This work is devoted to the study of initial boundary value problem for k-component system of semilinear wave equations with several fundamental boundary conditions(namely,the Dirichlet,Neumann,and Robin boundary cond...This work is devoted to the study of initial boundary value problem for k-component system of semilinear wave equations with several fundamental boundary conditions(namely,the Dirichlet,Neumann,and Robin boundary conditions).Blow-up results and lifespan estimates of solutions to the problem with two different types of weak damping terms and power nonlinearities in the sub-critical and critical cases on exterior domain are obtained.The test function technique is performed in the proofs.It is worth observing that our results in Theorem 1.1 in this article contain the results in[6]as a special case whenθ=0.To the best of our knowledge,the results in Theorems 1.1-1.2 are new.展开更多
Coupled thermo-mechanical analysis of two bonded functionally graded materials subjected to thermal loads is conducted in this study with the graded finite element method. The thermal-mechanical properties of the bi-m...Coupled thermo-mechanical analysis of two bonded functionally graded materials subjected to thermal loads is conducted in this study with the graded finite element method. The thermal-mechanical properties of the bi-material interfaces are classified based on discontinuity degrees of their material properties and their derivatives at the interfaces. Numerical results indicate that discontinuity exerts remarkable effect on the temperature profile and stress value at the interface of two bonded functionally-graded materials. Under the thermal flux loading conditions, the stronger the interface discontinuity is, the smaller the heat flux is.展开更多
In this paper the authors introduce some new ideas on generalized numbers and generalized weak functions. They prove that the product of any two weak functions is a generalized weak function. So in particular they sol...In this paper the authors introduce some new ideas on generalized numbers and generalized weak functions. They prove that the product of any two weak functions is a generalized weak function. So in particular they solve the problem of the multiplication of two generalized functions.展开更多
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,...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.展开更多
Toll-like receptor （TLR）-mediated inflammatory response could negatively affect bone metabolism. In this study, we determined how osteogenesis is regulated during inflammatory responses that are downstream of TLR si...Toll-like receptor （TLR）-mediated inflammatory response could negatively affect bone metabolism. In this study, we determined how osteogenesis is regulated during inflammatory responses that are downstream of TLR signaling. Human primary osteoblasts were cultured in collagen gels. Pam3CSK4 （P3C） and Escherichia coli lipopolysaccharide （EcLPS） were used as TLR2 and TLR4 ligand respectively. Porphyromonas gingivalis LPS having TLR2 activity with either TLR4 agonism （Pg1690） or TLR4 antagonism （Pg1449） and mutant E. coli LPS （LPxE/LPxF/WSK） were used. IL-lp, SH2-containing inositol phosphatase-1 （SHIP1） that has regulatory roles in osteogenesis, alkaline phosphatase and mineralization were analyzed. 3α-Aminocholestane （3AC） was used to inhibit SHIP1. Our results suggest that osteoblasts stimulated by P3C, poorly induced IL-1β but strongly upregulated SHIP1 and enhanced osteogenic mediators. On the contrary, EcLPS significantly induced IL-1β and osteogenic mediators were not induced. While Pg1690 downmodulated osteogenic mediators, Pg1449 enhanced osteogenic responses, suggesting that TLR4 signaling annuls osteogenesis even with TLR2 activity. Interestingly, mutant E. coli LPS that induces weak inflammation upregulated osteogenesis, but SHIP1 was not induced. Moreover, inhibiting SHIP1 significantly upregulated TLR2-mediated inflammatory response and downmodulated osteogenesis. In conclusion, these results suggest that induction of weak inflammatory response through TLR2 （with SHIP1 activity） and mutant TLR4 ligands could enhance osteogenesis.展开更多
The almost convergent function which was introduced by Raimi [6] and discussed by Ho [4], Das and Nanda [2, 3], is the continuous analogue of almost convergent sequences （see [5]）. In this paper, we establish the Ta...The almost convergent function which was introduced by Raimi [6] and discussed by Ho [4], Das and Nanda [2, 3], is the continuous analogue of almost convergent sequences （see [5]）. In this paper, we establish the Tauberian conditions and the Cauchy criteria for weak almost convergent functions on R2＋ .展开更多
This paper is a further continuation of the paper [1]. In the present paper Mellin transform and Miints formula of weak functions in complex domain will be treated.
This paper is a contionuation of [1] and is concerned with multiplication of weak functions. Here the weak functions are treated as generalized expansions in Hermite functions in [2].
