As an important type of polynomial approximation, approximation of functions by Bernstein operators is an important topic in approximation theory and computational theory. This paper gives global and pointwise estimat...As an important type of polynomial approximation, approximation of functions by Bernstein operators is an important topic in approximation theory and computational theory. This paper gives global and pointwise estimates for weighted approximation of functions with singularities by Bernstein operators. The main results are the Jackson's estimates of functions f∈ (Wwλ)2 andre Cw, which extends the result of (Della Vecchia et al., 2004).展开更多
A class of general modified split-step balanced methods proposed in the paper can be applied to solve stiff stochastic differential systems with m-dimensional multiplicative noise. Compared to some other already repor...A class of general modified split-step balanced methods proposed in the paper can be applied to solve stiff stochastic differential systems with m-dimensional multiplicative noise. Compared to some other already reported split-step balanced methods, the drift increment function of the methods can be taken from any chosen ane-step ordinary differential equations (ODEs) solver. The schemes is proved to be strong convergent with order one. For the mean-square stability analysis, the investigation is confined to two cases. Some numerical experiments are reported to testify the performance and the effectiveness of the methods.展开更多
The meaning to research the potential of VLBI for geodetic applications is summarized. And the observation models and their related parameters of geodetic interest are investigated. Then, the principle and method of u...The meaning to research the potential of VLBI for geodetic applications is summarized. And the observation models and their related parameters of geodetic interest are investigated. Then, the principle and method of using the random model in VLBI data processing are investigated. With the world wide VLBI data from 2000-2004, the conditions to compute the parameters of geodetic interest are introduced, and so are the computing methods and processes. And the computed resuits of the parameters of geodetic interest are analyzed.展开更多
The basic inference function of mathematical statistics, the score function, is a vector function. The author has introduced the scalar score, a scalar inference function, which reflects main features of a continuous ...The basic inference function of mathematical statistics, the score function, is a vector function. The author has introduced the scalar score, a scalar inference function, which reflects main features of a continuous probability distribution and which is simple. Its simplicity makes it possible to introduce new relevant numerical characteristics of continuous distributions. The t-mean and score variance are descriptions of distributions without the drawbacks of the mean and variance, which may not exist even in cases of regular distributions. Their sample counterparts appear to be alternative descriptions of the observed data. The scalar score itself appears to be a new mathematical tool, which could be used in solving traditional statistical problems for models far from the normal one, skewed and heavy-tailed.展开更多
There are many experimental approaches,field investigations and numerical calculations for movements of woods in a clear water and debris flow.However,kinematic conditions for accumulated logs and the interactions bet...There are many experimental approaches,field investigations and numerical calculations for movements of woods in a clear water and debris flow.However,kinematic conditions for accumulated logs and the interactions between a main flow and logs have not been fully evaluated.Mitigations for woods need taking into account the characteristics of tree species such as conifer and broad-leaf trees and of shapes such as root swells and crown.In the present study,we focus on the differences in specific weight of conifer and broad-leaf trees with some moisture in a sediment-water mixture flow with narrow flow width,and consider that conifer and broad-leaf tree are floating and submerged solid phase,respectively.Flume tests are conducted in steady flow of clear and debris flow over a rigid bed in order to evaluate conifer and broad-leaf tree movement in clear water and debris flow.Experimental data indicates that dimensionless transverse diffusion coefficient can be 0.1 to 0.4 and 0.3 to 0.9 in flow direction.Those diffusive characteristics seem to be independent of Reynolds number and Froude number,but dependent of bed slope,i.e.,gravity,though detailed considerations are needed to discuss about flow characteristics such as spatial eddy structures,momentum transfer induced by interactions of logs and so on.展开更多
