In this article, the computation of μ-values known as Structured Singular Values SSV for the companion matrices is presented. The comparison of lower bounds with the well-known MATLAB routine mussv is investigated. T...In this article, the computation of μ-values known as Structured Singular Values SSV for the companion matrices is presented. The comparison of lower bounds with the well-known MATLAB routine mussv is investigated. The Structured Singular Values provides important tools to analyze the stability and instability analysis of closed loop time invariant systems in the linear control theory as well as in structured eigenvalue perturbation theory.展开更多
This study analyzes the impact of profitability,firm size,and capital structure on firm value within the manufacturing sector.Utilizing a descriptive literature-based method,this research synthesizes various findings ...This study analyzes the impact of profitability,firm size,and capital structure on firm value within the manufacturing sector.Utilizing a descriptive literature-based method,this research synthesizes various findings from previous studies to provide a comprehensive overview of the relationships among these variables.Profitability,often measured by Return on Assets(ROA)or Return on Equity(ROE),is expected to have a positive relationship with firm value as it reflects a company’s ability to generate profits.Firm size,measured by total assets or the logarithm of sales,is also assumed to influence firm value,both through economies of scale and better access to capital markets.Meanwhile,capital structure,measured by Debt to Equity Ratio(DER)or Debt to Asset Ratio(DAR),has a complex impact;while debt can enhance firm value through tax shields,excessive debt levels can increase financial risk and potentially decrease firm value.The synthesis of literature indicates a general consensus on the importance of profitability and firm size in shaping firm value,though there is variation in the significance and direction of the relationship for capital structure variables.This study provides important implications for company managers and investors in making strategic decisions related to resource allocation and selecting an optimal capital structure to enhance firm value.展开更多
In this paper,we consider the discrete boundary value problem of the type{∆u1=0=∆un-1,∇(t_(k)^(N-1))φ(∆uk))+t_(k)^(N-1)fk(t_(k),u_(k),∆_(uk))=0,2≤k≤n-1,whereφ:(-a,a)→R,0<a<∞,is an increasing homeomorphism ...In this paper,we consider the discrete boundary value problem of the type{∆u1=0=∆un-1,∇(t_(k)^(N-1))φ(∆uk))+t_(k)^(N-1)fk(t_(k),u_(k),∆_(uk))=0,2≤k≤n-1,whereφ:(-a,a)→R,0<a<∞,is an increasing homeomorphism withφ(0)=0,such aφis called singular,N≥1,n≥3 are integers,tk are the grid points,uk:=u(tk),k=1,2,...,n,∇is the backward difference operator defined by∆uk=uk-uk-1,△is the forward difference operator defined by△uk=uk+1-uk,fk(2≤k≤n-1)are continuous functions.We prove the existence of solutions to this problem by employing the sign condition,the continuation lemma and the upper and lower solutions,respectively.On this basis,we also establish the Ambrosetti-Prodi type results for it.展开更多
The structural damage identification through modal data often leads to solving a set of linear equations. Special numerical treatment is sometimes required for an accurate and stable solution owing to the ill conditio...The structural damage identification through modal data often leads to solving a set of linear equations. Special numerical treatment is sometimes required for an accurate and stable solution owing to the ill conditioning of the equations. Based on the singular value decomposition (SVD) of the coefficient matrix, an error based truncation algorithm is proposed in this paper. By rejection of selected small singular values, the influence of noise can be reduced. A simply-supported beam is used as a simulation example to compare the results to other methods. Illustrative numerical examples demonstrate the good efficiency and stability of the algorithm in the nondestructive identification of structural damage through modal data.展开更多
The step-type contrast structure for a singular singularly perturbed problem is shown. By use of the method of boundary function, the formal asymptotic expansion is constructed. At the same time, based on sewing orbit...The step-type contrast structure for a singular singularly perturbed problem is shown. By use of the method of boundary function, the formal asymptotic expansion is constructed. At the same time, based on sewing orbit smooth, the existence of the step- type solution and the uniform validity of the asymptotic expansion are proved. Finally, an example is given to demonstrate the effectiveness of the present results.展开更多
A new digital watermarking algorithm based on the contourlet transform is proposed to improve the robustness and anti-attack performances of digital watermarking. The algorithm uses the Arnold scrambling technique and...A new digital watermarking algorithm based on the contourlet transform is proposed to improve the robustness and anti-attack performances of digital watermarking. The algorithm uses the Arnold scrambling technique and the singular value decomposition （SVD） scheme. The Arnold scrambling technique is used to preprocess the watermark, and the SVD scheme is used to find the best suitable hiding points. After the contourlet transform of the carrier image, intermediate frequency sub-bands are decomposed to obtain the singularity values. Then the watermark bits scrambled in the Arnold rules are dispersedly embedded into the selected SVD points. Finally, the inverse contourlet transform is applied to obtain the carrier image with the watermark. In the extraction part, the watermark can be extracted by the semi-blind watermark extracting algorithm. Simulation results show that the proposed algorithm has better hiding and robustness performances than the traditional contourlet watermarking algorithm and the contourlet watermarking algorithm with SVD. Meanwhile, it has good robustness performances when the embedded watermark is attacked by Gaussian noise, salt- and-pepper noise, multiplicative noise, image scaling and image cutting attacks, etc. while security is ensured.展开更多
