Algebraic reflexivity introduced by Hadwin is related to linear interpolation.In this paper,the concepts of weakly algebraic reflexivity and strongly algebraic reflexivity which are also related to linear interpolat...Algebraic reflexivity introduced by Hadwin is related to linear interpolation.In this paper,the concepts of weakly algebraic reflexivity and strongly algebraic reflexivity which are also related to linear interpolation are introduced.Some properties of them are obtained and some relations between them revealed展开更多
Rock mass classification systems are the very important part for underground projects and rock mass rating(RMR) is one of the most commonly applied classification systems in numerous civil and mining projects. The typ...Rock mass classification systems are the very important part for underground projects and rock mass rating(RMR) is one of the most commonly applied classification systems in numerous civil and mining projects. The type of rock mass consisting of an interbedding of strong and weak layers poses difficulties and uncertainties for determining the RMR. For this, the present paper uses the concept of rock bolt supporting factor(RSF) for modification of RMR system to be used in such rock mass types. The proposed method also demonstrates the importance of rock bolting practice in such rock masses. The geological parameters of the Shemshak Formation of the Alborz Tunnel in Iran are used as case examples for development of the theoretical approach.展开更多
It is proved that the quadratic system with a weak focus and a strong focus has at most one limit cycle around the strong focus, and as the weak focus is a 2nd order(or 3rd order) weak focus the quadratic system ha...It is proved that the quadratic system with a weak focus and a strong focus has at most one limit cycle around the strong focus, and as the weak focus is a 2nd order(or 3rd order) weak focus the quadratic system has at most two(one) limit cycles which have (1,1) distribution ((0,1) distribution).展开更多
In this paper, we first give the concept of weakly P-inversive semigroup S（P）. Then we describe the strong P-congruences on S（P） in terms of their P-kernel normal systems. It is proved that there is a bijection be...In this paper, we first give the concept of weakly P-inversive semigroup S（P）. Then we describe the strong P-congruences on S（P） in terms of their P-kernel normal systems. It is proved that there is a bijection between the strong P-congruences and the P-kernel normal systems. Finally, it is also prove that the lattice of strong P-congruences and the lattice of P-kernel normal systems on S（P） are isomorphic.展开更多
This article concerns the existence of weak solutions of the first boundary value problem for a kind of strongly degenerate quasilinear parabolic equation in the anisotropic Sobolev Space. With the theory of anisotrop...This article concerns the existence of weak solutions of the first boundary value problem for a kind of strongly degenerate quasilinear parabolic equation in the anisotropic Sobolev Space. With the theory of anisotropic Sobolev spaces an existence result is proved.展开更多
Using finite differences and entropy inequalities, the global existence of weak solutions to a multidimensional parabolic strongly coupled prey-predator model is obtained. The nonnegativity of the solutions is also sh...Using finite differences and entropy inequalities, the global existence of weak solutions to a multidimensional parabolic strongly coupled prey-predator model is obtained. The nonnegativity of the solutions is also shown.展开更多
Strong and weak limits as well as strong and weak differentials of multi-variable indeterminate forms are discussed based on the thorough exploration of differentiation to solve the strong and weak limits and differen...Strong and weak limits as well as strong and weak differentials of multi-variable indeterminate forms are discussed based on the thorough exploration of differentiation to solve the strong and weak limits and differentials of unitary indeterminate forms. The fruit of this work is going to be reported in three parts. The first part presents the standard analysis on this subject which supplements, systematizes and advances L. Hospital抯 principles on differential calculus by applying special ,general, and limit guaranteeing theories together with K(t) and XhK0 theories. The combination of theoretical analysis and geometric signification makes the derivation intuitional, visual and easy to perceive.展开更多
In this paper,we investigate three canonical forms of interval convex quadratic pro-gramming problems.Necessary and suficient conditions for checking weak and strong optimality of given vector corresponding to various...In this paper,we investigate three canonical forms of interval convex quadratic pro-gramming problems.Necessary and suficient conditions for checking weak and strong optimality of given vector corresponding to various forms of feasible region,are established respectively.By using the concept of feasible direction,these conditions are formulated in the form of linear systems with both equations and inequalities.In addition,we provide two specific examples to illustrate the efficiency of the conditions.展开更多
In this paper, some new iterative schemes for approximating the common element of the set of fixed points of strongly relatively nonexpansive mappings and the set of zero points of maximal monotone operators in a real...In this paper, some new iterative schemes for approximating the common element of the set of fixed points of strongly relatively nonexpansive mappings and the set of zero points of maximal monotone operators in a real uniformly smooth and uniformly convex Banach space are proposed. Some weak convergence theorems are obtained, which extend and complement some previous work.展开更多
