A new particle filter is presented for nonlinear tracking problems. Inpractice, maneuvering target-tracking systems are usually nonlinear and incompletely observed, andthe main difficulty of maneuvering target-trackin...A new particle filter is presented for nonlinear tracking problems. Inpractice, maneuvering target-tracking systems are usually nonlinear and incompletely observed, andthe main difficulty of maneuvering target-tracking problem lies in the fact that the maneuverabilityat every step is of high uncertainties. Here a new smoothing particle filter algorithm is proposed,which combines the particle filter to tackle the non-linear and non-Gaussian peculiarities of theproblem, together with smoothing of the PDF of system modes and thus settles the estimate problem ofthe target maneuverability. The simulation comparison with the auxiliary particle filters showsthat the approach has superiority and yields performance improvements in solving nonlinear trackingproblems.展开更多
A reconstructed edge-based smoothed triangular element, which is incorporated with the discrete shear gap (DSG) method, is formulated based on the global coordinate for analysis of Reissner-Mindlin plates. A symbolic ...A reconstructed edge-based smoothed triangular element, which is incorporated with the discrete shear gap (DSG) method, is formulated based on the global coordinate for analysis of Reissner-Mindlin plates. A symbolic integration combined with the smoothing technique is implemented to calculate the smoothed finite element matrices, which is integrated along the boundaries of each smoothing cell. Numerical results show that the proposed element is free from shear locking, and its results are in good agreement with the exact solutions, even for very thin plates with extremely distorted elements. The proposed element gives more accurate results than the original DSG element without smoothing, and it can be taken as an alternative element for analysis of Reissner-Mindlin plates. The prominent feature of the present element is that the integration scheme is unified in the smoothed form for all of the finite element matrices.展开更多
The combination of a 4-node quadrilateral mixed interpolation of tensorial components element(MITC4)and the cell-based smoothed finite element method(CSFEM)was formulated and implemented in this work for the analysis ...The combination of a 4-node quadrilateral mixed interpolation of tensorial components element(MITC4)and the cell-based smoothed finite element method(CSFEM)was formulated and implemented in this work for the analysis of free vibration and unidirectional buckling of shell structures.This formulation was applied to numerous numerical examples of non-woven fabrics.As CSFEM schemes do not require coordinate transformation,spurious modes and numerical instabilities are prevented using bilinear quadrilateral element subdivided into two,three and four smoothing cells.An improvement of the original CSFEM formulation was made regarding the calculation of outward unit normal vectors,which allowed to remove the integral operator in the strain smoothing operation.This procedure conducted both to the simplification of the developed formulation and the reduction of computational cost.A wide range of values for the thickness-to-length ratio and edge boundary conditions were analysed.The developed numerical model proved to overcome the shear locking phenomenon with success,revealing both reduced implementation effort and computational cost in comparison to the conventional FEM approach.The cell-based strain smoothing technique used in this work yields accurate results and generally attains higher convergence rate in energy at low computational cost.展开更多
In this paper, we propose a numerical method based on semi-Lagrangian approach for solving quasi-geostrophic (QG) equations on a sphere. Using potential vorticity and stream-function as prognostic variables, two-...In this paper, we propose a numerical method based on semi-Lagrangian approach for solving quasi-geostrophic (QG) equations on a sphere. Using potential vorticity and stream-function as prognostic variables, two-order centered difference is suggested on the latitude-longitude grid. In our proposed numerical scheme, advection terms are expressed in a Lagrangian frame of reference to circumvent the CFL restriction. The pole singularity associated with the latitude-longitude grid is eliminated by a smoothing technique for the initial flow. Error analysis is provided for the numerical scheme.展开更多
The paper＇s aim is how to forecast data with variations involving at times series data to get the best forecasting model. When researchers are going to forecast data with variations involving at times series data （i...The paper＇s aim is how to forecast data with variations involving at times series data to get the best forecasting model. When researchers are going to forecast data with variations involving at times series data （i.e., secular trends, cyclical variations, seasonal effects, and stochastic variations）, they believe the best forecasting model is the one which realistically considers the underlying causal factors in a situational relationship and therefore has the best ＂track records＂ in generating data. Paper＇s models can be adjusted for variations in related a time series which processes a great deal of randomness, to improve the accuracy of the financial forecasts. Because of Na＇fve forecasting models are based on