Existing multi-view deep subspace clustering methods aim to learn a unified representation from multi-view data,while the learned representation is difficult to maintain the underlying structure hidden in the origin s...Existing multi-view deep subspace clustering methods aim to learn a unified representation from multi-view data,while the learned representation is difficult to maintain the underlying structure hidden in the origin samples,especially the high-order neighbor relationship between samples.To overcome the above challenges,this paper proposes a novel multi-order neighborhood fusion based multi-view deep subspace clustering model.We creatively integrate the multi-order proximity graph structures of different views into the self-expressive layer by a multi-order neighborhood fusion module.By this design,the multi-order Laplacian matrix supervises the learning of the view-consistent self-representation affinity matrix;then,we can obtain an optimal global affinity matrix where each connected node belongs to one cluster.In addition,the discriminative constraint between views is designed to further improve the clustering performance.A range of experiments on six public datasets demonstrates that the method performs better than other advanced multi-view clustering methods.The code is available at https://github.com/songzuolong/MNF-MDSC(accessed on 25 December 2024).展开更多
In this paper, we apply the Legendre spectral-collocation method to obtain approximate solutions of nonlinear multi-order fractional differential equations (M-FDEs). The fractional derivative is described in the Caput...In this paper, we apply the Legendre spectral-collocation method to obtain approximate solutions of nonlinear multi-order fractional differential equations (M-FDEs). The fractional derivative is described in the Caputo sense. The study is conducted through illustrative example to demonstrate the validity and applicability of the presented method. The results reveal that the proposed method is very effective and simple. Moreover, only a small number of shifted Legendre polynomials are needed to obtain a satisfactory result.展开更多
"Beauty is truth, truth beauty"-the famous line in English romantic poet John Keats'Ode on a Grecian Urn-has triggered wide discussion and numerous interpretations. From the point of"negative capabi..."Beauty is truth, truth beauty"-the famous line in English romantic poet John Keats'Ode on a Grecian Urn-has triggered wide discussion and numerous interpretations. From the point of"negative capability", a phrase first coined by Keats himself, this paper is attempting to display the consistency between that poetic line and the poet's creation and life attitude on the whole. For this purpose, this paper will mainly introduce and interpret five of Keats'famous odes in the order of their display of his"rising acceptance of life": Ode to a Nightingale, Ode on a Grecian Urn, Ode to Autumn, Ode on Melancholy and Ode on Indolence. This paper would like to show in the first three Keats's positive quest in different aspects and on certain levels, the fourth the underlying tone of life's polyphonous song, and the final the"negative capability"that constitutes his healthy attitude toward creation and life. Finally, this paper hopes to demonstrate that it is such capability that enables the poet to growingly accept life, and it is also essential to him as a philosophical poet.展开更多
In this paper, we will present a new method for making first-order systems of nonlinear autonomous ODEs that exhibit limit cycles with a specific geometric shape in two and three dimensions, or systems of ODEs where s...In this paper, we will present a new method for making first-order systems of nonlinear autonomous ODEs that exhibit limit cycles with a specific geometric shape in two and three dimensions, or systems of ODEs where surfaces in three dimensions have attractor behavior. The method is to make the general solutions first by using the exponential function, sine and cosine. We are building up the general solutions bit for bit according to the constant terms that contain the formula of the desired limit cycle, and differentiating them. We will obtain a system of ODEs with the desired behavior. We design the general solutions for a distinct purpose. Using the methods described in this paper, it is possible to make some systems of nonlinear ODEs that are exhibiting limit cycles with a distinct geometric shape in two or three dimensions, and some surfaces having attractor behavior. The pictures show the result.展开更多
In this paper, we build the integral collocation method by using the second shifted Chebyshev polynomials. The numerical method solving the model non-linear such as Riccati differential equation, Logistic differential...In this paper, we build the integral collocation method by using the second shifted Chebyshev polynomials. The numerical method solving the model non-linear such as Riccati differential equation, Logistic differential equation and Multi-order ODEs. The properties of shifted Chebyshev polynomials of the second kind are presented. The finite difference method is used to solve this system of equations. Several numerical examples are provided to confirm the reliability and effectiveness of the proposed method.展开更多
