In the paper,by virtue of a general formula for any derivative of the ratio of two differentiable functions,with the aid of a recursive property of the Hessenberg determinants,the authors establish determinantal expre...In the paper,by virtue of a general formula for any derivative of the ratio of two differentiable functions,with the aid of a recursive property of the Hessenberg determinants,the authors establish determinantal expressions and recursive relations for the Bessel zeta function and for a sequence originating from a series expansion of the power of modified Bessel function of the first kind.展开更多
In this article, we study the regularity of weak solutions and the blow-up criteria for smooth solutions to the magneto-micropolar fluid equations in R3. We obtain the classical blow-up criteria for smooth solutions ...In this article, we study the regularity of weak solutions and the blow-up criteria for smooth solutions to the magneto-micropolar fluid equations in R3. We obtain the classical blow-up criteria for smooth solutions （u,w, b）, i.e., u ∈ Lq（0, T; LP（R3） for 2/q＋3/P≤ 1with 3〈P≤∞,u∈C（[0,T）;L3（R3））or△u∈Lq（0,T,LP）for 3/2〈P≤∞ satisfying 2/q＋3/P≤ 2. Moreover, our results indicate that the regularity of weak solutions is dominated by the velocity u of the fluid. In the end-point case p = ∞, the blow-up criteriacan be extended to more general spaces △u E L1 （0, T; B0∞,∞（R3）.展开更多
In this paper we prove a Schwarz-Pick lemma for the modulus of holomorphic mappings from the polydisk into the unit ball. This result extends some related results.
In the paper,the authors collect,discuss,and find out several connections,equivalences,closed-form formulas,and combinatorial identities concerning partial Bell polynomials,falling factorials,rising factorials,extende...In the paper,the authors collect,discuss,and find out several connections,equivalences,closed-form formulas,and combinatorial identities concerning partial Bell polynomials,falling factorials,rising factorials,extended binomial coefficients,and the Stirling numbers of the first and second kinds.These results are new,interesting,important,useful,and applicable in combinatorial number theory.展开更多
In this paper,we present monotonicity results of a function involving the inverse hyperbolic sine.From these,we obtain some lower bounds for the inverse hyperbolic sine.
Gas molecules(such as CH4,CO,H2O,H2S,NH_3)adsorption on the pure and Au-doped WO3(001)surface have been studied by Density functional theory calculations with generalized gradient approximation.Based on the the calcul...Gas molecules(such as CH4,CO,H2O,H2S,NH_3)adsorption on the pure and Au-doped WO3(001)surface have been studied by Density functional theory calculations with generalized gradient approximation.Based on the the calculation of adsorption energy,we found the most stable adsorption site for gas molecules by comparing the adsorption energies of different gas molecules on the WO3(001)surface.We have also compared the adsorption energy of five different gas molecules on the WO3(001)surface,our calculation results show that when the five kinds of gases are adsorbed on the pure WO3(001)surface,the order of the surface adsorption energy is CO>H2S>CH4>H2O>NH3.And the results show that NH3 is the most easily adsorbed gas among the other four gases adsorbed on the surface of pure WO3(001)surface.We also calculated the five different gases on the Au-doped WO3(001)surface.The order of adsorption energy was found to be different from the previous calculation:CO>CH4>H2S>H2O>NH3.These results provide a new route for the potential applications of Au-doped WO3 in gas molecules adsorption.展开更多
In this paper, the authors prove a general Schwarz lemma at the boundary for the holomorphic mapping f between unit balls B and B＇ in separable complex Hilbert spaces H and H＇, respectively. It is found that if the ...In this paper, the authors prove a general Schwarz lemma at the boundary for the holomorphic mapping f between unit balls B and B＇ in separable complex Hilbert spaces H and H＇, respectively. It is found that if the mapping f ∈ C^1＋α at z0 ∈ B with f（zo） = wo ∈ OB＇, then the Fr＆het derivative operator Df（z0） maps the tangent space Tz0（ B^n） to Tw0（ B＇）, the holomorphic tangent space Tz0^（1,0） to Tw0（1,0）（ B＇）,respectively.展开更多
By virtue of Cauchy’s integral formula in the theory of complex functions,the authors establish an integral representation for the weighted geometric mean,apply this newly established integral representation to show ...By virtue of Cauchy’s integral formula in the theory of complex functions,the authors establish an integral representation for the weighted geometric mean,apply this newly established integral representation to show that the weighted geometric mean is a complete Bernstein function,and find a new proof of the well-known weighted arithmetic-geometric mean inequality.展开更多
