Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach

This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.

Distributed Stochastic Optimization with Compression for Non-Strongly Convex Objectives

We are investigating the distributed optimization problem,where a network of nodes works together to minimize a global objective that is a finite sum of their stored local functions.Since nodes exchange optimization parameters through the wireless network,large-scale training models can create communication bottlenecks,resulting in slower training times.To address this issue,CHOCO-SGD was proposed,which allows compressing information with arbitrary precision without reducing the convergence rate for strongly convex objective functions.Nevertheless,most convex functions are not strongly convex(such as logistic regression or Lasso),which raises the question of whether this algorithm can be applied to non-strongly convex functions.In this paper,we provide the first theoretical analysis of the convergence rate of CHOCO-SGD on non-strongly convex objectives.We derive a sufficient condition,which limits the fidelity of compression,to guarantee convergence.Moreover,our analysis demonstrates that within the fidelity threshold,this algorithm can significantly reduce transmission burden while maintaining the same convergence rate order as its no-compression equivalent.Numerical experiments further validate the theoretical findings by demonstrating that CHOCO-SGD improves communication efficiency and keeps the same convergence rate order simultaneously.And experiments also show that the algorithm fails to converge with low compression fidelity and in time-varying topologies.Overall,our study offers valuable insights into the potential applicability of CHOCO-SGD for non-strongly convex objectives.Additionally,we provide practical guidelines for researchers seeking to utilize this algorithm in real-world scenarios.

Sub-Differential Characterizations of Non-Smooth Lower Semi-Continuous Pseudo-Convex Functions on Real Banach Spaces

In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of non-smooth convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the monotonicity of its sub-differentials to the lower semi-continuous pseudo-convex functions on real Banach spaces.

ON α-CONVEX FUNCTIONS WITH MISSING COEFFICIENTS

Let Jn(α,A,B),α≥0,-1≤B<A≤1,n≥1,denote the class of functions f(z)=z+∑k=n+1^∞αkZ^k which are analytic in E={z:|z|<1} and satisfy the conditions f(z)f′(z)/z≠0 and (1-α)zf′(z)/f(z)+α(1+zf″(z)/f′(z))-<1+Az/1+Bz for z∈E.In this paper we obtain incluion relations,distortion properties and estimates of |αn+2-λα^2n+1| for the class Jn(α,A,B),where λ is complex.

F-53B胁迫下污水厌氧处理系统及微生物群落的响应

通过构建厌氧反应体系,评估低浓度(1mg/L)和高浓度(10mg/L)氯化多氟醚磺酸盐(F-53B)胁迫下,厌氧处理系统出水水质、污泥性状和细菌群落的响应特征.结果表明,在F-53B的胁迫下,COD、氮(TN、NH_(4)^(+)-N)和磷(TP、PO_(4)^(3-)-P)在出水中的含量会升高,而污泥相对生物量(MLVSS/MLSS)则出现下降,且F-53B的浓度越高影响越大.高通量测序分析发现,相较于对照组(0mg/L F-53B),仅高浓度F-53B胁迫下细菌群落的多样性(ACE、Chao1和PD指数)出现了显著下降.同时,研究还发现,随着高浓度F-53B暴露时间的延长,厚壁菌门的相对丰度逐渐增大,而变形菌门、拟杆菌门和硝化螺旋菌门的相对丰度逐渐降低.此外,基于FAPROTAX功能预测分析发现,F-53B胁迫下微生物表现出更低的氮(N)代谢潜力和更高的化能异养和发酵能力.冗余分析(RDA)表明,厚壁菌门主要受F-53B的正向影响,并与TN和NH_(4)^(+)-N呈正相关;而变形菌门受F-53B的负向影响,并与COD、TP和PO_(4)^(3-)-P呈正相关.揭示了新型氟化物—F-53B对污水厌氧处理系统的胁迫机制.

THE SCHUR HARMONIC CONVEXITY FOR A CLASS OF SYMMETRIC FUNCTIONS

In this article, we prove that the symmetric function Fn（x,r）=∑i1＋i2＋……in=r（x1（i1x2^i2……xn^in）1/r is Schur harmonic convex for x ∈ R＋n and r ∈N -=（1, 2, 3,...} As its applications, some analytic inequalities are established.

SOME INEQUALITIES OF HERMITE-HADAMARD TYPE FOR s-CONVEX FUNCTIONS

In this paper several inequalities of the left-hand side of Hermite-Hadamard’s inequality are obtained for s-convex functions.

Differentiability of Convex Functions in Locally Convex Spaces（Ⅰ）──Continuous Convex Functions and Gateaux Differentiability

The aim of this paper is to investigate the differentiability(Gateaux differentiabllity and subdifferentiability) of continuous convex functions on locally convex spaces and to study the behaviour of some important results for this research area in locally convex spaces.

THE HADAMARD INEQUALITY FOR CONVEX FUNCTION VIA FRACTIONAL INTEGRALS

In this paper, we establish several inequalities for some differantiable mappings that are connected with the Riemann-Liouville fractional integrals. The analysis used in the proofs is fairly elementary.

DIFFERENTIABILITY OF CONVEX FUNCTIONS AND ASPLUND SPACES

Characterizations of differentiability are obtained for continuous convex functions defined on nonempty open convex sets of Banach spaces as a generalization and application of a mumber of mathematicians several years effort, and a characteristic theorem is given for Banach spaces which are (weak) Asplund spaces.

