Fredholm theory in ordered Banach algebras

This paper illustrates some initial steps taken in the e?ort of unifying the theory of positivity in ordered Banach algebas (OBAs) with the general Fredholm theory in Banach algebras. We introduce here upper Weyl and upper Browder elements in an OBA relative to an arbitrary Banach algebra homomorphism and investigate the spectra corresponding to the sets of upper Weyl and upper Browder elements, which we shall refer to as the upper Weyl and upper Browder spectra, respectively.     

有向图的上广义指数

本文得到了n阶k上本原有向图的第k重上广义指数的最大值,1≤k≤n,完全刻画了第k重上广义指数达到最大值的n阶有向图,讨论了第k重上广义指数可取得的值。     

Pawlak代数中下,上方逼近算子的若干性质

研究Pawlak代数(L,∧,∨,c,apr,apr)中下,上方逼近算子apr和apr的性质,利用它们构造F格L上的各种二元关系,探讨这些二元关系成为等价关系的条件,得到若干结果.     

Bohr Sets in Triple Products of Large Sets in Amenable Groups

We answer a question of Hegyvári and Ruzsa concerning effective estimates of the Bohr-regularity of certain triple sums of sets with positive upper Banach densities in the integers. Our proof also works for any discrete amenable group, and it does not require all addends in the triple products we consider to have positive (left) upper Banach densities; one of the addends is allowed to only have positive upper asymptotic density with respect to a (possibly very sparse) ergodic sequence.

     

Points of monotonicity in F-normed Orlicz function spaces

Aequationes mathematicae - In this paper points of lower strict monotonicity, upper strict monotonicity, lower local uniform monotonicity and upper local uniform monotonicity of Orlicz function...     

更新风险模型破产赤字概率的上界

本文给出了更新风险模型破产赤字上界的一种算法,这种算法通过引入一个单调积分算子,得到了比Cramer-Lundberg上界更好的一些结果。     

The number of edges in a bipartite graph of given radius

Vizing established an upper bound on the size of a graph of given order and radius. We find a sharp upper bound on the size of a bipartite graph of given order and radius.     

On weak completeness of products and direct sums in locally convex cones

We discuss the weak completeness of product and direct sum cones in the lower, upper and symmetric topologies. For the weak lower, upper and symmetric topology of a direct sum cone, there correspond bases of upper, respectively lower and symmetric, closed members in a coarser topology which leads us to investigate the weak completeness of direct sum cones.

     

Bounding the number of cycles in a graph in terms of its degree sequence

We give an upper bound on the number of cycles in a simple graph in terms of its degree sequence, and apply this bound to resolve several conjectures of Király (2009) and Arman and Tsaturian (2017) and to improve upper bounds on the maximum number of cycles in a planar graph.     

向量优化中有效点的存在性

分别在有pre-order的无线性结构的集合和拓扑空间中，给出了有效点的存在性。作为应用，讨论了向量优化问题中解的存在性。最后给出了紧、弱紧、锥紧、锥半紧、上序紧、下序紧、上序半紧、准上序半紧和准下序半紧等之间的关系。     

Extremum conditions for a nonsmooth function in terms of exhausters and coexhausters

The notions of upper and lower exhausters and coexhausters are discussed and necessary conditions for an unconstrained extremum of a nonsmooth function are derived. The necessary conditions for a minimum are formulated in terms of an upper exhauster (coexhauster) and the necessary conditions for a maximum are formulated in terms of a lower exhauster (coexhauster). This involves the problem of transforming an upper exhauster (coexhauster) into a lower exhauster (coexhauster) and vice versa. The transformation is carried out by means of a conversion operation (converter). Second-order approximations obtained with the help of second-order (upper and lower) coexhausters are considered. It is shown how a secondorder upper coexhauster can be converted into a lower coexhauster and vice versa. This problem is reduced to using a first-order conversion operator but in a space of a higher dimension. The obtained result allows one to construct second-order methods for the optimization of nonsmooth functions (Newton-type methods).     

上下解反序条件下二阶泛函微分方程Neumann边值问题解的存在性条件

主要利用上下解和单调迭代法,研究了带有N eum ann边界条件的二阶泛函微分方程在上下解反序条件下解的存在性条件.     

Lie products in incidence algebras

We give conditions when a strictly upper triangular element of an incidence algebra over a commutative ring is the Lie commutator of two elements of the incidence algebra, one of which is strictly upper triangular. In particular, it follows that this is the case for the ring of n × n upper triangular matrices, where n is either finite or infinite.     

Approximation of differentiation operator in the space L 2 on semiaxis

We establish an upper bound for the error of the best approximation of the first order differentiation operator by linear bounded operators on the set of twice differentiable functions in the space L ₂ on the half-line. This upper bound is close to a known lower bound and improves the previously known upper bound due to E. E. Berdysheva. We use a specific operator that is introduced and studied in the paper.     

Orlicz空间中支撑映射的上(下)半连续点

该文给出了赋Ｏｒｌｉｃｚ范数的Ｏｒｌｉｃｚ空间Ｌ°Ｍ中的点是支撑映射的上（下）半连续点的充分必要条件；推出了支撑映射为上（下）半连续的判别准则．     

On Upper Class of Increments of Fractional Brownian Motion

A series test for the upper upper class and lower upper class of increments of fractional brownian motion is provided.     

NBUE分布类应力-强度模型的概率上界

研究应力-强度模型的结构的可靠性分析,当元件应力变量分布属于NBUE类,强度变量服从指数分布,给出了应力-强度模型中概率的上界,由此讨论了n个元件组成系统的应力-强度模型概率上界.     

相关随机利率下的双二项模型的破产概率

研究带有相关随机利率的双二项风险模型,得到了破产概率的积分表达式,并利用鞅分析的方法得到了破产概率的经典Lundberg上界,另外给出了一个破产概率的比经典Lundberg上界更精确的上界.     

Mean value properties of nondifferentiation functions and their application in nonsmooth analysis

A calculus for (radial) upper convex approximations is developed and mean value properties of nondifferentiable functions are presented. The mean value theorems are formulated with radial upper convex approximations and are of equality type. Some applications in nonsmooth analysis are studied.     

Incentivizing advanced mathematics study at upper secondary level: the case of bonus points in Ireland

Secondary level mathematics education in Ireland has recently experienced a period of significant change with the introduction of new curricula and the addition of an incentive to study upper secondary mathematics at the most advanced level (Higher Level). This incentive, typically referred to as ‘bonus points’, appears to have aided a significant increase in the number of students studying upper secondary mathematics at Higher Level. However, thematic analysis of interviews with experienced upper secondary mathematics examiners and exploration of mathematics diagnostic test data outlined in this paper suggest that the difficulty of the Higher Level upper secondary mathematics final examination in Ireland has reduced since the introduction of the bonus points initiative. The sharp increase in students attempting this examination coupled with a policy of maintaining a consistent proportion of students achieving passing grades was identified as a key reason for this possible reduction in standards.