By the method of Knopp-Kojima, the generalized order of Dirichlet series is studied and some interesting relations on the maximum modulus, the maximum term and the coefficients of entire function defined by Dirichlet ...By the method of Knopp-Kojima, the generalized order of Dirichlet series is studied and some interesting relations on the maximum modulus, the maximum term and the coefficients of entire function defined by Dirichlet series of slow growth are obtained, which briefly extends some results of paper [1].展开更多
Some stochastic comparisons of generalized order statistics under the right spread order, the location independent riskier order and the total time transform order are investigated in this paper. The underlying distri...Some stochastic comparisons of generalized order statistics under the right spread order, the location independent riskier order and the total time transform order are investigated in this paper. The underlying distributions and parameters on which generalized order statistics are based are also surveyed to obtain the conditions for increasing the expectations of spacings between the first two generalized order statistics and between the last two generalized order statistics.展开更多
Moments of generalized order statistics appear in several areas of science and engineering.These moments are useful in studying properties of the random variables which are arranged in increasing order of importance,f...Moments of generalized order statistics appear in several areas of science and engineering.These moments are useful in studying properties of the random variables which are arranged in increasing order of importance,for example,time to failure of a computer system.The computation of these moments is sometimes very tedious and hence some algorithms are required.One algorithm is to use a recursive method of computation of these moments and is very useful as it provides the basis to compute higher moments of generalized order statistics from the corresponding lower-order moments.Generalized order statistics pro-vides several models of ordered data as a special case.The moments of general-ized order statistics also provide moments of order statistics and record values as a special case.In this research,the recurrence relations for single,product,inverse and ratio moments of generalized order statistics will be obtained for Lindley–Weibull distribution.These relations will be helpful for obtained moments of gen-eralized order statistics from Lindley–Weibull distribution recursively.Special cases of the recurrence relations will also be obtained.Some characterizations of the distribution will also be obtained by using moments of generalized order statistics.These relations for moments and characterizations can be used in differ-ent areas of computer sciences where data is arranged in increasing order.展开更多
Highway work zones are locations where severe traffic crashes tend to occur.Most of the extant research on work zone crash severity neglects the discrepancy in the injuries sustained by different drivers involved in t...Highway work zones are locations where severe traffic crashes tend to occur.Most of the extant research on work zone crash severity neglects the discrepancy in the injuries sustained by different drivers involved in the same crash.Admittedly,it is essential to analyse crash-level factors to their highest injury severity;but it is equally important to understand driver-level contributing factors to their injury severity to establish effective safety countermeasures to minimize drivers’injury severity.Thus,this research aims to identify the factors with significant impacts on the driver injury severity of work zone crashes and estimate their effects on each severity level.Data on 3880 drivers involved in 2134 work zone crashes are obtained from the Crash Report Sampling System(CRSS)database of the United States and employed for the empirical investigation.A Bayesian hierarchical generalized ordered probit model is advocated for analysing the driver injury severity.Model performance indices suggest that the advocated hierarchical model is superior to the generalized ordered probit model,and considerable within-crash correlation is found across the observed driver injury severity.The estimated parameters show that driver age and sex,alcohol use,vehicle age and type,speeding and speed limit,weather conditions,lighting conditions and crash type have significant effects on the driver injury severity in work zone crashes.Marginal effects of the significant factors on each divided injury severity level are also estimated.Countermeasures are proposed from the results to reduce severe injuries sustained by drivers involved in work zone crashes.展开更多
In this paper,we delve into a generalized higher order Camassa-Holm type equation,(or,an ghmCH equation for short).We establish local well-posedness for this equation under the condition that the initial data uo belon...In this paper,we delve into a generalized higher order Camassa-Holm type equation,(or,an ghmCH equation for short).We establish local well-posedness for this equation under the condition that the initial data uo belongs to the Sobolev space H'(R)for some s>2.In addition,we obtain the weak formulation of this equation and prove the existence of both single peakon solution and a multi-peakon dynamic system.展开更多
Spectrum distribution of the second order generalized distributed parameter system was discussed via the functional analysis and operator theory in Hilbert space. The solutions of the problem and the constructive expr...Spectrum distribution of the second order generalized distributed parameter system was discussed via the functional analysis and operator theory in Hilbert space. The solutions of the problem and the constructive expression of the solutions are given by the generalized inverse one of bounded linear operator. This is theoretically important for studying the stabilization and asymptotic stability of the second order generalized distributed parameter system.展开更多
Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized higher order algebraic differential equations.
