In this paper, we establish several inequalities for the the generalized linear distortion function λ（a, K） by using the monotonicity and convexity of certain combinations λ（a, K）.
In this paper, we define a functional optimization problem corresponding to smooth functions which its optimal solution is first derivative of these functions in a domain. These functional optimization problems are ap...In this paper, we define a functional optimization problem corresponding to smooth functions which its optimal solution is first derivative of these functions in a domain. These functional optimization problems are applied for non-smooth functions which by solving these problems we obtain a kind of generalized first derivatives. For this purpose, a linear programming problem corresponding functional optimization problem is obtained which their optimal solutions give the approximate generalized first derivative. We show the efficiency of our approach by obtaining derivative and generalized derivative of some smooth and nonsmooth functions respectively in some illustrative examples.展开更多
In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient proje...In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient projection method is given for solving the stochastic generalized linear complementarity problems. The global convergence of the conjugate gradient projection method is proved and the related numerical results are also reported.展开更多
In this article, we propose a generalized empirical likelihood inference for the parametric component in semiparametric generalized partially linear models with longitudinal data. Based on the extended score vector, a...In this article, we propose a generalized empirical likelihood inference for the parametric component in semiparametric generalized partially linear models with longitudinal data. Based on the extended score vector, a generalized empirical likelihood ratios function is defined, which integrates the within-cluster?correlation meanwhile avoids direct estimating the nuisance parameters in the correlation matrix. We show that the proposed statistics are asymptotically?Chi-squared under some suitable conditions, and hence it can be used to construct the confidence region of parameters. In addition, the maximum empirical likelihood estimates of parameters and the corresponding asymptotic normality are obtained. Simulation studies demonstrate the performance of the proposed method.展开更多
In this paper, we proposed a Extension Definition to derive, simultaneously, the first, second and high order generalized derivatives for non-smooth functions, in which the involved functions are Riemann integrable bu...In this paper, we proposed a Extension Definition to derive, simultaneously, the first, second and high order generalized derivatives for non-smooth functions, in which the involved functions are Riemann integrable but not necessarily locally Lipschitz or continuous. Indeed, we define a functional optimization problem corresponding to smooth functions where its optimal solutions are the first and second derivatives of these functions in a domain. Then by applying these functional optimization problems for non-smooth functions and using this method we obtain generalized first derivative (GFD) and generalized second derivative (GSD). Here, the optimization problem is approximated with a linear programming problem that by solving of which, we can obtain these derivatives, as simple as possible. We extend this approach for obtaining generalized high order derivatives (GHODs) of non-smooth functions, simultaneously. Finally, for efficiency of our approach some numerical examples have been presented.展开更多
By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = （A（u）Ux）x ＋ eB（u, Ux）. A complete classification of t...By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = （A（u）Ux）x ＋ eB（u, Ux）. A complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is listed. As a consequence, some approxi- mate solutions to the resulting perturbed equations are constructed via examples.展开更多
The virtual synchronous generator(VSG)technology has been proposed to address the problem of system frequency and active power oscillation caused by grid-connected new energy power sources.However,the traditional volt...The virtual synchronous generator(VSG)technology has been proposed to address the problem of system frequency and active power oscillation caused by grid-connected new energy power sources.However,the traditional voltage-current double-closed-loop control used in VSG has the disadvantages of poor disturbance immunity and insufficient dynamic response.In light of the issues above,a virtual synchronous generator voltage outer-loop control strategy based on improved linear autonomous disturbance rejection control(ILADRC)is put forth for consideration.Firstly,an improved first-order linear self-immunity control structure is established for the characteristics of the voltage outer loop;then,the effects of two key control parameters-observer bandwidthω_(0)and controller bandwidthω_(c)on the control system are analyzed,and the key parameters of ILADRC are optimally tuned online using improved gray wolf optimizer-radial basis function(IGWO-RBF)neural network.A simulationmodel is developed using MATLAB to simulate,analyze,and compare the method introduced in this paper.Simulations are performed with the traditional control strategy for comparison,and the results demonstrate that the proposed control method offers superior anti-interference performance.It effectively addresses power and frequency oscillation issues and enhances the stability of the VSG during grid-connected operation.展开更多