High-order strong stability preserving(SSP)time discretizations are often needed to ensure the nonlinear(and sometimes non-inner-product)strong stability properties of spatial discretizations specially designed for th...High-order strong stability preserving(SSP)time discretizations are often needed to ensure the nonlinear(and sometimes non-inner-product)strong stability properties of spatial discretizations specially designed for the solution of hyperbolic PDEs.Multi-derivative time-stepping methods have recently been increasingly used for evolving hyperbolic PDEs,and the strong stability properties of these methods are of interest.In our prior work we explored time discretizations that preserve the strong stability properties of spatial discretizations coupled with forward Euler and a second-derivative formulation.However,many spatial discretizations do not satisfy strong stability properties when coupled with this second-derivative formulation,but rather with a more natural Taylor series formulation.In this work we demonstrate sufficient conditions for an explicit two-derivative multistage method to preserve the strong stability properties of spatial discretizations in a forward Euler and Taylor series formulation.We call these strong stability preserving Taylor series(SSP-TS)methods.We also prove that the maximal order of SSP-TS methods is p=6,and define an optimization procedure that allows us to find such SSP methods.Several types of these methods are presented and their efficiency compared.Finally,these methods are tested on several PDEs to demonstrate the benefit of SSP-TS methods,the need for the SSP property,and the sharpness of the SSP time-step in many cases.展开更多
In this paper we study the strong and weak property of travelling wave front solutions for a class of degenerate parabolic equations. How the strong and weak property changes under the effects of wave speed and reacti...In this paper we study the strong and weak property of travelling wave front solutions for a class of degenerate parabolic equations. How the strong and weak property changes under the effects of wave speed and reaction diffusion terms are showed.展开更多
According to the meteorological conditions of sowing period and the characteristics of seedling in each key growth period,the measures of rushing drainage,rushing harvest stubble,rushing sow,implementing late sowing,s...According to the meteorological conditions of sowing period and the characteristics of seedling in each key growth period,the measures of rushing drainage,rushing harvest stubble,rushing sow,implementing late sowing,strengthening field management before winter and in spring are taken in Daiyue District during the autumn planting period of wheat,which reduce the influence of natural disasters and increase the yield of wheat.展开更多
This paper reports a new method of titration for very weak acids and bases using the appearance of incisions on oscillopolarogram to indicate the end-point.This method has the advantages of rapidity,simplicity,no indi...This paper reports a new method of titration for very weak acids and bases using the appearance of incisions on oscillopolarogram to indicate the end-point.This method has the advantages of rapidity,simplicity,no indicator needed as well as good precision.展开更多
Analytic method and identification direction for rational identification of lightning derivative disasters by strong convective weather monitoring data in southern China were introduced. Taking identification cases of...Analytic method and identification direction for rational identification of lightning derivative disasters by strong convective weather monitoring data in southern China were introduced. Taking identification cases of lightning disaster in Guangzhou Development Region as the background,according to the characteristics in the region that large high-precision enterprises were more,lightning derivative disasters occurred frequently in thunderstorm season,and the actual situation that time of the affected enterprise applying for lightning disaster scene identification lagged,combining Technical Specifications of Lightning Disaster Investigation（ QX / T103-2009）,qualitative analysis method of lightning derivative disaster was put forward under the weather condition of strong convection in southern China by using weather monitoring data（ Doppler sounding radar data,lightning positioning monitoring data,atmospheric electric field data,rainfall data,wind direction and force）,and was optimized by technical means（ ＂ metallographic method＂ and ＂ remanence law＂）. The research could put forward efficient and convenient analytical thinking and method for lightning derivative disaster,and further optimize accuracy and credibility of lightning disaster investigation.展开更多
In this paper we study the interaction of strong and weak singularities for hyperbolic system of conservation laws in multidimensional space. Under the assumption of transversal intersect of the shock front with the b...In this paper we study the interaction of strong and weak singularities for hyperbolic system of conservation laws in multidimensional space. Under the assumption of transversal intersect of the shock front with the bicharacteristics bearing weak singularities we proved a theorem on regularity propagation across the shock front.展开更多
The traditional methods of weak harmonic signal detection under strong chaotic interference often suffer from high computational complexity and poor performance. In this paper, an Extended Kalman Filter (EKF) based de...The traditional methods of weak harmonic signal detection under strong chaotic interference often suffer from high computational complexity and poor performance. In this paper, an Extended Kalman Filter (EKF) based detection method is proposed for the detection of weak harmonic signal. The EKF method avoids matrix inversion by iterating measurement equation and state equation, which simultaneously improves the robustness and reduces the complexity. Compared with the existing detection methods, the proposed method has the following advantages: 1) it has better performance than the neural network method;2) it has similar performance with the optimal filtering method, but with lower computational complexity;3) it is more robust compared with the optimal filtering method.展开更多
基金Supported in part by the National Natural Science Foundation of China(1 9771 0 72 ) .