By dint of the summer precipitation data from 21 stations in the Dongting Lake region during 1960-2008 and the sea surface temperature(SST) data from NOAA,the spatial and temporal distributions of summer precipitation...By dint of the summer precipitation data from 21 stations in the Dongting Lake region during 1960-2008 and the sea surface temperature(SST) data from NOAA,the spatial and temporal distributions of summer precipitation and their correlations with SST are analyzed.The coupling relationship between the anomalous distribution in summer precipitation and the variation of SST has between studied with the Singular Value Decomposition(SVD) analysis.The increase or decrease of summer precipitation in the Dongting Lake region is closely associated with the SST anomalies in three key regions.The variation of SST in the three key regions has been proved to be a significant previous signal to anomaly of summer rainfall in Dongting region.展开更多
The singularly perturbed elliptic equation boundary value problem with turning point is considered. Using the method of multiple scales and the comparison theorem, the asymptotic behavior of solution for the boundary ...The singularly perturbed elliptic equation boundary value problem with turning point is considered. Using the method of multiple scales and the comparison theorem, the asymptotic behavior of solution for the boundary value problem is studied.展开更多
A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems i...A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems is studied.展开更多
From 700 m to 1900 m on the northern slope of Changbai Mountain, 13 plots with an interval of 100 m in elevation were investigated to study the variations of population structure and important value of the main edific...From 700 m to 1900 m on the northern slope of Changbai Mountain, 13 plots with an interval of 100 m in elevation were investigated to study the variations of population structure and important value of the main edificators along the elevation gradient. In their core distribution areas, most of the edificators had healthy population structure and could regenerate smoothly except Larix olgensis, but important value of Larix olgensis had no obvious variations with elevation changes, which showed that Larix olgensis had its own particularity and strong adaptability. At high elevation above 1800 m, Betula ermanii was the only species that could form a mono-dominant community. Important values of Pinus koraiensis and Acer mono had similar changing trends, and they had the similar ecological adaptabilities.展开更多
Vibration acceleration signals are often measured from case surface of arunning machine to monitor its condition. If the measured vibration signals display to have periodicimpulse components with a certain frequency, ...Vibration acceleration signals are often measured from case surface of arunning machine to monitor its condition. If the measured vibration signals display to have periodicimpulse components with a certain frequency, there may exist a corresponding local fault in themachine, and if further extracting the periodic impulse components from the vibration signals, theseverity of the local fault can be estimated and tracked. However, the signal-to-noise ratios (SNRs)of the vibration acceleration signals are often so small that the periodic impulse components aresubmersed in much background noises and other components, and it is difficult or inconvenient for usto detect and extract the periodic impulse components with the current common analyzing methods forvibration signals. Therefore, another technique, called singular value decomposition (SVD), istried to be introduced to solve the problem. First, the principle of detecting and extracting thesignal periodic components using singular value decomposition is summarized and discussed. Second,the infeasibility of the direct use of the existing SVD based detecting and extracting approach ispointed out. Third, the approach to construct the matrix for SVD from the signal series is improvedlargely, which is the key program to improve the SVD technique; Other associated improvement is alsoproposed. Finally, a simulating application example and a real-life application example ondetecting and extracting the periodic impulse components are given, which showed that the introducedand improved SVD technique is feasible.展开更多
This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2...This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2, where p is an element of (Graphics) and f is singular at t = 0, t = 1 and u = 0. Under suitable weaker conditions than those of [1], it is proved by constructing a special cone in C[0, 2pi] and employing the fixed point index theory that the problem has at least one or at least two positive solutions.展开更多
This paper deals with the existence of positive solutions to the singular boundary value problemwhere q(t) may be singular at t = 0 and t = 1, f(t,y) may be superlinear at y =∞ and singular, at y = 0.