General linear model (GLM) is the most popular method for functional magnetic resource imaging (fMRI) data analysis . However, its theory is imperfect. The key of this model is how to constitute the design-matrix to m...General linear model (GLM) is the most popular method for functional magnetic resource imaging (fMRI) data analysis . However, its theory is imperfect. The key of this model is how to constitute the design-matrix to model the interesting effects better and separate noises better. For the purpose of detecting brain function activation , according to the principle of GLM,a new convolution model is presented by a new dynamic function convolving with design-matrix,which combining with t-test can be used to detect brain active signal. The fMRI imaging result of visual stimulus experiment indicates that brain activities mainly concentrate among v1and v2 areas of visual cortex, and also verified the validity of this technique.展开更多
A new vector-valued Pad′e-type approximation is defined by introducing a gener- alized vector-valued linear functional from a scalar polynomial space to a vector space. Some algebraic properties and error formulas ar...A new vector-valued Pad′e-type approximation is defined by introducing a gener- alized vector-valued linear functional from a scalar polynomial space to a vector space. Some algebraic properties and error formulas are presented. The expressions of this Pad′e-type ap- proximants are provided with the generating function form and the determinant form.展开更多
The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicat...The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicate the corresponding relationship.展开更多
To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Padé-type approximation is defined. By means of the power series expansion of the s...To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Padé-type approximation is defined. By means of the power series expansion of the solution, this method can construct an approximate solution to solve the given integral equation. On the basis of the orthogonal polynomials, two useful determinant expressions of the numerator polynomial and the denominator polynomial for Padé-type approximation are explicitly given.展开更多
An estimation method for solutions to the general linear system of Volterra- type integral inequalities containing several iterated integral functionals is obtained. This method is based on a result proved by the pres...An estimation method for solutions to the general linear system of Volterra- type integral inequalities containing several iterated integral functionals is obtained. This method is based on a result proved by the present second author in Journ. Math. Anal. Appl.(1984). A certain two-dimensional system of nonlinear ordinary differential equations is also discussed to demonstrate the usefulness of our method.展开更多
In this paper a new method to realize rational generalized transfer functions of linearshift-variant digital filters through state feedback is presented In some practical applications therequired characteristics of th...In this paper a new method to realize rational generalized transfer functions of linearshift-variant digital filters through state feedback is presented In some practical applications therequired characteristics of the filter change slowly.Under these circumstances,the proposedmethod is very effective and the resulting filter structure is simple.A numerical example isprovided to show the performance of the method.展开更多
In this paper we introduce an appealing nonparametric method for estimating variance and conditional variance functions in generalized linear models （GLMs）, when designs are fixed points and random variables respect...In this paper we introduce an appealing nonparametric method for estimating variance and conditional variance functions in generalized linear models （GLMs）, when designs are fixed points and random variables respectively, Bias-corrected confidence bands are proposed for the （conditional） variance by local linear smoothers. Nonparametric techniques are developed in deriving the bias-corrected confidence intervals of the （conditional） variance. The asymptotic distribution of the proposed estimator is established and show that the bias-corrected confidence bands asymptotically have the correct coverage properties. A small simulation is performed when unknown regression parameter is estimated by nonparametric quasi-likelihood. The results are also applicable to nonparamctric autoregressive times series model with heteroscedastic conditional variance.展开更多
