This paper deals with the some oscillation criteria for the two dimensional difference system of the form: . Examples illustrating the results are inserted.
In this paper,we generalize the concept of asymptotic Hankel operators on H2(D)to the Hardy space H2(Dn)(over polydisk)in terms of asymptotic Hankel and partial asymptotic Hankel operators and investigate some propert...In this paper,we generalize the concept of asymptotic Hankel operators on H2(D)to the Hardy space H2(Dn)(over polydisk)in terms of asymptotic Hankel and partial asymptotic Hankel operators and investigate some properties in case of its weak and strong convergence.Meanwhile,we introduce ith-partial Hankel operators on H2(Dn)and obtain a characterization of its compactness for n>1.Our main results include the containment of Toeplitz algebra in the collection of all strong partial asymptotic Hankel operators on H2(Dn).It is also shown that a Toeplitz operator with symbolφis asymptotic Hankel if and only if φ is holomorphic function in L∞(Tn).展开更多
Model selection strategies have been routinely employed to determine a model for data analysis in statistics, and further study and inference then often proceed as though the selected model were the true model that we...Model selection strategies have been routinely employed to determine a model for data analysis in statistics, and further study and inference then often proceed as though the selected model were the true model that were known a priori. Model averaging approaches, on the other hand, try to combine estimators for a set of candidate models. Specifically, instead of deciding which model is the ’right’ one, a model averaging approach suggests to fit a set of candidate models and average over the estimators using data adaptive weights.In this paper we establish a general frequentist model averaging framework that does not set any restrictions on the set of candidate models. It broaden, the scope of the existing methodologies under the frequentist model averaging development. Assuming the data is from an unknown model, we derive the model averaging estimator and study its limiting distributions and related predictions while taking possible modeling biases into account.We propose a set of optimal weights to combine the individual estimators so that the expected mean squared error of the average estimator is minimized. Simulation studies are conducted to compare the performance of the estimator with that of the existing methods. The results show the benefits of the proposed approach over traditional model selection approaches as well as existing model averaging methods.展开更多
In this paper,we focus on studying the asymptotic stability of the monotone decreasing kink profile solitary wave solutions for the generalized KdV-Burgers equation.We obtain the estimate of the firstorder and second-...In this paper,we focus on studying the asymptotic stability of the monotone decreasing kink profile solitary wave solutions for the generalized KdV-Burgers equation.We obtain the estimate of the firstorder and second-order derivatives for monotone decreasing kink profile solitary wave solutions,and overcome the difficulties caused by high-order nonlinear terms in the generalized KdV-Burgers equation in the estimate by using L2 energy estimating method and Young inequality.We prove that the monotone decreasing kink profile solitary wave solutions are asymptotically stable in H1.Moreover,we obtain the decay rate of the perturbationψin the sense of L^2 and L^∞norm,respectively,which are(1+t)^-1/2 and(1+t)^-1/4 by using Gargliado-Nirenberg inequality.展开更多
This paper considers a nonparametric M-estimator of a regression function for functional stationary ergodic data.More precisely,in the ergodic data setting,we consider the regression of a real random variable Y over a...This paper considers a nonparametric M-estimator of a regression function for functional stationary ergodic data.More precisely,in the ergodic data setting,we consider the regression of a real random variable Y over an explanatory random variable X taking values in some semi-metric abstract space.Under some mild conditions,the weak consistency and the asymptotic normality of the M-estimator are established.Furthermore,a simulated example is provided to examine the finite sample performance of the M-estimator.展开更多
Recently proposed two swampland criteria that arising from string theory landscape leads to the important challenge of the realization of single-field inflationary models. Especially one of swampland criteria which im...Recently proposed two swampland criteria that arising from string theory landscape leads to the important challenge of the realization of single-field inflationary models. Especially one of swampland criteria which implies a large tensor-to-scalar ratio is strongly in tension with recent observational results. In this paper, we explore the possibility the swampland conjectures could be compatible with single-field inflationary scenarios if the effects due to the quantum theory of gravity are considered. We show that the quantum gravitational effects due to the nonlinear dispersion relation provides significant modifications on the amplitude of both the scalar and tensor perturbation spectra. Such modifications could be either raise or reduce the perturbation spectra depending on the values of the parameters in the nonlinear terms of the dispersion relations. Therefore, these effects can reduce the tensor-to-scalar ratio to a smaller value, which helps to relax the tension between the swampland conjecture and observational data.展开更多
