属性粗糙集的新型近似算子

由等价类中元素属性测度的上、下确界定义的属性粗糙集,没有充分反映等价类中其它元素的作用,在信息处理中不免造成元素信息的丢失.为此提出一种新的属性粗糙集近似算子的表示方法,给出了相应的性质并实例说明了这一方法的合理性.     

粗糙直觉模糊集的近似表示

在粗糙直觉模糊集的基础上,从新的角度提出了不确定目标概念的近似表示和处理的方法(通过近似模糊集和近似精确集刻画).首先将已有的直觉模糊集相似概念和均值直觉模糊集概念引入到该模型,定义了Pawlak近似空间U/R下的阶梯直觉模糊集、0.5-精确集的概念,然后得到了均值直觉模糊集(0.5-精确集)是所有直觉模糊集中与目标直觉模糊集最接近的直觉模糊集(近似精确集),接着分析了均值直觉模糊集、0.5-精确集分别与目标直觉模糊集的相似度随着知识粒度变化的变化规律.     

Strict positive definiteness on products of compact two-point homogeneous spaces

We present an explicit characterization for the real, continuous, isotropic and strictly positive definite kernels on a product of compact two-point homogeneous spaces, covering almost all possible choices for the spaces. The result complements similar characterizations previously obtained for products of high-dimensional spheres.     

Aubry–Mather Sets for Relativistic Oscillators with Anharmonic Potentials

In this paper, by the Aubry–Mather theory, it is proved that there are many periodic solutions and usual or generalized quasiperiodic solutions for relativistic oscillator with anharmonic potentials models d/dt(x/(1-|x|~2~(1/2))+ |x|~(α-1)x=p(t),where p(t) ∈ C~0(R~1) is 1-periodic and α 0.     

Structural Properties of Cubic Sets in Regular LA-semihypergroups

In this article we characterize the regular LA-semihypergroups in terms of $({\in }_{\Gamma },{\in }_{\Gamma }\vee q_{\Delta })$-cubic (left, right, two sided, bi, generalized bi, interior, quasi)-hyperideals of LA-semihypergroups. Meanwhile, some illustrative examples are given to show the rationality of the definitions popularized in the present paper.     

A weighted version of a result of Hamada on minihypers and on linear codes meeting the Griesmer bound

Minihypers were introduced by Hamada to investigate linear codes meeting the Griesmer bound. Hamada (Bull Osaka Women’s Univ 24:1–47, 1985; Discrete Math 116:229–268, 1993) characterized the non-weighted minihypers having parameters , with k−1 > λ₁ > λ₂ > ... > λ _h ≥ 0, as the union of a λ₁-dimensional space, λ₂-dimensional space, ..., λ _h -dimensional space, which all are pairwise disjoint. We present in this article a weighted version of this result. We prove that a weighted -minihyper , with k−1 > λ₁ > λ₂ > ... > λ _h ≥ 0, is a sum of a λ₁-dimensional space, λ₂-dimensional space, ..., and λ _h -dimensional space. This research was supported by the Project Combined algorithmic and theoretical study of combinatorial structures between the Fund for Scientific Research Flanders-Belgium (FWO-Flanders) and the Bulgarian Academy of Sciences. This research is also part of the FWO-Flanders project nr. G.0317.06 Linear codes and cryptography.     

On the topological structure of univoque sets

Erd?s, Horváth and Joó discovered some years ago that for some real numbers 1<q<2 there exists only one sequence ci of zeroes and ones such that ∑ciq−i=1. Subsequently, the set U of these numbers was characterized algebraically in [P. Erd?s, I. Joó, V. Komornik, Characterization of the unique expansions 1=∑q−ni and related problems, Bull. Soc. Math. France 118 (1990) 377-390] and [V. Komornik, P. Loreti, Subexpansions, superexpansions and uniqueness properties in non-integer bases, Period. Math. Hungar. 44 (2) (2002) 195-216]. We establish an analogous characterization of the closure of U. This allows us to clarify the topological structure of these sets: is a countable dense set of , so the latter set is perfect. Moreover, since U is known to have zero Lebesgue measure, is a Cantor set.     

Boundary functions in L2 H $$(\mathbb{B}^n )$$

We solve the Dirichlet problem for line integrals of holomorphic functions in the unit ball For a function u which is lower semi-continuous on we give necessary and sufficient conditions in order that there exists a holomorphic function f ∈ such that