In this paper,we study the generalized lower order of entire functions defined by Dirichlet series.By constructing the Newton polygon based on Knopp-Kojima’s formula,we obtain a relation between the coefficients of t...In this paper,we study the generalized lower order of entire functions defined by Dirichlet series.By constructing the Newton polygon based on Knopp-Kojima’s formula,we obtain a relation between the coefficients of the Dirichlet series and its generalized lower order.展开更多
By extending the usual Wigner operator to the s-parameterized one as 1/4π2 integral （dyduexp [iu（q-Q）＋iy（p-P）＋is/2yu]） from n=- ∞ to ∞ with s beng a,real parameter,we propose a generalized Weyl quantization...By extending the usual Wigner operator to the s-parameterized one as 1/4π2 integral （dyduexp [iu（q-Q）＋iy（p-P）＋is/2yu]） from n=- ∞ to ∞ with s beng a,real parameter,we propose a generalized Weyl quantization scheme which accompanies a new generalized s-parameterized ordering rule.This rule recovers P-Q ordering,Q-P ordering,and Weyl ordering of operators in s = 1,1,0 respectively.Hence it differs from the Cahill-Glaubers’ ordering rule which unifies normal ordering,antinormal ordering,and Weyl ordering.We also show that in this scheme the s-parameter plays the role of correlation between two quadratures Q and P.The formula that can rearrange a given operator into its new s-parameterized ordering is presented.展开更多
In this paper, the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some e...In this paper, the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some exact explicit travelling solitary wave solutions for the above equation are obtained. As a result, some minor errors and some known results in the previousl literature are clarified and improved.展开更多
In this paper, based on a new more general ansitz, a new algebraic method, named generalized Riccati equation rational expansion method, is devised for constructing travelling wave solutions for nonlinear evolution eq...In this paper, based on a new more general ansitz, a new algebraic method, named generalized Riccati equation rational expansion method, is devised for constructing travelling wave solutions for nonlinear evolution equations with nonlinear terms of any order. Compared with most existing tanh methods for finding travelling wave solutions, the proposed method not only recovers the results by most known algebraic methods, but also provides new and more general solutions. We choose the generalized Burgers-Fisher equation with nonlinear terms of any order to illustrate our method. As a result, we obtain several new kinds of exact solutions for the equation. This approach can also be applied to other nonlinear evolution equations with nonlinear terms of any order.展开更多
The nonlocal symmetry of the generalized fifth order KdV equation(FOKdV) is first obtained by using the related Lax pair and then localizing it in a new enlarged system by introducing some new variables. On this basis...The nonlocal symmetry of the generalized fifth order KdV equation(FOKdV) is first obtained by using the related Lax pair and then localizing it in a new enlarged system by introducing some new variables. On this basis, new Ba¨cklund transformation is obtained through Lie’s first theorem. Furthermore, the general form of Lie point symmetry for the enlarged FOKdV system is found and new interaction solutions for the generalized FOKdV equation are explored by using a symmetry reduction method.展开更多
By using the theory of compensated compactness,we prove that there exists a sequence {uδε} converges nearly everywhere to the solution of the initial-value problem of generalized KdV equation with high order perturb...By using the theory of compensated compactness,we prove that there exists a sequence {uδε} converges nearly everywhere to the solution of the initial-value problem of generalized KdV equation with high order perturbation terms,namely we prove the existence of the weak solution.展开更多
In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators...In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators.The existence,uniqueness,and stability of the proposed model are discussed.Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models.Comparative studies with generalized fifth-order Runge-Kutta method are given.Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented.We have showcased the efficiency of the proposed method and garnered robust empirical support for our theoretical findings.展开更多
A new method that uses a modified ordered subsets （MOS） algorithm to improve the convergence rate of space-alternating generalized expectation-maximization （SAGE） algorithm for positron emission tomography （PET）...A new method that uses a modified ordered subsets （MOS） algorithm to improve the convergence rate of space-alternating generalized expectation-maximization （SAGE） algorithm for positron emission tomography （PET） image reconstruction is proposed.In the MOS-SAGE algorithm,the number of projections and the access order of the subsets are modified in order to improve the quality of the reconstructed images and accelerate the convergence speed.The number of projections in a subset increases as follows：2,4,8,16,32 and 64.This sequence means that the high frequency component is recovered first and the low frequency component is recovered in the succeeding iteration steps.In addition,the neighboring subsets are separated as much as possible so that the correlation of projections can be decreased and the convergences can be speeded up.The application of the proposed method to simulated and real images shows that the MOS-SAGE algorithm has better performance than the SAGE algorithm and the OSEM algorithm in convergence and image quality.展开更多
