Strong approximation for ρ-mixing sequences

We establish strong invariance principles for sums of stationary ??-mixing random variables with finite and infinite second moments under weaker mixing rates. Some earlier results are improved. As applications, some results of the law of the iterated logarithm with finite and infinite variance are obtained, also a conjecture raised by Shao in 1993 is solved.     

σ-asymptotically lacunary statistical equivalent sequences

This paper presents the following definitions which is a natural combination of the definition for asymptotically equivalent, statistically limit, lacunary sequences, and σ-convergence. Let ϑ be a lacunary sequence; Two nonnegative sequences [x] and [y] are S _σ,8-asymptotically equivalent of multiple L provided that for every ε > 0

Auslander–Reiten sequences on schemes

Auslander–Reiten sequences are the central item of Auslander–Reiten theory, which is one of the most important techniques for the investigation of the structure of abelian categories. This note considers X, a smooth projective scheme of dimension at least 1 over the field k, and , an indecomposable coherent sheaf on X. It is proved that in the category of quasi-coherent sheaves on X, there is an Auslander–Reiten sequence ending in .     

表达式x（δf／δx）＋y（δf／δy）和x（δf／δy）-y（δf／δx）的若干性质

讨论了偏导数表达式x(δf/δx) y(δf/δy)和x(δf/δy)-y(δf/δx)的若干性质，尤其是它们的积分性质。     

Strong approximation for ρ-mixing sequences

We establish strong invariance principles for sums of stationary ρ-mixing random variables with finite and infinite second moments under weaker mixing rates.Some earlier results are improved.As applications,some results of the law of the iterated logarithm with finite and infinite variance are obtained,also a conjecture raised by Shao in 1993 is solved.     

The k–Fibonacci difference sequences

In this paper we apply the concept of difference relation to the sequences of k–Fibonacci numbers. We will obtain general formulas to find any term of the ith k–Fibonacci difference sequence from the initial k–Fibonacci numbers. We also find formulas for the sum of the elements of these new sequences as well as their generating functions. Finally, we study the k–Fibonacci Newton polynomial interpolation.     

0,1 distribution in the highest level sequences of primitive sequences over Z_(2~e)

In this paper, we discuss the 0,1 distribution in the highest level sequence αe-1 of primitive sequence over Z2e generated by a primitive polynomial of degree n. First we get an estimate of the 0,1 distribution by using the estimates of exponential sums over Galois rings, which is tight for e relatively small to n. We also get an estimate which is suitable for e relatively large to n. Combining the two bounds, we obtain an estimate depending only on n, which shows that the larger n is, the closer to 1/2 the proportion of 1 will be.     

How do random Fibonacci sequences grow?

We study the random Fibonacci sequences defined by ${F_1 = F_2 = \widetilde F_1 = \widetilde F_2 = 1}$ and for n ≥ 1, F _n+2 = F _n+1 ± F _n (linear case) and ${\widetilde F_{n+2} = |\widetilde F_{n+1} \pm \widetilde F_{n}|}$ (non-linear case), where each ± sign is independent and either + with probability p or ? with probability 1 ? p (0 < p ≤ 1). Our main result is that the exponential growth of F _n for 0 < p ≤ 1, and of ${\widetilde F_{n}}$ for 1/3 ≤ p ≤ 1 is almost surely given by $${\int \limits _0^\infty \log x\, d\nu_\alpha (x),}$$ where α is an explicit function of p depending on the case we consider, and ν _α is an explicit probability distribution on ${\mathbb{R}_+}$ defined inductively on Stern–Brocot intervals. In the non-linear case, the largest Lyapunov exponent is not an analytic function of p, since we prove that it is equal to zero for 0 < p ≤ 1/3. We also give some results about the variations of the largest Lyapunov exponent, and provide a formula for its derivative.     

Matrix realizations of littlewood—richardson sequences

In this paper we consider the problem of characterizing the invariant factors of three matrices A B, and C, such that AB — C Our matrices have entries over a principal ideal domain or over a local domain. In Section 2 we show that this problem is localizablc

The above problem lias a well-known solution in terms of Littlewood-Richardson sequences. We introduce the concept of a matrix realization of a Littlewood-Richardson sequence. The main result is an explicit construction of a sequence of matrices which realizes a previously given Littlewood Richardson sequence. Our methods offer a matrix theoretical proof of a well-known result of T, Klein on extensions of p-modules.     

On generalized quasi-β-power increasing sequences

The paper deals with absolute summability factors for infinite series. The main purpose of this paper is to generalize a recent paper of Savas (2009) [2].     

Spectral sequences in (∞,1)-categories

We explain how to set up the homotopy spectral sequence of a (co)simplicial object in an ∞-category, with an emphasis on how to construct the differentials in a model-invariant manner.     

Interpolating sequences for H∞(BH)

We prove that under the extended Carleson’s condition, a sequence (x_n) ? B_H is linear interpolating for H^∞(B_H) for an infinite dimensional Hilbert space H. In particular, we construct the interpolating functions for each sequence and find a bound for the constant of interpolation.     

The invariance principle for ϕ-mixing sequences

Summary In this paper we investigate the invariance principle for -mixing sequences, satisfying restrictions on the variances which are a weak form of stationarity. No mixing rate is assumed. For -mixing strictly stationary sequences we give a necessary and sufficient condition for the invariance principle.     

ALTERNATING BAND CRANK-NICOLSON METHOD FOR δu／δt=δ^2u／δx^2＋δ^2u／δy^2

the Alternating Segment Crank-Nicolson scheme for one-dimensional diffusion equation has been developed in [1],and the Alternating Block Crank-Nicolson method for two-dimensional problem in [2].The methods have the advantages of parallel computing,stability and good accuracy.In this paper for the two-dimensional diffusion equation,the net region is divided into bands,a special kind of block.This method is called the alternating Band Crank-Nicolson method.     

Thin sequences in the corona of H ∞

In this paper we consider several conditions for sequences of points in M(H ^∞) and establish relations between them. We show that every interpolating sequence for QA of nontrivial points in the corona $M(H^\infty )\backslash \mathbb{D}$ of H ^∞ is a thin sequence for H ^∞, which satisfies an additional topological condition. The discrete sequences in the Shilov boundary of H ^∞ necessarily satisfy the same condition.