Addition formulas exist in trigonometric functions.Double-angle and half-angle formulas can be derived from these formulas.Moreover,the relation equation between the trigonometric function and the hyperbolic function ...Addition formulas exist in trigonometric functions.Double-angle and half-angle formulas can be derived from these formulas.Moreover,the relation equation between the trigonometric function and the hyperbolic function can be derived using an imaginary number.The inverse hyperbolic function arsinher(r)■ro 1/√1+t^(2)dt p1tt2 dt is similar to the inverse trigonometric function arcsiner(r)■ro 1/√1+t^(2)dt p1t2 dt,such as the second degree of a polynomial and the constant term 1,except for the sign−and+.Such an analogy holds not only when the degree of the polynomial is 2,but also for higher degrees.As such,a function exists with respect to the leaf function through the imaginary number i,such that the hyperbolic function exists with respect to the trigonometric function through this imaginary number.In this study,we refer to this function as the hyperbolic leaf function.By making such a definition,the relation equation between the leaf function and the hyperbolic leaf function makes it possible to easily derive various formulas,such as addition formulas of hyperbolic leaf functions based on the addition formulas of leaf functions.Using the addition formulas,we can also derive the double-angle and half-angle formulas.We then verify the consistency of these formulas by constructing graphs and numerical data.展开更多
Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach. This approach can also be applied to other nonlinear differential-difference...Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach. This approach can also be applied to other nonlinear differential-difference equations.展开更多
A hyperbolic Lindstedt-Poincare method is presented to determine the homoclinic solutions of a kind of nonlinear oscillators, in which critical value of the homoclinic bifurcation parameter can be determined. The gene...A hyperbolic Lindstedt-Poincare method is presented to determine the homoclinic solutions of a kind of nonlinear oscillators, in which critical value of the homoclinic bifurcation parameter can be determined. The generalized Lienard oscillator is studied in detail, and the present method's predictions are compared with those of Runge-Kutta method to illustrate its accuracy.展开更多
A hyperbolic function is introduced to reflect the attenuation effect of one firm's default to its partner. If two firms are competitors (copartners), the default intensity of one firm will decrease (increase) ab...A hyperbolic function is introduced to reflect the attenuation effect of one firm's default to its partner. If two firms are competitors (copartners), the default intensity of one firm will decrease (increase) abruptly when the other firm defaults. As time goes on, the impact will decrease gradually until extinct. In this model, the joint distribution and marginal distributions of default times are derived by employing the change of measure, and the fair swap premium of a credit default swap (CDS) can be valued.展开更多
In this paper, we discuss some analytic properties of hyperbolic tangent function and estimate some approximation errors of neural network operators with the hyperbolic tan- gent activation function. Firstly, an equat...In this paper, we discuss some analytic properties of hyperbolic tangent function and estimate some approximation errors of neural network operators with the hyperbolic tan- gent activation function. Firstly, an equation of partitions of unity for the hyperbolic tangent function is given. Then, two kinds of quasi-interpolation type neural network operators are con- structed to approximate univariate and bivariate functions, respectively. Also, the errors of the approximation are estimated by means of the modulus of continuity of function. Moreover, for approximated functions with high order derivatives, the approximation errors of the constructed operators are estimated.展开更多
An approximate solution of the Dirac equation for a spin-1/2 particle under the influence of q-deformed hyperbolic P ¨oschl–Teller potential combined with trigonometric Scarf II non-central potential is studied ...An approximate solution of the Dirac equation for a spin-1/2 particle under the influence of q-deformed hyperbolic P ¨oschl–Teller potential combined with trigonometric Scarf II non-central potential is studied analytically. It is assumed that the scalar potential equals the vector potential in order to obtain analytical solutions. Both radial and angular parts of the Dirac equation are solved using the Nikiforov–Uvarov method. A relativistic energy spectrum and the relation between quantum numbers can be obtained using this method. Several quantum wave functions corresponding to several states are also presented in terms of the Jacobi Polynomials.展开更多