In this paper,by deriving an inequality involving the generating function of the Bernoulli numbers,the author introduces a new ratio of finitely many gamma functions,finds complete monotonicity of the second logarithm...In this paper,by deriving an inequality involving the generating function of the Bernoulli numbers,the author introduces a new ratio of finitely many gamma functions,finds complete monotonicity of the second logarithmic derivative of the ratio,and simply reviews the complete monotonicity of several linear combinations of finitely many digamma or trigamma functions.展开更多
Generalized H2 （GH2） stability analysis and controller design of the uncertain discrete-time Takagi-Sugeno （T-S） fuzzy systems with state delay are studied based on a switching fuzzy model and piecewise Lyapunov f...Generalized H2 （GH2） stability analysis and controller design of the uncertain discrete-time Takagi-Sugeno （T-S） fuzzy systems with state delay are studied based on a switching fuzzy model and piecewise Lyapunov function. GH2 stability sufficient conditions are derived in terms of linear matrix inequalities （LMIs）. The interactions among the fuzzy subsystems are considered. Therefore, the proposed conditions are less conservative than the previous results. Since only a set of LMIs is involved, the controller design is quite simple and numerically tractable. To illustrate the validity of the proposed method, a design example is provided.展开更多
A significant proportion of urban crashes,especially serious and fatal crashes,occur at traffic signals.Many of the black-spots in both Australia and New Zealand cities occur at high volume and/or high-speed traffic s...A significant proportion of urban crashes,especially serious and fatal crashes,occur at traffic signals.Many of the black-spots in both Australia and New Zealand cities occur at high volume and/or high-speed traffic signals.Given this,crash reduction studies often focus on the major signalised intersections.However,there is limited information that links the phasing configuration,degree of saturation and overall cycle time to crashes.While a number of analysis tools are available for assessing the efficiency of intersections,there are very few tools that can assist engineers in assessing the safety effects of intersection upgrades and new intersections.Safety performance functions have been developed to help quantify the safety impact of various traffic signal phasing configurations and level of intersection congestion at low and high-speed traffic signals in New Zealand and Australia.Data from 238 signalised intersection sites in Auckland,Wellington,Christchurch,Hamilton,Dunedin and Melbourne was used to develop crash prediction models for key crash-causing movements at traffic signals.Different variables(road features)effect each crash type.The models indicate that the safety of intersections can be improved by longer cycle times and longer lost inter-green times,especially all-red time,using fully protected right turns and by extending the length of right turn bays.The exception is at intersections with lots of pedestrians where shorter cycle times are preferred as pedestrian crashes increase with longer wait times.A number of factors have a negative impact on safety including,free left turns,more approach lanes,intersection arms operating near or over capacity in peak periods and higher speed limits.展开更多
目的比较功能定量磁化率成像(fQSM)和血氧水平依赖(BOLD)成像在对指任务功能MRI(fMRI)中检测脑激活的能力。方法前瞻性招募24例健康成人志愿者,采用3.0 T MRI设备同步采集对指运动任务的fMRI幅度及相位图。采用一般线性模型(GLM)和独立...目的比较功能定量磁化率成像(fQSM)和血氧水平依赖(BOLD)成像在对指任务功能MRI(fMRI)中检测脑激活的能力。方法前瞻性招募24例健康成人志愿者,采用3.0 T MRI设备同步采集对指运动任务的fMRI幅度及相位图。采用一般线性模型(GLM)和独立成分分析(ICA)成像提取任务诱发的BOLD以及fQSM脑激活图。采用相关分析探讨BOLD和f QSM脑激活成分时间序列的相似性,采用配对t检验或置换检验比较BOLD和fQSM脑激活成分动态范围和分数低频振幅的差别。结果GLM显示BOLD激活脑区主要位于双侧中央前后回和小脑运动区,而fQSM未检测到激活的脑区(体素水平P<0.001,团块水平FWEc校正P<0.05)。即使降低阈值,fQSM检测到的激活也远少于BOLD,且两者在小脑运动区的时间序列呈显著负相关。头动和空间平滑对BOLD及fQSM激活强度的影响不显著。固定成分数(90)的ICA显示,BOLD能敏感检测到与对指任务时序密切关联的脑激活独立成分,而fQSM未能检测到与任务相关的脑激活,BOLD和fQSM各激活成分时间序列相关性较弱,且BOLD激活成分时间序列的动态范围和分数低频振幅显著高于fQSM(P<0.05,Bonferroni校正)。此外,自动成分数选择的ICA识别到3个与运动显著关联的f QSM脑激活成分,包括感觉运动、内侧前额叶和小脑运动网络,且后者与BOLD感觉运动网络存在显著负相关。结论fQSM技术在手指运动相关脑激活方面的检测能力低于BOLD技术,使用自动成分数选择的ICA有助于提高fQSM脑激活检测能力。展开更多
Under the assumption that in the generalized linear model (GLM) the expectation of the response variable has a correct specification and some other smooth conditions, it is shown that with probability one the quasi-li...Under the assumption that in the generalized linear model (GLM) the expectation of the response variable has a correct specification and some other smooth conditions, it is shown that with probability one the quasi-likelihood equation for the GLM has a solution when the sample size n is sufficiently large. The rate of this solution tending to the true value is determined. In an important special case, this rate is the same as specified in the LIL for iid partial sums and thus cannot be improved anymore.展开更多
基金Supported by the National Natural Science Foundation of China(11071069, 11171307)the Natural Science Foundation of Hunan Province(09JJ6003)
文摘In this paper, we establish several inequalities for the the generalized linear distortion function λ（a, K） by using the monotonicity and convexity of certain combinations λ（a, K）.
