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.

Second Note on the Definition of S₁-Convexity

In this note, we discuss the definition of the S1-convexity Phenomenon. We first make use of some results we have attained for?? in the past, such as those contained in [1], to refine the definition of the phenomenon. We then observe that easy counter-examples to the claim extends K0 are found. Finally, we make use of one theorem from [2] and a new theorem that appears to be a supplement to that one to infer that? does not properly extend K0 in both its original and its revised version.

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.

First Note on the Definition of s<i>1</i>-Convexity

In this note, we analyze a few major claims about . As a consequence, we rewrite a major theorem, nullify its proof and one remark of importance, and offer a valid proof for it. The most important gift of this paper is probably the reasoning involved in all: We observe that a constant, namely t, has been changed into a variable, and we then tell why such a move could not have been made, we observe the discrepancy between the claimed domain and the actual domain of a supposed function that is created and we then explain why such a function could not, or should not, have been created, along with others.

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.

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

We give a new characterization of q 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.

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.

The Optimality Conditions for Multiobjective Semi-infinite Programming Involving Generalized Unified （C, α, p, d）-convexity

The definition of generalized unified (C, α, ρ, d)-convex function is given. The concepts of generalized unified (C, α, ρ, d)-quasiconvexity, generalized unified (C, α, ρ, d)-pseudoconvexity and generalized unified (C, α, ρ, d)-strictly pseudoconvex functions are presented. The sufficient optimality conditions for multiobjective nonsmooth semi-infinite programming are obtained involving these generalized convexity lastly.

Stratified Convexity &Concavity of Gradient Flows on Manifolds with Boundary

As has been observed by Morse [1], any generic vector field v on a compact smooth manifold X with boundary gives rise to a stratification of the boundary by compact submanifolds , where . Our main observation is that this stratification re-flects the stratified convexity/concavity of the boundary ?with respect to the ?v-flow. We study the behavior of this stratification under deformations of the vector field v. We also investigate the restrictions that the existence of a convex/concave traversing ?v-flow imposes on the topology of X. Let be the orthogonal projection of on the tangent bundle of . We link the dynamics of theon the boundary with the property of in X being convex/concave. This linkage is an instance of more general phenomenon that we call “holography of traversing fields”—a subject of a different paper to follow.

BERNSTEIN-TYPE OPERATORS, CONVEXITY AND LIPSCHITZ CLASSES

In the present paper we extend previous results about the monotoaicity of Bernstein-type operators rdtiwe to convex functions and about the preservation of Lipschitz classes.

On the Convexity of Generalized Grotzsch Ring Function

In this paper,the authors study the monotoneity and convexity of certain combinations and composites defined in terms of the generalized Grotzsch ring function μa (r), which appears in Ramanujan' s generalized modular equations,and obtain some inequalities for this function.

A Sufficient Convexity Condition for Parametric Bézier Surface over Rectangle

Surface convexity is a key issue in computer aided geometric design, which is widely applied in geometric modeling field, such as physical models, industrial design, automatic manufacturing, etc. In this paper, a sufficient convexity condition of the parametric Bézier surface over rectangles is proposed, which is firstly considered as a sufficient convexity condition for the Bézier control grid. The condition is proved by De Casteljau surface subdivision arithmetic, in which the recursive expressions elaborate that the control grid eventually converges to the surface. At last, two examples for the modeling of interpolation-type surface are discussed, one of which is a general surface and the other is a degenerate surface.

Schur Convexity and the Dual Simpson’s Formula

In this paper, we show that some functions related to the dual Simpson’s formula and Bullen- Simpson’s formula are Schur-convex provided that f is four-convex. These results should be compared to that of Simpson’s formula in Applied Math. Lett. (24) (2011), 1565-1568.

ANALYSIS SOLUTION OF BULGING CONVEXITY OF THE HYDRAULIC ELASTIC BULGING ROLL

ＡＮＡＬＹＳＩＳＳＯＬＵＴＩＯＮＯＦＢＵＬＧＩＮＧＣＯＮＶＥＸＩＴＹＯＦＴＨＥＨＹＤＲＡＵＬＩＣＥＬＡＳＴＩＣＢＵＬＧＩＮＧＲＯＬＬＡＮＡＬＹＳＩＳＳＯＬＵＴＩＯＮＯＦＢＵＬＧＩＮＧＣＯＮＶＥＸＩＴＹＯＦＴＨＥＨＹＤＲＡＵＬＩＣＥＬＡＳＴＩＣＢＵＬＧ...

Convexity Properties for a Function of Two Integer Variables

Sufficient conditions are given for any local minimum of a function of two integer variables to be a global minimum. An example is given to show that a function of two integer variables need not be discrete convex for this condition to hold.

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.

First Note on the Definition of S2-Convexity

In this short, but fundamental, note, we start progressing towards a mathematically sound definition of the real functional classes

Addendum to: An Approach to Hierarchical Clustering via Level Surfaces and Convexity

This article is an addendum to the 2001 paper [1] which investigated an approach to hierarchical clustering based on the level sets of a density function induced on data points in a d-dimensional feature space. We refer to this as the “level-sets approach” to hierarchical clustering. The density functions considered in [1] were those formed as the sum of identical radial basis functions centered at the data points, each radial basis function assumed to be continuous, monotone decreasing, convex on every ray, and rising to positive infinity at its center point. Such a framework can be investigated with respect to both the Euclidean (L2) and Manhattan (L1) metrics. The addendum here puts forth some observations and questions about the level-sets approach that go beyond those in [1]. In particular, we detail and ask the following questions. How does the level-sets approach compare with other related approaches? How is the resulting hierarchical clustering affected by the choice of radial basis function? What are the structural properties of a function formed as the sum of radial basis functions? Can the levels-sets approach be theoretically validated? Is there an efficient algorithm to implement the level-sets approach?