an extrapolation of past values for future. These models may be adjusted for seasonal, secular, and cyclical trends in related data. When a data series processes a great deal of randomness, smoothing techniques, such as moving averages and exponential smoothing, may improve the accuracy of the financial forecasts. But neither Na＇fve models nor smoothing techniques are capable of identifying major future changes in the direction of a situational data series. Hereby, nonlinear techniques, like direct and sequential search approaches, overcome those shortcomings can be used. The methodology which we have used is based on inferential analysis. To build the models to identify the major future changes in the direction of a situational data series, a comparative model building is applied. Hereby, the paper suggests using some of the nonlinear techniques, like direct and sequential search approaches, to reduce the technical shortcomings. The final result of the paper is to manipulate, to prepare, and to integrate heuristic non-linear searching methods to serve calculating adjusted factors to produce the best forecast data.展开更多
Support vector machines （SVMs） have been extensively studied and have shown remarkable success in many applications. A new family of twice continuously differentiable piecewise smooth functions are used to smooth th...Support vector machines （SVMs） have been extensively studied and have shown remarkable success in many applications. A new family of twice continuously differentiable piecewise smooth functions are used to smooth the objective function of uncon- strained SVMs. The three-order piecewise smooth support vector machine （TPWSSVMd） is proposed. The piecewise functions can get higher and higher approximation accuracy as required with the increase of parameter d. The global convergence proof of TPWSSVMd is given with the rough set theory. TPWSSVMd can efficiently handle large scale and high dimensional problems. Nu- merical results demonstrate TPWSSVMa has better classification performance and learning efficiency than other competitive base- lines.展开更多
AIM: To investigate the effect and the possible mechanism of ginsenoside Rb1 on small intestinal smooth muscle motility in mice. METHODS: Intestinal smooth muscle strips were isolated from male ICR mice (5 wk old), an...AIM: To investigate the effect and the possible mechanism of ginsenoside Rb1 on small intestinal smooth muscle motility in mice. METHODS: Intestinal smooth muscle strips were isolated from male ICR mice (5 wk old), and the effect of ginsenoside Rb1 on spontaneous contraction was recorded with an electrophysiolograph. The effect of ginsenoside Rb1 on ion channel currents, including the voltage-gated K + channel current (IK V ), calcium-activated potassium channel currents (IK Ca ), spontaneous transient outward currents and ATP-sensitive potassium channel current (IK ATP ), was recorded on freshly isolated single cells using the whole-cell patch clamp technique. RESULTS: Ginsenoside Rb1 dose-dependently inhibited the spontaneous contraction of intestinal smooth muscle by 21.15% ± 3.31%, 42.03% ± 8.23% and 67.23% ± 5.63% at concentrations of 25 μmol/L, 50 μmol/L and 100 μmol/L, respectively (n=5,P<0.05). The inhibitory effect of ginsenoside Rb1 on spontaneous contraction was significantly but incompletely blocked by 10 mmol/L tetraethylammonium or 0.5 mmol/L 4-aminopyridine, respectively (n=5, P<0.05). However, the inhibitory effect of ginsenoside Rb1 on spontaneous contraction was not affected by 10 μmol/L glibenclamide or 0.4 μmol/L tetrodotoxin. At the cell level, ginsenoside Rb1 increased outward potassium currents, and IK V was enhanced from 1137.71 ± 171.62 pA to 1449.73 ± 162.39 pA by 50 μmol/L Rb1 at +60 mV (n=6, P<0.05). Ginsenoside Rb1 increased IK Ca and enhanced the amplitudes of spontaneous transient outward currents from 582.77 ± 179.09 mV to 788.12 ± 278.34 mV (n=5, P<0.05). However, ginsenoside Rb1 (50 μmol/L) had no significant effect on IK ATP (n=3, P<0.05). CONCLUSION: These results suggest that ginsenoside Rb1 has an inhibitory effect on the spontaneous contraction of mouse intestinal smooth muscle mediated by the activation of IK V and IK Ca , but the K ATP channel was not involved in this effect.展开更多
In this paper,we propose an algorithm for a nonsmooth convex optimization problem arising in very large-scale integrated circuit placement.The objective function is the sum of a large number of Half-Perimeter Wire Len...In this paper,we propose an algorithm for a nonsmooth convex optimization problem arising in very large-scale integrated circuit placement.The objective function is the sum of a large number of Half-Perimeter Wire Length(HPWL)functions and a strongly convex function.The algorithm is based on Nesterov’s smoothing and excessive gap techniques.The main advantage of the algorithm is that it can capture the HPWL information in the process of optimization,and every subproblem has an explicit solution in the process of optimization.The convergence rate of the algorithm is Oe1=k2T;where k is the iteration counter,which is optimal.We also present preliminary experiments on nine placement contest benchmarks.Numerical examples confirm the theoretical results.展开更多
