Quasi Controlled K-Metric Spaces over C^(*)-Algebras with an Application to Stochastic Integral Equations

Generally,the field of fixed point theory has attracted the attention of researchers in different fields of science and engineering due to its use in proving the existence and uniqueness of solutions of real-world dynamic models.C^(∗)-algebra is being continually used to explain a physical system in quantum field theory and statistical mechanics and has subsequently become an important area of research.The concept of a C^(∗)-algebra-valued metric space was introduced in 2014 to generalize the concept of metric space.In fact,It is a generalization by replacing the set of real numbers with a C^(∗)-algebra.After that,this line of research continued,where several fixed point results have been obtained in the framework of C^(∗)-algebra valued metric,aswell as(more general)C^(∗)-algebra-valued b-metric spaces andC^(∗)-algebra-valued extended b-metric spaces.Very recently,based on the concept and properties of C^(∗)-algebras,we have studied the quasi-case of such spaces to give a more general notion of relaxing the triangular inequality in the asymmetric case.In this paper,we first introduce the concept of C^(∗)-algebra-valued quasi-controlledK-metric spaces and prove some fixed point theorems that remain valid in this setting.To support our main results,we also furnish some exampleswhichdemonstrate theutility of ourmainresult.Finally,as an application,we useour results to prove the existence and uniqueness of the solution to a nonlinear stochastic integral equation.

自由积C^(*)-代数中的0-1率

在自由概率论框架下,刻画了非交换情形的Kolmogorov型0-1率和Hewitt-Savage型0-1率。

12C^(6+)辐射对菊苣根黄酮类物质及抗氧化活性的影响

为探究12C^(6+)辐射对菊苣中黄酮类物质及抗氧化活性的影响,以菊苣根为试验材料,测定不同12C^(6+)辐射剂量下总黄酮含量及抗氧化活性。利用超高效液相色谱-电喷雾串联四级杆质谱仪(UPLC-ESI-MS/MS),对总黄酮含量显著增加的20、40 Gy辐射组与对照组中黄酮类物质进行靶向代谢组学分析。结果表明,10~40 Gy12C^(6+)辐射均提高了菊苣根总黄酮含量,其中20、40 Gy辐射组含量提升最显著;鉴定出5类11种黄酮类代谢物,橙皮素、氯化矢车菊素-3-O-芸香糖苷是响应12C^(6+)辐射致菊苣根总黄酮含量升高的关键差异代谢物,12C^(6+)辐射影响了紫云英苷、异鼠李素-3-O-葡萄糖苷、木犀草素和橙皮素的合成。类黄酮生物合成途径(ko00941)、黄酮和黄酮醇的生物合成途径(ko00944)富集显著。20、40 Gy剂量辐射提高了菊苣根黄酮提取液的1,1-二苯基-2-三硝基苯肼(DPPH)、2,2’-联氮-双-(3-乙基苯并噻唑啉-6-磺酸)二铵盐(ABTS+)自由基清除能力及铁离子还原能力(FRAP),显著增强了其抗氧化活性。综上,20、40 Gy剂量的12C^(6+)辐射能提高菊苣根中总黄酮含量,改变菊苣根中黄酮类物质种类及含量,并增强其抗氧化活性。本研究结果为进一步研究菊苣辐射诱变育种提供了理论依据。