In this article, we are interested in least squares estimator for a class of pathdependent McKean-Vlasov stochastic differential equations (SDEs). More precisely, we investigate the consistency and asymptotic distribu...In this article, we are interested in least squares estimator for a class of pathdependent McKean-Vlasov stochastic differential equations (SDEs). More precisely, we investigate the consistency and asymptotic distribution of the least squares estimator for the unknown parameters involved by establishing an appropriate contrast function. Comparing to the existing results in the literature, the innovations of this article lie in three aspects:(i) We adopt a tamed Euler-Maruyama algorithm to establish the contrast function under the monotone condition, under which the Euler-Maruyama scheme no longer works;(ii) We take the advantage of linear interpolation with respect to the discrete-time observations to approximate the functional solution;(iii) Our model is more applicable and practice as we are dealing with SDEs with irregular coefficients (for example, Holder continuous) and pathdistribution dependent.展开更多
The advection-diffusion equation ytε-εyxxε+ M yxε= 0,(x, t) ∈(0, 1) ×(0, T) is null controllable for any strictly positive values of the diffusion coefficient ε and of the controllability time T. We discuss...The advection-diffusion equation ytε-εyxxε+ M yxε= 0,(x, t) ∈(0, 1) ×(0, T) is null controllable for any strictly positive values of the diffusion coefficient ε and of the controllability time T. We discuss here the behavior of the cost of control when the coefficient ε goes to zero, according to the values of T. It is actually known that this cost is uniformly bounded with respect to ε if T is greater than a minimal time TM, with TM in the interval [1, 2×31/2]/M for M > 0 and in the interval [2×21/2, 2(1 +31/2)]/|M | for M < 0. The exact value of TM is however unknown.We investigate in this work the determination of the minimal time TM employing two distincts but complementary approaches. In a first one, we numerically estimate the cost of controllability, reformulated as the solution of a generalized eigenvalue problem for the underlying control operator, with respect to the parameter T and ε. This allows notably to exhibit the structure of initial data leading to large costs of control. At the practical level, this evaluation requires the non trivial and challenging approximation of null controls for the advection-diffusion equation. In the second approach, we perform an asymptotic analysis, with respect to the parameter ε, of the optimality system associated to the control of minimal L2-norm. The matched asymptotic expansion method is used to describe the multiple boundary layers.展开更多
The asymptotic curve is widely used in astronomy, mechanics and numerical optimization. Moreover, it shows great application potentials in architecture. We focus on the problem how to cover bounded asymptotic curves b...The asymptotic curve is widely used in astronomy, mechanics and numerical optimization. Moreover, it shows great application potentials in architecture. We focus on the problem how to cover bounded asymptotic curves by a freeform surface. The paper presents the necessary and sufficient conditions for quadrilateral with non-inflection being asymptotic boundary curves of a surface. And then, with given corner data, we model quintic Bezier asymptotic quadrilateral interpolated by a smooth Bezier surface of bi-eleven degree. We handle the available degrees of freedom during the construction to get an optimized result. Some representative surfaces bounded by asymptotic curves with lines or inflections are also discussed by examples. The presented interpolation scheme for the construction of tensor-product Bezier surfaces is compatible with the CAD systems.展开更多
Zero-utility principle is one of the main premium pricing principles,which has been widely used in insurance practice.In this paper,the nonparametric estimation of zero-utility premium is given.In addition,the consist...Zero-utility principle is one of the main premium pricing principles,which has been widely used in insurance practice.In this paper,the nonparametric estimation of zero-utility premium is given.In addition,the consistency and asymptotic normality of the estimation are proved.Some special cases including linear,exponential and quadratic utility are discussed.Finally,the Monte Carlo method is used to show the convergence rate of premium estimation.Furthermore,the histogram and Normal-Probability-Plot are given to investigate the asymptotic normality of the estimators.The results show that our estimations are good enough to use in practice.展开更多
The behavior of the Kozachenko–Leonenko estimates for the(differential) Shannon entropy is studied when the number of i.i.d. vector-valued observations tends to infinity. The asymptotic unbiasedness and L^2-consisten...The behavior of the Kozachenko–Leonenko estimates for the(differential) Shannon entropy is studied when the number of i.i.d. vector-valued observations tends to infinity. The asymptotic unbiasedness and L^2-consistency of the estimates are established. The conditions employed involve the analogues of the Hardy–Littlewood maximal function. It is shown that the results are valid in particular for the entropy estimation of any nondegenerate Gaussian vector.展开更多