In this paper, we establish the following limiting weak-type behaviors of Littlewood-Paley g-function g_φ: for nonnegative function f∈ L^1(R^n),■and ■where f_t(x) =t^(-n)f(t^(-1) x) for t > 0. Meanwhile, the co...In this paper, we establish the following limiting weak-type behaviors of Littlewood-Paley g-function g_φ: for nonnegative function f∈ L^1(R^n),■and ■where f_t(x) =t^(-n)f(t^(-1) x) for t > 0. Meanwhile, the corresponding results for Marcinkiewicz integral and its fractional version with kernels satisfying L_α~q-Dini condition are also given.展开更多
In this paper, we show that many risk measures arising in Actuarial Sciences, Finance, Medicine, Welfare analysis, etc. are gathered in classes of Weighted Mean Loss or Gain (WMLG) statistics. Some of them are Upper T...In this paper, we show that many risk measures arising in Actuarial Sciences, Finance, Medicine, Welfare analysis, etc. are gathered in classes of Weighted Mean Loss or Gain (WMLG) statistics. Some of them are Upper Threshold Based (UTH) or Lower Threshold Based (LTH). These statistics may be time-dependent when the scene is monitored in the time and depend on specific functions w and d. This paper provides time-dependent and uniformly functional weak asymptotic laws that allow temporal and spatial studies of the risk as well as comparison among statistics in terms of dependence and mutual influence. The results are particularized for usual statistics like the Kakwani and Shorrocks ones that are mainly used in welfare analysis. Data-driven applications based on pseudo-panel data are provided.展开更多
In this paper,a new subclass of close-to-convex harmonic functions defined by differential operators is introduced.Some properties for functions belonging to that,such as,representation theorem,sufficient conditions,i...In this paper,a new subclass of close-to-convex harmonic functions defined by differential operators is introduced.Some properties for functions belonging to that,such as,representation theorem,sufficient conditions,inclusion relations,coefficient inequalities,growth and convex combination problems are obtained.In addition,the radius of starlike,the radius of convexity and convolution properties of this class are obtained.展开更多
The main purpose of this paper is to investigate the singularities of solutions to the single Tricomi equation with derivative term and combined memory term.In addition,the blow-up of the solution to the weakly couple...The main purpose of this paper is to investigate the singularities of solutions to the single Tricomi equation with derivative term and combined memory term.In addition,the blow-up of the solution to the weakly coupled system with memory term is also considered,where one is a power nonlinear term and the other is a derivative nonlinear term.Upper bound lifespan estimates of solution are obtained in the sub-critical by utilizing the test function method and iteration technique.The innovation of this paper focuses on the lifespan estimates of the solutions,which extends the well-known Strauss and Glassey conjectures.展开更多
基金Supported by Fundamental Research Program of Shanxi Province(20210302123045,20210302123182)National Natural Science Foundation of China(11601446)。
文摘This work is devoted to the study of initial boundary value problem for k-component system of semilinear wave equations with several fundamental boundary conditions(namely,the Dirichlet,Neumann,and Robin boundary conditions).Blow-up results and lifespan estimates of solutions to the problem with two different types of weak damping terms and power nonlinearities in the sub-critical and critical cases on exterior domain are obtained.The test function technique is performed in the proofs.It is worth observing that our results in Theorem 1.1 in this article contain the results in[6]as a special case whenθ=0.To the best of our knowledge,the results in Theorems 1.1-1.2 are new.
基金supported by the National Natural Science Foundation of China(Nos.10902046,11032006and11121202)the Fundamental Research Funds for the Central Universities(lzujbky-2012-2)+1 种基金the Fund of Ministry of Education of the Program of Changjiang Scholars and Innovative Research Team in University(No.IRT0628)the Science Foundation of the Ministry of Education of China for Ph.D.program
文摘Coupled thermo-mechanical analysis of two bonded functionally graded materials subjected to thermal loads is conducted in this study with the graded finite element method. The thermal-mechanical properties of the bi-material interfaces are classified based on discontinuity degrees of their material properties and their derivatives at the interfaces. Numerical results indicate that discontinuity exerts remarkable effect on the temperature profile and stress value at the interface of two bonded functionally-graded materials. Under the thermal flux loading conditions, the stronger the interface discontinuity is, the smaller the heat flux is.
文摘In this paper the authors introduce some new ideas on generalized numbers and generalized weak functions. They prove that the product of any two weak functions is a generalized weak function. So in particular they solve the problem of the multiplication of two generalized functions.
文摘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.