12C^(6+)辐照对不同品种油橄榄种子萌发及幼苗生长的影响

【目的】为油橄榄辐照诱变育种提供理论参考。【方法】以‘皮削利’‘切姆拉尔’‘豆果’‘奇迹’‘阿尔波萨纳’5个品种的种子为试验材料,以5种剂量(0、50、100、150和250 Gy)的12C^(6+)辐照油橄榄种子,播种后统计不同处理下的发芽率、存活率、鲜质量、株高、总叶数量、根长和侧根数量等7项指标,运用隶属函数法综合评价不同辐照剂量对不同品种油橄榄种子萌发及幼苗生长的影响,并计算半致死辐照剂量。【结果】12C^(6+)辐照对不同品种油橄榄种子发芽率的影响存在差异。随着辐照剂量增加,‘皮削利’和‘切姆拉尔’种子发芽率先升高后降低,‘豆果’‘奇迹’‘阿尔波萨纳’种子发芽率逐渐降低,250 Gy辐照处理下发芽率分别降至11.46%、8.33%、14.58%、7.29%和11.46%。12C^(6+)辐照对各品种油橄榄幼苗的生长有抑制作用。随着辐照剂量增加,鲜质量、株高、总叶数量、根长和侧根数量均逐渐下降,250 Gy辐照处理下均降至最低。12C^(6+)辐照对油橄榄幼苗具有一定的致死效应,且与辐照剂量紧密相关。与种子发芽后40 d时相比,发芽后90 d时各辐照处理下不同品种油橄榄幼苗的存活率均有不同程度的下降。隶属函数分析结果表明,各辐照剂量按照5个品种的总得分由高到低排序,依次均为0、50、100、150、250 Gy,表明不同剂量辐照处理(50~250 Gy)均不同程度地影响了不同品种油橄榄幼苗的长势。5个油橄榄品种按照种子半致死剂量由高到低排序,依次分别为‘豆果’(153.7 Gy)、‘皮削利’(143.5 Gy)、‘切姆拉尔’(129.9 Gy)、‘奇迹’(115.3 Gy)、‘阿尔波萨纳’(108.1 Gy)。【结论】12C^(6+)辐照对不同品种油橄榄种子萌发及幼苗生长整体上有抑制作用,且辐照剂量越大,抑制作用越强。综合考虑发芽率、存活率、幼苗生长等情况,油橄榄种子的适宜辐照剂量为100~150 Gy。

Gelfand-Naimark Theorem of Commutative Hopf C^＊ -Algebras

Let A be a commutative C^＊ -algebra. By the Gelfand-Naimark theorem, there exists a locally compact space G such that A is isomorphic to Co（G）, the C^＊-algebra of all complex continuous functions on G vanishing at infinity. The result is generalized to the ease of Hopf C^＊-algebra, where G is altered by a locally compact group. Using the isomorphic representation, the counit ε and the antipode S of a commutative Hopf C^＊-algebra are proposed.

^(12)C^(16)O_(2)分子位于1.57μm的饱和吸收光谱

本文展示了基于光梳锁频-光腔衰荡光谱装置测量的^(12)C^(16)O_(2)分子位于1.57μm附近的30012←00001振动带中转动量子数最高为68的共计37根振转跃迁的饱和吸收光谱,其频率确定至kHz水平;文献和CDSD2019数据库中的多普勒光谱确定的30012振动态的振转能级与本工作确定的数值存在超过1 MHz的偏差.

Some convergence theorems of fuzzy concave integral on fuzzyσ-algebra

In this paper,we consider the extension of the concave integral from classical crispσ-algebra to fuzzyσ-algebra of fuzzy sets.Firstly,the concept of fuzzy concave integral on a fuzzy set is introduced.Secondly,some important properties of such integral are discussed.Finally,various kinds of convergence theorems of a sequence of fuzzy concave integrals are proved.

Elementary C^(*)-Algebras and Haagerup Tensor Products

In this note,we give a new characterization of elementary C^(*)-algebras in terms of completely compact maps and Haagerup tensor products.

Hilbert C^(*)-模中g-Riesz基的对偶性

本文研究Hilbert C^(*)-模中g-Riesz基的对偶性问题.利用算子理论方法,获得了Hilbert C^(*)-模中的给定序列是g-Riesz基且有唯一对偶g-框架的充要条件,g-Riesz基的对偶g-框架是g-Riesz基的充要条件,以及g-Riesz基成为无冗g-框架的充分条件,所得结果进一步展示了g-框架理论在Hilbert C^(*)-模与Hilbert空间中的差异性.