The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler...The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler numbers of higher order were extended.展开更多
There is a close relationship between the Painlevéintegrability and other integrability of nonlinear evolution equation.By using the Weiss-Tabor-Carnevale(WTC)method and the symbolic computation of Maple,the Pain...There is a close relationship between the Painlevéintegrability and other integrability of nonlinear evolution equation.By using the Weiss-Tabor-Carnevale(WTC)method and the symbolic computation of Maple,the Painlevétest is used for the higher order generalized non-autonomous equation and the third order Korteweg-de Vries equation with variable coefficients.Finally the Painlevéintegrability condition of this equation is gotten.展开更多
The paper deals with growth estimates and approximation（not necessarily entire） of solutions of certain elliptic partial differential equations. These solutions are called generalized bi-axially symmetric potentials...The paper deals with growth estimates and approximation（not necessarily entire） of solutions of certain elliptic partial differential equations. These solutions are called generalized bi-axially symmetric potentials（GBASP＇s）. To obtain more refined measure of growth, we have defined q-proximate order and obtained the characterization of generalized q-type and generalized lower q-type with respect to q-proximate order of a GBASP in terms of approximation errors and ratio of these errors in sup norm.展开更多
In the present paper, we study the polynomial approximation of entire functions of several complex variables. The characterizations of generalized order and generalized type of entire functions of slow growth are obta...In the present paper, we study the polynomial approximation of entire functions of several complex variables. The characterizations of generalized order and generalized type of entire functions of slow growth are obtained in terms of approximation and interpolation errors.展开更多
Two kinds of selection combining schemes including generalized selection combining (GSC) and generalized order selection combining (GOSC) are investigated. In the GSC scheme, L strongest diversity branches from a tota...Two kinds of selection combining schemes including generalized selection combining (GSC) and generalized order selection combining (GOSC) are investigated. In the GSC scheme, L strongest diversity branches from a total of R diversity branches are selected and coherently combined by maximal ratio combining. GOSC means that the Lth strongest diversity branch from R diversity branches is selected for reception. Closed-form expressions for the average signal-to-noise ratios of maximum ratio transmission with GSC and GOSC are derived in Rayleigh fading channels.展开更多
基金supported by the National Natural Science Foundation of China(11101096)the National Natural Science Foundation of China(11201083)+1 种基金the National Natural Science Foundation of China(11301140)the Guangdong Natural Science Foundation(S2012010010376)
文摘By the method of Knopp-Kojima, the generalized order of Dirichlet series is studied and some interesting relations on the maximum modulus, the maximum term and the coefficients of entire function defined by Dirichlet series of slow growth are obtained, which briefly extends some results of paper [1].
基金Supported by Program for Young Talents in Artillery College.
文摘Some stochastic comparisons of generalized order statistics under the right spread order, the location independent riskier order and the total time transform order are investigated in this paper. The underlying distributions and parameters on which generalized order statistics are based are also surveyed to obtain the conditions for increasing the expectations of spacings between the first two generalized order statistics and between the last two generalized order statistics.
基金The work was funded by the University of Jeddah,Saudi Arabia under Grant Number UJ–02–093–DR.The authors,therefore,acknowledge with thanks the University for technical and financial support.
文摘Moments of generalized order statistics appear in several areas of science and engineering.These moments are useful in studying properties of the random variables which are arranged in increasing order of importance,for example,time to failure of a computer system.The computation of these moments is sometimes very tedious and hence some algorithms are required.One algorithm is to use a recursive method of computation of these moments and is very useful as it provides the basis to compute higher moments of generalized order statistics from the corresponding lower-order moments.Generalized order statistics pro-vides several models of ordered data as a special case.The moments of general-ized order statistics also provide moments of order statistics and record values as a special case.In this research,the recurrence relations for single,product,inverse and ratio moments of generalized order statistics will be obtained for Lindley–Weibull distribution.These relations will be helpful for obtained moments of gen-eralized order statistics from Lindley–Weibull distribution recursively.Special cases of the recurrence relations will also be obtained.Some characterizations of the distribution will also be obtained by using moments of generalized order statistics.These relations for moments and characterizations can be used in differ-ent areas of computer sciences where data is arranged in increasing order.