Development of asymptotic magnitude Bode plots for integer-order transfer functions is a well-established topic in the control theory.However,construction of such plots for the fractional-order transfer functions has ...Development of asymptotic magnitude Bode plots for integer-order transfer functions is a well-established topic in the control theory.However,construction of such plots for the fractional-order transfer functions has not received much attention in the existing literature.In the present paper,we investigate in this direction and derive the procedures for sketching asymptotic magnitude Bode plots for some of the popular fractional-order controllers such as PI^α,[PI]^α,PD^β,[PD]^β,and PI^αD^β.In addition,we deduce these plots for general fractional commensurate-order transfer functions as well.As applications of this work,we illustrate 1)the analysis of the designed fractional-control loop and 2)the identification of fractional-order transfer function from a given plot.展开更多
This paper investigates the asymptotic state estimation problem for linear systems with sensor and actuator faults,where the faults are modeled via multiple modes.For the case of sensor faults,we first introduce a new...This paper investigates the asymptotic state estimation problem for linear systems with sensor and actuator faults,where the faults are modeled via multiple modes.For the case of sensor faults,we first introduce a new notion of detectability,i.e.,detectability of system against sensor faults.The notion helps to address the question of whether it is possible to asymptotically estimate the system state by using the control input and system output,irrespective of which mode the system is in and what values the fault signals are.A necessary and sufficient condition for the system to be detectable against sensor faults is given,and then two switched observers are proposed for asymptotic state estimation with the help of maximin strategy.For the system with l fault modes,we provide the explicit form of the switched observer,which is based on a bank of"l(l+1)/2"Luenberger-like or sliding-mode observers.Furthermore,extensions to the case of sensor and actuator faults are further studied.Finally,a simulation example of a reduced-order aircraft system is provided to show the effectiveness of the proposed approaches.展开更多
This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covarianc...This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covariance structures. The focus is on the existence and uniqueness of the classical (square integrable) solution (mild solution, weak solution). It is also concerned with the Feynman-Kac formula for the solution;Feynman-Kac formula for the moments of the solution;and their applications to the asymptotic moment bounds of the solution. It also briefly touches the exact asymptotics of the moments of the solution.展开更多
The drift parameter estimation problem of the complex Ornstein-Uhlenbeck process driven by a complexα-stable motion is considered.Based on discrete observations,an estimator of the unknown drift parameter is construc...The drift parameter estimation problem of the complex Ornstein-Uhlenbeck process driven by a complexα-stable motion is considered.Based on discrete observations,an estimator of the unknown drift parameter is constructed by using the least squares method.Moreover,the strong consistency and the asymptotic distribution of the least squares estimator are derived under some assumptions.展开更多
In this study, we investigate the tail probability of the discounted aggregate claim sizes in a dependent risk model. In this model, the claim sizes are observed to follow a one-sided linear process with independent a...In this study, we investigate the tail probability of the discounted aggregate claim sizes in a dependent risk model. In this model, the claim sizes are observed to follow a one-sided linear process with independent and identically distributed innovations. Investment return is described as a general stochastic process with cadlag paths. In the case of heavy-tailed innovation distributions, we are able to derive some asymptotic estimates for tail probability and to provide some asymptotic upper bounds to improve the applicability of our study.展开更多
We study the asymptotic behavior of an incompressible viscous fluid flow in a biological body lined by a thin biological film with a cellular microstructure,varying thickness,and a heterogeneous viscosity regulated by...We study the asymptotic behavior of an incompressible viscous fluid flow in a biological body lined by a thin biological film with a cellular microstructure,varying thickness,and a heterogeneous viscosity regulated by a time random process.Let ting the thickness of the film tend to zero,we derive an effective biological slip boundary condition on the boundary of the body.This law relates the tangential fluxes to the tangential velocities via a proportional coefficient corresponding to the energy of some local problem.This law describes the ability of the biological film to function as a lubricant reducing friction at the wall of the body.The tangential velocities are functions of the random trajectories of a finely concentrated biological particle.展开更多
Based on a Tweedie-type formula developed under the Laplace distribution,this paper proposes a new bias-corrected estimator of the regression parameters in a simple linear model when the measurement error follows a La...Based on a Tweedie-type formula developed under the Laplace distribution,this paper proposes a new bias-corrected estimator of the regression parameters in a simple linear model when the measurement error follows a Laplace distribution.Large sample properties,including the consistency and the asymptotic normality,are investigated.The finite sample performance of the proposed estimators are evaluated via simulation studies,as well as comparison studies with some existing estimation procedures.展开更多
文摘This paper deals with the some oscillation criteria for the two dimensional difference system of the form: . Examples illustrating the results are inserted.
