Gamma 算子在 Lp (1≤p ≤∞)空间带权同时逼近的强逆不等式

该文利用修正的带权 K- 泛函K²σ f, t²)_w,p, 考虑Gamma算子在L_p~ (1≤p ≤∞)空间带权同时逼近, 给出了它的 B -型强逆不等式.     

Kernel density in the study of the strong stability of the queueing system

We use kernel density with correction of boundary effects to study the strong stability of the M/M/1 system after perturbation of arrival flow (respectively service times), to evaluate the proximity of G/M/1 (respectively M/G/1) and M/M/1 systems when the distribution G is unknown. Simulation studies are performed to support the results.     

A note on a paper “A regularization method for the proximal point algorithm”

In this note, a small gap is corrected in the proof of H.K. Xu [Theorem 3.3, A regularization method for the proximal point algorithm, J. Glob. Optim. 36, 115–125 (2006)], and some strict restriction is removed also.      

环上的模糊理想幂格及其强截集诱导的格

给出了环上模糊理想幂格的概念,得到相关性质。进而由环上模糊理想强截集诱导出格,讨论了它不是分配格,但为模格。同时,将环上升为主理想环,得到了模糊理想乘积的强截集等于强截集的乘积,且都为环的理想。最后,讨论了Boolean环的模糊子集为模糊理想与其伴随构成交半格的关系。     

Non-collision periodic solutions of second order singular dynamical systems

We study the existence of non-collision periodic solutions for second order singular dynamical systems. The repulsive case and the attractive case are dealt with using a unified topological approach. The proof is based on a well-known fixed point theorem for completely continuous operators, involving a new type of cone. We do not need to consider so-called strong force conditions. Moreover, for the repulsive case, the critical case can be covered. Recent results in the literature, even in the scalar case, are complemented, generalized and improved.     

<Emphasis Type="Italic">G</Emphasis>-compactness and groups

Lascar described E _KP as a composition of E _L and the topological closure of E _L (Casanovas et al. in J Math Log 1(2):305–319). We generalize this result to some other pairs of equivalence relations. Motivated by an attempt to construct a new example of a non-G-compact theory, we consider the following example. Assume G is a group definable in a structure M. We define a structure M′ consisting of M and X as two sorts, where X is an affine copy of G and in M′ we have the structure of M and the action of G on X. We prove that the Lascar group of M′ is a semi-direct product of the Lascar group of M and G/G _L . We discuss the relationship between G-compactness of M and M′. This example may yield new examples of non-G-compact theories. The first author is supported by the Polish Goverment grant N N201 384134. The second author is supported by the Polish Goverment grant N201 032 32/2231.     

Weakly Pseudocompact Frames

We define the notion of weak pseudocompactness for frames and present several characterizations. Among them are characterizations in terms of strong inclusions, uniformities and cozero bases. Noteworthy is the fact that these internal characterizations are not translated from characterizations of weakly pseudocompact spaces.      

Convergence of series of dependent φ-subgaussian random variables

The almost sure convergence of weighted sums of φ-subgaussian m-acceptable random variables is investigated. As corollaries, the main results are applied to the case of negatively dependent and m-dependent subgaussian random variables. Finally, an application to random Fourier series is presented.     

多通道Assembly-like排队系统的强逼近

借助于强逼近理论和修正系统，本文较为详细地研究了多路到达、多服务台Ａｓｓｅｍｂｌｙ－ｌｉｋｅ排队系统，得到了队长过程、离去过程、负荷和虚等待时间过程的强逼近定理。     

A note on wavelet density deconvolution for weakly dependent data

In this paper we investigate the performance of a linear wavelet-type deconvolution estimator for weakly dependent data. We show that the rates of convergence which are optimal in the case of i.i.d. data are also (almost) attained for strongly mixing observations, provided the mixing coefficients decay fast enough. The results are applied to a discretely observed continuous-time stochastic volatility model.