This article considers Cauchy problem for quasilinear hyperbolic systems in diagonal form. A necessary and sufficient condition in guaranteeing that Cauchy problem admits a unique global classical solution on t ≥ 0 i...This article considers Cauchy problem for quasilinear hyperbolic systems in diagonal form. A necessary and sufficient condition in guaranteeing that Cauchy problem admits a unique global classical solution on t ≥ 0 is obtained, and a sharp estimate of the life span for the classical solution is given.展开更多
In this paper we derive LPS＇s criterion for the breakdown of classical solutions to the incompressible nematic liquid crystal flow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution o...In this paper we derive LPS＇s criterion for the breakdown of classical solutions to the incompressible nematic liquid crystal flow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution of nematic liquid crystals in R^3. We show that if 0 〈 T 〈 ＋∞ is the maximal time interval for the unique smooth solution u ∈ C^∞（[0, T）,R^3）,then ｜u｜＋｜△d｜∈L^q（[0,T],L^p（R^3））,where p and q satisfy the Ladyzhenskaya-Prodi-Serrin＇s condition：3/p＋2/q=1 and p∈（3,＋∞].展开更多
With recent advances in numerical modeling, design of underground structures increasingly relies on numerical modeling-based analysis approaches. While modeling tools like the discrete element method(DEM) and the comb...With recent advances in numerical modeling, design of underground structures increasingly relies on numerical modeling-based analysis approaches. While modeling tools like the discrete element method(DEM) and the combined finite-discrete element method(FDEM) are useful for investigating small-scale damage processes, continuum models remain the primary practical tool for most field-scale problems.The results obtained from such models are significantly dependent on the selection of an appropriate yield criterion and dilation angle. Towards improving its capabilities in handling mining-related problems, the authors have previously developed a new yield criterion(called progressive S-shaped criterion). The focus of the current study is to demonstrate its use in modeling rock pillars through a comparative analysis against four other yield criteria. In addition to the progressive S-shaped criterion,only one out of the four other criteria predicted a trend in strength consistent with an empirical pillar strength database compiled from the literature. Given the closely-knit relationship between yield criteria and dilation angle in controlling the overall damage process, a separate comparison was conducted using a mobilized dilation model, a zero degree dilation angle and a constant non-zero dilation angle. This study also investigates the impact of meso-scale heterogeneity in mechanical properties on the overall model response by assigning probability distributions to the input parameters. The comparisons revealed that an isotropic model using a combination of progressive S-shaped criterion and mobilized dilation angle model is sufficient in capturing the behaviors of rock pillars. Subsequently, the pillar model was used to assess the effect of L/W(length/width) ratio on the peak strength.展开更多
This article studies on Cauchy’s function f （z） and its integral, （2πi）J[ f （z）] ≡ ■C f （t）dt/（t z） taken along a closed simple contour C, in regard to their comprehensive properties over the entire z =...This article studies on Cauchy’s function f （z） and its integral, （2πi）J[ f （z）] ≡ ■C f （t）dt/（t z） taken along a closed simple contour C, in regard to their comprehensive properties over the entire z = x ＋ iy plane consisted of the simply connected open domain D ＋ bounded by C and the open domain D outside C. （1） With f （z） assumed to be C n （n ∞-times continuously differentiable） z ∈ D ＋ and in a neighborhood of C, f （z） and its derivatives f （n） （z） are proved uniformly continuous in the closed domain D ＋ = [D ＋ ＋ C]. （2） Cauchy’s integral formulas and their derivatives z ∈ D ＋ （or z ∈ D ） are proved to converge uniformly in D ＋ （or in D = [D ＋C]）, respectively, thereby rendering the integral formulas valid over the entire z-plane. （3） The same claims （as for f （z） and J[ f （z）]） are shown extended to hold for the complement function F（z）, defined to be C n z ∈ D and about C. （4） The uniform convergence theorems for f （z） and F（z） shown for arbitrary contour C are adapted to find special domains in the upper or lower half z-planes and those inside and outside the unit circle ｜z｜ = 1 such that the four general- ized Hilbert-type integral transforms are proved. （5） Further, the singularity distribution of f （z） in D is elucidated by considering the direct problem exemplified with several typ- ical singularities prescribed in D . （6） A comparative study is made between generalized integral formulas and Plemelj’s formulas on their differing basic properties. （7） Physical sig- nificances of these formulas are illustrated with applicationsto nonlinear airfoil theory. （8） Finally, an unsolved inverse problem to determine all the singularities of Cauchy function f （z） in domain D , based on the continuous numerical value of f （z） z ∈ D ＋ = [D ＋ ＋ C], is presented for resolution as a conjecture.展开更多
A simple method for solving Cauchy’s problem of wave equations in higher space dimensions with initial condition of separated variables, has been given by using D’Alembert’s formula and some examples have been shown.