1 Introduction Currently, categorical data are world applications, particularly widely used in many realin the biomedical and social sciences. Unlike the numeric case, when the data are cate- gorical, choosing the app...1 Introduction Currently, categorical data are world applications, particularly widely used in many realin the biomedical and social sciences. Unlike the numeric case, when the data are cate- gorical, choosing the appropriate similarity or dissimilarity measure between two different categorical objects became a difficult task for many applications. What＇s more, in this case, the set mean, i.e., the averaging value of a finite set of data objects, is an undefined concept. This means that the well known K-means [ 1 ] and its numerous variants cannot be directly used for center-based clustering of categorical data.展开更多
This paper proposes a dwindling filter line search algorithm for nonlinear equality constrained optimization. A dwindling filter, which is a modification of the traditional filter, is employed in the algorithm. The en...This paper proposes a dwindling filter line search algorithm for nonlinear equality constrained optimization. A dwindling filter, which is a modification of the traditional filter, is employed in the algorithm. The envelope of the dwindling filter becomes thinner and thinner as the step size approaches zero. This new algorithm has more flexibility for the acceptance of the trial step and requires less computational costs compared with traditional filter algorithm. The global and local convergence of the proposed algorithm are given under some reasonable conditions. The numerical experiments are reported to show the effectiveness of the dwindling filter algorithm.展开更多
This paper proposes a nonmonotone line search filter method with reduced Hessian updating for solving nonlinear equality constrained optimization.In order to deal with large scale problems,a reduced Hessian matrix is ...This paper proposes a nonmonotone line search filter method with reduced Hessian updating for solving nonlinear equality constrained optimization.In order to deal with large scale problems,a reduced Hessian matrix is approximated by BFGS updates.The new method assures global convergence without using a merit function.By Lagrangian function in the filter and nonmonotone scheme,the authors prove that the method can overcome Maratos effect without using second order correction step so that the locally superlinear convergence is achieved.The primary numerical experiments are reported to show effectiveness of the proposed algorithm.展开更多
The authors prove a general Schwarz lemma at the boundary for holomorphic mappings from the polydisc to the unit ball in any dimensions.For the special case of one complex variable,the obtained results give the classi...The authors prove a general Schwarz lemma at the boundary for holomorphic mappings from the polydisc to the unit ball in any dimensions.For the special case of one complex variable,the obtained results give the classic boundary Schwarz lemma.展开更多
This paper proposes a filter secant method with nonmonotone line search for non-linearequality constrained optimization.The Hessian of the Lagrangian is approximated using the BFGSsecant update.This new method has mor...This paper proposes a filter secant method with nonmonotone line search for non-linearequality constrained optimization.The Hessian of the Lagrangian is approximated using the BFGSsecant update.This new method has more flexibility for the acceptance of the trial step and requires lesscomputational costs compared with the monotone one.The global and local convergence of the proposedmethod are given under some reasonable conditions.Further,two-step Q-superlinear convergence rateis established by introducing second order correction step.The numerical experiments are reported toshow the effectiveness of the proposed algorithm.展开更多
The author studies the Cauchy problem of the dissipative quasi-geostrophic equation in weak Morrey spaces. The global well-posedness is established for any small initial data in the weak space Mp^＊,γ（R^n）, with 1...The author studies the Cauchy problem of the dissipative quasi-geostrophic equation in weak Morrey spaces. The global well-posedness is established for any small initial data in the weak space Mp^＊,γ（R^n）, with 1〈p〈∞and A = n-（2α-1）p, and for a small external force in a time-weighted weak Morrey space.展开更多
基金The first author,Mrs.Yan Hong,was partially supported by the Natural Science Foundation of Inner Mongolia(Grant No.2019MS01007)by the Science Research Fund of Inner Mongolia University for Nationalities(Grant No.NMDBY15019)by the Foun-dation of the Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region(Grant Nos.NJZY19157 and NJZY20119)in China。
文摘In the paper,by virtue of a general formula for any derivative of the ratio of two differentiable functions,with the aid of a recursive property of the Hessenberg determinants,the authors establish determinantal expressions and recursive relations for the Bessel zeta function and for a sequence originating from a series expansion of the power of modified Bessel function of the first kind.