基金Support of UGC Research Grant[Ref.No.:21/12/2014(ii)EU-V,Sr.No.2121440601]to second author for carrying out the research work is gratefully acknowledged.
文摘In this paper,we generalize the concept of asymptotic Hankel operators on H2(D)to the Hardy space H2(Dn)(over polydisk)in terms of asymptotic Hankel and partial asymptotic Hankel operators and investigate some properties in case of its weak and strong convergence.Meanwhile,we introduce ith-partial Hankel operators on H2(Dn)and obtain a characterization of its compactness for n>1.Our main results include the containment of Toeplitz algebra in the collection of all strong partial asymptotic Hankel operators on H2(Dn).It is also shown that a Toeplitz operator with symbolφis asymptotic Hankel if and only if φ is holomorphic function in L∞(Tn).
基金National Science Foundation of USA (Grant Nos.DMS1812048,DMS-1737857,DMS-1513483 and DMS-1418042)National Natural Science Foundation of China (Grant No.11529101).
文摘Model selection strategies have been routinely employed to determine a model for data analysis in statistics, and further study and inference then often proceed as though the selected model were the true model that were known a priori. Model averaging approaches, on the other hand, try to combine estimators for a set of candidate models. Specifically, instead of deciding which model is the ’right’ one, a model averaging approach suggests to fit a set of candidate models and average over the estimators using data adaptive weights.In this paper we establish a general frequentist model averaging framework that does not set any restrictions on the set of candidate models. It broaden, the scope of the existing methodologies under the frequentist model averaging development. Assuming the data is from an unknown model, we derive the model averaging estimator and study its limiting distributions and related predictions while taking possible modeling biases into account.We propose a set of optimal weights to combine the individual estimators so that the expected mean squared error of the average estimator is minimized. Simulation studies are conducted to compare the performance of the estimator with that of the existing methods. The results show the benefits of the proposed approach over traditional model selection approaches as well as existing model averaging methods.
基金the National Natural Science Foundation of China under Grant No.11471215.
文摘In this paper,we focus on studying the asymptotic stability of the monotone decreasing kink profile solitary wave solutions for the generalized KdV-Burgers equation.We obtain the estimate of the firstorder and second-order derivatives for monotone decreasing kink profile solitary wave solutions,and overcome the difficulties caused by high-order nonlinear terms in the generalized KdV-Burgers equation in the estimate by using L2 energy estimating method and Young inequality.We prove that the monotone decreasing kink profile solitary wave solutions are asymptotically stable in H1.Moreover,we obtain the decay rate of the perturbationψin the sense of L^2 and L^∞norm,respectively,which are(1+t)^-1/2 and(1+t)^-1/4 by using Gargliado-Nirenberg inequality.
基金National Natural Science Foundation of China(No.11301084)Natural Science Foundation of Fujian Province,China(No.2014J01010).
文摘This paper considers a nonparametric M-estimator of a regression function for functional stationary ergodic data.More precisely,in the ergodic data setting,we consider the regression of a real random variable Y over an explanatory random variable X taking values in some semi-metric abstract space.Under some mild conditions,the weak consistency and the asymptotic normality of the M-estimator are established.Furthermore,a simulated example is provided to examine the finite sample performance of the M-estimator.
基金Supported by National Natural Science Foundation of China under Grant No.11675143the Fundamental Research for the Provincial Universities of Zhejiang in China under Grant No.RF-A2019015.
文摘Recently proposed two swampland criteria that arising from string theory landscape leads to the important challenge of the realization of single-field inflationary models. Especially one of swampland criteria which implies a large tensor-to-scalar ratio is strongly in tension with recent observational results. In this paper, we explore the possibility the swampland conjectures could be compatible with single-field inflationary scenarios if the effects due to the quantum theory of gravity are considered. We show that the quantum gravitational effects due to the nonlinear dispersion relation provides significant modifications on the amplitude of both the scalar and tensor perturbation spectra. Such modifications could be either raise or reduce the perturbation spectra depending on the values of the parameters in the nonlinear terms of the dispersion relations. Therefore, these effects can reduce the tensor-to-scalar ratio to a smaller value, which helps to relax the tension between the swampland conjecture and observational data.