The present paper aims at giving some general ideas concerning the micromechanical approach of the strength of a porous material. It is shown that its determination theoretically amounts to solving a nonlinear boundar...The present paper aims at giving some general ideas concerning the micromechanical approach of the strength of a porous material. It is shown that its determination theoretically amounts to solving a nonlinear boundary value problem defined on a representative elementary volume(REV). The principle of nonlinear homogenization is illustrated based on the case of a solid phase having a Green’s strength criterion. An original refinement of the so-called secant method(based on two reference strains) is also provided. The paper also describes the main feature of the Gurson’s model which implements the principle of limit analysis on a conceptual model of hollow sphere. The last part of the paper gives some ideas concerning poromechanical couplings.展开更多
In this paper, we presented a sufficient condition on the frequency domain for the absolutely stable analysis of the Takagi-Sugeno (T-S)fuzzy control system, based on the Popov’s criterion. we use some numerical exam...In this paper, we presented a sufficient condition on the frequency domain for the absolutely stable analysis of the Takagi-Sugeno (T-S)fuzzy control system, based on the Popov’s criterion. we use some numerical examples to illustrate the efficiency of frequency domain-based condition.展开更多
In this paper, we give two characterizations of multi-Cauchy-Jensen mappings. One of them reduces the system of n equations defining these mappings to a single functional equation. We also prove, using the fixed point...In this paper, we give two characterizations of multi-Cauchy-Jensen mappings. One of them reduces the system of n equations defining these mappings to a single functional equation. We also prove, using the fixed point method, the generalized Hyers-Ulam stability of this equation. Our results generalize some known outcomes.展开更多
Inspired by Cardano＇s method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor （DSDT） is revisited from a new view- point. This decomposition simplifies the cubic tenso...Inspired by Cardano＇s method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor （DSDT） is revisited from a new view- point. This decomposition simplifies the cubic tensor equation, decouples the spher- ical/deviatoric strain energy density, and lays the foundation for the von Mises yield criterion. Besides, it is verified that under the precondition of energy decoupling and the simplest form, the DSDT is the only possible form of the additive decomposition with physical meanings.展开更多
As is well known,the definitions of fractional sum and fractional difference of f(z)on non-uniform lattices x(z)=c1z^(2)+c2z+c3 or x(z)=c1q^(z)+c2q^(-z)+c3 are more difficult and complicated.In this article,for the fi...As is well known,the definitions of fractional sum and fractional difference of f(z)on non-uniform lattices x(z)=c1z^(2)+c2z+c3 or x(z)=c1q^(z)+c2q^(-z)+c3 are more difficult and complicated.In this article,for the first time we propose the definitions of the fractional sum and fractional difference on non-uniform lattices by two different ways.The analogue of Euler’s Beta formula,Cauchy’Beta formula on non-uniform lattices are established,and some fundamental theorems of fractional calculas,the solution of the generalized Abel equation on non-uniform lattices are obtained etc.展开更多
In this paper, an efficient weight initialization method is proposed using Cauchy’s inequality based on sensitivity analy- sis to improve the convergence speed in single hidden layer feedforward neural networks. The ...In this paper, an efficient weight initialization method is proposed using Cauchy’s inequality based on sensitivity analy- sis to improve the convergence speed in single hidden layer feedforward neural networks. The proposed method ensures that the outputs of hidden neurons are in the active region which increases the rate of convergence. Also the weights are learned by minimizing the sum of squared errors and obtained by solving linear system of equations. The proposed method is simulated on various problems. In all the problems the number of epochs and time required for the proposed method is found to be minimum compared with other weight initialization methods.展开更多