基金partially supported by the National Natural Science Foun-dation of China (10771052)Program for Science & Technology Innovation Talents in Universities of Henan Province (2009HASTIT007)+1 种基金Doctor Fund of Henan Polytechnic University (B2008-62)Innovation Scientists and Technicians Troop Construction Projects of Henan Province
文摘In this article, we study the regularity of weak solutions and the blow-up criteria for smooth solutions to the magneto-micropolar fluid equations in R3. We obtain the classical blow-up criteria for smooth solutions （u,w, b）, i.e., u ∈ Lq（0, T; LP（R3） for 2/q＋3/P≤ 1with 3〈P≤∞,u∈C（[0,T）;L3（R3））or△u∈Lq（0,T,LP）for 3/2〈P≤∞ satisfying 2/q＋3/P≤ 2. Moreover, our results indicate that the regularity of weak solutions is dominated by the velocity u of the fluid. In the end-point case p = ∞, the blow-up criteriacan be extended to more general spaces △u E L1 （0, T; B0∞,∞（R3）.
基金supported by the National Natural Science Foundation of China(11201199)the Scientific Research Foundation of Jinling Institute of Technology(Jit-b-201221)Qing Lan Project
文摘In this paper we prove a Schwarz-Pick lemma for the modulus of holomorphic mappings from the polydisk into the unit ball. This result extends some related results.
基金supported in part by the National Natural Science Foundation of China(Grant No.12061033)by the Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region(Grants No.NJZY20119)by the Natural Science Foundation of Inner Mongolia(Grant No.2019MS01007),China.
文摘In the paper,the authors collect,discuss,and find out several connections,equivalences,closed-form formulas,and combinatorial identities concerning partial Bell polynomials,falling factorials,rising factorials,extended binomial coefficients,and the Stirling numbers of the first and second kinds.These results are new,interesting,important,useful,and applicable in combinatorial number theory.
文摘In this paper,we present monotonicity results of a function involving the inverse hyperbolic sine.From these,we obtain some lower bounds for the inverse hyperbolic sine.
基金the Key Projects of National Natural Science Foundation of China(U1704255)the National Natural Science Foundation of China(11804081)+6 种基金the National Natural Science Foundation of China(Grant No.21603109)the Henan Joint Fund of the National Natural Science Foundation of China(Grant No.U1404216)the Natural Science Foundation of Henan Province(182102210305)the Natural Science Foundation of Henan Province(19B430003,20A430016,182300410288)the Key Research Project for the Universities of Henan Province(19A140009)the Doctoral Foundation of Henan Polytechnic University(B2018-38)the Open Project of Key Laboratory of Radio Frequency and Micro-Nano Electronics of Jiangsu Province(LRME201601)。
文摘Gas molecules(such as CH4,CO,H2O,H2S,NH_3)adsorption on the pure and Au-doped WO3(001)surface have been studied by Density functional theory calculations with generalized gradient approximation.Based on the the calculation of adsorption energy,we found the most stable adsorption site for gas molecules by comparing the adsorption energies of different gas molecules on the WO3(001)surface.We have also compared the adsorption energy of five different gas molecules on the WO3(001)surface,our calculation results show that when the five kinds of gases are adsorbed on the pure WO3(001)surface,the order of the surface adsorption energy is CO>H2S>CH4>H2O>NH3.And the results show that NH3 is the most easily adsorbed gas among the other four gases adsorbed on the surface of pure WO3(001)surface.We also calculated the five different gases on the Au-doped WO3(001)surface.The order of adsorption energy was found to be different from the previous calculation:CO>CH4>H2S>H2O>NH3.These results provide a new route for the potential applications of Au-doped WO3 in gas molecules adsorption.
基金supported by the National Natural Science Foundation of China(Nos.11671361,11571256)the Zhejiang Provincial Natural Science Foundation of China(No.LY14A010008)
文摘In this paper, the authors prove a general Schwarz lemma at the boundary for the holomorphic mapping f between unit balls B and B＇ in separable complex Hilbert spaces H and H＇, respectively. It is found that if the mapping f ∈ C^1＋α at z0 ∈ B with f（zo） = wo ∈ OB＇, then the Fr＆het derivative operator Df（z0） maps the tangent space Tz0（ B^n） to Tw0（ B＇）, the holomorphic tangent space Tz0^（1,0） to Tw0（1,0）（ B＇）,respectively.
