for p-tert-butylcalix [8] arene. Taking the yield of bridged calixarene as a compar-sion standard, the activity decreases with the increasing of the number of phenolic units in calixarene.     

The microscopic approach of sdgIBM-1 and its application to nucleus<Superscript>154</Superscript>Gd

Based on the Dyson expansion theory, a microscopic approach of sdgIBM-1 is presented and applied to nucleus¹⁵⁴Gd in this paper. The energy spectra andE2 transition have been calculated. Good agreement is obtained in comparison with experimental results. Foundation item: Supported by the Foundation of Administration of Education of China Biography: Sang Jian ping (1959), male. Ph. D. Professor, research direction: nuclear physics     

Walsh spectrum properties of rotation symmetric boolean function

Rotation symmetric function was presented by Pieprzyk. The algebraic configuration of rotation symmetric（RotS） function is special. For a Rots n variables function f（x1, x2, …, xn） we have f（ρn^k （x1, x2, …xn））=f（x1, x2, …, xn） for k=0, 1, …, n-1. In this paper, useing probability method we find that when the parameters of RotS function is under circular translation of indices, its walsh spectrum is invariant. And we prove the result is both sufficient and necessary.