This is a series of studies on Wu＇s conjecture and on its resolution to be presented herein. Both are devoted to expound all the comprehensive properties of Cauchy＇s function f（z） （z = x ＋ iy） and its integral ...This is a series of studies on Wu＇s conjecture and on its resolution to be presented herein. Both are devoted to expound all the comprehensive properties of Cauchy＇s function f（z） （z = x ＋ iy） and its integral J[f（z）]≡（2πi）-∮cf（t）（t-z）-1dt taken along the unit circle as contour C,inside which（the open domain D＋） f（z） is regular but has singularities distributed in open domain Doutside C. Resolution is given to the inverse problem that the singularities of f（z） can be determined in analytical form in terms of the values f（t） of f（z） numerically prescribed on C（｜t｜ = 1） ,as so enunciated by Wu＇s conjecture. The case of a single singularity is solved using complex algebra and analysis to acquire the solution structure for a standard reference. Multiple singularities are resolved by reducing them to a single one by elimination in principle,for which purpose a general asymptotic method is developed here for resolution to the conjecture by induction,and essential singularities are treated with employing the generalized Hilbert transforms. These new methods are applicable to relevant problems in mathematics,engineering and technology in analogy with resolving the inverse problem presented here.展开更多
In this paper,we discussed the local integral solution operators of imhomogeneous Cauchy Riemann equations on an open set with piecewise C k boundary in C n,as a generalization of the solution opertators for Leray map...In this paper,we discussed the local integral solution operators of imhomogeneous Cauchy Riemann equations on an open set with piecewise C k boundary in C n,as a generalization of the solution opertators for Leray map S(z,ζ) which do not depends holomorphic on z∈D in Koppelman formula is obtained and the L s norm estimates for the solution operators are the same as that [10] in forms.展开更多
A frequency-domain-based sufficient condition is derived to guarantee the globally asymptotic stability of the simplest Takagi-Sugeno （T-S） fuzzy control system by using the circle criterion. The analysis is perform...A frequency-domain-based sufficient condition is derived to guarantee the globally asymptotic stability of the simplest Takagi-Sugeno （T-S） fuzzy control system by using the circle criterion. The analysis is performed in the frequency domain, and hence the condition is of great significance when the frequency-response method, which is widely used in the linear control theory and practice, is employed to synthesize the simplest T-S fuzzy controller. Besides, this sufficient condition is featured by a graphical interpretation, which makes the condition straightforward to be used. Comparisons are drawn between the performance of the simplest T-S fuzzy controller and that of the linear compensator. Two numerical examples are presented to demonstrate how this sufficient condition can be applied to both stable and unstable plants.展开更多
基金Project supported by the NSF of China! (19971O62)the NSF of Fujian Province!(A97020) the NSF of Educational Committee of
文摘This article considers Cauchy problem for quasilinear hyperbolic systems in diagonal form. A necessary and sufficient condition in guaranteeing that Cauchy problem admits a unique global classical solution on t ≥ 0 is obtained, and a sharp estimate of the life span for the classical solution is given.
基金Supported by National Natural Science Foundation of China (10976026, 11271305, 11301439, 11226174)
文摘In this paper we derive LPS＇s criterion for the breakdown of classical solutions to the incompressible nematic liquid crystal flow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution of nematic liquid crystals in R^3. We show that if 0 〈 T 〈 ＋∞ is the maximal time interval for the unique smooth solution u ∈ C^∞（[0, T）,R^3）,then ｜u｜＋｜△d｜∈L^q（[0,T],L^p（R^3））,where p and q satisfy the Ladyzhenskaya-Prodi-Serrin＇s condition：3/p＋2/q=1 and p∈（3,＋∞].