In this paper, a 3rd order combination method with three processes and a 4th order combination method with five processes for solving ODEs are discussed. These methods are the Runge-Kutta method combined with a linear...In this paper, a 3rd order combination method with three processes and a 4th order combination method with five processes for solving ODEs are discussed. These methods are the Runge-Kutta method combined with a linear multistep method, which overcomes the defect of the 3rd order parallel Runge-Kutta method discussed in [1].展开更多
In this paper, we define an exponential function whose exponent is the product of a real number and the upper limit of integration in a non-elementary integral that can be arbitrary. We are using Abel’s methods, desc...In this paper, we define an exponential function whose exponent is the product of a real number and the upper limit of integration in a non-elementary integral that can be arbitrary. We are using Abel’s methods, described by Armitage and Eberlein. The key is to start with a non-elementary integral function, differentiating and inverting, and then define a set of functions. Differentiating these functions twice give second-order nonlinear ODEs that have the defined set of functions as solutions.展开更多
Yinshan anticline is the product of tectono-dynamic deformation - metamorphism .Along the axis of the anticline exists a brittle-ductile shearing zone which obviously controls the ore-formation . Mineralization occurs...Yinshan anticline is the product of tectono-dynamic deformation - metamorphism .Along the axis of the anticline exists a brittle-ductile shearing zone which obviously controls the ore-formation . Mineralization occurs along the axis of the anticline in a width of about 1000m .In the mining area .volcano- subvolcanic rocks of Early Yanshan period are divided into three cycles :Ⅰ intermediate acidic dacite lava and dacite porphyry ;Ⅱ acidic amphibole liparite and quartz porphyry;Ⅲ intermediate andesite porphyrite . Among them activities of ⅠandⅡ cycles are more intensive and are intimately related to the mineralization . Yinshan ore deposit is the result of combinative processes of tectono -dynamic and volcano -magmatic hydrothermal fluids, so that mere are two centers of metallogenic zoning, one being the axial strain zone of Yinshan anticline which is the center of first order, and the other being porphyry stock , 2nd order.展开更多
This paper is presenting a new method for making first-order systems of nonlinear autonomous ODEs that exhibit limit cycles with a specific geometric shape in two and three dimensions, or systems of ODEs where surface...This paper is presenting a new method for making first-order systems of nonlinear autonomous ODEs that exhibit limit cycles with a specific geometric shape in two and three dimensions, or systems of ODEs where surfaces in three dimensions have attractor behavior. The method is to make the general solutions first by using the exponential function, sine, and cosine. We are building up the general solutions bit for bit according to constant terms that contain the formula of the desired limit cycle, and differentiating them. In Part One, we used only formulas for closed curves where all parts of the formula were of the same degree. In order to use many other formulas for closed curves, the method in this paper is to introduce an additional variable, and we will get an additional ODE. We will choose the part of the formula with the highest degree and multiply the other parts with an extra variable, so that all parts of the formula have the same degree, creating a constant term containing this new formula. We will place it under the fraction line in the solutions, building up the rest of the solutions according to this constant term and differentiating. Keeping this extra variable constant, we will achieve almost the desired result. Using the methods described in this paper, it is possible to make some systems of nonlinear ODEs that are exhibiting limit cycles with a distinct geometric shape in two or three dimensions and some surfaces having attractor behavior, where not all parts of the formulas are the same degree. The pictures show the result.展开更多
In this paper, a group of Gauss-Legendre iterative methods with cubic convergence for solving nonlinear systems are proposed. We construct the iterative schemes based on Gauss-Legendre quadrature formula. The cubic co...In this paper, a group of Gauss-Legendre iterative methods with cubic convergence for solving nonlinear systems are proposed. We construct the iterative schemes based on Gauss-Legendre quadrature formula. The cubic convergence and error equation are proved theoretically, and demonstrated numerically. Several numerical examples for solving the system of nonlinear equations and boundary-value problems of nonlinear ordinary differential equations (ODEs) are provided to illustrate the efficiency and performance of the suggested iterative methods.展开更多
The Soote Season and Spring,the sweet Spring are two lyrics that sing the praise of spring.The common feature of the two lyrics is that the two poets depict a series of pictures of the sweet spring by rich and varied ...The Soote Season and Spring,the sweet Spring are two lyrics that sing the praise of spring.The common feature of the two lyrics is that the two poets depict a series of pictures of the sweet spring by rich and varied imagery for readers.When these pictures are presented to readers,readers feel as if they are participating in them,and the enchanting beauty of spring makes readers feel intoxicated with happiness.The two poets express their different feelings toward nature.展开更多
基金supported by the National Key R&D Program of China(2023YFC3304600).