CERTAIN SUFFICIENT CONDITIONS FOR STARLIKENESS AND CONVEXITY OF MEROMORPHICALLY MULTIVALENT FUNCTIONS

In this paper we derive certain sufficient conditions for starlikeness and convexity of order α of meromorphically multivalent functions in the punctured unit disk.

Third Hankel Determinant for the Inverse of Starlike and Convex Functions

Denote S to be the class of functions which are analytic,normalized and univalent in the open unit disk U={z:|z|<1}.The important subclasses of S are the class of starlike and convex functions,which we denote by S and C.In this paper,we obtain the third Hankel determinant for the inverse of functions f(z)=z+∞Σn=2 anz^n belonging to S^*and C.

On new classes of strongly Janowski type functions of complex order

We investigate some new subclasses of analytic functions of Janowski type of complex order.We also study inclusion properties,distortion theorems,coefficient bounds and radius of convexity of the functions.Moreover,analytic properties of these classes under certain integral operator are also discussed.Our findings are more comprehensive than the existing results in the literature.

动力系统中F-传递性与F-混合性的一个注记

对一维动力系统的混合性及传递性进行了一般性讨论。设(I,f)是一个拓扑动力系统(简称动力系统或系统),其中I为紧致度量空间(度量为d),f:X→X是连续映射。基于Furstenberg族,研究了一维动力系统(I,f)和它的泛函包络系统(L^(1)(I,I),H_(f))的一些性质,在前人研究的混合性和传递性的基础上,引进了F–混合与F–传递的概念,并证明了如果(I,f)是F–混合的,则(L^(1)(I,I),H_(f))是F–传递的。

APPROXIMATE CONVEXITY AND CONCAVITY OFGENERALIZED GROTZSCH RING FUNCTION

In this paper, the so-called approximate convexity and concavity properties of generalized Groetzsch ring function μa （r） by studying the monotonieity,convexity or concavity of certain composites of μa（r） are obtained.

THE FEKETE-SZEG PROBLEM FOR CLOSE-TO-CONVEX FUNCTIONS WITH RESPECT TO THE KOEBE FUNCTION

An analytic function f in the unit disk D ：= {z ∈ C ： ｜z｜ 〈 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k（z） ：= z/（1-z）2, z ∈ D, if there exists δ ∈ （-π/2,π/2） such that Re {eiδ（1-z）2f′（z）} 〉 0, z ∈ D. For the class C（k） of all close-to-convex functions with respect to k, related to the class of functions convex in the positive direction of the imaginary axis, the Fekete-Szego problem is studied.

Inequalities for Tφ-convex functions

In this paper, the Tφ-convex functions were introduced as a generalizations of convex functions. Then the characteristics of the Tφ-convex functions were discussed. Furthermore, some new inequalities for the Tφ-convex functions were derived.

Convexity for New Integral Operator on k-uniformly p-valent a-convex Functions of Complex Order

In this paper, we obtain the convexity of new general integral operator on some classes of k-uniformly p-valent a-convex functions of complex order. These results extend some known theorems.

基于^(18)F-Florbetaben PET显像可视化阿尔茨海默病脑内β-淀粉样蛋白异常沉积

目的基于氟[^(18)F]贝他苯(^(18)F-FBB)淀粉样蛋白(Aβ)PET显像,分析不同认知损害严重程度阿尔茨海默病(AD)患者不同脑区的Aβ异常沉积特征,以及与认知功能的相关性。资料与方法回顾性纳入2022年8月—2023年10月在复旦大学附属华山医院就诊的18例临床诊断高度可能AD患者,且^(18)F-FBB PET显像均证实存在脑内Aβ异常沉积。根据症状严重程度分为AD源性轻度认知损害(MCI)组8例和痴呆组10例,另纳入正常对照者12例。基于脑部结构相MRI和自动解剖标记模板对3组受试者额叶、外侧顶叶、外侧颞叶、前后扣带回及复合皮质脑区Aβ异常沉积标准化摄取值比值进行半定量分析,并比较组间差异,分析AD患者脑内Aβ沉积程度与简易智能测试量表、蒙特利尔认知评估评分的相关性。结果AD源性MCI和痴呆组在额叶、外侧颞叶、外侧顶叶、前后扣带回及复合皮质Aβ异常沉积的标准化摄取值比值均显著高于对照组(t=7.442~9.151,P均<0.05);但AD源性MCI与痴呆组上述脑区Aβ异常沉积的标准化摄取值比值差异无统计学意义(t=0.312~0.996,P均>0.05)。AD源性MCI和痴呆组脑内Aβ沉积程度与简易智能测试量表、蒙特利尔认知评估评分均无显著相关性(r=-0.049~0.050,P均>0.05)。结论AD源性MCI和痴呆组患者脑内Aβ异常沉积均显著高于正常对照组。但Aβ沉积无法鉴别不同认知损害程度的AD患者,在反映Aβ沉积评估AD临床症状的严重程度方面具有一定局限性。

Several Hermite-Hadamard Type Inequalities for Harmonically Convex Functions in the Second Sense with Applications

In this paper, we first introduce the concept ＂harmonically convex functions＂ in the second sense and establish several Hermite-Hadamard type inequalities for harmonically convex functions in the second sense. Finally, some applications to special mean are shown.