文摘In this article, we are interested in least squares estimator for a class of pathdependent McKean-Vlasov stochastic differential equations (SDEs). More precisely, we investigate the consistency and asymptotic distribution of the least squares estimator for the unknown parameters involved by establishing an appropriate contrast function. Comparing to the existing results in the literature, the innovations of this article lie in three aspects:(i) We adopt a tamed Euler-Maruyama algorithm to establish the contrast function under the monotone condition, under which the Euler-Maruyama scheme no longer works;(ii) We take the advantage of linear interpolation with respect to the discrete-time observations to approximate the functional solution;(iii) Our model is more applicable and practice as we are dealing with SDEs with irregular coefficients (for example, Holder continuous) and pathdistribution dependent.
文摘The advection-diffusion equation ytε-εyxxε+ M yxε= 0,(x, t) ∈(0, 1) ×(0, T) is null controllable for any strictly positive values of the diffusion coefficient ε and of the controllability time T. We discuss here the behavior of the cost of control when the coefficient ε goes to zero, according to the values of T. It is actually known that this cost is uniformly bounded with respect to ε if T is greater than a minimal time TM, with TM in the interval [1, 2×31/2]/M for M > 0 and in the interval [2×21/2, 2(1 +31/2)]/|M | for M < 0. The exact value of TM is however unknown.We investigate in this work the determination of the minimal time TM employing two distincts but complementary approaches. In a first one, we numerically estimate the cost of controllability, reformulated as the solution of a generalized eigenvalue problem for the underlying control operator, with respect to the parameter T and ε. This allows notably to exhibit the structure of initial data leading to large costs of control. At the practical level, this evaluation requires the non trivial and challenging approximation of null controls for the advection-diffusion equation. In the second approach, we perform an asymptotic analysis, with respect to the parameter ε, of the optimality system associated to the control of minimal L2-norm. The matched asymptotic expansion method is used to describe the multiple boundary layers.
基金The authors are grateful to the reviewers for their helpful comments and suggestions. This work is partly supported by the National Natural Science Foundation of China (Nos. 11671068, 11271060, 11401077).
文摘The asymptotic curve is widely used in astronomy, mechanics and numerical optimization. Moreover, it shows great application potentials in architecture. We focus on the problem how to cover bounded asymptotic curves by a freeform surface. The paper presents the necessary and sufficient conditions for quadrilateral with non-inflection being asymptotic boundary curves of a surface. And then, with given corner data, we model quintic Bezier asymptotic quadrilateral interpolated by a smooth Bezier surface of bi-eleven degree. We handle the available degrees of freedom during the construction to get an optimized result. Some representative surfaces bounded by asymptotic curves with lines or inflections are also discussed by examples. The presented interpolation scheme for the construction of tensor-product Bezier surfaces is compatible with the CAD systems.
基金the National Natural Science Foundation of China under Grant Nos.71761019 and 71563021the Natural science foundation of Jiangxi Province under Grant No.20171ACB21022.
文摘Zero-utility principle is one of the main premium pricing principles,which has been widely used in insurance practice.In this paper,the nonparametric estimation of zero-utility premium is given.In addition,the consistency and asymptotic normality of the estimation are proved.Some special cases including linear,exponential and quadratic utility are discussed.Finally,the Monte Carlo method is used to show the convergence rate of premium estimation.Furthermore,the histogram and Normal-Probability-Plot are given to investigate the asymptotic normality of the estimators.The results show that our estimations are good enough to use in practice.
文摘The behavior of the Kozachenko–Leonenko estimates for the(differential) Shannon entropy is studied when the number of i.i.d. vector-valued observations tends to infinity. The asymptotic unbiasedness and L^2-consistency of the estimates are established. The conditions employed involve the analogues of the Hardy–Littlewood maximal function. It is shown that the results are valid in particular for the entropy estimation of any nondegenerate Gaussian vector.