基于C^(*)准则的最优控制灵敏度设计方法

为优化侧杆负载及控制灵敏度特性设计流程,提出一种基于C^(*)准则的最优控制灵敏度设计方法。依托国外相关经验,结合C^(*)准则设计参数;介绍驾驶员人机工程学及侧杆性能对飞行体验的影响,引出侧杆最优力感特性的设计方法,结合传统的飞行品质规范搭建人机闭环模型验证。实验结果表明:侧杆在不同速度下对纵向角速率和过载控制权重不同,响应均满足C^(*)准则的一级设计要求,仿真验证了侧杆参数和飞行品质结合优化的有效性。

基于C^(2)R模型的反舰导弹突防策略研究

随着现代战争形态的改变,反舰导弹与舰艇防御的攻防对抗一直是研究领域的热点。为制定并选取反舰导弹最有效的突防策略,以反舰导弹、空射诱饵和舰空导弹为研究对象,构建了编队突防模型,运用数据包络分析的方法,给出了五种C^(2)R模型,对反舰导弹突防的所有预期结果进行了评价并排序,在排序中进行策略优选。最后经过仿真试验,验证了模型的可行性和适用性,并有效地对空射诱饵伴随反舰导弹突防的兵器组合策略进行了排序优选,提升了指挥决策效率。

基于C^(#)的光伏压花玻璃厚度在线检测仪设计

该文针对光伏压花玻璃设计并制作了一款在线厚度检测仪器。该仪器使用光谱共焦传感器,采用C^(#)上位机进行核心的交互控制以及数据处理,组合利用可编程逻辑控制器(PLC)和伺服电机控制测量位置。经测试,该仪器操作便捷、测量高效准确,可以取代传统压花玻璃生产过程中繁琐的人工厚度检测。

Asymptotic Direct System of C^(*)-algebras and Locally AF-algebra

We define the direct limit of the asymptotic direct system of C^(*)-algebras and give some properties of it.Finally,we prove that a C^(*)-algebra is a locally AF-algebra,if and only if it is the direct limit of an asymptotic direct system of finite-dimensional C^(*)-algebras.

ISOMORPHISMS AND DERIVATIONS IN C*-ALGEBRAS

In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality：‖f （x） ＋ f （y） ＋ 2f （z） ＋ 2f （w）‖ ≤‖ 2f x ＋ y2 ＋ z ＋ w ‖（0.1）This is applied to investigate isomorphisms between C＊-algebras, Lie C＊-algebras and JC＊-algebras, and derivations on C＊-algebras, Lie C＊-algebras and JC＊-algebras, associated with the Cauchy-Jensen functional equation 2f （x ＋ y/2 ＋ z ＋ w） = f（x） ＋ f（y） ＋ 2f（z） ＋ 2f（w）.

THE CLASSIFICATION OF NILPOTENT LEIBNIZ 3-ALGEBRAS

The notions of the nilpotent and the strong-nilpotent Leibniz 3-algebras are defined. And the three dimensional two-step nilpotent, strong-nilpotent Leibniz 3-algebras are classified.

CHAIN CONDITIONS FOR C＊-ALGEBRAS COMING FROM HILBERT C＊-MODULES

In this paper we define and study chain conditions for Hilbert C＊-modules through their C＊-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that these chain conditions are passed from the C＊-algebra to its Hilbert module under certain conditions. We also study chain conditions for Hilbert modules coming from inclusion of C＊-algebra with a faithful conditional expectation.

Diagonal Invariant Ideals of Topologically Graded C~*-algebras

We study diagonal invariant ideals of topologically graded C*-algebras over discrete groups. Since all Toeplitz algebras defined on discrete groups are topologically graded, the results in this paper have improved the first author's previous works on this topic.

C^＊-Structure of Quantum Double for Finite Hopf C^＊-Algebra

Let H be a finite Hopf C^＊ -algebra and H′be its dual Hopf algebra. Drinfeld＇s quantum double D（H） of H is a Hopf^＊-algebra. There is a faithful positive linear functional θ on D（H）. Through the associated Gelfand-Naimark-Segal （GNS） representation, D（H） has a faithful^＊ -representation so that it becomes a Hopf C^＊ -algebra. The canonical embedding map of H into D（H） is isometric.

LINEAR *-DERIVATIONS ON JB*-ALGEBRAS

It is shown that for a derivation on a JB* -algebra B, there exists a unique C-linear *-derivation D:B→B near the derivation.

On BCL⁺-Algebras

This paper presents the BCL+-algebras, which is derived the fundamental properties. Results are generalized with version of BCL-algebras [5], using some unusual for a binary relation * and a constant 1 (one) in a non-empty set X, one may take different axiom systems for BCL+-algebras.