Information analysis of high dimensional data was carried out through similarity measure application. High dimensional data were considered as the a typical structure. Additionally, overlapped and non-overlapped data ...Information analysis of high dimensional data was carried out through similarity measure application. High dimensional data were considered as the a typical structure. Additionally, overlapped and non-overlapped data were introduced, and similarity measure analysis was also illustrated and compared with conventional similarity measure. As a result, overlapped data comparison was possible to present similarity with conventional similarity measure. Non-overlapped data similarity analysis provided the clue to solve the similarity of high dimensional data. Considering high dimensional data analysis was designed with consideration of neighborhoods information. Conservative and strict solutions were proposed. Proposed similarity measure was applied to express financial fraud among multi dimensional datasets. In illustrative example, financial fraud similarity with respect to age, gender, qualification and job was presented. And with the proposed similarity measure, high dimensional personal data were calculated to evaluate how similar to the financial fraud. Calculation results show that the actual fraud has rather high similarity measure compared to the average, from minimal 0.0609 to maximal 0.1667.展开更多
Background: It has been reported that strenuous exercise increases the number of bone marrow-derived progenitor cells such as CD34+ cells in the blood, but no previous studies have investigated the changes in circul...Background: It has been reported that strenuous exercise increases the number of bone marrow-derived progenitor cells such as CD34+ cells in the blood, but no previous studies have investigated the changes in circulating CD34+ cells following resistance exercise. This study tested the hypothesis that the number of CD34+ cells in the blood would increase after eccentric exercise of the elbow flexors, but decrease in recovery, and the magnitude of the changes would be dependent on the magnitude of muscle damage. Methods: Nine men (28.0 ± 6.6 years) performed exercises consisting of 10 sets of six maximal voluntary eccentric contractions of the elbow flexors with their non-dominant arm. Six of them performed the same exercise with the same ann 4 weeks later. Changes in indirect markers of muscle damage were measured before, within 10 min after, and at 24, 48, 72, and 96 h after eccentric exercise. Differential leukocyte counts (total leukocytes, neutrophils, lymphocytes, monocytes) and CD34+ cells in the blood were measured before, immediately after, and at 2, 24, 48, 72, and 96 h following the exercises. Results: After eccentric exercise, significant (p 〈 0.05) decreases in maximal voluntary isometric contraction torque and increases in delayed onset muscle soreness and plasma creatine kinase activity were observed. However, no significant changes in leukocytes and CD34+ cells were evident. The changes in muscle damage markers were significantly (p 〈 0.05) smaller following the second exercise session as compared with the first exercise session, but the changes in leukocytes and CD34+ cells were not significantly different between sessions. Conclusion: These results did not support the hypothesis, and showed that eccentric exercise-induced muscle damage to the elbow flexors did not influence the number of circulating CD34+ cells.展开更多
Fermented chile pepper mash is a major food product in New Mexico. There are few reports on the fermentation process or on methods to monitor it, In the current study we examined a pour plate procedure with an overlay...Fermented chile pepper mash is a major food product in New Mexico. There are few reports on the fermentation process or on methods to monitor it, In the current study we examined a pour plate procedure with an overlay using plate count agar and 3 MTM PetrifilmTM Aerobic Count (AC) plates for determination of total aerobic bacterial counts during the fermentation of chile mash. Fifty chile mash samples were obtained directly from commercial fermentation vats and examined within 2 h of collection. Serial dilutions of the chile mash were prepared in Butterfield's Phosphate Buffer. 1 mL portions of the diluted samples were aliquoted in duplicate onto the AC plates and into empty Petri dishes. Plate count agar was poured and once the plates had solidified, they were overlaid with about 10 mL of PCA to minimize spreaders. Plates were incubated at 30 ℃ for 48 h and enumerated. Paired difference tests were conducted on log transformed data to compare the results of the two plating procedures. For commercial chile mash samples, we did not show any significant differences between the AC plate counts and the pour plate counts (α = 0.05), 3 MTM PetrifilmTM AC plates are a good alternative to pour plates for the determination of the total aerobic counts in fermented chile mashes.展开更多
An equation of state (EOS) for high-pressure liquids, i.e., Tait EOS, is deduced according to isothermal 1 3V compressibility KT= -1/V· (2V/2p)T·.Based on the equation, a generalized EOS for high pressu...An equation of state (EOS) for high-pressure liquids, i.e., Tait EOS, is deduced according to isothermal 1 3V compressibility KT= -1/V· (2V/2p)T·.Based on the equation, a generalized EOS for high pressure-liquids is established by using the reduced state principle and introducing a characteristic parameter-configuration factor ξ. Reasonably satisfactory P-V-T data for many organic compounds, including some polar components, were calculated by using the equation.展开更多