文摘Algebraic reflexivity introduced by Hadwin is related to linear interpolation.In this paper,the concepts of weakly algebraic reflexivity and strongly algebraic reflexivity which are also related to linear interpolation are introduced.Some properties of them are obtained and some relations between them revealed
文摘Rock mass classification systems are the very important part for underground projects and rock mass rating(RMR) is one of the most commonly applied classification systems in numerous civil and mining projects. The type of rock mass consisting of an interbedding of strong and weak layers poses difficulties and uncertainties for determining the RMR. For this, the present paper uses the concept of rock bolt supporting factor(RSF) for modification of RMR system to be used in such rock mass types. The proposed method also demonstrates the importance of rock bolting practice in such rock masses. The geological parameters of the Shemshak Formation of the Alborz Tunnel in Iran are used as case examples for development of the theoretical approach.
文摘It is proved that the quadratic system with a weak focus and a strong focus has at most one limit cycle around the strong focus, and as the weak focus is a 2nd order(or 3rd order) weak focus the quadratic system has at most two(one) limit cycles which have (1,1) distribution ((0,1) distribution).
基金the Science Research Foundation of Qingdao Technological University(C2002-214)
文摘In this paper, we first give the concept of weakly P-inversive semigroup S（P）. Then we describe the strong P-congruences on S（P） in terms of their P-kernel normal systems. It is proved that there is a bijection between the strong P-congruences and the P-kernel normal systems. Finally, it is also prove that the lattice of strong P-congruences and the lattice of P-kernel normal systems on S（P） are isomorphic.
基金The project is supported by NNSF of China (10371116)
文摘This article concerns the existence of weak solutions of the first boundary value problem for a kind of strongly degenerate quasilinear parabolic equation in the anisotropic Sobolev Space. With the theory of anisotropic Sobolev spaces an existence result is proved.
基金supported by the National Natural Science Foundation of China (Nos. 10701024, 10601011)
文摘Using finite differences and entropy inequalities, the global existence of weak solutions to a multidimensional parabolic strongly coupled prey-predator model is obtained. The nonnegativity of the solutions is also shown.
文摘Strong and weak limits as well as strong and weak differentials of multi-variable indeterminate forms are discussed based on the thorough exploration of differentiation to solve the strong and weak limits and differentials of unitary indeterminate forms. The fruit of this work is going to be reported in three parts. The first part presents the standard analysis on this subject which supplements, systematizes and advances L. Hospital抯 principles on differential calculus by applying special ,general, and limit guaranteeing theories together with K(t) and XhK0 theories. The combination of theoretical analysis and geometric signification makes the derivation intuitional, visual and easy to perceive.
基金Supported by the Natural Science Foundation of Zhejiang Province(LY21A010021)the National Natural Science Foundation of China(11701506)。
文摘In this paper,we investigate three canonical forms of interval convex quadratic pro-gramming problems.Necessary and suficient conditions for checking weak and strong optimality of given vector corresponding to various forms of feasible region,are established respectively.By using the concept of feasible direction,these conditions are formulated in the form of linear systems with both equations and inequalities.In addition,we provide two specific examples to illustrate the efficiency of the conditions.