We propose a smoothing trust region filter algorithm for nonsmooth nonconvex least squares problems. We present convergence theorems of the proposed algorithm to a Clarke stationary point or a global minimizer of the ...We propose a smoothing trust region filter algorithm for nonsmooth nonconvex least squares problems. We present convergence theorems of the proposed algorithm to a Clarke stationary point or a global minimizer of the objective function under certain conditions. Preliminary numerical experiments show the efficiency of the proposed algorithm for finding zeros of a system of polynomial equations with high degrees on the sphere and solving differential variational inequalities.展开更多
A series of ten numerical tests are carried out using smoothing techniques in the PSU/NACR mesoscale model MM5 initial field in order to study the development reasons of a pre-summer uncommon explosive event which too...A series of ten numerical tests are carried out using smoothing techniques in the PSU/NACR mesoscale model MM5 initial field in order to study the development reasons of a pre-summer uncommon explosive event which took place in East Asia from 1—2 June.1993.The integration fields are compared with that of original results obtained by non-smoothed initial field.The results show that:(1)After the northern trough is smoothed,its corresponding cold air can not move downward and southward.Only a weak cyclone system forms south of 25°N after 24 h integration. (2)After the southern strong moisture transportation channel is smoothed,the northem trough system can only form a weak trough along the east coast of China after 24 h integration.(3)These two separate low trough systems in the southern and northern jet systems,with strong warm moisture transportation channel and cold air respectively,are both necessary for explosive cyclone development.In such an unfavorable season and location for explosive cyclone to take place,only after these two low troughs merged into a strong low vortex can the surface cyclone he developed explosively.Both the northern trough system and the southern moisture transportation channel are all indispensable for the explosive cyclone development.This explosive cyclone event is the result of the interaction of northern and southern systems.展开更多
The authors are concerned with a class of derivative nonlinear Schr¨odinger equation iu_t + u_(xx) + i?f(u, ū, ωt)u_x=0,(t, x) ∈ R × [0, π],subject to Dirichlet boundary condition, where the nonlinearity...The authors are concerned with a class of derivative nonlinear Schr¨odinger equation iu_t + u_(xx) + i?f(u, ū, ωt)u_x=0,(t, x) ∈ R × [0, π],subject to Dirichlet boundary condition, where the nonlinearity f(z1, z2, ?) is merely finitely differentiable with respect to all variables rather than analytic and quasi-periodically forced in time. By developing a smoothing and approximation theory, the existence of many quasi-periodic solutions of the above equation is proved.展开更多
Support vector machines （SVMs） have shown remarkable success in many applications. However, the non-smooth feature of objective function is a limitation in practical application of SVMs. To overcome this disadvantag...Support vector machines （SVMs） have shown remarkable success in many applications. However, the non-smooth feature of objective function is a limitation in practical application of SVMs. To overcome this disadvantage, a twice continuously differentiable piecewise-smooth function is constructed to smooth the objective function of unconstrained support vector machine （SVM）, and it issues a piecewise-smooth support vector machine （PWESSVM）. Comparing to the other smooth approximation functions, the smooth precision has an obvious improvement. The theoretical analysis shows PWESSVM is globally convergent. Numerical results and comparisons demonstrate the classification performance of our algorithm is better than other competitive baselines.展开更多
Support vector machines （SVMs） have been intensively applied in the domains of speech recognmon, text categorization, and faults detection. However, the practical application of SVMs is limited by the non-smooth fea...Support vector machines （SVMs） have been intensively applied in the domains of speech recognmon, text categorization, and faults detection. However, the practical application of SVMs is limited by the non-smooth feature of objective function. To overcome this problem, a novel smooth function based on the geometry of circle tangent is constructed. It smoothes the non-differentiable term of unconstrained SVM, and also proposes a circle tangent smooth SVM （CTSSVM）. Compared with other smooth approaching functions, its smooth precision had an obvious improvement. Theoretical analysis proved the global convergence of CTSSVM. Numerical experiments and comparisons showed CTSSVM had better classification and learning efficiency than competitive baselines.展开更多
文摘A new particle filter is presented for nonlinear tracking problems. Inpractice, maneuvering target-tracking systems are usually nonlinear and incompletely observed, andthe main difficulty of maneuvering target-tracking problem lies in the fact that the maneuverabilityat every step is of high uncertainties. Here a new smoothing particle filter algorithm is proposed,which combines the particle filter to tackle the non-linear and non-Gaussian peculiarities of theproblem, together with smoothing of the PDF of system modes and thus settles the estimate problem ofthe target maneuverability. The simulation comparison with the auxiliary particle filters showsthat the approach has superiority and yields performance improvements in solving nonlinear trackingproblems.