This paper presents a new and efficient approach for constructing exact solutions to nonlinear differential-difference equations (NLDDEs) and lattice equation. By using this method via symbolic computation system MA...This paper presents a new and efficient approach for constructing exact solutions to nonlinear differential-difference equations (NLDDEs) and lattice equation. By using this method via symbolic computation system MAPLE, we obtained abundant soliton-like and/or period-form solutions to the (2+1)-dimensional Toda equation. It seems that solitary wave solutions are merely special cases in one family. Furthermore, the method can also be applied to other nonlinear differential-difference equations.展开更多
To date no analytical solution of the pile ultimate lateral capacity for the general c–φ soil has been obtained. In the present study, a new dimensionless embedded ratio was proposed and the analytical solutions of ...To date no analytical solution of the pile ultimate lateral capacity for the general c–φ soil has been obtained. In the present study, a new dimensionless embedded ratio was proposed and the analytical solutions of ultimate lateral capacity and rotation center of rigid pile in c–φ soils were obtained. The results showed that both the dimensionless ultimate lateral capacity and dimensionless rotation center were the univariate functions of the embedded ratio. Also,the ultimate lateral capacity in the c–φ soil was the combination of the ultimate lateral capacity(f;) in the clay, and the ultimate lateral capacity(f;) in the sand. Therefore, the Broms chart for clay, solution for clay(φ=0) put forward by Poulos and Davis, solution for sand(c=0) obtained by Petrasovits and Awad, and Kondner’s ultimate bending moment were all proven to be the special cases of the general solution in the present study. A comparison of the field and laboratory tests in 93 cases showed that the average ratios of the theoretical values to the experimental value ranged from 0.85 to 1.15. Also, the theoretical values displayed a good agreement with the test values.展开更多
The hyperbolic function proposed by Abbo- Sloan was employed not only to approach the Mohr- Coulomb criterion but also to express the plastic potential function. A better approximation to the Mohr-Coulomb yield and po...The hyperbolic function proposed by Abbo- Sloan was employed not only to approach the Mohr- Coulomb criterion but also to express the plastic potential function. A better approximation to the Mohr-Coulomb yield and potential surfaces was achieved by increasing the transition angle and proven to be highly efficient in numerical convergence. When a Gaussian integral point goes into plastic state, two cases on yield stress adjustments were introduced. They may avoid solving the second derivative of the plastic potential function and the inverse matrix compared with the existing subroutine. Based on the above approaches, a fully implicit backward Euler integral regression algorithm was adopted. The two- and three-di- mensional user subroutines which can consider the asso- ciated or non-associated flow rule were developed on the platform of the finite element program--ABAQUS. To verify the reliability of these two subroutines, firstly, the numerical simulations of the indoor conventional triaxial compression and uniaxial tensile tests were performed, and their results were compared with those of the embedded Mohr-Coulomb model and the analytical approach. Then the main influential factors including the associated or non- associated flow rule, the judgment criteria of slope failure, and the tensile strength of soil were analyzed, and the application of the two-dimensional subroutine in the sta- bility analysis of a typical soil slope was discussed in detail through comparisons with the embedded model and the limit analysis method, which shows that this subroutine is more applicable and reliable than the latter two.展开更多
The evolution of solitons in Bose-Einstein condensates (BECs) with time-dependent atomic scattering length in an expulsive parabolic potential is studied. Based on the extended hyperbolic function method, we success...The evolution of solitons in Bose-Einstein condensates (BECs) with time-dependent atomic scattering length in an expulsive parabolic potential is studied. Based on the extended hyperbolic function method, we successfully obtain the bright and dark soliton solutions. In addition, some new soliton solutions in this model are found. The results in this paper include some in the literature (Phys. Rev. Lett. 94(2005)050402 and Chin. Phys. Lett. 22(2005) 1855).展开更多