Surface reconstruction from unorganized data points is a challenging problem in Computer Aided Design and Geometric Modeling. In this paper, we extend the mathematical model proposed by Juttler and Felis (Adv. Comput...Surface reconstruction from unorganized data points is a challenging problem in Computer Aided Design and Geometric Modeling. In this paper, we extend the mathematical model proposed by Juttler and Felis (Adv. Comput. Math., 17 (2002), pp. 135-152) based on tensor product algebraic spline surfaces from fixed meshes to adaptive meshes. We start with a tensor product algebraic B-spline surface defined on an initial mesh to fit the given data based on an optimization approach. By measuring the fitting errors over each cell of the mesh, we recursively insert new knots in cells over which the errors are larger than some given threshold, and construct a new algebraic spline surface to better fit the given data locally. The algorithm terminates when the error over each cell is less than the threshold. We provide some examples to demonstrate our algorithm and compare it with Juttler's method. Examples suggest that our method is effective and is able to produce reconstruction surfaces of high quality.展开更多
Pressure losses in flow components are generally characterized either by pressure loss coefficients or by discharge coefficients. The pressure drop for incompressible flow across a screen of fractional free area a is ...Pressure losses in flow components are generally characterized either by pressure loss coefficients or by discharge coefficients. The pressure drop for incompressible flow across a screen of fractional free area a is often calculated from widely used correlation provided in Perry's Handbook. This correlation was developed based on experimental work which have covered a wide range of fractional free area (a = 0.14 to 0.79). The present work aims at validation for a flow in plain square mesh screen with a particular fractional free area (porosity, a) of 0.25 using CFD (Computational Fluid Dynamics) approach. The simulations are carried out for wide range of screen Reynolds number (Re = 0.1 to 105) covering both laminar and turbulent flow regimes. Initial simulations are carried out for incompressible fluid (water) and further extended to compressible fluid (air). Discharge coefficients obtained from the simulations are compared with experimental values. Effect of compressibility on discharge coefficients is described.展开更多
This paper presents a novel class of semiparametric estimating functions for the additive model with right-censored data that are obtained from general biased-sampling. The new estimator can be obtained using a weight...This paper presents a novel class of semiparametric estimating functions for the additive model with right-censored data that are obtained from general biased-sampling. The new estimator can be obtained using a weighted estimating equation for the covariate coefficients, by embedding the biased-sampling data into left-truncated and right-censored data. The asymptotic properties(consistency and asymptotic normality) of the proposed estimator are derived via the modern empirical processes theory. Based on the cumulative residual processes, we also propose graphical and numerical methods to assess the adequacy of the additive risk model.The good finite-sample performance of the proposed estimator is demonstrated by simulation studies and two applications of real datasets.展开更多
This paper considers a semi-varying coefficient model for panel data with fixed effects,proposes the profile-likelihood-based estimators for the parametric and nonparametric components,and establishes convergence rate...This paper considers a semi-varying coefficient model for panel data with fixed effects,proposes the profile-likelihood-based estimators for the parametric and nonparametric components,and establishes convergence rates and asymptotic normality properties for both estimators.Simulation results show that the proposed estimators behave well in finite sample cases.展开更多
In this paper,a necessary and sufficient condition for the existence of a kind of bivariate vector valued rational interpolants over rectangular grids is given.This criterion is an algebraic method,i.e.,by solving a s...In this paper,a necessary and sufficient condition for the existence of a kind of bivariate vector valued rational interpolants over rectangular grids is given.This criterion is an algebraic method,i.e.,by solving a system of equations based on the given data,we can directly test whether the relevant interpolant exists or not.By coming up with our method, the problem of how to deal with scalar equations and vector equations in the same system of equations is solved.After testing existence,an expression of the corresponding bivariate vector-valued rational interpolant can be constructed consequently.In addition,the way to get the expression is different from the one by making use of Thiele-type bivariate branched vector-valued continued fractions and Samelson inverse which are commonly used to construct the bivariate vector-valued rational interpolants.Compared with the Thiele-type method,the one given in this paper is more direct.Finally,some numerical examples are given to illustrate the result.展开更多