基金funded by The National Institute for Occupational Safety and Health,USA(NIOSH)(Grant No.200-2016-90154)
文摘With recent advances in numerical modeling, design of underground structures increasingly relies on numerical modeling-based analysis approaches. While modeling tools like the discrete element method(DEM) and the combined finite-discrete element method(FDEM) are useful for investigating small-scale damage processes, continuum models remain the primary practical tool for most field-scale problems.The results obtained from such models are significantly dependent on the selection of an appropriate yield criterion and dilation angle. Towards improving its capabilities in handling mining-related problems, the authors have previously developed a new yield criterion(called progressive S-shaped criterion). The focus of the current study is to demonstrate its use in modeling rock pillars through a comparative analysis against four other yield criteria. In addition to the progressive S-shaped criterion,only one out of the four other criteria predicted a trend in strength consistent with an empirical pillar strength database compiled from the literature. Given the closely-knit relationship between yield criteria and dilation angle in controlling the overall damage process, a separate comparison was conducted using a mobilized dilation model, a zero degree dilation angle and a constant non-zero dilation angle. This study also investigates the impact of meso-scale heterogeneity in mechanical properties on the overall model response by assigning probability distributions to the input parameters. The comparisons revealed that an isotropic model using a combination of progressive S-shaped criterion and mobilized dilation angle model is sufficient in capturing the behaviors of rock pillars. Subsequently, the pillar model was used to assess the effect of L/W(length/width) ratio on the peak strength.
文摘This article studies on Cauchy’s function f （z） and its integral, （2πi）J[ f （z）] ≡ ■C f （t）dt/（t z） taken along a closed simple contour C, in regard to their comprehensive properties over the entire z = x ＋ iy plane consisted of the simply connected open domain D ＋ bounded by C and the open domain D outside C. （1） With f （z） assumed to be C n （n ∞-times continuously differentiable） z ∈ D ＋ and in a neighborhood of C, f （z） and its derivatives f （n） （z） are proved uniformly continuous in the closed domain D ＋ = [D ＋ ＋ C]. （2） Cauchy’s integral formulas and their derivatives z ∈ D ＋ （or z ∈ D ） are proved to converge uniformly in D ＋ （or in D = [D ＋C]）, respectively, thereby rendering the integral formulas valid over the entire z-plane. （3） The same claims （as for f （z） and J[ f （z）]） are shown extended to hold for the complement function F（z）, defined to be C n z ∈ D and about C. （4） The uniform convergence theorems for f （z） and F（z） shown for arbitrary contour C are adapted to find special domains in the upper or lower half z-planes and those inside and outside the unit circle ｜z｜ = 1 such that the four general- ized Hilbert-type integral transforms are proved. （5） Further, the singularity distribution of f （z） in D is elucidated by considering the direct problem exemplified with several typ- ical singularities prescribed in D . （6） A comparative study is made between generalized integral formulas and Plemelj’s formulas on their differing basic properties. （7） Physical sig- nificances of these formulas are illustrated with applicationsto nonlinear airfoil theory. （8） Finally, an unsolved inverse problem to determine all the singularities of Cauchy function f （z） in domain D , based on the continuous numerical value of f （z） z ∈ D ＋ = [D ＋ ＋ C], is presented for resolution as a conjecture.
基金Supported by the Natural Science Foundation of Hubei Province!(992P0 30 7) the National Natural Science Foun-dation of Chi
文摘A simple method for solving Cauchy’s problem of wave equations in higher space dimensions with initial condition of separated variables, has been given by using D’Alembert’s formula and some examples have been shown.
文摘The present paper aims at giving some general ideas concerning the micromechanical approach of the strength of a porous material. It is shown that its determination theoretically amounts to solving a nonlinear boundary value problem defined on a representative elementary volume(REV). The principle of nonlinear homogenization is illustrated based on the case of a solid phase having a Green’s strength criterion. An original refinement of the so-called secant method(based on two reference strains) is also provided. The paper also describes the main feature of the Gurson’s model which implements the principle of limit analysis on a conceptual model of hollow sphere. The last part of the paper gives some ideas concerning poromechanical couplings.
文摘In this paper, we presented a sufficient condition on the frequency domain for the absolutely stable analysis of the Takagi-Sugeno (T-S)fuzzy control system, based on the Popov’s criterion. we use some numerical examples to illustrate the efficiency of frequency domain-based condition.
