In this paper,some kinds of singular integral equations of convolution type with reflection and translation shift are discussed and they are turned into Riemann boundary value problems with both discontinuous coeffici...In this paper,some kinds of singular integral equations of convolution type with reflection and translation shift are discussed and they are turned into Riemann boundary value problems with both discontinuous coefficients and reflection by using the Fourier transform.In spite of the classical method for solution,we are to give another method,therefore the general solution and condition of solvability are obtained in class{0}.展开更多
In this paper, some approximation formulae for a class of convolution type double singular integral operators depending on three parameters of the type(T_λf)(x, y) = ∫_a^b ∫_a^b f(t, s)K_λ(t-x,s-y)dsdt, x,y ∈(a,...In this paper, some approximation formulae for a class of convolution type double singular integral operators depending on three parameters of the type(T_λf)(x, y) = ∫_a^b ∫_a^b f(t, s)K_λ(t-x,s-y)dsdt, x,y ∈(a,b), λ ∈ Λ [0,∞),(0.1)are given. Here f belongs to the function space L_1( <a,b >~2), where <a,b> is an arbitrary interval in R. In this paper three theorems are proved, one for existence of the operator(T_λf)(x, y) and the others for its Fatou-type pointwise convergence to f(x_0, y_0), as(x,y,λ) tends to(x_0, y_0, λ_0). In contrast to previous works, the kernel functions K_λ(u,v)don't have to be 2π-periodic, positive, even and radial. Our results improve and extend some of the previous results of [1, 6, 8, 10, 11, 13] in three dimensional frame and especially the very recent paper [15].展开更多
In this paper, we propose and discuss a class of singular integral equation of convolution type with csc(τ- θ) kernel in class L2[-π, π]. Using discrete Fourier transform and the lemma, this kind of equations is t...In this paper, we propose and discuss a class of singular integral equation of convolution type with csc(τ- θ) kernel in class L2[-π, π]. Using discrete Fourier transform and the lemma, this kind of equations is transformed to discrete system of equations, and then we obtain the solvable conditions and the explicit solutions in class L2[-π, π].展开更多
For the existing aspect category sentiment analysis research,most of the aspects are given for sentiment extraction,and this pipeline method is prone to error accumulation,and the use of graph convolutional neural net...For the existing aspect category sentiment analysis research,most of the aspects are given for sentiment extraction,and this pipeline method is prone to error accumulation,and the use of graph convolutional neural network for aspect category sentiment analysis does not fully utilize the dependency type information between words,so it cannot enhance feature extraction.This paper proposes an end-to-end aspect category sentiment analysis(ETESA)model based on type graph convolutional networks.The model uses the bidirectional encoder representation from transformers(BERT)pretraining model to obtain aspect categories and word vectors containing contextual dynamic semantic information,which can solve the problem of polysemy;when using graph convolutional network(GCN)for feature extraction,the fusion operation of word vectors and initialization tensor of dependency types can obtain the importance values of different dependency types and enhance the text feature representation;by transforming aspect category and sentiment pair extraction into multiple single-label classification problems,aspect category and sentiment can be extracted simultaneously in an end-to-end way and solve the problem of error accumulation.Experiments are tested on three public datasets,and the results show that the ETESA model can achieve higher Precision,Recall and F1 value,proving the effectiveness of the model.展开更多
In this paper, two kinds of convolution integral equations with both Cauchy kernel and reflection are discussed. Using Fourier transformation theory they can be transformed into Riemann boundary value problems with bo...In this paper, two kinds of convolution integral equations with both Cauchy kernel and reflection are discussed. Using Fourier transformation theory they can be transformed into Riemann boundary value problems with both discontinuous coefficients and reflection. And we give a new method, by which the general solution and the condition of solvability are obtained respectively.展开更多
基金Supported by the Qufu Normal University Youth Fund(XJ201218)
文摘In this paper,some kinds of singular integral equations of convolution type with reflection and translation shift are discussed and they are turned into Riemann boundary value problems with both discontinuous coefficients and reflection by using the Fourier transform.In spite of the classical method for solution,we are to give another method,therefore the general solution and condition of solvability are obtained in class{0}.
文摘In this paper, some approximation formulae for a class of convolution type double singular integral operators depending on three parameters of the type(T_λf)(x, y) = ∫_a^b ∫_a^b f(t, s)K_λ(t-x,s-y)dsdt, x,y ∈(a,b), λ ∈ Λ [0,∞),(0.1)are given. Here f belongs to the function space L_1( <a,b >~2), where <a,b> is an arbitrary interval in R. In this paper three theorems are proved, one for existence of the operator(T_λf)(x, y) and the others for its Fatou-type pointwise convergence to f(x_0, y_0), as(x,y,λ) tends to(x_0, y_0, λ_0). In contrast to previous works, the kernel functions K_λ(u,v)don't have to be 2π-periodic, positive, even and radial. Our results improve and extend some of the previous results of [1, 6, 8, 10, 11, 13] in three dimensional frame and especially the very recent paper [15].
基金Supported by the Qufu Normal University Youth Fund(XJ201218)
文摘In this paper, we propose and discuss a class of singular integral equation of convolution type with csc(τ- θ) kernel in class L2[-π, π]. Using discrete Fourier transform and the lemma, this kind of equations is transformed to discrete system of equations, and then we obtain the solvable conditions and the explicit solutions in class L2[-π, π].
基金Supported by the National Key Research and Development Program of China(No.2018YFB1702601).
文摘For the existing aspect category sentiment analysis research,most of the aspects are given for sentiment extraction,and this pipeline method is prone to error accumulation,and the use of graph convolutional neural network for aspect category sentiment analysis does not fully utilize the dependency type information between words,so it cannot enhance feature extraction.This paper proposes an end-to-end aspect category sentiment analysis(ETESA)model based on type graph convolutional networks.The model uses the bidirectional encoder representation from transformers(BERT)pretraining model to obtain aspect categories and word vectors containing contextual dynamic semantic information,which can solve the problem of polysemy;when using graph convolutional network(GCN)for feature extraction,the fusion operation of word vectors and initialization tensor of dependency types can obtain the importance values of different dependency types and enhance the text feature representation;by transforming aspect category and sentiment pair extraction into multiple single-label classification problems,aspect category and sentiment can be extracted simultaneously in an end-to-end way and solve the problem of error accumulation.Experiments are tested on three public datasets,and the results show that the ETESA model can achieve higher Precision,Recall and F1 value,proving the effectiveness of the model.
文摘In this paper, two kinds of convolution integral equations with both Cauchy kernel and reflection are discussed. Using Fourier transformation theory they can be transformed into Riemann boundary value problems with both discontinuous coefficients and reflection. And we give a new method, by which the general solution and the condition of solvability are obtained respectively.