In this paper, we use Riccati equation to construct new solitary wave solutions of the nonlinear evolution equations (NLEEs). Through the new function transformation, the Riccati equation is solved, and many new solit...In this paper, we use Riccati equation to construct new solitary wave solutions of the nonlinear evolution equations (NLEEs). Through the new function transformation, the Riccati equation is solved, and many new solitary wave solutions are obtained. Then it is substituted into the (2 + 1)-dimensional BLMP equation and (2 + 1)-dimensional KDV equation as an auxiliary equation. Many types of solitary wave solutions are obtained by choosing different coefficient p<sub>1</sub> and q<sub>1</sub> in the Riccati equation, and some of them have not been found in other documents. These solutions that we obtained in this paper will be helpful to understand the physics of the NLEEs.展开更多
On the power unit vector presented by Yang Wenxiong, it for the mathematical theory of k multiplier is extended to create a new mathematical branch. The extended k multiplier is yet to concern the negative pavers. Enu...On the power unit vector presented by Yang Wenxiong, it for the mathematical theory of k multiplier is extended to create a new mathematical branch. The extended k multiplier is yet to concern the negative pavers. Enumerating the combinatorial variaties and its functions can satisfy the various conditions, formulas, integrations, and equations etc. derived by Yang Wenxiong. The theory of k multiplier will be applied further to establish the theory of supperlight of a particle and its motion with the natural wave-panicle duality etc.展开更多
A new nonlinear wave equation of a finite deformation elastic circular rod simultaneously introducing transverse inertia and shearing strain was derived by means of Hamilton principle. The nonlinear equation includes ...A new nonlinear wave equation of a finite deformation elastic circular rod simultaneously introducing transverse inertia and shearing strain was derived by means of Hamilton principle. The nonlinear equation includes two nonlinear terms caused by finite deformation and double geometric dispersion effects caused by transverse inertia and transverse shearing strain. Nonlinear wave equation and corresponding truncated nonlinear wave equation were solved by the hyperbolic secant function finite expansion method. The solitary wave solutions of these nonlinear equations were obtained. The necessary condition of these solutions existence was given also.展开更多
In this paper, the Toda equation and the discrete nonlinear Schrdinger equation with a saturable nonlinearity via the discrete " (G′/G")-expansion method are researched. As a result, with the aid of the symbolic ...In this paper, the Toda equation and the discrete nonlinear Schrdinger equation with a saturable nonlinearity via the discrete " (G′/G")-expansion method are researched. As a result, with the aid of the symbolic computation, new hyperbolic function solution and trigonometric function solution with parameters of the Toda equation are obtained. At the same time, new envelop hyperbolic function solution and envelop trigonometric function solution with parameters of the discrete nonlinear Schro¨dinger equation with a saturable nonlinearity are obtained. This method can be applied to other nonlinear differential-difference equations in mathematical physics.展开更多
The so-called extended hyperbolic complex (EHC) function method is used to study further the stationary axisymmetric Einstein Maxwell theory with p Abelian gauge fields (EM-p theory, for short), Two EHC structural...The so-called extended hyperbolic complex (EHC) function method is used to study further the stationary axisymmetric Einstein Maxwell theory with p Abelian gauge fields (EM-p theory, for short), Two EHC structural Riemann- Hilbert (RH) transformations are constructed and are then shown to give an infinite-dimensional symmetry group of the EM-p theory. This symmetry group is verified to have the structure of semidirect product of Kac-Moody group SU(p + 1, 1) and Virasoro group. Moreover, the infinitesimal forms of these two RH transformations are calculated and found to give exactly the same infinitesimal transformations as in previous author's paper by a different scheme, This demonstrates that the results obtained in the present paper provide some exponentiations of all the infinitesimal symmetry transformations obtained before.展开更多
