不同权的Bloch型空间之间的加权复合算子再刻画

本文研究了单位圆中从空间β_L到β_α的加权复合算子uC_φ为有界算子和紧算子的条件.利用阶估计等方法,获得了有界性和紧性的简捷充要条件,推广了叶善力的相应结果.     

THE COMPACT COMPOSITION OPERATOR ON THE μ-BERGMAN SPACE IN THE UNIT BALL

nAbstract Let p 0 and μ be a normal function on [0, 1), ν(r) =(1-r~2)~(1+(n/p)) μ(r) for r ∈ [0, 1). In this article, the bounded or compact weighted composition operator T_φ,ψfrom the μ-Bergman space A~p(μ) to the normal weight Bloch type space β_ν in the unit ball is characterized. The briefly sufficient and necessary condition that the composition operator C_φis compact from A~p(μ) to β_ν is given. At the same time, the authors give the briefly sufficient and necessary condition that C_φis compact on β_μ for a 1.     

Comments on “A note on “A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets””

In a recently published paper “A note on “A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets””, Khalil and Hassan pointed out that assertions (3) and (4) of Theorem 3.2 in our previous paper “A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets” are not true [2]. Furthermore, they introduced the notions of a generalized trapezoidal interval type-2 fuzzy soft subset and a generalized trapezoidal interval type-2 fuzzy soft equal and used these two notions to correct the flaw in assertions (3) and (4) of Theorem 3.2 in our previous paper. In this paper, we show by a counterexample that Khalil and Hassan's correction is incorrect and provide the modified versions of assertions (3) and (4) of Theorem 3.2, along with a strict proof. In addition, Khalil and Hassan pointed out by a counterexample that assertions (3)–(6) of Theorem 3.5 in our paper are not true and proposed the corrections of those assertions. In this paper, we show that Khalil and Hassan's counterexample and corrections are incorrect and provide a new example to verify the inaccuracies of assertions (3) and (5) of Theorem 3.5 in our paper. Moreover, we offer the modified versions of assertions (3) and (5) of Theorem 3.5 and prove them. Finally, Khalil and Hassan's statement that assertions (4) and (6) of Theorem 3.5 in our previous paper are not true is proven to be incorrect, i.e. assertions (4) and (6) of Theorem 3.5 in our previous paper are true.     

双参数非线性非局部奇摄动抛物型初始-边值问题的广义解

研究了一类广义抛物型方程奇摄动问题.首先在一定的条件下, 提出了一类具有两参数的非线性非局部广义抛物型方程初始 边值问题.其次证明了相应问题解的存在性.然后, 通过Fredholm积分方程得到了初始 边值问题的外部解.再利用泛函分析理论和伸长变量及多重尺度法, 分别构造了初始 边值问题广义解的边界层、初始层项,从而得到了问题的形式渐近展开式.最后利用不动点理论证明了对应的非线性非局部广义抛物型方程的奇异摄动初始 边值问题的广义解的渐近展开式的一致有效性.     

激光脉冲放大器增益通量耦合系统解

研究了一个激光脉冲放大器增益通量系统解的问题.首先讨论了较一般的系统, 然后引入一个同伦映射.再利用映射的性质, 引进一个人工参数, 将求解非线性问题转化为求解一系列线性问题.再逐次地求出对应的线性问题的解, 最后得到了原模型解的近似展开式.可以看出, 同伦映射方法是一个解析的方法.它是通过函数的解析运算并用初等函数来表达近似解,其不同于用离散数值运算的数值计算方法.因此通过同伦映射解, 还可以对它继续进行解析运算, 从而可以进行微分和积分等运算来得到与激光脉冲放大器增益通量相关的其他物理量的性态.     

Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games

We consider the problem of computing the set of initial states of a dynamical system such that there exists a control strategy to ensure that the trajectories satisfy a temporal logic specification with probability 1 (almost-surely). We focus on discrete-time, stochastic linear dynamics and specifications given as formulas of the Generalized Reactivity(1) fragment of Linear Temporal Logic over linear predicates in the states of the system. We propose a solution based on iterative abstraction-refinement, and turn-based 2-player probabilistic games. While the theoretical guarantee of our algorithm after any finite number of iterations is only a partial solution, we show that if our algorithm terminates, then the result is the set of all satisfying initial states. Moreover, for any (partial) solution our algorithm synthesizes witness control strategies to ensure almost-sure satisfaction of the temporal logic specification. While the proposed algorithm guarantees progress and soundness in every iteration, it is computationally demanding. We offer an alternative, more efficient solution for the reachability properties that decomposes the problem into a series of smaller problems of the same type. All algorithms are demonstrated on an illustrative case study.     

A novel feature selection for RNA-seq analysis

RNA-seq data are challenging existing omics data analytics for its volume and complexity. Although quite a few computational models were proposed from different standing points to conduct differential expression (D.E.) analysis, almost all these methods do not provide a rigorous feature selection for high-dimensional RNA-seq count data. Instead, most or even all genes are invited into differential calls no matter they have real contributions to data variations or not. Thus, it would inevitably affect the robustness of D.E. analysis and lead to the increase of false positive ratios.In this study, we presented a novel feature selection method: nonnegative singular value approximation (NSVA) to enhance RNA-seq differential expression analysis by taking advantage of RNA-seq count data's non-negativity. As a variance-based feature selection method, it selects genes according to its contribution to the first singular value direction of input data in a data-driven approach. It demonstrates robustness to depth bias and gene length bias in feature selection in comparison with its five peer methods. Combining with state-of-the-art RNA-seq differential expression analysis, it contributes to enhancing differential expression analysis by lowering false discovery rates caused by the biases. Furthermore, we demonstrated the effectiveness of the proposed feature selection by proposing a data-driven differential expression analysis: NSVA-seq, besides conducting network marker discovery.     

Cartesian Closed Extensions of Subcategories of CONT

In this paper we give a uniform way of proving cartesian closedness for many new subcategories of continuous posets. We define C-P to be the category of continuous posets whose D–completions are isomorphic to objects from C, where C is a subcategory of the category CONT of domains. The main result is that if C is a cartesian closed full subcategory of ALG _⊥ or BC, then C-P is also a cartesian closed subcategory of the category CONTP of continuous posets and Scott continuous functions. In particular, we have the following cartesian closed categories : BC-P, LAT-P, aL-P, aBC-P, B-P, aLAT-P, ω -B-P, ω -aLAT-P, etc.     

A note on the convexity of ruin probabilities

Conditions for the convexity of compound geometric tails and compound geometric convolution tails are established. The results are then applied to analyze the convexity of the ruin probability and the Laplace transform of the time to ruin in the classical compound Poisson risk model with and without diffusion. An application to an optimization problem is given.