文摘Development of asymptotic magnitude Bode plots for integer-order transfer functions is a well-established topic in the control theory.However,construction of such plots for the fractional-order transfer functions has not received much attention in the existing literature.In the present paper,we investigate in this direction and derive the procedures for sketching asymptotic magnitude Bode plots for some of the popular fractional-order controllers such as PI^α,[PI]^α,PD^β,[PD]^β,and PI^αD^β.In addition,we deduce these plots for general fractional commensurate-order transfer functions as well.As applications of this work,we illustrate 1)the analysis of the designed fractional-control loop and 2)the identification of fractional-order transfer function from a given plot.
基金This work was supported in part by National Natural Science Foundation of China(Grant Nos.61733005,61673172,61663013,61803155,51565012)Science and Technology Research Project of Jiangxi Education Department(Grant No.170376).
文摘This paper investigates the asymptotic state estimation problem for linear systems with sensor and actuator faults,where the faults are modeled via multiple modes.For the case of sensor faults,we first introduce a new notion of detectability,i.e.,detectability of system against sensor faults.The notion helps to address the question of whether it is possible to asymptotically estimate the system state by using the control input and system output,irrespective of which mode the system is in and what values the fault signals are.A necessary and sufficient condition for the system to be detectable against sensor faults is given,and then two switched observers are proposed for asymptotic state estimation with the help of maximin strategy.For the system with l fault modes,we provide the explicit form of the switched observer,which is based on a bank of"l(l+1)/2"Luenberger-like or sliding-mode observers.Furthermore,extensions to the case of sensor and actuator faults are further studied.Finally,a simulation example of a reduced-order aircraft system is provided to show the effectiveness of the proposed approaches.
基金an NSERC grant and a startup fund of University of Alberta.
文摘This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covariance structures. The focus is on the existence and uniqueness of the classical (square integrable) solution (mild solution, weak solution). It is also concerned with the Feynman-Kac formula for the solution;Feynman-Kac formula for the moments of the solution;and their applications to the asymptotic moment bounds of the solution. It also briefly touches the exact asymptotics of the moments of the solution.
基金Key Natural Science Foundation of Anhui Education Commission, China (No.KJ2017A568)Natural Science Foundation of Anhui Province, China (No.1808085MA02)Natural Science Foundation of Bengbu University, China (No. 2018CXY045)。
文摘The drift parameter estimation problem of the complex Ornstein-Uhlenbeck process driven by a complexα-stable motion is considered.Based on discrete observations,an estimator of the unknown drift parameter is constructed by using the least squares method.Moreover,the strong consistency and the asymptotic distribution of the least squares estimator are derived under some assumptions.
基金National Natural Science Foundation of China (Grant No. 71501100)the Open Project of Jiangsu Key Laboratory of Financial Engineering (Grant No. NSK2015-02)+1 种基金supported by National Natural Science Foundation of China (Grant No. 71271042)the stage results of the Major Bidding Project of the Chinese National Social Science Foundation (Grant No. 17ZDA072)。
文摘In this study, we investigate the tail probability of the discounted aggregate claim sizes in a dependent risk model. In this model, the claim sizes are observed to follow a one-sided linear process with independent and identically distributed innovations. Investment return is described as a general stochastic process with cadlag paths. In the case of heavy-tailed innovation distributions, we are able to derive some asymptotic estimates for tail probability and to provide some asymptotic upper bounds to improve the applicability of our study.
文摘We study the asymptotic behavior of an incompressible viscous fluid flow in a biological body lined by a thin biological film with a cellular microstructure,varying thickness,and a heterogeneous viscosity regulated by a time random process.Let ting the thickness of the film tend to zero,we derive an effective biological slip boundary condition on the boundary of the body.This law relates the tangential fluxes to the tangential velocities via a proportional coefficient corresponding to the energy of some local problem.This law describes the ability of the biological film to function as a lubricant reducing friction at the wall of the body.The tangential velocities are functions of the random trajectories of a finely concentrated biological particle.
基金Jianhong Shi's research is supported by the National Science Foundation of Shanxi Province of China under Grant No.2013011002-1Weixing Song's research is supported by the Division of Mathematical Science,National Science Foundation under Grant No.1205276.
文摘Based on a Tweedie-type formula developed under the Laplace distribution,this paper proposes a new bias-corrected estimator of the regression parameters in a simple linear model when the measurement error follows a Laplace distribution.Large sample properties,including the consistency and the asymptotic normality,are investigated.The finite sample performance of the proposed estimators are evaluated via simulation studies,as well as comparison studies with some existing estimation procedures.