基金supported by the National Natural Science Foundation of China (Grants 11272118, 11372106)Fundamental Research Fund of the Central Universities (Grant 227201401203)
文摘A reconstructed edge-based smoothed triangular element, which is incorporated with the discrete shear gap (DSG) method, is formulated based on the global coordinate for analysis of Reissner-Mindlin plates. A symbolic integration combined with the smoothing technique is implemented to calculate the smoothed finite element matrices, which is integrated along the boundaries of each smoothing cell. Numerical results show that the proposed element is free from shear locking, and its results are in good agreement with the exact solutions, even for very thin plates with extremely distorted elements. The proposed element gives more accurate results than the original DSG element without smoothing, and it can be taken as an alternative element for analysis of Reissner-Mindlin plates. The prominent feature of the present element is that the integration scheme is unified in the smoothed form for all of the finite element matrices.
基金supported by the Portuguese Foundation for Science and Technology(FCT)through project UID/CTM/00264/2019 of 2C2T—Centro de Ciência e Tecnologia Têxtil,hold by National Founds of FCT/MCTES,and project UID/EEA/04436/2013,COMPETE 2020 with the code POCI-01-0145-FEDER-006941.
文摘The combination of a 4-node quadrilateral mixed interpolation of tensorial components element(MITC4)and the cell-based smoothed finite element method(CSFEM)was formulated and implemented in this work for the analysis of free vibration and unidirectional buckling of shell structures.This formulation was applied to numerous numerical examples of non-woven fabrics.As CSFEM schemes do not require coordinate transformation,spurious modes and numerical instabilities are prevented using bilinear quadrilateral element subdivided into two,three and four smoothing cells.An improvement of the original CSFEM formulation was made regarding the calculation of outward unit normal vectors,which allowed to remove the integral operator in the strain smoothing operation.This procedure conducted both to the simplification of the developed formulation and the reduction of computational cost.A wide range of values for the thickness-to-length ratio and edge boundary conditions were analysed.The developed numerical model proved to overcome the shear locking phenomenon with success,revealing both reduced implementation effort and computational cost in comparison to the conventional FEM approach.The cell-based strain smoothing technique used in this work yields accurate results and generally attains higher convergence rate in energy at low computational cost.
文摘In this paper, we propose a numerical method based on semi-Lagrangian approach for solving quasi-geostrophic (QG) equations on a sphere. Using potential vorticity and stream-function as prognostic variables, two-order centered difference is suggested on the latitude-longitude grid. In our proposed numerical scheme, advection terms are expressed in a Lagrangian frame of reference to circumvent the CFL restriction. The pole singularity associated with the latitude-longitude grid is eliminated by a smoothing technique for the initial flow. Error analysis is provided for the numerical scheme.
