CONVEXITY OF THE FREE BOUNDARY FOR AN AXISYMMETRIC INCOMPRESSIBLE IMPINGING JET

This paper is devoted to the study of the shape of the free boundary for a threedimensional axisymmetric incompressible impinging jet.To be more precise,we will show that the free boundary is convex to the fluid,provided that the uneven ground is concave to the fluid.

On the Application of Mixed Models of Probability and Convex Set for Time-Variant Reliability Analysis

In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems typically involve a complexmultilevel nested optimization problem,which can result in an enormous amount of computation.To this end,this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model.In this method,the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a timeindependent reliability problem.Further,to solve the double nested optimization problem in hybrid reliability calculation,an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point(MPP).The limit state function is linearized at these points,and an innovative random variable is defined to solve the equivalent static reliability analysis model.The effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem.

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.

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.

Accelerated Primal-Dual Projection Neurodynamic Approach With Time Scaling for Linear and Set Constrained Convex Optimization Problems

The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on unconstrained smooth con-vex optimization problems.In this paper,on the basis of primal-dual dynamical approach,Nesterov accelerated dynamical approach,projection operator and directional gradient,we present two accelerated primal-dual projection neurodynamic approaches with time scaling to address convex optimization problems with smooth and nonsmooth objective functions subject to linear and set constraints,which consist of a second-order ODE(ordinary differential equation)or differential conclusion system for the primal variables and a first-order ODE for the dual vari-ables.By satisfying specific conditions for time scaling,we demonstrate that the proposed approaches have a faster conver-gence rate.This only requires assuming convexity of the objective function.We validate the effectiveness of our proposed two accel-erated primal-dual projection neurodynamic approaches through numerical experiments.

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.

THE SCHUR CONVEXITY OF GINI MEAN VALUES IN THE SENSE OF HARMONIC MEAN

We prove that the Gini mean values S（a,b; x,y） are Schur harmonic convex with respect to （x,y）∈（0,∞）×（0,∞） if and only if （a, b） ∈{（a, b）：a≥0,a ≥ b,a＋b＋1≥0}∪{（a,b）：b≥0,b≥a,a＋b＋1≥0} and Schur harmonic concave with respect to （x,y） ∈ （0,∞）×（0,∞） if and only if （a,b）∈{（a,b）：a≤0,b≤0,a｜b｜1≤0}.

MONOTONICITY,CONVEXITY AND INEQUALITIES INVOLVING THE GENERALIZED ELLIPTIC INTEGRALS

We establish the monotonicity and convexity properties for several special functions involving the generalized elliptic integrals, and present some new analytic inequalities.

NORMAL STRUCTURE AND SOME GEOMETRIC PARAMETERS RELATED TO THE MODULUS OF U-CONVEXITY IN BANACH SPACES

We present a short and simple proof of the recent result of Yang and Wang [12]. Stimulated by their idea, two geometric parameters Uax（ε） and βx （ε）, both related to Gao＇s modulus of U-convexity of a Banach space X, are introduced. Their properties and the relationships with normal structure are studied. Some existing results involving normal structure and fixed points for non-expansive mappings in Banach spaces are improved.

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.

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

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

Risk measures with comonotonic subadditivity or convexity on product spaces

In this paper, by an axiomatic approach, we propose the concepts of comonotonic subadditivity and comonotonic convex risk measures for portfolios, which are extensions of the ones introduced by Song and Yan （2006）. Representation results for these new introduced risk measures for portfolios are given in terms of Choquet integrals. Links of these newly introduced risk measures to multi-period comonotonic risk measures are represented. Finally, applications of the newly introduced comonotonic coherent risk measures to capital allocations are provided.

ON CRITERIA FOR STARLIKENESS AND CONVEXITY OF ANALYTIC FUNCTIONS

In this paper the authors study (1-γ+zf(?)(z)/f'(z))/(zf'(z)/f(z)) as a criteria for starlikeness and convexity. Sharp upper bound of |α2| and of the Fekete-Szego functional |α3-μα22| is given for a class of analytic functions defined by using this expression.

Convexity and Positivity of Bivariate Quadratic Bézier Surfaces over a Rectangle

With the help of several discriminants about the zero points of a quartic polynomial, the sufficient and necessary conditions for the positivity and nonnegativity of the quartic polynomial over an interval I(-∞,+∞) was derived. Based on these conclusions, the sufficient and necessary conditions for the positivity and convexity of the 2×2 Bézier surface over a rectangle were obtained. A simple sufficient condition was deduced also and finally several examples were given.

基于Convexity模型的航空公司利率风险管理

国际性特征日趋明显的中国航空公司正面临着金融市场上的诸多不确定性,其中利率风险日益凸显。将Convexity模型这一在西方发达国家较为成熟的风险管理工具引入中国,并将其应用到中国航空公司的风险管理实践,对利率风险进行了极为精确的量化评估,最后给出了相应的规避方法。

THE MODULUS OF CONVEXITY AND THE EQUIVALENT CONDITIONS OF UNIFORMLY NON-SQUARE SPACES

This paper shows that X is uniformly non-square iff P(η_o)】0 for someη_o∈(0,2).Thus X is super-reflexive if and only if for X there exists an equivalent normwhich meets the above condition.By virtue of the before mentioned result,the author derives the necessary,and suffi-cient conditions for X and l^p(X_j)being uniformly non-square,respectively,and gives acharacterization of finite-dimensional spaces which are uniformly non-square.

Characterization of Uniform PL-convexity of Complex Banach Space by Functions with Two Variables

We give a new characterization ofq-uniform PL-convexity of complex Banach space by using the existence of a kind of functions with two variables and then prove a sharp weak (1, 1)-type inequality for analytic martingales with values in the Banach space.

ON A GENERALIZED MODULUS OF CONVEXITY AND UNIFORM NORMAL STRUCTURE

In this article, the authors study a generalized modulus of convexity, δ（α） （ε）. Certain related geometrical properties of this modulus are analyzed. Their main result is that Banach space X has uniform normal structure if there exists ε, 0 ≤e≤ 1, such that δ^（α）（1＋ε ） 〉 （1- α）ε.

Minima Domain Intervals and the S-Convexity, as well as the Convexity, Phenomenon

In this paper, we propose a refinement in the analytical definition of the s2-convex classes of functions aiming to progress further in the direction of including s2-convexity properly in the body of Real Analysis.