We present an integrated mathematical model of vehicle-following control for the establishment, maintenance, and re-establishment of the previous or new safe and efficient steady-following state. The hyperbolic functi...We present an integrated mathematical model of vehicle-following control for the establishment, maintenance, and re-establishment of the previous or new safe and efficient steady-following state. The hyperbolic functions are introduced to establish the corresponding mathematical models, which can describe the behavioral adjustment of the following vehicle steered by a well-experienced driver under complex vehicle following situations. According to the proposed mathematical models, the control laws of the following vehicle adjusting its own behavior can be calculated for its moving in safety,efficiency, and smoothness(comfort). Simulation results show that the safe and efficient steady-following state can be well established, maintained, and re-established by its own smooth(comfortable) behavioral adjustment with the synchronous control of the following vehicle’s velocity, acceleration, and the actual following distance.展开更多
Necessary and sufficient conditions are obtained for the boundedness of Berezin transformation on Lebesgue space Lp(B,dVβ) in the real unit ball B in Rn. As an application, we prove that Gleason type problem is solva...Necessary and sufficient conditions are obtained for the boundedness of Berezin transformation on Lebesgue space Lp(B,dVβ) in the real unit ball B in Rn. As an application, we prove that Gleason type problem is solvable in hyperbolic harmonic Bergman spaces. Furthermore we investigate the boundary behavior of the solutions of Gleason type problem.展开更多
We propose a hyperbolic function form of the Cardassian component in the Cardassian model. Using the repartition of this Cardassian component, we can obtain a non-zero gravitational interaction between the time deriva...We propose a hyperbolic function form of the Cardassian component in the Cardassian model. Using the repartition of this Cardassian component, we can obtain a non-zero gravitational interaction between the time derivative of Ricci scalar curvature and the baryon/lepton number current in the radiation-dominated universe. Furthermore, the other term that acts like a non-zero cosmological constant would give an accelerated expansion of current universe and the features of this model do not violate our desired requirements.展开更多
In this paper,we introduce for the first time a new eligible kernel function with a hyperbolic barrier term for semidefinite programming(SDP).This add a new type of functions to the class of eligible kernel functions....In this paper,we introduce for the first time a new eligible kernel function with a hyperbolic barrier term for semidefinite programming(SDP).This add a new type of functions to the class of eligible kernel functions.We prove that the interior-point algorithm based on the new kernel function meets O(n3/4 logε/n)iterations as the worst case complexity bound for the large-update method.This coincides with the complexity bound obtained by the first kernel function with a trigonometric barrier term proposed by El Ghami et al.in2012,and improves with a factor n(1/4)the obtained iteration bound based on the classic kernel function.We present some numerical simulations which show the effectiveness of the algorithm developed in this paper.展开更多
文摘Addition formulas exist in trigonometric functions.Double-angle and half-angle formulas can be derived from these formulas.Moreover,the relation equation between the trigonometric function and the hyperbolic function can be derived using an imaginary number.The inverse hyperbolic function arsinher(r)■ro 1/√1+t^(2)dt p1tt2 dt is similar to the inverse trigonometric function arcsiner(r)■ro 1/√1+t^(2)dt p1t2 dt,such as the second degree of a polynomial and the constant term 1,except for the sign−and+.Such an analogy holds not only when the degree of the polynomial is 2,but also for higher degrees.As such,a function exists with respect to the leaf function through the imaginary number i,such that the hyperbolic function exists with respect to the trigonometric function through this imaginary number.In this study,we refer to this function as the hyperbolic leaf function.By making such a definition,the relation equation between the leaf function and the hyperbolic leaf function makes it possible to easily derive various formulas,such as addition formulas of hyperbolic leaf functions based on the addition formulas of leaf functions.Using the addition formulas,we can also derive the double-angle and half-angle formulas.We then verify the consistency of these formulas by constructing graphs and numerical data.