文摘Existing multi-view deep subspace clustering methods aim to learn a unified representation from multi-view data,while the learned representation is difficult to maintain the underlying structure hidden in the origin samples,especially the high-order neighbor relationship between samples.To overcome the above challenges,this paper proposes a novel multi-order neighborhood fusion based multi-view deep subspace clustering model.We creatively integrate the multi-order proximity graph structures of different views into the self-expressive layer by a multi-order neighborhood fusion module.By this design,the multi-order Laplacian matrix supervises the learning of the view-consistent self-representation affinity matrix;then,we can obtain an optimal global affinity matrix where each connected node belongs to one cluster.In addition,the discriminative constraint between views is designed to further improve the clustering performance.A range of experiments on six public datasets demonstrates that the method performs better than other advanced multi-view clustering methods.The code is available at https://github.com/songzuolong/MNF-MDSC(accessed on 25 December 2024).
文摘In this paper, we apply the Legendre spectral-collocation method to obtain approximate solutions of nonlinear multi-order fractional differential equations (M-FDEs). The fractional derivative is described in the Caputo sense. The study is conducted through illustrative example to demonstrate the validity and applicability of the presented method. The results reveal that the proposed method is very effective and simple. Moreover, only a small number of shifted Legendre polynomials are needed to obtain a satisfactory result.
文摘"Beauty is truth, truth beauty"-the famous line in English romantic poet John Keats'Ode on a Grecian Urn-has triggered wide discussion and numerous interpretations. From the point of"negative capability", a phrase first coined by Keats himself, this paper is attempting to display the consistency between that poetic line and the poet's creation and life attitude on the whole. For this purpose, this paper will mainly introduce and interpret five of Keats'famous odes in the order of their display of his"rising acceptance of life": Ode to a Nightingale, Ode on a Grecian Urn, Ode to Autumn, Ode on Melancholy and Ode on Indolence. This paper would like to show in the first three Keats's positive quest in different aspects and on certain levels, the fourth the underlying tone of life's polyphonous song, and the final the"negative capability"that constitutes his healthy attitude toward creation and life. Finally, this paper hopes to demonstrate that it is such capability that enables the poet to growingly accept life, and it is also essential to him as a philosophical poet.
文摘In this paper, we will present a new method for making first-order systems of nonlinear autonomous ODEs that exhibit limit cycles with a specific geometric shape in two and three dimensions, or systems of ODEs where surfaces in three dimensions have attractor behavior. The method is to make the general solutions first by using the exponential function, sine and cosine. We are building up the general solutions bit for bit according to the constant terms that contain the formula of the desired limit cycle, and differentiating them. We will obtain a system of ODEs with the desired behavior. We design the general solutions for a distinct purpose. Using the methods described in this paper, it is possible to make some systems of nonlinear ODEs that are exhibiting limit cycles with a distinct geometric shape in two or three dimensions, and some surfaces having attractor behavior. The pictures show the result.