文摘In this paper, we define a functional optimization problem corresponding to smooth functions which its optimal solution is first derivative of these functions in a domain. These functional optimization problems are applied for non-smooth functions which by solving these problems we obtain a kind of generalized first derivatives. For this purpose, a linear programming problem corresponding functional optimization problem is obtained which their optimal solutions give the approximate generalized first derivative. We show the efficiency of our approach by obtaining derivative and generalized derivative of some smooth and nonsmooth functions respectively in some illustrative examples.
文摘In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient projection method is given for solving the stochastic generalized linear complementarity problems. The global convergence of the conjugate gradient projection method is proved and the related numerical results are also reported.
文摘In this article, we propose a generalized empirical likelihood inference for the parametric component in semiparametric generalized partially linear models with longitudinal data. Based on the extended score vector, a generalized empirical likelihood ratios function is defined, which integrates the within-cluster?correlation meanwhile avoids direct estimating the nuisance parameters in the correlation matrix. We show that the proposed statistics are asymptotically?Chi-squared under some suitable conditions, and hence it can be used to construct the confidence region of parameters. In addition, the maximum empirical likelihood estimates of parameters and the corresponding asymptotic normality are obtained. Simulation studies demonstrate the performance of the proposed method.
文摘In this paper, we proposed a Extension Definition to derive, simultaneously, the first, second and high order generalized derivatives for non-smooth functions, in which the involved functions are Riemann integrable but not necessarily locally Lipschitz or continuous. Indeed, we define a functional optimization problem corresponding to smooth functions where its optimal solutions are the first and second derivatives of these functions in a domain. Then by applying these functional optimization problems for non-smooth functions and using this method we obtain generalized first derivative (GFD) and generalized second derivative (GSD). Here, the optimization problem is approximated with a linear programming problem that by solving of which, we can obtain these derivatives, as simple as possible. We extend this approach for obtaining generalized high order derivatives (GHODs) of non-smooth functions, simultaneously. Finally, for efficiency of our approach some numerical examples have been presented.
基金Project supported by the National Natural Science Foundation of China(Grant No.10671156)the Natural Science Foundation of Shaanxi Province of China(Grant No.SJ08A05)
文摘By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = （A（u）Ux）x ＋ eB（u, Ux）. A complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is listed. As a consequence, some approxi- mate solutions to the resulting perturbed equations are constructed via examples.
基金supported by the Lanzhou Jiaotong University-Southwest Jiaotong University Joint Innovation Fund(LH2024027).