基金supported by the Open Fund of the Key Laboratory of Highway Engineering of Ministry of Education(Changsha University of Science&Technology)(Grant No.kfj230301).
文摘Highway work zones are locations where severe traffic crashes tend to occur.Most of the extant research on work zone crash severity neglects the discrepancy in the injuries sustained by different drivers involved in the same crash.Admittedly,it is essential to analyse crash-level factors to their highest injury severity;but it is equally important to understand driver-level contributing factors to their injury severity to establish effective safety countermeasures to minimize drivers’injury severity.Thus,this research aims to identify the factors with significant impacts on the driver injury severity of work zone crashes and estimate their effects on each severity level.Data on 3880 drivers involved in 2134 work zone crashes are obtained from the Crash Report Sampling System(CRSS)database of the United States and employed for the empirical investigation.A Bayesian hierarchical generalized ordered probit model is advocated for analysing the driver injury severity.Model performance indices suggest that the advocated hierarchical model is superior to the generalized ordered probit model,and considerable within-crash correlation is found across the observed driver injury severity.The estimated parameters show that driver age and sex,alcohol use,vehicle age and type,speeding and speed limit,weather conditions,lighting conditions and crash type have significant effects on the driver injury severity in work zone crashes.Marginal effects of the significant factors on each divided injury severity level are also estimated.Countermeasures are proposed from the results to reduce severe injuries sustained by drivers involved in work zone crashes.
文摘In this paper,we delve into a generalized higher order Camassa-Holm type equation,(or,an ghmCH equation for short).We establish local well-posedness for this equation under the condition that the initial data uo belongs to the Sobolev space H'(R)for some s>2.In addition,we obtain the weak formulation of this equation and prove the existence of both single peakon solution and a multi-peakon dynamic system.
文摘Spectrum distribution of the second order generalized distributed parameter system was discussed via the functional analysis and operator theory in Hilbert space. The solutions of the problem and the constructive expression of the solutions are given by the generalized inverse one of bounded linear operator. This is theoretically important for studying the stabilization and asymptotic stability of the second order generalized distributed parameter system.
文摘Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized higher order algebraic differential equations.
基金the National Natural Science Foundation of China(11501127)Natural Science Foundation of Guangdong Province(2018A030313954).
文摘In this paper,we study the generalized lower order of entire functions defined by Dirichlet series.By constructing the Newton polygon based on Knopp-Kojima’s formula,we obtain a relation between the coefficients of the Dirichlet series and its generalized lower order.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11175113 and 11147009)the Natural Science Foundation of Shandong Province of China (Grant No. ZR2010AQ027)the Program of Higher Educational Science and Technology of Shandong Province,China (Grant No. J10LA15)
文摘By extending the usual Wigner operator to the s-parameterized one as 1/4π2 integral （dyduexp [iu（q-Q）＋iy（p-P）＋is/2yu]） from n=- ∞ to ∞ with s beng a,real parameter,we propose a generalized Weyl quantization scheme which accompanies a new generalized s-parameterized ordering rule.This rule recovers P-Q ordering,Q-P ordering,and Weyl ordering of operators in s = 1,1,0 respectively.Hence it differs from the Cahill-Glaubers’ ordering rule which unifies normal ordering,antinormal ordering,and Weyl ordering.We also show that in this scheme the s-parameter plays the role of correlation between two quadratures Q and P.The formula that can rearrange a given operator into its new s-parameterized ordering is presented.
基金supported by the Research Foundation of Education Bureau of Hubei Province,China (Grant No Z200612001)the Natural Science Foundation of Yangtze University (Grant No 20061222)
文摘In this paper, the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some exact explicit travelling solitary wave solutions for the above equation are obtained. As a result, some minor errors and some known results in the previousl literature are clarified and improved.