文摘In this paper, we give two characterizations of multi-Cauchy-Jensen mappings. One of them reduces the system of n equations defining these mappings to a single functional equation. We also prove, using the fixed point method, the generalized Hyers-Ulam stability of this equation. Our results generalize some known outcomes.
基金supported by the National Natural Science Foundation of China(Nos.11072125 and11272175)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20130002110044)the China Postdoctoral Science Foundation(No.2015M570035)
文摘Inspired by Cardano＇s method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor （DSDT） is revisited from a new view- point. This decomposition simplifies the cubic tensor equation, decouples the spher- ical/deviatoric strain energy density, and lays the foundation for the von Mises yield criterion. Besides, it is verified that under the precondition of energy decoupling and the simplest form, the DSDT is the only possible form of the additive decomposition with physical meanings.
基金Supported by the National Natural Science Foundation Fujian province of China(2016J01032).
文摘As is well known,the definitions of fractional sum and fractional difference of f(z)on non-uniform lattices x(z)=c1z^(2)+c2z+c3 or x(z)=c1q^(z)+c2q^(-z)+c3 are more difficult and complicated.In this article,for the first time we propose the definitions of the fractional sum and fractional difference on non-uniform lattices by two different ways.The analogue of Euler’s Beta formula,Cauchy’Beta formula on non-uniform lattices are established,and some fundamental theorems of fractional calculas,the solution of the generalized Abel equation on non-uniform lattices are obtained etc.
文摘In this paper, an efficient weight initialization method is proposed using Cauchy’s inequality based on sensitivity analy- sis to improve the convergence speed in single hidden layer feedforward neural networks. The proposed method ensures that the outputs of hidden neurons are in the active region which increases the rate of convergence. Also the weights are learned by minimizing the sum of squared errors and obtained by solving linear system of equations. The proposed method is simulated on various problems. In all the problems the number of epochs and time required for the proposed method is found to be minimum compared with other weight initialization methods.
文摘This is a series of studies on Wu＇s conjecture and on its resolution to be presented herein. Both are devoted to expound all the comprehensive properties of Cauchy＇s function f（z） （z = x ＋ iy） and its integral J[f（z）]≡（2πi）-∮cf（t）（t-z）-1dt taken along the unit circle as contour C,inside which（the open domain D＋） f（z） is regular but has singularities distributed in open domain Doutside C. Resolution is given to the inverse problem that the singularities of f（z） can be determined in analytical form in terms of the values f（t） of f（z） numerically prescribed on C（｜t｜ = 1） ,as so enunciated by Wu＇s conjecture. The case of a single singularity is solved using complex algebra and analysis to acquire the solution structure for a standard reference. Multiple singularities are resolved by reducing them to a single one by elimination in principle,for which purpose a general asymptotic method is developed here for resolution to the conjecture by induction,and essential singularities are treated with employing the generalized Hilbert transforms. These new methods are applicable to relevant problems in mathematics,engineering and technology in analogy with resolving the inverse problem presented here.
文摘In this paper,we discussed the local integral solution operators of imhomogeneous Cauchy Riemann equations on an open set with piecewise C k boundary in C n,as a generalization of the solution opertators for Leray map S(z,ζ) which do not depends holomorphic on z∈D in Koppelman formula is obtained and the L s norm estimates for the solution operators are the same as that [10] in forms.
文摘A frequency-domain-based sufficient condition is derived to guarantee the globally asymptotic stability of the simplest Takagi-Sugeno （T-S） fuzzy control system by using the circle criterion. The analysis is performed in the frequency domain, and hence the condition is of great significance when the frequency-response method, which is widely used in the linear control theory and practice, is employed to synthesize the simplest T-S fuzzy controller. Besides, this sufficient condition is featured by a graphical interpretation, which makes the condition straightforward to be used. Comparisons are drawn between the performance of the simplest T-S fuzzy controller and that of the linear compensator. Two numerical examples are presented to demonstrate how this sufficient condition can be applied to both stable and unstable plants.