Define the incremental fractional Brownian field with parameter H ∈ (0, 1) by ZH(τ, s) = BH(s-+τ) - BH(S), where BH(s) is a fractional Brownian motion with Hurst parameter H ∈ (0, 1). We firstly deriv...Define the incremental fractional Brownian field with parameter H ∈ (0, 1) by ZH(τ, s) = BH(s-+τ) - BH(S), where BH(s) is a fractional Brownian motion with Hurst parameter H ∈ (0, 1). We firstly derive the exact tail asymptoties for the maximum MH*(T) = max(τ,s)∈[a,b]×[0,T] ZH(τ, s)/τH of the standardised fractional Brownian motion field, with any fixed 0 〈 a 〈 b 〈 ∞ and T 〉 0; and we, furthermore, extend the obtained result to the ease that T is a positive random variable independent of {BH(s), s ≥ 0}. As a by-product, we obtain the Gumbel limit law for MH*r(T) as T →∞.展开更多
This paper studies estimation in partial functional linear quantile regression in which the dependent variable is related to both a vector of finite length and a function-valued random variable as predictor variables....This paper studies estimation in partial functional linear quantile regression in which the dependent variable is related to both a vector of finite length and a function-valued random variable as predictor variables. The slope function is estimated by the functional principal component basis. The asymptotic distribution of the estimator of the vector of slope parameters is derived and the global convergence rate of the quantile estimator of unknown slope function is established under suitable norm. It is showed that this rate is optirnal in a minimax sense under some smoothness assumptions on the covariance kernel of the covariate and the slope function. The convergence rate of the mean squared prediction error for the proposed estimators is also established. Finite sample properties of our procedures are studied through Monte Carlo simulations. A real data example about Berkeley growth data is used to illustrate our proposed methodology.展开更多
文摘As an important type of polynomial approximation, approximation of functions by Bernstein operators is an important topic in approximation theory and computational theory. This paper gives global and pointwise estimates for weighted approximation of functions with singularities by Bernstein operators. The main results are the Jackson's estimates of functions f∈ (Wwλ)2 andre Cw, which extends the result of (Della Vecchia et al., 2004).
基金National Natural Science Foundation of China(No.11171352)
文摘A class of general modified split-step balanced methods proposed in the paper can be applied to solve stiff stochastic differential systems with m-dimensional multiplicative noise. Compared to some other already reported split-step balanced methods, the drift increment function of the methods can be taken from any chosen ane-step ordinary differential equations (ODEs) solver. The schemes is proved to be strong convergent with order one. For the mean-square stability analysis, the investigation is confined to two cases. Some numerical experiments are reported to testify the performance and the effectiveness of the methods.
基金Funded by the National 973 Program of China (No.2006CB701301)the Project of University Education and Research of HubeiProvince (No.20053039).
文摘The meaning to research the potential of VLBI for geodetic applications is summarized. And the observation models and their related parameters of geodetic interest are investigated. Then, the principle and method of using the random model in VLBI data processing are investigated. With the world wide VLBI data from 2000-2004, the conditions to compute the parameters of geodetic interest are introduced, and so are the computing methods and processes. And the computed resuits of the parameters of geodetic interest are analyzed.
文摘The basic inference function of mathematical statistics, the score function, is a vector function. The author has introduced the scalar score, a scalar inference function, which reflects main features of a continuous probability distribution and which is simple. Its simplicity makes it possible to introduce new relevant numerical characteristics of continuous distributions. The t-mean and score variance are descriptions of distributions without the drawbacks of the mean and variance, which may not exist even in cases of regular distributions. Their sample counterparts appear to be alternative descriptions of the observed data. The scalar score itself appears to be a new mathematical tool, which could be used in solving traditional statistical problems for models far from the normal one, skewed and heavy-tailed.
