Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences最新文献

Abstract

In this paper, we study unicity of meromorphic functions concerning differential-difference polynomials and mainly prove: Let (k_{1},k_{2},cdots,k_{n}) be nonnegative integers and (k=) max({k_{1},k_{2},cdots,k_{n}}), let (l) be the number of distinct values of ({0,c_{1},c_{2},cdots,c_{n}}), let (s) be the number of distinct values of ({c_{1},c_{2},cdots,c_{n}}), let (f(z)) be a nonconstant meromorphic function of finite order satisfying (N(r,f)leqfrac{1}{8(lk+l+2s-1)+1}T(r,f)), let (m_{1}(z),m_{2}(z),cdots,m_{n}(z),)(a(z),b(z)) be small functions of (f(z)) such that (a(z)notequiv b(z)), let ((c_{1},k_{1}),(c_{2},k_{2}),)(cdots,(c_{n},k_{n})) be distinct and let (F(z)=m_{1}(z)f^{(k_{1})}(z+c_{1})+m_{2}(z)f^{(k_{2})}(z+c_{2})+cdots+m_{n}(z)f^{(k_{n})}(z+c_{n})). If (f(z)) and (F(z)) share (a(z),b(z)) CM, then (f(z)equiv F(z)). Our results improve and extend some results due to [1, 18, 20].

Abstract

The paper is concerned with the statistical estimation of the spectral parameters of stationary models with tapered data. As estimators of the unknown parameters we consider the tapered Whittle estimator and the simplified tapered Whittle estimators. We show that under broad regularity conditions on the spectral density of the model these estimators are asymptotically statistically equivalent, in the sense that these estimators possess the same asymptotic properties. The processes considered will be discrete-time and continuous-time Gaussian, linear or Lévy-driven linear processes with memory.

Abstract

The concept of covariogram is extended from bounded convex bodies in (mathbb{R}^{d}) to the entire space (mathbb{R}^{d}) by obtaining integral representations for the distribution and probability density functions of the Euclidean distance between two (d)-dimensional Gaussian points that have correlated coordinates governed by a covariance matrix. When (d=2), a closed-form expression for the density function is obtained. Precise bounds for the moments of the considered distance are found in terms of the extreme eigenvalues of the covariance matrix.

Abstract

Various types of movability for abstract classical pro-morphisms or coherent mappings, and for abstract classical or strong shape morphisms was given by the same authors in some previous paper [10–12]. In the present paper we introduce and study the notions of (uniform) movability, and (uniform) co-movability for a new type of pro-morphisms and shape morphisms belonging to the so called enriched pro-category (pro^{J})-(mathcal{C}) and to the corresponding shape category (Sh^{J}_{(mathcal{C},mathcal{D})}), which were introduced by Uglešić [27].

Abstract

For Higman’s sequence building operation (omega_{m}) and for any integer sequences set ({mathcal{B}}) the subgroup (A_{omega_{m}{mathcal{B}}}) is benign in a free group (G) as soon as (A_{mathcal{B}}) is benign in (G). Higman used this property as a key step to prove that a finitely generated group is embeddable into a finitely presented group if and only if it is recursively presented. We build the explicit analog of this fact, i.e., we explicitly give a finitely presented overgroup (K_{omega_{m}{mathcal{B}}}) of (G) and its finitely generated subgroup (L_{omega_{m}{mathcal{B}}}leq K_{omega_{m}{mathcal{B}}}) such that (Gcap L_{omega_{m}{mathcal{B}}}=A_{omega_{m}{mathcal{B}}}) holds. Our construction can be used in explicit embeddings of finitely generated groups into finitely presented groups, which are theoretically possible by Higman’s theorem. To build our construction we suggest some auxiliary ‘‘nested’’ free constructions based on free products with amalgamation and HNN-extensions.

Abstract

In this paper, we have dealt with the uniqueness problem of a general meromorphic function with (mathcal{L}) function in terms of two shared sets. In our main theorem, we deal with general meromorphic functions instead of meromorphic functions having finitely many poles. As a corollary of our main theorem, we have shown that our result not only fills the gap of some theorems of [3] and [1] for (m=n-1) but also reduces the cardinality of the main range set and hence our result significantly improves all the results in this direction.

Abstract

In this note, we consider the problem of aggregation of estimators in order to denoise a signal. The main contribution is a short proof of the fact that the exponentially weighted aggregate satisfies a sharp oracle inequality. While this result was already known for a wide class of symmetric noise distributions, the extension to asymmetric distributions presented in this note is new.

Abstract

In this paper, we prove that for a transcendental entire function (f) of finite order such that (lambda(f-a)<rho(f)), where (a) is an entire function and satisfies (rho(a)<rho(f)), (ninmathbb{N}), if (Delta_{c}^{n}f) and (f) share the entire function (b) satisfying (rho(b)<rho(f)) CM, where (cinmathbb{C}) satisfies (Delta_{c}^{n}fnotequiv 0), then (f(z)=a(z)+de^{cz}), where (d,c) are two nonzero constants. In particular, if (a=b), then (a) reduces to a constant. This result improves and generalizes the recent results of Chen and Chen [3], Liao and Zhang [10] and Lü et al. [11] in a large scale. Also we exhibit some relevant examples to fortify our results.

Abstract

The purpose of this note is to recall one remarkable theorem of Khinchin about the special role of the Gaussian distribution. This theorem allows us to give a new interpretation of the Lindeberg condition: it guarantees the uniform integrability of the squares of normed sums of random variables and, thus, the passage to the limit under the expectation sign. The latter provides a simple proof of the central limit theorem for independent random variables.

Abstract

In this paper, we will present the expression of meromorphic solutions on the crossing differential or difference Malmquist systems of certain types using Nevanlinna theory. For instance, we consider the admissible meromorphic solutions of the crossing differential Malmquist system

where (a_{1}(z)d_{1}(z)notequiv a_{0}(z)) and (a_{2}(z)d_{2}(z)notequiv b_{0}(z)).