基金The project partially supported by the State Key Basic Research Program of China under Grant No. 2004CB318000
文摘In this paper, based on a new more general ansitz, a new algebraic method, named generalized Riccati equation rational expansion method, is devised for constructing travelling wave solutions for nonlinear evolution equations with nonlinear terms of any order. Compared with most existing tanh methods for finding travelling wave solutions, the proposed method not only recovers the results by most known algebraic methods, but also provides new and more general solutions. We choose the generalized Burgers-Fisher equation with nonlinear terms of any order to illustrate our method. As a result, we obtain several new kinds of exact solutions for the equation. This approach can also be applied to other nonlinear evolution equations with nonlinear terms of any order.
基金supported by the National Natural Science Foundation of China(Grant Nos.11347183,11405110,11275129,and 11305106)the Natural Science Foundation of Zhejiang Province of China(Grant Nos.Y7080455 and LQ13A050001)
文摘The nonlocal symmetry of the generalized fifth order KdV equation(FOKdV) is first obtained by using the related Lax pair and then localizing it in a new enlarged system by introducing some new variables. On this basis, new Ba¨cklund transformation is obtained through Lie’s first theorem. Furthermore, the general form of Lie point symmetry for the enlarged FOKdV system is found and new interaction solutions for the generalized FOKdV equation are explored by using a symmetry reduction method.
基金Supported by the Innovation Talents of Science and Technology of Henan University(2009-HASTIT-007)Supported by the Natural Science Program of Department of Education(2011A110006)
文摘By using the theory of compensated compactness,we prove that there exists a sequence {uδε} converges nearly everywhere to the solution of the initial-value problem of generalized KdV equation with high order perturbation terms,namely we prove the existence of the weak solution.
文摘In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators.The existence,uniqueness,and stability of the proposed model are discussed.Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models.Comparative studies with generalized fifth-order Runge-Kutta method are given.Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented.We have showcased the efficiency of the proposed method and garnered robust empirical support for our theoretical findings.
基金The National Basic Research Program of China (973Program) (No.2003CB716102).
文摘A new method that uses a modified ordered subsets （MOS） algorithm to improve the convergence rate of space-alternating generalized expectation-maximization （SAGE） algorithm for positron emission tomography （PET） image reconstruction is proposed.In the MOS-SAGE algorithm,the number of projections and the access order of the subsets are modified in order to improve the quality of the reconstructed images and accelerate the convergence speed.The number of projections in a subset increases as follows：2,4,8,16,32 and 64.This sequence means that the high frequency component is recovered first and the low frequency component is recovered in the succeeding iteration steps.In addition,the neighboring subsets are separated as much as possible so that the correlation of projections can be decreased and the convergences can be speeded up.The application of the proposed method to simulated and real images shows that the MOS-SAGE algorithm has better performance than the SAGE algorithm and the OSEM algorithm in convergence and image quality.
基金Supported by the NNSF of China(10001016) SF for the Prominent Youth of Henan Province
文摘The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler numbers of higher order were extended.
基金Supported by the Shanxi Education Department Project(Grant No.J2020398)Key Natural Science Projects of Shanxi Energy Institute(Grant No.ZZ-2018003)。
文摘There is a close relationship between the Painlevéintegrability and other integrability of nonlinear evolution equation.By using the Weiss-Tabor-Carnevale(WTC)method and the symbolic computation of Maple,the Painlevétest is used for the higher order generalized non-autonomous equation and the third order Korteweg-de Vries equation with variable coefficients.Finally the Painlevéintegrability condition of this equation is gotten.
文摘The paper deals with growth estimates and approximation（not necessarily entire） of solutions of certain elliptic partial differential equations. These solutions are called generalized bi-axially symmetric potentials（GBASP＇s）. To obtain more refined measure of growth, we have defined q-proximate order and obtained the characterization of generalized q-type and generalized lower q-type with respect to q-proximate order of a GBASP in terms of approximation errors and ratio of these errors in sup norm.
文摘In the present paper, we study the polynomial approximation of entire functions of several complex variables. The characterizations of generalized order and generalized type of entire functions of slow growth are obtained in terms of approximation and interpolation errors.
文摘Two kinds of selection combining schemes including generalized selection combining (GSC) and generalized order selection combining (GOSC) are investigated. In the GSC scheme, L strongest diversity branches from a total of R diversity branches are selected and coherently combined by maximal ratio combining. GOSC means that the Lth strongest diversity branch from R diversity branches is selected for reception. Closed-form expressions for the average signal-to-noise ratios of maximum ratio transmission with GSC and GOSC are derived in Rayleigh fading channels.