基金supported by Research Budget from Research and Development Center,NIPPON KOEI Co.,Ltd (Research theme:Modeling for debris flow with woods and their applicability)
文摘There are many experimental approaches,field investigations and numerical calculations for movements of woods in a clear water and debris flow.However,kinematic conditions for accumulated logs and the interactions between a main flow and logs have not been fully evaluated.Mitigations for woods need taking into account the characteristics of tree species such as conifer and broad-leaf trees and of shapes such as root swells and crown.In the present study,we focus on the differences in specific weight of conifer and broad-leaf trees with some moisture in a sediment-water mixture flow with narrow flow width,and consider that conifer and broad-leaf tree are floating and submerged solid phase,respectively.Flume tests are conducted in steady flow of clear and debris flow over a rigid bed in order to evaluate conifer and broad-leaf tree movement in clear water and debris flow.Experimental data indicates that dimensionless transverse diffusion coefficient can be 0.1 to 0.4 and 0.3 to 0.9 in flow direction.Those diffusive characteristics seem to be independent of Reynolds number and Froude number,but dependent of bed slope,i.e.,gravity,though detailed considerations are needed to discuss about flow characteristics such as spatial eddy structures,momentum transfer induced by interactions of logs and so on.
基金Project(RDF 11-02-03)supported by the Research Development Fund of XJTLU,China
文摘Information analysis of high dimensional data was carried out through similarity measure application. High dimensional data were considered as the a typical structure. Additionally, overlapped and non-overlapped data were introduced, and similarity measure analysis was also illustrated and compared with conventional similarity measure. As a result, overlapped data comparison was possible to present similarity with conventional similarity measure. Non-overlapped data similarity analysis provided the clue to solve the similarity of high dimensional data. Considering high dimensional data analysis was designed with consideration of neighborhoods information. Conservative and strict solutions were proposed. Proposed similarity measure was applied to express financial fraud among multi dimensional datasets. In illustrative example, financial fraud similarity with respect to age, gender, qualification and job was presented. And with the proposed similarity measure, high dimensional personal data were calculated to evaluate how similar to the financial fraud. Calculation results show that the actual fraud has rather high similarity measure compared to the average, from minimal 0.0609 to maximal 0.1667.
文摘Background: It has been reported that strenuous exercise increases the number of bone marrow-derived progenitor cells such as CD34+ cells in the blood, but no previous studies have investigated the changes in circulating CD34+ cells following resistance exercise. This study tested the hypothesis that the number of CD34+ cells in the blood would increase after eccentric exercise of the elbow flexors, but decrease in recovery, and the magnitude of the changes would be dependent on the magnitude of muscle damage. Methods: Nine men (28.0 ± 6.6 years) performed exercises consisting of 10 sets of six maximal voluntary eccentric contractions of the elbow flexors with their non-dominant arm. Six of them performed the same exercise with the same ann 4 weeks later. Changes in indirect markers of muscle damage were measured before, within 10 min after, and at 24, 48, 72, and 96 h after eccentric exercise. Differential leukocyte counts (total leukocytes, neutrophils, lymphocytes, monocytes) and CD34+ cells in the blood were measured before, immediately after, and at 2, 24, 48, 72, and 96 h following the exercises. Results: After eccentric exercise, significant (p 〈 0.05) decreases in maximal voluntary isometric contraction torque and increases in delayed onset muscle soreness and plasma creatine kinase activity were observed. However, no significant changes in leukocytes and CD34+ cells were evident. The changes in muscle damage markers were significantly (p 〈 0.05) smaller following the second exercise session as compared with the first exercise session, but the changes in leukocytes and CD34+ cells were not significantly different between sessions. Conclusion: These results did not support the hypothesis, and showed that eccentric exercise-induced muscle damage to the elbow flexors did not influence the number of circulating CD34+ cells.