文摘In this paper, we build the integral collocation method by using the second shifted Chebyshev polynomials. The numerical method solving the model non-linear such as Riccati differential equation, Logistic differential equation and Multi-order ODEs. The properties of shifted Chebyshev polynomials of the second kind are presented. The finite difference method is used to solve this system of equations. Several numerical examples are provided to confirm the reliability and effectiveness of the proposed method.
文摘In this paper, a 3rd order combination method with three processes and a 4th order combination method with five processes for solving ODEs are discussed. These methods are the Runge-Kutta method combined with a linear multistep method, which overcomes the defect of the 3rd order parallel Runge-Kutta method discussed in [1].
文摘In this paper, we define an exponential function whose exponent is the product of a real number and the upper limit of integration in a non-elementary integral that can be arbitrary. We are using Abel’s methods, described by Armitage and Eberlein. The key is to start with a non-elementary integral function, differentiating and inverting, and then define a set of functions. Differentiating these functions twice give second-order nonlinear ODEs that have the defined set of functions as solutions.
文摘Yinshan anticline is the product of tectono-dynamic deformation - metamorphism .Along the axis of the anticline exists a brittle-ductile shearing zone which obviously controls the ore-formation . Mineralization occurs along the axis of the anticline in a width of about 1000m .In the mining area .volcano- subvolcanic rocks of Early Yanshan period are divided into three cycles :Ⅰ intermediate acidic dacite lava and dacite porphyry ;Ⅱ acidic amphibole liparite and quartz porphyry;Ⅲ intermediate andesite porphyrite . Among them activities of ⅠandⅡ cycles are more intensive and are intimately related to the mineralization . Yinshan ore deposit is the result of combinative processes of tectono -dynamic and volcano -magmatic hydrothermal fluids, so that mere are two centers of metallogenic zoning, one being the axial strain zone of Yinshan anticline which is the center of first order, and the other being porphyry stock , 2nd order.
文摘This paper is presenting a new method for making first-order systems of nonlinear autonomous ODEs that exhibit limit cycles with a specific geometric shape in two and three dimensions, or systems of ODEs where surfaces in three dimensions have attractor behavior. The method is to make the general solutions first by using the exponential function, sine, and cosine. We are building up the general solutions bit for bit according to constant terms that contain the formula of the desired limit cycle, and differentiating them. In Part One, we used only formulas for closed curves where all parts of the formula were of the same degree. In order to use many other formulas for closed curves, the method in this paper is to introduce an additional variable, and we will get an additional ODE. We will choose the part of the formula with the highest degree and multiply the other parts with an extra variable, so that all parts of the formula have the same degree, creating a constant term containing this new formula. We will place it under the fraction line in the solutions, building up the rest of the solutions according to this constant term and differentiating. Keeping this extra variable constant, we will achieve almost the desired result. Using the methods described in this paper, it is possible to make some systems of nonlinear ODEs that are exhibiting limit cycles with a distinct geometric shape in two or three dimensions and some surfaces having attractor behavior, where not all parts of the formulas are the same degree. The pictures show the result.
文摘In this paper, a group of Gauss-Legendre iterative methods with cubic convergence for solving nonlinear systems are proposed. We construct the iterative schemes based on Gauss-Legendre quadrature formula. The cubic convergence and error equation are proved theoretically, and demonstrated numerically. Several numerical examples for solving the system of nonlinear equations and boundary-value problems of nonlinear ordinary differential equations (ODEs) are provided to illustrate the efficiency and performance of the suggested iterative methods.
文摘The Soote Season and Spring,the sweet Spring are two lyrics that sing the praise of spring.The common feature of the two lyrics is that the two poets depict a series of pictures of the sweet spring by rich and varied imagery for readers.When these pictures are presented to readers,readers feel as if they are participating in them,and the enchanting beauty of spring makes readers feel intoxicated with happiness.The two poets express their different feelings toward nature.