基金Project supported by the National Natural Science Foundation of China (Grant No 10461006), the Natural Science Foundation (Grant No 200408020103), the High Education Science Research Program (Grant No NJ02035) of Inner Mongolia, China and the Youth Foundation (Grant No QN004024) of Inner Mongolia Normal University, China.
文摘Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach. This approach can also be applied to other nonlinear differential-difference equations.
基金supported by the National Natural Science Foundation of China (10672193)Sun Yat-sen University (Fu Lan Scholarship)the University of Hong Kong (CRGC grant).
文摘A hyperbolic Lindstedt-Poincare method is presented to determine the homoclinic solutions of a kind of nonlinear oscillators, in which critical value of the homoclinic bifurcation parameter can be determined. The generalized Lienard oscillator is studied in detail, and the present method's predictions are compared with those of Runge-Kutta method to illustrate its accuracy.
基金the National Basic Research Program of China(973 Program)(No.2007CB814903)the National Natural Science Foundation of China(No.70671069)
文摘A hyperbolic function is introduced to reflect the attenuation effect of one firm's default to its partner. If two firms are competitors (copartners), the default intensity of one firm will decrease (increase) abruptly when the other firm defaults. As time goes on, the impact will decrease gradually until extinct. In this model, the joint distribution and marginal distributions of default times are derived by employing the change of measure, and the fair swap premium of a credit default swap (CDS) can be valued.
基金Supported by the National Natural Science Foundation of China(61179041,61272023,and 11401388)
文摘In this paper, we discuss some analytic properties of hyperbolic tangent function and estimate some approximation errors of neural network operators with the hyperbolic tan- gent activation function. Firstly, an equation of partitions of unity for the hyperbolic tangent function is given. Then, two kinds of quasi-interpolation type neural network operators are con- structed to approximate univariate and bivariate functions, respectively. Also, the errors of the approximation are estimated by means of the modulus of continuity of function. Moreover, for approximated functions with high order derivatives, the approximation errors of the constructed operators are estimated.
文摘An approximate solution of the Dirac equation for a spin-1/2 particle under the influence of q-deformed hyperbolic P ¨oschl–Teller potential combined with trigonometric Scarf II non-central potential is studied analytically. It is assumed that the scalar potential equals the vector potential in order to obtain analytical solutions. Both radial and angular parts of the Dirac equation are solved using the Nikiforov–Uvarov method. A relativistic energy spectrum and the relation between quantum numbers can be obtained using this method. Several quantum wave functions corresponding to several states are also presented in terms of the Jacobi Polynomials.
基金supported by the National Natural Science Foundation of Chinathe Natural Science Foundation of Shandong Province in China (Grant No Y2007G64)
文摘This paper presents a new and efficient approach for constructing exact solutions to nonlinear differential-difference equations (NLDDEs) and lattice equation. By using this method via symbolic computation system MAPLE, we obtained abundant soliton-like and/or period-form solutions to the (2+1)-dimensional Toda equation. It seems that solitary wave solutions are merely special cases in one family. Furthermore, the method can also be applied to other nonlinear differential-difference equations.
基金financially supported by the National Natural Science Foundation of China(Grant No.51379132)
文摘To date no analytical solution of the pile ultimate lateral capacity for the general c–φ soil has been obtained. In the present study, a new dimensionless embedded ratio was proposed and the analytical solutions of ultimate lateral capacity and rotation center of rigid pile in c–φ soils were obtained. The results showed that both the dimensionless ultimate lateral capacity and dimensionless rotation center were the univariate functions of the embedded ratio. Also,the ultimate lateral capacity in the c–φ soil was the combination of the ultimate lateral capacity(f;) in the clay, and the ultimate lateral capacity(f;) in the sand. Therefore, the Broms chart for clay, solution for clay(φ=0) put forward by Poulos and Davis, solution for sand(c=0) obtained by Petrasovits and Awad, and Kondner’s ultimate bending moment were all proven to be the special cases of the general solution in the present study. A comparison of the field and laboratory tests in 93 cases showed that the average ratios of the theoretical values to the experimental value ranged from 0.85 to 1.15. Also, the theoretical values displayed a good agreement with the test values.