文摘Fermented chile pepper mash is a major food product in New Mexico. There are few reports on the fermentation process or on methods to monitor it, In the current study we examined a pour plate procedure with an overlay using plate count agar and 3 MTM PetrifilmTM Aerobic Count (AC) plates for determination of total aerobic bacterial counts during the fermentation of chile mash. Fifty chile mash samples were obtained directly from commercial fermentation vats and examined within 2 h of collection. Serial dilutions of the chile mash were prepared in Butterfield's Phosphate Buffer. 1 mL portions of the diluted samples were aliquoted in duplicate onto the AC plates and into empty Petri dishes. Plate count agar was poured and once the plates had solidified, they were overlaid with about 10 mL of PCA to minimize spreaders. Plates were incubated at 30 ℃ for 48 h and enumerated. Paired difference tests were conducted on log transformed data to compare the results of the two plating procedures. For commercial chile mash samples, we did not show any significant differences between the AC plate counts and the pour plate counts (α = 0.05), 3 MTM PetrifilmTM AC plates are a good alternative to pour plates for the determination of the total aerobic counts in fermented chile mashes.
文摘An equation of state (EOS) for high-pressure liquids, i.e., Tait EOS, is deduced according to isothermal 1 3V compressibility KT= -1/V· (2V/2p)T·.Based on the equation, a generalized EOS for high pressure-liquids is established by using the reduced state principle and introducing a characteristic parameter-configuration factor ξ. Reasonably satisfactory P-V-T data for many organic compounds, including some polar components, were calculated by using the equation.
基金supported by the National Key Basic Research Project of China(No.2004CB318000)One Hundred Talent Project of the Chinese Academy of Sciences,the NSF of China(No.60225002,No.60533060)Doctorial Program of MOE of China and the 111 Project(No.B07033).
文摘Surface reconstruction from unorganized data points is a challenging problem in Computer Aided Design and Geometric Modeling. In this paper, we extend the mathematical model proposed by Juttler and Felis (Adv. Comput. Math., 17 (2002), pp. 135-152) based on tensor product algebraic spline surfaces from fixed meshes to adaptive meshes. We start with a tensor product algebraic B-spline surface defined on an initial mesh to fit the given data based on an optimization approach. By measuring the fitting errors over each cell of the mesh, we recursively insert new knots in cells over which the errors are larger than some given threshold, and construct a new algebraic spline surface to better fit the given data locally. The algorithm terminates when the error over each cell is less than the threshold. We provide some examples to demonstrate our algorithm and compare it with Juttler's method. Examples suggest that our method is effective and is able to produce reconstruction surfaces of high quality.
文摘Pressure losses in flow components are generally characterized either by pressure loss coefficients or by discharge coefficients. The pressure drop for incompressible flow across a screen of fractional free area a is often calculated from widely used correlation provided in Perry's Handbook. This correlation was developed based on experimental work which have covered a wide range of fractional free area (a = 0.14 to 0.79). The present work aims at validation for a flow in plain square mesh screen with a particular fractional free area (porosity, a) of 0.25 using CFD (Computational Fluid Dynamics) approach. The simulations are carried out for wide range of screen Reynolds number (Re = 0.1 to 105) covering both laminar and turbulent flow regimes. Initial simulations are carried out for incompressible fluid (water) and further extended to compressible fluid (air). Discharge coefficients obtained from the simulations are compared with experimental values. Effect of compressibility on discharge coefficients is described.
基金supported by National Natural Science Foundation of China(Grant Nos.11771133 and 11401194)the Natural Science Foundation of Hunan Province of China(Grant No.2017JJ3021)+2 种基金Zhao’s work was supported by National Natural Science Foundation of China(Grant No.11771366)Zhou’s work was supported by the State Key Program of National Natural Science Foundation of China(Grant No.71331006)the State Key Program in the Major Research Plan of National Natural Science Foundation of China(Grant No.91546202)
文摘This paper presents a novel class of semiparametric estimating functions for the additive model with right-censored data that are obtained from general biased-sampling. The new estimator can be obtained using a weighted estimating equation for the covariate coefficients, by embedding the biased-sampling data into left-truncated and right-censored data. The asymptotic properties(consistency and asymptotic normality) of the proposed estimator are derived via the modern empirical processes theory. Based on the cumulative residual processes, we also propose graphical and numerical methods to assess the adequacy of the additive risk model.The good finite-sample performance of the proposed estimator is demonstrated by simulation studies and two applications of real datasets.
