Cauchy-Rassias Stability of Cauchy-Jensen Additive Mappings in Banach Spaces

Let X, Y be vector spaces. It is shown that if a mapping f ： X → Y satisfies f（（x＋y）/2＋z）＋f（（x-y）/2＋z=f（x）＋2f（z）,（0.1） f（（x＋y）/2＋z）-f（（x-y）/2＋z）f（y）,（0.2） or 2f（（x＋y）/2＋x）=f（x）＋f（y）＋2f（z）（0.3）for all x, y, z ∈ X, then the mapping f ： X →Y is Cauchy additive. Furthermore, we prove the Cauchy-Rassias stability of the functional equations （0.1）, （0.2） and （0.3） in Banach spaces. The results are applied to investigate isomorphisms between unital Banach algebras.     

关于一类含有Dziok-Srivastava算子的多叶解析函数的包含关系和卷积性质

该文引进和研究了一类含有Dziok-Srivastava算子的新的多叶解析函数. 得到了这一函数类中的一些有趣的性质, 如包含关系, 卷积性质等. 这些结果改进和拓展了早期的一些工作. 同时也得到了其他一些新的结果.     

急件订单干扰下虚拟单元重调度

虚拟单元生产中,针对急件订单干扰情况,研究了考虑序位相似性,即尽量保持初始工序的加工次序的虚拟单元重调度问题。为了应对急件订单干扰,设置了各工件工序可用机器集合和相应的加工时间集合,构建了以序位相似性最大和急件订单完工时间、系统总流程时间最短为目标的多目标非线性整数规划模型。针对模型自身特征,采用了遗传—蚁群算法相结合的优化算法求解模型。最后,以船舶实际生产为例,验证了模型的可行和优越性,以及算法的有效性。     

A formula for gap between two closed operators

Aim of this short note is to obtain a formula for the gap between two densely defined unbounded closed operators. It is interesting to note that the formula is very similar to the corresponding formula for the gap between two bounded operators.     

The mean first passage time of a three-level atomic optical bistable system subjected to noise

The transient properties of a three-level atomic optical bistable system in the presence of multiplicative and additive noises are investigated. The explicit expressions of the mean first-passage time (MFPT) of the transition from the high intracavity intensity state to the low one are obtained by numerical computations. The impacts of the intensities of the multiplicative noise D M and the additive noise D A , the intensity of correlation between two noises λ , and the intensity of the incident light y on the MFPT are discussed, respectively. Our results show: (i) for the case of no correlation between two noises (λ = 0.0), the increase in D M and D A can lead to an increase in the probability of the transition to the low intracavity intensity state, while the increase in y can lead to a retardation of the transition; and (ii) for the case of correlation between two noises (λ = 0.0), the increase in λ can cause an increase in the probability of the transition, and the increase in D A can cause a retardation of the transition firstly and then an increase in the probability of the transition, i.e., the noise-enhanced stability is observed for the case of correlation between two noises.     

Categorical Abstract Algebraic Logic: Subdirect Representation of Pofunctors

Pa?asińska and Pigozzi developed a theory of partially ordered varieties and quasi-varieties of algebras with the goal of addressing issues pertaining to the theory of algebraizability of logics involving an abstract form of the connective of logical implication. Following their lead, the author has abstracted the theory to cover the case of algebraic systems, systems that replace algebras in the theory of categorical abstract algebraic logic. In this note, an order subdirect representation theorem for partially ordered algebraic systems is proven. This is an analog of the Order Subdirect Representation Theorem of Pa?asińska and Pigozzi, which, in turn, generalizes the well-known Subdirect Representation Theorem of Universal Algebra.     

K促进的纳米片状水滑石衍生CoAlO金属氧化物催化碳烟燃烧

采用水热法合成了负载K的纳米片状水滑石衍生CoAlO金属氧化物,其表现出优异的催化碳烟燃烧活性.氢气-程序升温还原（H₂-TPR）实验结果表明,K与Co之间的相互作用提高了催化剂的氧化还原性能.X射线光电子能谱（XPS）分析结果表明,K的负载增大了表面Co²⁺/Co³⁺的比例,促进了氧空位的产生,提高了催化剂对气相氧的吸附能力.碳烟-程序升温还原（Soot-TPR）实验结果表明,K的负载增加了表面吸附氧数量.动力学实验结果表明,K的负载增加了单位质量催化剂上的活性氧数量、反应速率和转化频率（TOF）,从而提高了催化剂的本征活性.另外,碳烟颗粒可以分散在纳米片的层间,与活性位点的接触效率得到提高,也有利于提高催化碳烟燃烧活性.     

Probability measures in -algebras in Hilbert spaces with conjugation

Let be a real -algebra of -real bounded operators containing no central summand of type in a complex Hilbert space with conjugation . Denote by the quantum logic of all -orthogonal projections in the von Neumann algebra . Let be a probability measure. It is shown that contains a finite central summand and there exists a normal finite trace on such that , .

     

Crystal structure of a new precursor of radical-clock based on the norbornenyl framework

The crystal of 5-phenyl-2-endo-(propane-2-sulfonyl)-bicyclo[2-2-1]hept-5-ene-2-carbonitrile1, a new radical-clock is described. The structure has confirmed the configuration for the positions of the phenyl and sulfonyl groups. In the crystal, the radical precursor carbon atom of the propane group is not neighbouring with the double bond of the norbornene. Nevertheless, in solution, it may be expected an ideal conformation with a short intergroup distance leading to a cyclization process. Crystal data: C₁₇H₁₉NO₂S, triclinic, space group P−1,a=6.567 (3),b=10.407(5),c=12.610(6), α=110.48(2), β=95.88(2), λ=102.67(3).