文摘The hyperbolic function proposed by Abbo- Sloan was employed not only to approach the Mohr- Coulomb criterion but also to express the plastic potential function. A better approximation to the Mohr-Coulomb yield and potential surfaces was achieved by increasing the transition angle and proven to be highly efficient in numerical convergence. When a Gaussian integral point goes into plastic state, two cases on yield stress adjustments were introduced. They may avoid solving the second derivative of the plastic potential function and the inverse matrix compared with the existing subroutine. Based on the above approaches, a fully implicit backward Euler integral regression algorithm was adopted. The two- and three-di- mensional user subroutines which can consider the asso- ciated or non-associated flow rule were developed on the platform of the finite element program--ABAQUS. To verify the reliability of these two subroutines, firstly, the numerical simulations of the indoor conventional triaxial compression and uniaxial tensile tests were performed, and their results were compared with those of the embedded Mohr-Coulomb model and the analytical approach. Then the main influential factors including the associated or non- associated flow rule, the judgment criteria of slope failure, and the tensile strength of soil were analyzed, and the application of the two-dimensional subroutine in the sta- bility analysis of a typical soil slope was discussed in detail through comparisons with the embedded model and the limit analysis method, which shows that this subroutine is more applicable and reliable than the latter two.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 1057508 and 10302018), the Natural Science Foundation of Zhejiang Province, China (Grant No Y605056).
文摘The evolution of solitons in Bose-Einstein condensates (BECs) with time-dependent atomic scattering length in an expulsive parabolic potential is studied. Based on the extended hyperbolic function method, we successfully obtain the bright and dark soliton solutions. In addition, some new soliton solutions in this model are found. The results in this paper include some in the literature (Phys. Rev. Lett. 94(2005)050402 and Chin. Phys. Lett. 22(2005) 1855).
文摘In this paper, we use Riccati equation to construct new solitary wave solutions of the nonlinear evolution equations (NLEEs). Through the new function transformation, the Riccati equation is solved, and many new solitary wave solutions are obtained. Then it is substituted into the (2 + 1)-dimensional BLMP equation and (2 + 1)-dimensional KDV equation as an auxiliary equation. Many types of solitary wave solutions are obtained by choosing different coefficient p<sub>1</sub> and q<sub>1</sub> in the Riccati equation, and some of them have not been found in other documents. These solutions that we obtained in this paper will be helpful to understand the physics of the NLEEs.
文摘On the power unit vector presented by Yang Wenxiong, it for the mathematical theory of k multiplier is extended to create a new mathematical branch. The extended k multiplier is yet to concern the negative pavers. Enumerating the combinatorial variaties and its functions can satisfy the various conditions, formulas, integrations, and equations etc. derived by Yang Wenxiong. The theory of k multiplier will be applied further to establish the theory of supperlight of a particle and its motion with the natural wave-panicle duality etc.
基金Project supported by the National Natural Science Foundation of China (No.10472076)the Natural Science Foundation of Shanxi Province of China (No.2006021005)
文摘A new nonlinear wave equation of a finite deformation elastic circular rod simultaneously introducing transverse inertia and shearing strain was derived by means of Hamilton principle. The nonlinear equation includes two nonlinear terms caused by finite deformation and double geometric dispersion effects caused by transverse inertia and transverse shearing strain. Nonlinear wave equation and corresponding truncated nonlinear wave equation were solved by the hyperbolic secant function finite expansion method. The solitary wave solutions of these nonlinear equations were obtained. The necessary condition of these solutions existence was given also.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.61072147,11071159)the Natural Science Foundation of Shanghai Municipality (Grant No.09ZR1410800)+1 种基金the Science Foundation of Key Laboratory of Mathematics Mechanization (Grant No.KLMM0806)the Shanghai Leading Academic Discipline Project (Grant Nos.J50101, S30104)
文摘In this paper, the Toda equation and the discrete nonlinear Schrdinger equation with a saturable nonlinearity via the discrete " (G′/G")-expansion method are researched. As a result, with the aid of the symbolic computation, new hyperbolic function solution and trigonometric function solution with parameters of the Toda equation are obtained. At the same time, new envelop hyperbolic function solution and envelop trigonometric function solution with parameters of the discrete nonlinear Schro¨dinger equation with a saturable nonlinearity are obtained. This method can be applied to other nonlinear differential-difference equations in mathematical physics.