The singularly perturbed nonlinear boundary value problems are considered.Using the stretched variable and the method of boundary layer correction,the formal asymptotic expansion of solution is obtained.And then the u...The singularly perturbed nonlinear boundary value problems are considered.Using the stretched variable and the method of boundary layer correction,the formal asymptotic expansion of solution is obtained.And then the uniform validity of solution is proved by using the differential inequalities.展开更多
Extracting implicit anomaly information through deformation monitoring data mining is highly significant to determining dam safety status.As an intelligent singular value diagnostic method for concrete dam deformation...Extracting implicit anomaly information through deformation monitoring data mining is highly significant to determining dam safety status.As an intelligent singular value diagnostic method for concrete dam deformation monitoring, shallow neural network models result in local optima and overfitting, and require manual feature extraction.To obtain an intelligent singular value diagnosis model that can be used for dam safety monitoring, a convolutional neural network (CNN) model that has advantages of deep learning (DL), such as automatic feature extraction, good model fitting, and strong generalizability, was trained in this study.An engineering example shows that the predicted result of the intelligent singular value diagnostic method based on CNN is highly compatible with the confusion matrix, with a precision of 92.41%, receiver operating characteristic (ROC) coordinates of (0.03, 0.97), an area-under-curve (AUC) value of 0.99, and an F1-score of 0.91.Moreover, the performance of the CNN model is better than those of models based on decision tree (DT) and k-nearest neighbor (KNN) methods.Therefore, the intelligent singular value diagnostic method based on CNN is simple to operate, highly intelligent, and highly reliable, and it has a high potential for application in engineering.展开更多
The singular value decomposition is derived when the Radon transform is restricted to functions which are square integrable on the unit ball in R-n with respect to the weight W-lambda(x). It fulfilles mainly by means ...The singular value decomposition is derived when the Radon transform is restricted to functions which are square integrable on the unit ball in R-n with respect to the weight W-lambda(x). It fulfilles mainly by means of the projection-slice theorem. The range of the Radon transform is spanned by products of Gegenbauer polynomials and spherical harmonics. The inverse transform of the those basis functions are given. This immediately leads to an inversion formula by series expansion and range characterizations.展开更多
The existence and asymptotic behavior of solution for a class of quasilinear singularly perturbed boundary value problems are discussed under suitable conditions by the theory of differential inequalities and matching...The existence and asymptotic behavior of solution for a class of quasilinear singularly perturbed boundary value problems are discussed under suitable conditions by the theory of differential inequalities and matching principle.展开更多
In this paper, a class of strongly nonlinear singular perturbed boundary value problems are coasidered by the theory of differential inequalities and the correction of boundary layer, under which the existence of solu...In this paper, a class of strongly nonlinear singular perturbed boundary value problems are coasidered by the theory of differential inequalities and the correction of boundary layer, under which the existence of solution is proved and the uniformly valid asymptotic expansions is obtained as well.展开更多
The traditional K-singular value decomposition(K-SVD)algorithm has poor imagedenoising performance under strong noise.An image-denoising algorithm is proposed based on improved K-SVD and dictionary atom optimization.F...The traditional K-singular value decomposition(K-SVD)algorithm has poor imagedenoising performance under strong noise.An image-denoising algorithm is proposed based on improved K-SVD and dictionary atom optimization.First,a correlation coefficient-matching criterion is used to obtain a sparser representation of the image dictionary.The dictionary noise atom is detected according to structural complexity and noise intensity and removed to optimize the dictionary.Then,non-local regularity is incorporated into the denoising model to further improve image-denoising performance.Results of the simulated dictionary recovery problem and application on a transmission line dataset show that the proposed algorithm improves the smoothness of homogeneous regions while retaining details such as texture and edge.展开更多
The singularly perturbed boundary value problem for the nonlinear boundary conditions is considered.Under suitable conditions,the asymptotic behavior of solution for the original problems is studied by using theory of...The singularly perturbed boundary value problem for the nonlinear boundary conditions is considered.Under suitable conditions,the asymptotic behavior of solution for the original problems is studied by using theory of differential inequalities.展开更多
文摘In this article, the computation of μ-values known as Structured Singular Values SSV for the companion matrices is presented. The comparison of lower bounds with the well-known MATLAB routine mussv is investigated. The Structured Singular Values provides important tools to analyze the stability and instability analysis of closed loop time invariant systems in the linear control theory as well as in structured eigenvalue perturbation theory.