基金Supported by the National Natural Science Foundation of China(10771050)the Natural Science Foun-dation of Hebei Province(A2010001482)
文摘In this paper, some new iterative schemes for approximating the common element of the set of fixed points of strongly relatively nonexpansive mappings and the set of zero points of maximal monotone operators in a real uniformly smooth and uniformly convex Banach space are proposed. Some weak convergence theorems are obtained, which extend and complement some previous work.
文摘High-order strong stability preserving(SSP)time discretizations are often needed to ensure the nonlinear(and sometimes non-inner-product)strong stability properties of spatial discretizations specially designed for the solution of hyperbolic PDEs.Multi-derivative time-stepping methods have recently been increasingly used for evolving hyperbolic PDEs,and the strong stability properties of these methods are of interest.In our prior work we explored time discretizations that preserve the strong stability properties of spatial discretizations coupled with forward Euler and a second-derivative formulation.However,many spatial discretizations do not satisfy strong stability properties when coupled with this second-derivative formulation,but rather with a more natural Taylor series formulation.In this work we demonstrate sufficient conditions for an explicit two-derivative multistage method to preserve the strong stability properties of spatial discretizations in a forward Euler and Taylor series formulation.We call these strong stability preserving Taylor series(SSP-TS)methods.We also prove that the maximal order of SSP-TS methods is p=6,and define an optimization procedure that allows us to find such SSP methods.Several types of these methods are presented and their efficiency compared.Finally,these methods are tested on several PDEs to demonstrate the benefit of SSP-TS methods,the need for the SSP property,and the sharpness of the SSP time-step in many cases.
文摘In this paper we study the strong and weak property of travelling wave front solutions for a class of degenerate parabolic equations. How the strong and weak property changes under the effects of wave speed and reaction diffusion terms are showed.
文摘According to the meteorological conditions of sowing period and the characteristics of seedling in each key growth period,the measures of rushing drainage,rushing harvest stubble,rushing sow,implementing late sowing,strengthening field management before winter and in spring are taken in Daiyue District during the autumn planting period of wheat,which reduce the influence of natural disasters and increase the yield of wheat.
文摘This paper reports a new method of titration for very weak acids and bases using the appearance of incisions on oscillopolarogram to indicate the end-point.This method has the advantages of rapidity,simplicity,no indicator needed as well as good precision.
文摘Analytic method and identification direction for rational identification of lightning derivative disasters by strong convective weather monitoring data in southern China were introduced. Taking identification cases of lightning disaster in Guangzhou Development Region as the background,according to the characteristics in the region that large high-precision enterprises were more,lightning derivative disasters occurred frequently in thunderstorm season,and the actual situation that time of the affected enterprise applying for lightning disaster scene identification lagged,combining Technical Specifications of Lightning Disaster Investigation（ QX / T103-2009）,qualitative analysis method of lightning derivative disaster was put forward under the weather condition of strong convection in southern China by using weather monitoring data（ Doppler sounding radar data,lightning positioning monitoring data,atmospheric electric field data,rainfall data,wind direction and force）,and was optimized by technical means（ ＂ metallographic method＂ and ＂ remanence law＂）. The research could put forward efficient and convenient analytical thinking and method for lightning derivative disaster,and further optimize accuracy and credibility of lightning disaster investigation.
文摘In this paper we study the interaction of strong and weak singularities for hyperbolic system of conservation laws in multidimensional space. Under the assumption of transversal intersect of the shock front with the bicharacteristics bearing weak singularities we proved a theorem on regularity propagation across the shock front.
基金the National Natural Science Foundation of China (Grant No. 61871102 and 61731006)Sichuan province science and technology support program under Grant N0. 2017GZ0345.
文摘The traditional methods of weak harmonic signal detection under strong chaotic interference often suffer from high computational complexity and poor performance. In this paper, an Extended Kalman Filter (EKF) based detection method is proposed for the detection of weak harmonic signal. The EKF method avoids matrix inversion by iterating measurement equation and state equation, which simultaneously improves the robustness and reduces the complexity. Compared with the existing detection methods, the proposed method has the following advantages: 1) it has better performance than the neural network method;2) it has similar performance with the optimal filtering method, but with lower computational complexity;3) it is more robust compared with the optimal filtering method.
