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,provi...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.展开更多
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....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.展开更多
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.
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 i...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.展开更多
We establish the monotonicity and convexity properties for several special functions involving the generalized elliptic integrals, and present some new analytic inequalities.
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 sp...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.展开更多
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 ...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.展开更多
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 martinga...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.展开更多
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(-∞,+...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.展开更多
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 ...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.展开更多
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 unif...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.展开更多
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 ...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.展开更多
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.
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 mo...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.展开更多
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 suff...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.展开更多
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 ...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.展开更多
Sufficient conditions are given for any local minimum of a function of two integer variables to be a global minimum. An example is given </span><span style="font-family:Verdana;">to</span>&...Sufficient conditions are given for any local minimum of a function of two integer variables to be a global minimum. An example is given </span><span style="font-family:Verdana;">to</span><span style="font-family:Verdana;"> show that a function of two integer variables need not be discrete convex for this condition to hold.展开更多
The hydraulic elastic bulging roll system is a new roll system being developed in recent years.It is the first time in home that dead load test and study on this system has been made.Based on the experiment,the analys...The hydraulic elastic bulging roll system is a new roll system being developed in recent years.It is the first time in home that dead load test and study on this system has been made.Based on the experiment,the analysis solution of the bulging convexity of the hydraulic elastic bulging roll was obtained by selecting appropriate displacement function and adopting inverse solution of the elasticity theory.In evaluating,a variable displacement function and its solving method was advanced.The analysis results are in accord with the experiment's.Some conclusions have laid the foundation of establishing close-loop controlled mathematical model of the hydraulic elastic bulging roll system.展开更多
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 inequa...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.展开更多
基金supported in part by the National Natural Science Foundation of China(12101088)the Natural Science Foundation of Sichuan Province(2022NSFSC1858)。
文摘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.
文摘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.
文摘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.
文摘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.
基金supported by the Natural Science Foundation of China(11701176,61673169,11301127,11626101,11601485)the Science and Technology Research Program of Zhejiang Educational Committee(Y201635325)
文摘We establish the monotonicity and convexity properties for several special functions involving the generalized elliptic integrals, and present some new analytic inequalities.
文摘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.
文摘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.
文摘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.
文摘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.
基金Supported by Education Foundation of Henan Province(2003110006)
文摘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.
基金Supported by the Science Foundation of Shaanxi Provincial Educational Department Natural Science Foundation of China(06JK152) Supported by the Graduate Innovation Project of Yanan uni- versity(YCX201003)
文摘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.
文摘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.
文摘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.
文摘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.
文摘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.
文摘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.
文摘Sufficient conditions are given for any local minimum of a function of two integer variables to be a global minimum. An example is given </span><span style="font-family:Verdana;">to</span><span style="font-family:Verdana;"> show that a function of two integer variables need not be discrete convex for this condition to hold.
文摘The hydraulic elastic bulging roll system is a new roll system being developed in recent years.It is the first time in home that dead load test and study on this system has been made.Based on the experiment,the analysis solution of the bulging convexity of the hydraulic elastic bulging roll was obtained by selecting appropriate displacement function and adopting inverse solution of the elasticity theory.In evaluating,a variable displacement function and its solving method was advanced.The analysis results are in accord with the experiment's.Some conclusions have laid the foundation of establishing close-loop controlled mathematical model of the hydraulic elastic bulging roll system.
基金supported by NSFC (60850005)NSF of Zhejiang Province(D7080080, Y7080185, Y607128)
文摘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.