文摘This study analyzes the impact of profitability,firm size,and capital structure on firm value within the manufacturing sector.Utilizing a descriptive literature-based method,this research synthesizes various findings from previous studies to provide a comprehensive overview of the relationships among these variables.Profitability,often measured by Return on Assets(ROA)or Return on Equity(ROE),is expected to have a positive relationship with firm value as it reflects a company’s ability to generate profits.Firm size,measured by total assets or the logarithm of sales,is also assumed to influence firm value,both through economies of scale and better access to capital markets.Meanwhile,capital structure,measured by Debt to Equity Ratio(DER)or Debt to Asset Ratio(DAR),has a complex impact;while debt can enhance firm value through tax shields,excessive debt levels can increase financial risk and potentially decrease firm value.The synthesis of literature indicates a general consensus on the importance of profitability and firm size in shaping firm value,though there is variation in the significance and direction of the relationship for capital structure variables.This study provides important implications for company managers and investors in making strategic decisions related to resource allocation and selecting an optimal capital structure to enhance firm value.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1236104012461035)+1 种基金the Outstanding Youth Fund of Gansu Province(Grant No.24JRRA121)the Scientific Research Ability Improvement Program for Young Teachers of Northwest Normal University(Grant No.NWNU-LKQN2021-17)。
文摘In this paper,we consider the discrete boundary value problem of the type{∆u1=0=∆un-1,∇(t_(k)^(N-1))φ(∆uk))+t_(k)^(N-1)fk(t_(k),u_(k),∆_(uk))=0,2≤k≤n-1,whereφ:(-a,a)→R,0<a<∞,is an increasing homeomorphism withφ(0)=0,such aφis called singular,N≥1,n≥3 are integers,tk are the grid points,uk:=u(tk),k=1,2,...,n,∇is the backward difference operator defined by∆uk=uk-uk-1,△is the forward difference operator defined by△uk=uk+1-uk,fk(2≤k≤n-1)are continuous functions.We prove the existence of solutions to this problem by employing the sign condition,the continuation lemma and the upper and lower solutions,respectively.On this basis,we also establish the Ambrosetti-Prodi type results for it.
文摘The structural damage identification through modal data often leads to solving a set of linear equations. Special numerical treatment is sometimes required for an accurate and stable solution owing to the ill conditioning of the equations. Based on the singular value decomposition (SVD) of the coefficient matrix, an error based truncation algorithm is proposed in this paper. By rejection of selected small singular values, the influence of noise can be reduced. A simply-supported beam is used as a simulation example to compare the results to other methods. Illustrative numerical examples demonstrate the good efficiency and stability of the algorithm in the nondestructive identification of structural damage through modal data.
基金Project supported by the National Natural Science Foundation of China(No.11071075)the Natural Science Foundation of Shanghai(No.10ZR1409200)
文摘The step-type contrast structure for a singular singularly perturbed problem is shown. By use of the method of boundary function, the formal asymptotic expansion is constructed. At the same time, based on sewing orbit smooth, the existence of the step- type solution and the uniform validity of the asymptotic expansion are proved. Finally, an example is given to demonstrate the effectiveness of the present results.