文摘The virtual synchronous generator(VSG)technology has been proposed to address the problem of system frequency and active power oscillation caused by grid-connected new energy power sources.However,the traditional voltage-current double-closed-loop control used in VSG has the disadvantages of poor disturbance immunity and insufficient dynamic response.In light of the issues above,a virtual synchronous generator voltage outer-loop control strategy based on improved linear autonomous disturbance rejection control(ILADRC)is put forth for consideration.Firstly,an improved first-order linear self-immunity control structure is established for the characteristics of the voltage outer loop;then,the effects of two key control parameters-observer bandwidthω_(0)and controller bandwidthω_(c)on the control system are analyzed,and the key parameters of ILADRC are optimally tuned online using improved gray wolf optimizer-radial basis function(IGWO-RBF)neural network.A simulationmodel is developed using MATLAB to simulate,analyze,and compare the method introduced in this paper.Simulations are performed with the traditional control strategy for comparison,and the results demonstrate that the proposed control method offers superior anti-interference performance.It effectively addresses power and frequency oscillation issues and enhances the stability of the VSG during grid-connected operation.
基金Supported by National Natural Science Foundation of China (No.90208003, 30200059), the 973 Project (No. 2003CB716106), Doctor training Fund of MOE, P.R.C., and Fok Ying Tong Education Foundation (No.91041)
文摘General linear model (GLM) is the most popular method for functional magnetic resource imaging (fMRI) data analysis . However, its theory is imperfect. The key of this model is how to constitute the design-matrix to model the interesting effects better and separate noises better. For the purpose of detecting brain function activation , according to the principle of GLM,a new convolution model is presented by a new dynamic function convolving with design-matrix,which combining with t-test can be used to detect brain active signal. The fMRI imaging result of visual stimulus experiment indicates that brain activities mainly concentrate among v1and v2 areas of visual cortex, and also verified the validity of this technique.
基金The work is supported by the National Natural Science Foundation of China (10271074).
文摘A new vector-valued Pad′e-type approximation is defined by introducing a gener- alized vector-valued linear functional from a scalar polynomial space to a vector space. Some algebraic properties and error formulas are presented. The expressions of this Pad′e-type ap- proximants are provided with the generating function form and the determinant form.
文摘The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicate the corresponding relationship.
基金Project supported by the National Natural Science Foundation of China (No. 10271074)
文摘To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Padé-type approximation is defined. By means of the power series expansion of the solution, this method can construct an approximate solution to solve the given integral equation. On the basis of the orthogonal polynomials, two useful determinant expressions of the numerator polynomial and the denominator polynomial for Padé-type approximation are explicitly given.
基金This project is supported in part by the Guangdong Provincial NSP the SF of Key Discipline of theState Council Office of O
文摘An estimation method for solutions to the general linear system of Volterra- type integral inequalities containing several iterated integral functionals is obtained. This method is based on a result proved by the present second author in Journ. Math. Anal. Appl.(1984). A certain two-dimensional system of nonlinear ordinary differential equations is also discussed to demonstrate the usefulness of our method.
文摘In this paper a new method to realize rational generalized transfer functions of linearshift-variant digital filters through state feedback is presented In some practical applications therequired characteristics of the filter change slowly.Under these circumstances,the proposedmethod is very effective and the resulting filter structure is simple.A numerical example isprovided to show the performance of the method.
基金Supported by the National Natural Science Foundation of China （No.10471140）.
文摘In this paper we introduce an appealing nonparametric method for estimating variance and conditional variance functions in generalized linear models （GLMs）, when designs are fixed points and random variables respectively, Bias-corrected confidence bands are proposed for the （conditional） variance by local linear smoothers. Nonparametric techniques are developed in deriving the bias-corrected confidence intervals of the （conditional） variance. The asymptotic distribution of the proposed estimator is established and show that the bias-corrected confidence bands asymptotically have the correct coverage properties. A small simulation is performed when unknown regression parameter is estimated by nonparametric quasi-likelihood. The results are also applicable to nonparamctric autoregressive times series model with heteroscedastic conditional variance.
基金partially supported by the National Nature Science Foundation of China(12061033)。
文摘In this paper,by deriving an inequality involving the generating function of the Bernoulli numbers,the author introduces a new ratio of finitely many gamma functions,finds complete monotonicity of the second logarithmic derivative of the ratio,and simply reviews the complete monotonicity of several linear combinations of finitely many digamma or trigamma functions.