文摘The paper＇s aim is how to forecast data with variations involving at times series data to get the best forecasting model. When researchers are going to forecast data with variations involving at times series data （i.e., secular trends, cyclical variations, seasonal effects, and stochastic variations）, they believe the best forecasting model is the one which realistically considers the underlying causal factors in a situational relationship and therefore has the best ＂track records＂ in generating data. Paper＇s models can be adjusted for variations in related a time series which processes a great deal of randomness, to improve the accuracy of the financial forecasts. Because of Na＇fve forecasting models are based on an extrapolation of past values for future. These models may be adjusted for seasonal, secular, and cyclical trends in related data. When a data series processes a great deal of randomness, smoothing techniques, such as moving averages and exponential smoothing, may improve the accuracy of the financial forecasts. But neither Na＇fve models nor smoothing techniques are capable of identifying major future changes in the direction of a situational data series. Hereby, nonlinear techniques, like direct and sequential search approaches, overcome those shortcomings can be used. The methodology which we have used is based on inferential analysis. To build the models to identify the major future changes in the direction of a situational data series, a comparative model building is applied. Hereby, the paper suggests using some of the nonlinear techniques, like direct and sequential search approaches, to reduce the technical shortcomings. The final result of the paper is to manipulate, to prepare, and to integrate heuristic non-linear searching methods to serve calculating adjusted factors to produce the best forecast data.
基金supported by the National Natural Science Foundation of China(6110016561100231+6 种基金5120530961472307)the Natural Science Foundation of Shaanxi Province(2012JQ80442014JM83132010JQ8004)the Foundation of Education Department of Shaanxi Province(2013JK1096)the New Star Team of Xi’an University of Posts and Telecommunications
文摘Support vector machines （SVMs） have been extensively studied and have shown remarkable success in many applications. A new family of twice continuously differentiable piecewise smooth functions are used to smooth the objective function of uncon- strained SVMs. The three-order piecewise smooth support vector machine （TPWSSVMd） is proposed. The piecewise functions can get higher and higher approximation accuracy as required with the increase of parameter d. The global convergence proof of TPWSSVMd is given with the rough set theory. TPWSSVMd can efficiently handle large scale and high dimensional problems. Nu- merical results demonstrate TPWSSVMa has better classification performance and learning efficiency than other competitive base- lines.
基金Supported by The National Natural Science Foundation of China, No. 30873328The State Administration of Traditional Chinese Medicine of the People’s Republic of China, No. 06-075930
文摘AIM: To investigate the effect and the possible mechanism of ginsenoside Rb1 on small intestinal smooth muscle motility in mice. METHODS: Intestinal smooth muscle strips were isolated from male ICR mice (5 wk old), and the effect of ginsenoside Rb1 on spontaneous contraction was recorded with an electrophysiolograph. The effect of ginsenoside Rb1 on ion channel currents, including the voltage-gated K + channel current (IK V ), calcium-activated potassium channel currents (IK Ca ), spontaneous transient outward currents and ATP-sensitive potassium channel current (IK ATP ), was recorded on freshly isolated single cells using the whole-cell patch clamp technique. RESULTS: Ginsenoside Rb1 dose-dependently inhibited the spontaneous contraction of intestinal smooth muscle by 21.15% ± 3.31%, 42.03% ± 8.23% and 67.23% ± 5.63% at concentrations of 25 μmol/L, 50 μmol/L and 100 μmol/L, respectively (n=5,P<0.05). The inhibitory effect of ginsenoside Rb1 on spontaneous contraction was significantly but incompletely blocked by 10 mmol/L tetraethylammonium or 0.5 mmol/L 4-aminopyridine, respectively (n=5, P<0.05). However, the inhibitory effect of ginsenoside Rb1 on spontaneous contraction was not affected by 10 μmol/L glibenclamide or 0.4 μmol/L tetrodotoxin. At the cell level, ginsenoside Rb1 increased outward potassium currents, and IK V was enhanced from 1137.71 ± 171.62 pA to 1449.73 ± 162.39 pA by 50 μmol/L Rb1 at +60 mV (n=6, P<0.05). Ginsenoside Rb1 increased IK Ca and enhanced the amplitudes of spontaneous transient outward currents from 582.77 ± 179.09 mV to 788.12 ± 278.34 mV (n=5, P<0.05). However, ginsenoside Rb1 (50 μmol/L) had no significant effect on IK ATP (n=3, P<0.05). CONCLUSION: These results suggest that ginsenoside Rb1 has an inhibitory effect on the spontaneous contraction of mouse intestinal smooth muscle mediated by the activation of IK V and IK Ca , but the K ATP channel was not involved in this effect.
基金supported partially by National Natural Science Foundation of China(Nos.61170308 and 11331003)National Key Basic Research Science Foundation of China(No.2011CB808003).