基金The National Natural Science Foundation of China( No. 69092008)
文摘A new digital watermarking algorithm based on the contourlet transform is proposed to improve the robustness and anti-attack performances of digital watermarking. The algorithm uses the Arnold scrambling technique and the singular value decomposition （SVD） scheme. The Arnold scrambling technique is used to preprocess the watermark, and the SVD scheme is used to find the best suitable hiding points. After the contourlet transform of the carrier image, intermediate frequency sub-bands are decomposed to obtain the singularity values. Then the watermark bits scrambled in the Arnold rules are dispersedly embedded into the selected SVD points. Finally, the inverse contourlet transform is applied to obtain the carrier image with the watermark. In the extraction part, the watermark can be extracted by the semi-blind watermark extracting algorithm. Simulation results show that the proposed algorithm has better hiding and robustness performances than the traditional contourlet watermarking algorithm and the contourlet watermarking algorithm with SVD. Meanwhile, it has good robustness performances when the embedded watermark is attacked by Gaussian noise, salt- and-pepper noise, multiplicative noise, image scaling and image cutting attacks, etc. while security is ensured.
基金Supported by The Special Foundation of Chinese Meteorological Bureau Climate Changes Program(200920)The Special Foundation of Hunan Major Scientific and Technological Research Program(2008FJ1006)~~
文摘By dint of the summer precipitation data from 21 stations in the Dongting Lake region during 1960-2008 and the sea surface temperature(SST) data from NOAA,the spatial and temporal distributions of summer precipitation and their correlations with SST are analyzed.The coupling relationship between the anomalous distribution in summer precipitation and the variation of SST has between studied with the Singular Value Decomposition(SVD) analysis.The increase or decrease of summer precipitation in the Dongting Lake region is closely associated with the SST anomalies in three key regions.The variation of SST in the three key regions has been proved to be a significant previous signal to anomaly of summer rainfall in Dongting region.
文摘The singularly perturbed elliptic equation boundary value problem with turning point is considered. Using the method of multiple scales and the comparison theorem, the asymptotic behavior of solution for the boundary value problem is studied.
文摘A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems is studied.
基金This research was supported by Chinese Academy of Sciences '100 people'project National Natural Science Foundation of China (39970123) and Changbai Mountain Open Research Station.
文摘From 700 m to 1900 m on the northern slope of Changbai Mountain, 13 plots with an interval of 100 m in elevation were investigated to study the variations of population structure and important value of the main edificators along the elevation gradient. In their core distribution areas, most of the edificators had healthy population structure and could regenerate smoothly except Larix olgensis, but important value of Larix olgensis had no obvious variations with elevation changes, which showed that Larix olgensis had its own particularity and strong adaptability. At high elevation above 1800 m, Betula ermanii was the only species that could form a mono-dominant community. Important values of Pinus koraiensis and Acer mono had similar changing trends, and they had the similar ecological adaptabilities.
基金This project is supported by National Natural Science Foundation of China (No.59905011, 60275041).
文摘Vibration acceleration signals are often measured from case surface of arunning machine to monitor its condition. If the measured vibration signals display to have periodicimpulse components with a certain frequency, there may exist a corresponding local fault in themachine, and if further extracting the periodic impulse components from the vibration signals, theseverity of the local fault can be estimated and tracked. However, the signal-to-noise ratios (SNRs)of the vibration acceleration signals are often so small that the periodic impulse components aresubmersed in much background noises and other components, and it is difficult or inconvenient for usto detect and extract the periodic impulse components with the current common analyzing methods forvibration signals. Therefore, another technique, called singular value decomposition (SVD), istried to be introduced to solve the problem. First, the principle of detecting and extracting thesignal periodic components using singular value decomposition is summarized and discussed. Second,the infeasibility of the direct use of the existing SVD based detecting and extracting approach ispointed out. Third, the approach to construct the matrix for SVD from the signal series is improvedlargely, which is the key program to improve the SVD technique; Other associated improvement is alsoproposed. Finally, a simulating application example and a real-life application example ondetecting and extracting the periodic impulse components are given, which showed that the introducedand improved SVD technique is feasible.