基金Project supported by the Science Foundation from Education Department of Liaoning Province, China (Grant No 202142036) and the National Natural Science Foundation of China (Grant No 10475036).
文摘The so-called extended hyperbolic complex (EHC) function method is used to study further the stationary axisymmetric Einstein Maxwell theory with p Abelian gauge fields (EM-p theory, for short), Two EHC structural Riemann- Hilbert (RH) transformations are constructed and are then shown to give an infinite-dimensional symmetry group of the EM-p theory. This symmetry group is verified to have the structure of semidirect product of Kac-Moody group SU(p + 1, 1) and Virasoro group. Moreover, the infinitesimal forms of these two RH transformations are calculated and found to give exactly the same infinitesimal transformations as in previous author's paper by a different scheme, This demonstrates that the results obtained in the present paper provide some exponentiations of all the infinitesimal symmetry transformations obtained before.
基金supported by the National Natural Science Foundation of China(Grant No.61174183)
文摘We present an integrated mathematical model of vehicle-following control for the establishment, maintenance, and re-establishment of the previous or new safe and efficient steady-following state. The hyperbolic functions are introduced to establish the corresponding mathematical models, which can describe the behavioral adjustment of the following vehicle steered by a well-experienced driver under complex vehicle following situations. According to the proposed mathematical models, the control laws of the following vehicle adjusting its own behavior can be calculated for its moving in safety,efficiency, and smoothness(comfort). Simulation results show that the safe and efficient steady-following state can be well established, maintained, and re-established by its own smooth(comfortable) behavioral adjustment with the synchronous control of the following vehicle’s velocity, acceleration, and the actual following distance.
基金supported by the National Natural Science Fountation of China(Grant No.10001030)the Post-doctoral Fellowship of University of Aveiro,UI&D"Matematica e Aplicacoes".
文摘Necessary and sufficient conditions are obtained for the boundedness of Berezin transformation on Lebesgue space Lp(B,dVβ) in the real unit ball B in Rn. As an application, we prove that Gleason type problem is solvable in hyperbolic harmonic Bergman spaces. Furthermore we investigate the boundary behavior of the solutions of Gleason type problem.
文摘We propose a hyperbolic function form of the Cardassian component in the Cardassian model. Using the repartition of this Cardassian component, we can obtain a non-zero gravitational interaction between the time derivative of Ricci scalar curvature and the baryon/lepton number current in the radiation-dominated universe. Furthermore, the other term that acts like a non-zero cosmological constant would give an accelerated expansion of current universe and the features of this model do not violate our desired requirements.
文摘In this paper,we introduce for the first time a new eligible kernel function with a hyperbolic barrier term for semidefinite programming(SDP).This add a new type of functions to the class of eligible kernel functions.We prove that the interior-point algorithm based on the new kernel function meets O(n3/4 logε/n)iterations as the worst case complexity bound for the large-update method.This coincides with the complexity bound obtained by the first kernel function with a trigonometric barrier term proposed by El Ghami et al.in2012,and improves with a factor n(1/4)the obtained iteration bound based on the classic kernel function.We present some numerical simulations which show the effectiveness of the algorithm developed in this paper.