基金supported by Elam M. and Georgina E.Hack Memorial Research Funds,Department of Periodontics,University of Washington,Seattle,WA,USAsupported by WVCTSI funds,West Virginia University,Morgantown,WV,USA
文摘Toll-like receptor （TLR）-mediated inflammatory response could negatively affect bone metabolism. In this study, we determined how osteogenesis is regulated during inflammatory responses that are downstream of TLR signaling. Human primary osteoblasts were cultured in collagen gels. Pam3CSK4 （P3C） and Escherichia coli lipopolysaccharide （EcLPS） were used as TLR2 and TLR4 ligand respectively. Porphyromonas gingivalis LPS having TLR2 activity with either TLR4 agonism （Pg1690） or TLR4 antagonism （Pg1449） and mutant E. coli LPS （LPxE/LPxF/WSK） were used. IL-lp, SH2-containing inositol phosphatase-1 （SHIP1） that has regulatory roles in osteogenesis, alkaline phosphatase and mineralization were analyzed. 3α-Aminocholestane （3AC） was used to inhibit SHIP1. Our results suggest that osteoblasts stimulated by P3C, poorly induced IL-1β but strongly upregulated SHIP1 and enhanced osteogenic mediators. On the contrary, EcLPS significantly induced IL-1β and osteogenic mediators were not induced. While Pg1690 downmodulated osteogenic mediators, Pg1449 enhanced osteogenic responses, suggesting that TLR4 signaling annuls osteogenesis even with TLR2 activity. Interestingly, mutant E. coli LPS that induces weak inflammation upregulated osteogenesis, but SHIP1 was not induced. Moreover, inhibiting SHIP1 significantly upregulated TLR2-mediated inflammatory response and downmodulated osteogenesis. In conclusion, these results suggest that induction of weak inflammatory response through TLR2 （with SHIP1 activity） and mutant TLR4 ligands could enhance osteogenesis.
文摘The almost convergent function which was introduced by Raimi [6] and discussed by Ho [4], Das and Nanda [2, 3], is the continuous analogue of almost convergent sequences （see [5]）. In this paper, we establish the Tauberian conditions and the Cauchy criteria for weak almost convergent functions on R2＋ .
文摘This paper is a further continuation of the paper [1]. In the present paper Mellin transform and Miints formula of weak functions in complex domain will be treated.
文摘This paper is a contionuation of [1] and is concerned with multiplication of weak functions. Here the weak functions are treated as generalized expansions in Hermite functions in [2].
文摘In this paper, we establish the following limiting weak-type behaviors of Littlewood-Paley g-function g_φ: for nonnegative function f∈ L^1(R^n),■and ■where f_t(x) =t^(-n)f(t^(-1) x) for t > 0. Meanwhile, the corresponding results for Marcinkiewicz integral and its fractional version with kernels satisfying L_α~q-Dini condition are also given.
文摘In this paper, we show that many risk measures arising in Actuarial Sciences, Finance, Medicine, Welfare analysis, etc. are gathered in classes of Weighted Mean Loss or Gain (WMLG) statistics. Some of them are Upper Threshold Based (UTH) or Lower Threshold Based (LTH). These statistics may be time-dependent when the scene is monitored in the time and depend on specific functions w and d. This paper provides time-dependent and uniformly functional weak asymptotic laws that allow temporal and spatial studies of the risk as well as comparison among statistics in terms of dependence and mutual influence. The results are particularized for usual statistics like the Kakwani and Shorrocks ones that are mainly used in welfare analysis. Data-driven applications based on pseudo-panel data are provided.
基金Supported by the Natural Science Foundation of Inner Mongolia(Grant Nos.2024MS01014,2022MS01004)the Higher-School Science Foundation of Inner Mongolia(Grant No.NJZZ19209)。
文摘In this paper,a new subclass of close-to-convex harmonic functions defined by differential operators is introduced.Some properties for functions belonging to that,such as,representation theorem,sufficient conditions,inclusion relations,coefficient inequalities,growth and convex combination problems are obtained.In addition,the radius of starlike,the radius of convexity and convolution properties of this class are obtained.
基金Supported by National Natural Science Foundation of China Under Grant(12401647)Supported by Fundamental Research Program of Shanxi Province(202203021212336)+2 种基金Taiyuan Institute of Technology Scientific Research Initial Funding(2023KJ057,2024KJ007,2024LJ005)Supported by Scientific and Technologial Innovation Programs of Higher Education Institutions in Shanxi(2024L358)Youth Program of Taiyuan University(24TYQN10)。
文摘The main purpose of this paper is to investigate the singularities of solutions to the single Tricomi equation with derivative term and combined memory term.In addition,the blow-up of the solution to the weakly coupled system with memory term is also considered,where one is a power nonlinear term and the other is a derivative nonlinear term.Upper bound lifespan estimates of solution are obtained in the sub-critical by utilizing the test function method and iteration technique.The innovation of this paper focuses on the lifespan estimates of the solutions,which extends the well-known Strauss and Glassey conjectures.