文摘In this paper,we propose an algorithm for a nonsmooth convex optimization problem arising in very large-scale integrated circuit placement.The objective function is the sum of a large number of Half-Perimeter Wire Length(HPWL)functions and a strongly convex function.The algorithm is based on Nesterov’s smoothing and excessive gap techniques.The main advantage of the algorithm is that it can capture the HPWL information in the process of optimization,and every subproblem has an explicit solution in the process of optimization.The convergence rate of the algorithm is Oe1=k2T;where k is the iteration counter,which is optimal.We also present preliminary experiments on nine placement contest benchmarks.Numerical examples confirm the theoretical results.
基金supported by Hong Kong Research Grant Council(Grant No.Poly U5001/12p)National Natural Science Foundation of China(Grant No.11101231)
文摘We propose a smoothing trust region filter algorithm for nonsmooth nonconvex least squares problems. We present convergence theorems of the proposed algorithm to a Clarke stationary point or a global minimizer of the objective function under certain conditions. Preliminary numerical experiments show the efficiency of the proposed algorithm for finding zeros of a system of polynomial equations with high degrees on the sphere and solving differential variational inequalities.
文摘A series of ten numerical tests are carried out using smoothing techniques in the PSU/NACR mesoscale model MM5 initial field in order to study the development reasons of a pre-summer uncommon explosive event which took place in East Asia from 1—2 June.1993.The integration fields are compared with that of original results obtained by non-smoothed initial field.The results show that:(1)After the northern trough is smoothed,its corresponding cold air can not move downward and southward.Only a weak cyclone system forms south of 25°N after 24 h integration. (2)After the southern strong moisture transportation channel is smoothed,the northem trough system can only form a weak trough along the east coast of China after 24 h integration.(3)These two separate low trough systems in the southern and northern jet systems,with strong warm moisture transportation channel and cold air respectively,are both necessary for explosive cyclone development.In such an unfavorable season and location for explosive cyclone to take place,only after these two low troughs merged into a strong low vortex can the surface cyclone he developed explosively.Both the northern trough system and the southern moisture transportation channel are all indispensable for the explosive cyclone development.This explosive cyclone event is the result of the interaction of northern and southern systems.
基金supported by the National Natural Science Foundation of China(No.11201292)Shanghai Natural Science Foundation(No.12ZR1444300)the Key Discipline"Applied Mathematics"of Shanghai Second Polytechnic University(No.XXKZD1304)
文摘The authors are concerned with a class of derivative nonlinear Schr¨odinger equation iu_t + u_(xx) + i?f(u, ū, ωt)u_x=0,(t, x) ∈ R × [0, π],subject to Dirichlet boundary condition, where the nonlinearity f(z1, z2, ?) is merely finitely differentiable with respect to all variables rather than analytic and quasi-periodically forced in time. By developing a smoothing and approximation theory, the existence of many quasi-periodic solutions of the above equation is proved.
基金supported by the National Natural Science Foundation of China (61100165, 61100231, 61105064, 51205309)the Natural Science Foundation of Shaanxi Province (2012JQ8044, 2011JM8003, 2010JQ8004)the Foundation of Education Department of Shanxi Province (2013JK1096)
文摘Support vector machines （SVMs） have shown remarkable success in many applications. However, the non-smooth feature of objective function is a limitation in practical application of SVMs. To overcome this disadvantage, a twice continuously differentiable piecewise-smooth function is constructed to smooth the objective function of unconstrained support vector machine （SVM）, and it issues a piecewise-smooth support vector machine （PWESSVM）. Comparing to the other smooth approximation functions, the smooth precision has an obvious improvement. The theoretical analysis shows PWESSVM is globally convergent. Numerical results and comparisons demonstrate the classification performance of our algorithm is better than other competitive baselines.
文摘Support vector machines （SVMs） have been intensively applied in the domains of speech recognmon, text categorization, and faults detection. However, the practical application of SVMs is limited by the non-smooth feature of objective function. To overcome this problem, a novel smooth function based on the geometry of circle tangent is constructed. It smoothes the non-differentiable term of unconstrained SVM, and also proposes a circle tangent smooth SVM （CTSSVM）. Compared with other smooth approaching functions, its smooth precision had an obvious improvement. Theoretical analysis proved the global convergence of CTSSVM. Numerical experiments and comparisons showed CTSSVM had better classification and learning efficiency than competitive baselines.