文摘This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2, where p is an element of (Graphics) and f is singular at t = 0, t = 1 and u = 0. Under suitable weaker conditions than those of [1], it is proved by constructing a special cone in C[0, 2pi] and employing the fixed point index theory that the problem has at least one or at least two positive solutions.
文摘This paper deals with the existence of positive solutions to the singular boundary value problemwhere q(t) may be singular at t = 0 and t = 1, f(t,y) may be superlinear at y =∞ and singular, at y = 0.
文摘The singularly perturbed nonlinear boundary value problems are considered.Using the stretched variable and the method of boundary layer correction,the formal asymptotic expansion of solution is obtained.And then the uniform validity of solution is proved by using the differential inequalities.
基金supported by the National Natural Science Foundation of China(Grant No.51579207)the Open Foundation of State Key Laboratory Base of Eco-Hydraulic Engineering in Arid Area(Grant No.2016ZZKT-8)the Key Projects of Natural Science Basic Research Program of Shaanxi Province(Grant No.2018JZ5010)
文摘Extracting implicit anomaly information through deformation monitoring data mining is highly significant to determining dam safety status.As an intelligent singular value diagnostic method for concrete dam deformation monitoring, shallow neural network models result in local optima and overfitting, and require manual feature extraction.To obtain an intelligent singular value diagnosis model that can be used for dam safety monitoring, a convolutional neural network (CNN) model that has advantages of deep learning (DL), such as automatic feature extraction, good model fitting, and strong generalizability, was trained in this study.An engineering example shows that the predicted result of the intelligent singular value diagnostic method based on CNN is highly compatible with the confusion matrix, with a precision of 92.41%, receiver operating characteristic (ROC) coordinates of (0.03, 0.97), an area-under-curve (AUC) value of 0.99, and an F1-score of 0.91.Moreover, the performance of the CNN model is better than those of models based on decision tree (DT) and k-nearest neighbor (KNN) methods.Therefore, the intelligent singular value diagnostic method based on CNN is simple to operate, highly intelligent, and highly reliable, and it has a high potential for application in engineering.
文摘The singular value decomposition is derived when the Radon transform is restricted to functions which are square integrable on the unit ball in R-n with respect to the weight W-lambda(x). It fulfilles mainly by means of the projection-slice theorem. The range of the Radon transform is spanned by products of Gegenbauer polynomials and spherical harmonics. The inverse transform of the those basis functions are given. This immediately leads to an inversion formula by series expansion and range characterizations.
基金Supported by the NNSF of China（10901003） Supported by the Natural Science Foundation from the Education Bureau of Anhui Province（KJ2011A135）
文摘The existence and asymptotic behavior of solution for a class of quasilinear singularly perturbed boundary value problems are discussed under suitable conditions by the theory of differential inequalities and matching principle.
基金Supported by the Natural Science Foundation of Zhejiang Provivce (102009)Supported by the Natural Foundation of Huzhou Teacher's College(200302)
文摘In this paper, a class of strongly nonlinear singular perturbed boundary value problems are coasidered by the theory of differential inequalities and the correction of boundary layer, under which the existence of solution is proved and the uniformly valid asymptotic expansions is obtained as well.
基金supported by Science and Technology Research Program of Hubei Provincial Department of Education(T201805)Major Technological Innovation Projects of Hubei(No.2018AAA028)+1 种基金National Natural Science Foundation of China(Grant No.61703201)NSF of Jiangsu Province(BK20170765).
文摘The traditional K-singular value decomposition(K-SVD)algorithm has poor imagedenoising performance under strong noise.An image-denoising algorithm is proposed based on improved K-SVD and dictionary atom optimization.First,a correlation coefficient-matching criterion is used to obtain a sparser representation of the image dictionary.The dictionary noise atom is detected according to structural complexity and noise intensity and removed to optimize the dictionary.Then,non-local regularity is incorporated into the denoising model to further improve image-denoising performance.Results of the simulated dictionary recovery problem and application on a transmission line dataset show that the proposed algorithm improves the smoothness of homogeneous regions while retaining details such as texture and edge.
文摘The singularly perturbed boundary value problem for the nonlinear boundary conditions is considered.Under suitable conditions,the asymptotic behavior of solution for the original problems is studied by using theory of differential inequalities.
