Polynomial splines have played an important role in image processing, medical imaging and wavelet theory. Exponential splines which are of more general concept have been recently investigated.We focus on cardinal expo...Polynomial splines have played an important role in image processing, medical imaging and wavelet theory. Exponential splines which are of more general concept have been recently investigated.We focus on cardinal exponential splines and develop a method to implement the exponential B-splines which form a Riesz basis of the space of cardinal exponential splines with finite energy.展开更多
In this paper, some conclusions related to the prime number theorem, such as the Mertens formula are improved by the improved Abelian summation formula, and some problems such as “Dirichlet” function and “W(n)” fu...In this paper, some conclusions related to the prime number theorem, such as the Mertens formula are improved by the improved Abelian summation formula, and some problems such as “Dirichlet” function and “W(n)” function are studied.展开更多
The determination of material formula needs try-and-error experiment,and consumes large amount of time and fund.In order to solve the problem,a comprehensive method is established,via the experiment of artificial-simi...The determination of material formula needs try-and-error experiment,and consumes large amount of time and fund.In order to solve the problem,a comprehensive method is established,via the experiment of artificial-similar material formula of a mine slope.We controlled the samples by the compactness,and arranged the formula of the test group with the method of the uniform formula experiment.The physical and mechanical parameters of these samples were analyzed using the method of the partial least-squares regression(PLS).And a mathematical model of the indexes of physical and mechanics parameters relating to the factors of formulation constituents was established eventually.We used the model to analyze the effect of each formulation constituent on physical and mechanics parameters of samples.The experiment results and analysis illustrates that1)in the formulation of similar material,the effect of raw materials on the internal friction angleφand cohesion C is opposite;2)The method can highly facilitate the process of the of preparing artificial-similar materials,more economic and effective.展开更多
The quarter-circular caisson breakwater （QCB） is a new type of breakwater, and it can be applied in deepwater. The stability of QCB under wave force action can be enhanced, and the rubble mound engineering can be le...The quarter-circular caisson breakwater （QCB） is a new type of breakwater, and it can be applied in deepwater. The stability of QCB under wave force action can be enhanced, and the rubble mound engineering can be less than that of semi-circular breakwaters in deepwater. In order to study the wave force distribution acting on the QCB, to find wave force formula for this type of breakwater, firstly in this paper, the distribution characteristics of the horizontal force, the downward vertical force and the uplift force on the breakwater were gotten based on physical model wave flume experiments and on the analysis of the wave pressure experimental data. Based on a series of physical model tests acted by irregular waves, a kind of calculation method, which was modified by Goda formula, was proposed to carry out the wave force on the QCB. Secondly, the reliability method with correlated variables was adopted to analyze the QCB, considering the high correlation between wave forces or moments. Utilizing the observed wave data in engineering field, the reliability index and failure probability of QCB were obtained. Finally, a factor Q=0.9 is given to modify the zero pressure height above SWL of QCB, and wave force partial coefficient 1.34 to the design expressions of QCB for anti-sliding, as well as 1.67 for anti-overturning, were presented.展开更多
The Koppelman-Leray formula on complex manifolds is obtained, and under suitable condition the continuous solution of partial derivative-equation on complex manifolds is obtained.
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
文摘Polynomial splines have played an important role in image processing, medical imaging and wavelet theory. Exponential splines which are of more general concept have been recently investigated.We focus on cardinal exponential splines and develop a method to implement the exponential B-splines which form a Riesz basis of the space of cardinal exponential splines with finite energy.
文摘In this paper, some conclusions related to the prime number theorem, such as the Mertens formula are improved by the improved Abelian summation formula, and some problems such as “Dirichlet” function and “W(n)” function are studied.
基金Projects(41372312,51379194)supported by the National Natural Science Foundation of ChinaProject(CUGL140817)supported by the Fundamental Research Funds for the Central Universities of China University of Geosciences(Wuhan)+1 种基金Project(2014CFB894)supported by the Natural Science Foundation of Hubei Province of ChinaProject(2014M552113)supported by the China Postdoctoral Science Foundation
文摘The determination of material formula needs try-and-error experiment,and consumes large amount of time and fund.In order to solve the problem,a comprehensive method is established,via the experiment of artificial-similar material formula of a mine slope.We controlled the samples by the compactness,and arranged the formula of the test group with the method of the uniform formula experiment.The physical and mechanical parameters of these samples were analyzed using the method of the partial least-squares regression(PLS).And a mathematical model of the indexes of physical and mechanics parameters relating to the factors of formulation constituents was established eventually.We used the model to analyze the effect of each formulation constituent on physical and mechanics parameters of samples.The experiment results and analysis illustrates that1)in the formulation of similar material,the effect of raw materials on the internal friction angleφand cohesion C is opposite;2)The method can highly facilitate the process of the of preparing artificial-similar materials,more economic and effective.
基金Supported by the Natural Science Foundation of Hebei Province （Grant No. E2012201057） the Scientific and Technological Projects of Hebei Province （Grant No. 2009056） the Natural Science Foundation of Tianjin （Grant No. 10JCYBJC03700）
文摘The quarter-circular caisson breakwater （QCB） is a new type of breakwater, and it can be applied in deepwater. The stability of QCB under wave force action can be enhanced, and the rubble mound engineering can be less than that of semi-circular breakwaters in deepwater. In order to study the wave force distribution acting on the QCB, to find wave force formula for this type of breakwater, firstly in this paper, the distribution characteristics of the horizontal force, the downward vertical force and the uplift force on the breakwater were gotten based on physical model wave flume experiments and on the analysis of the wave pressure experimental data. Based on a series of physical model tests acted by irregular waves, a kind of calculation method, which was modified by Goda formula, was proposed to carry out the wave force on the QCB. Secondly, the reliability method with correlated variables was adopted to analyze the QCB, considering the high correlation between wave forces or moments. Utilizing the observed wave data in engineering field, the reliability index and failure probability of QCB were obtained. Finally, a factor Q=0.9 is given to modify the zero pressure height above SWL of QCB, and wave force partial coefficient 1.34 to the design expressions of QCB for anti-sliding, as well as 1.67 for anti-overturning, were presented.
文摘The Koppelman-Leray formula on complex manifolds is obtained, and under suitable condition the continuous solution of partial derivative-equation on complex manifolds is obtained.
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.