基金supported by the National Natural Science Foundation of China under Grant No.11101452the Natural Science Foundation Project of CQ CSTC under Grant No.2012jjA00035+2 种基金the National Basic Research Program of China under Grant No.2011CB808000the National Social Science Foundation of China under Grant No.12XTJ001the Natural Science Foundation Project of CTBU of China under Grant No.1352001
文摘This paper considers a semi-varying coefficient model for panel data with fixed effects,proposes the profile-likelihood-based estimators for the parametric and nonparametric components,and establishes convergence rates and asymptotic normality properties for both estimators.Simulation results show that the proposed estimators behave well in finite sample cases.
基金the National Natural Science Foundation of China (No. 60473114) the Natural Science Foundation of Auhui Province (No. 070416227)+2 种基金 the Natural Science Research Scheme of Education Department of Anhui Province (No. KJ2008B246) Colleges and Universities in Anhui Province Young Teachers Subsidy Scheme (No. 2008jq1110) the Science Research Foundation of Chaohu College (No. XLY-200705).
文摘In this paper,a necessary and sufficient condition for the existence of a kind of bivariate vector valued rational interpolants over rectangular grids is given.This criterion is an algebraic method,i.e.,by solving a system of equations based on the given data,we can directly test whether the relevant interpolant exists or not.By coming up with our method, the problem of how to deal with scalar equations and vector equations in the same system of equations is solved.After testing existence,an expression of the corresponding bivariate vector-valued rational interpolant can be constructed consequently.In addition,the way to get the expression is different from the one by making use of Thiele-type bivariate branched vector-valued continued fractions and Samelson inverse which are commonly used to construct the bivariate vector-valued rational interpolants.Compared with the Thiele-type method,the one given in this paper is more direct.Finally,some numerical examples are given to illustrate the result.
基金supported by National Natural Science Foundation of China(Grant Nos.11326175 and 71471090)Natural Science Foundation of Zhejiang Province of China(Grant No.LQ14A010012)+2 种基金Research Start-up Foundation of Jiaxing University(Grant No.70512021)China Postdoctoral Science Foundation(Grant No.2014T70449)Natural Science Foundation of Jiangsu Province of China(Grant No.BK20131339)
文摘Define the incremental fractional Brownian field with parameter H ∈ (0, 1) by ZH(τ, s) = BH(s-+τ) - BH(S), where BH(s) is a fractional Brownian motion with Hurst parameter H ∈ (0, 1). We firstly derive the exact tail asymptoties for the maximum MH*(T) = max(τ,s)∈[a,b]×[0,T] ZH(τ, s)/τH of the standardised fractional Brownian motion field, with any fixed 0 〈 a 〈 b 〈 ∞ and T 〉 0; and we, furthermore, extend the obtained result to the ease that T is a positive random variable independent of {BH(s), s ≥ 0}. As a by-product, we obtain the Gumbel limit law for MH*r(T) as T →∞.
基金supported by National Natural Science Foundation of China(Grant No.11071120)
文摘This paper studies estimation in partial functional linear quantile regression in which the dependent variable is related to both a vector of finite length and a function-valued random variable as predictor variables. The slope function is estimated by the functional principal component basis. The asymptotic distribution of the estimator of the vector of slope parameters is derived and the global convergence rate of the quantile estimator of unknown slope function is established under suitable norm. It is showed that this rate is optirnal in a minimax sense under some smoothness assumptions on the covariance kernel of the covariate and the slope function. The convergence rate of the mean squared prediction error for the proposed estimators is also established. Finite sample properties of our procedures are studied through Monte Carlo simulations. A real data example about Berkeley growth data is used to illustrate our proposed methodology.