文摘Generalized H2 （GH2） stability analysis and controller design of the uncertain discrete-time Takagi-Sugeno （T-S） fuzzy systems with state delay are studied based on a switching fuzzy model and piecewise Lyapunov function. GH2 stability sufficient conditions are derived in terms of linear matrix inequalities （LMIs）. The interactions among the fuzzy subsystems are considered. Therefore, the proposed conditions are less conservative than the previous results. Since only a set of LMIs is involved, the controller design is quite simple and numerically tractable. To illustrate the validity of the proposed method, a design example is provided.
文摘A significant proportion of urban crashes,especially serious and fatal crashes,occur at traffic signals.Many of the black-spots in both Australia and New Zealand cities occur at high volume and/or high-speed traffic signals.Given this,crash reduction studies often focus on the major signalised intersections.However,there is limited information that links the phasing configuration,degree of saturation and overall cycle time to crashes.While a number of analysis tools are available for assessing the efficiency of intersections,there are very few tools that can assist engineers in assessing the safety effects of intersection upgrades and new intersections.Safety performance functions have been developed to help quantify the safety impact of various traffic signal phasing configurations and level of intersection congestion at low and high-speed traffic signals in New Zealand and Australia.Data from 238 signalised intersection sites in Auckland,Wellington,Christchurch,Hamilton,Dunedin and Melbourne was used to develop crash prediction models for key crash-causing movements at traffic signals.Different variables(road features)effect each crash type.The models indicate that the safety of intersections can be improved by longer cycle times and longer lost inter-green times,especially all-red time,using fully protected right turns and by extending the length of right turn bays.The exception is at intersections with lots of pedestrians where shorter cycle times are preferred as pedestrian crashes increase with longer wait times.A number of factors have a negative impact on safety including,free left turns,more approach lanes,intersection arms operating near or over capacity in peak periods and higher speed limits.
文摘目的比较功能定量磁化率成像(fQSM)和血氧水平依赖(BOLD)成像在对指任务功能MRI(fMRI)中检测脑激活的能力。方法前瞻性招募24例健康成人志愿者,采用3.0 T MRI设备同步采集对指运动任务的fMRI幅度及相位图。采用一般线性模型(GLM)和独立成分分析(ICA)成像提取任务诱发的BOLD以及fQSM脑激活图。采用相关分析探讨BOLD和f QSM脑激活成分时间序列的相似性,采用配对t检验或置换检验比较BOLD和fQSM脑激活成分动态范围和分数低频振幅的差别。结果GLM显示BOLD激活脑区主要位于双侧中央前后回和小脑运动区,而fQSM未检测到激活的脑区(体素水平P<0.001,团块水平FWEc校正P<0.05)。即使降低阈值,fQSM检测到的激活也远少于BOLD,且两者在小脑运动区的时间序列呈显著负相关。头动和空间平滑对BOLD及fQSM激活强度的影响不显著。固定成分数(90)的ICA显示,BOLD能敏感检测到与对指任务时序密切关联的脑激活独立成分,而fQSM未能检测到与任务相关的脑激活,BOLD和fQSM各激活成分时间序列相关性较弱,且BOLD激活成分时间序列的动态范围和分数低频振幅显著高于fQSM(P<0.05,Bonferroni校正)。此外,自动成分数选择的ICA识别到3个与运动显著关联的f QSM脑激活成分,包括感觉运动、内侧前额叶和小脑运动网络,且后者与BOLD感觉运动网络存在显著负相关。结论fQSM技术在手指运动相关脑激活方面的检测能力低于BOLD技术,使用自动成分数选择的ICA有助于提高fQSM脑激活检测能力。
基金This work was supported by the National Natural Science Foundation of China.
文摘Under the assumption that in the generalized linear model (GLM) the expectation of the response variable has a correct specification and some other smooth conditions, it is shown that with probability one the quasi-likelihood equation for the GLM has a solution when the sample size n is sufficiently large. The rate of this solution tending to the true value is determined. In an important special case, this rate is the same as specified in the LIL for iid partial sums and thus cannot be improved anymore.