文摘By virtue of Cauchy’s integral formula in the theory of complex functions,the authors establish an integral representation for the weighted geometric mean,apply this newly established integral representation to show that the weighted geometric mean is a complete Bernstein function,and find a new proof of the well-known weighted arithmetic-geometric mean inequality.
基金This work was supported by the National Natural Science Foundation of China （Grant No. 61672157）, and the Innovative Research Team of Probability and Statistics： Theory and Application （IRTL1704）.
文摘1 Introduction Currently, categorical data are world applications, particularly widely used in many realin the biomedical and social sciences. Unlike the numeric case, when the data are cate- gorical, choosing the appropriate similarity or dissimilarity measure between two different categorical objects became a difficult task for many applications. What＇s more, in this case, the set mean, i.e., the averaging value of a finite set of data objects, is an undefined concept. This means that the well known K-means [ 1 ] and its numerous variants cannot be directly used for center-based clustering of categorical data.
基金supported by the National Natural Science Foundation of China under Grant Nos.11201304,11371253the Innovation Program of Shanghai Municipal Education Commission under Grant No.12YZ174Group of Accounting and Governance Disciplines(10kq03)
文摘This paper proposes a dwindling filter line search algorithm for nonlinear equality constrained optimization. A dwindling filter, which is a modification of the traditional filter, is employed in the algorithm. The envelope of the dwindling filter becomes thinner and thinner as the step size approaches zero. This new algorithm has more flexibility for the acceptance of the trial step and requires less computational costs compared with traditional filter algorithm. The global and local convergence of the proposed algorithm are given under some reasonable conditions. The numerical experiments are reported to show the effectiveness of the dwindling filter algorithm.
基金supported by the National Science Foundation of China under Grant No.10871130the Ph.D Foundation under Grant No.20093127110005+1 种基金the Shanghai Leading Academic Discipline Project under Grant No.S30405the Innovation Program of Shanghai Municipal Education Commission under Grant No.12YZ174
文摘This paper proposes a nonmonotone line search filter method with reduced Hessian updating for solving nonlinear equality constrained optimization.In order to deal with large scale problems,a reduced Hessian matrix is approximated by BFGS updates.The new method assures global convergence without using a merit function.By Lagrangian function in the filter and nonmonotone scheme,the authors prove that the method can overcome Maratos effect without using second order correction step so that the locally superlinear convergence is achieved.The primary numerical experiments are reported to show effectiveness of the proposed algorithm.
基金supported by the National Science Foundation of China(Nos.11671361,11571256)
文摘The authors prove a general Schwarz lemma at the boundary for holomorphic mappings from the polydisc to the unit ball in any dimensions.For the special case of one complex variable,the obtained results give the classic boundary Schwarz lemma.
基金supported by the National Science Foundation of China under Grant No. 10871130the Ph.D. Foundation under Grant No. 20093127110005+1 种基金the Shanghai Leading Academic Discipline Project under Grant No. S30405the Shanghai Finance Budget Project under Grant Nos. 1139IA0013 and 1130IA15
文摘This paper proposes a filter secant method with nonmonotone line search for non-linearequality constrained optimization.The Hessian of the Lagrangian is approximated using the BFGSsecant update.This new method has more flexibility for the acceptance of the trial step and requires lesscomputational costs compared with the monotone one.The global and local convergence of the proposedmethod are given under some reasonable conditions.Further,two-step Q-superlinear convergence rateis established by introducing second order correction step.The numerical experiments are reported toshow the effectiveness of the proposed algorithm.
基金the China Postdoctoral Science Foundation (No.20060390530)Natural Science Foundation of Henan Province (No.0611055500)
文摘The author studies the Cauchy problem of the dissipative quasi-geostrophic equation in weak Morrey spaces. The global well-posedness is established for any small initial data in the weak space Mp^＊,γ（R^n）, with 1〈p〈∞and A = n-（2α-1）p, and for a small external force in a time-weighted weak Morrey space.
