In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. B...In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. By the criterion algorithm, the global controllability can be determined in finite steps of arithmetic operations. The algorithm is imposed on the coefficients of the polynomials only and the analysis technique is based on Sturm Theorem in real algebraic geometry and its modern progress. Finally, the authors will give some examples to show the application of our results.展开更多
As per Hawking and Bekenstein’s work on black holes, information resides on the surface and there is a limit on it amounting to a bit for every Planck area. It would seem therefore that extra dimensions would logical...As per Hawking and Bekenstein’s work on black holes, information resides on the surface and there is a limit on it amounting to a bit for every Planck area. It would seem therefore that extra dimensions would logically lead to a hyper-surface for a black hole and consequently a reduction of the corresponding information density due to the dilution effect of these additional dimensions. The present paper argues that the counterintuitive opposite of the above is what should be expected. This surprising result is a consequence of a well known theorem on measure concentration due to I. Dvoretzky.展开更多
In this article, I consider the right triangle as the simplex in the Euclidean plane, and extend this definition to higher dimensions. The n-dimensional simplex has one hypotenuse and (n−1)legs (catheti). The (n−1)leg...In this article, I consider the right triangle as the simplex in the Euclidean plane, and extend this definition to higher dimensions. The n-dimensional simplex has one hypotenuse and (n−1)legs (catheti). The (n−1)legs define an orthogonal path of edges in the solid with perpendicular adjacent edges along the path. The length of the hypotenuse and the volume of the solid can be calculated without the Cayley-Menger determinant, by direct extension of the corresponding right triangle formulas. I give a proof of the existence of these shapes, describe the distribution of right angles in them, give an algebraic proof of the Coxeter trisection of a right tetrahedron into three smaller right tetrahedra, and generalize this construction to n-dimensional spaces. Finally, I investigate the connection between the Coxeter partition and the Hadwiger conjecture on the partition of the simplex into orthoschemes, which I call Pythagorean simplexes.展开更多
This paper proposes one method of feature selection by using Bayes＇ theorem. The purpose of the proposed method is to reduce the computational complexity and increase the classification accuracy of the selected featu...This paper proposes one method of feature selection by using Bayes＇ theorem. The purpose of the proposed method is to reduce the computational complexity and increase the classification accuracy of the selected feature subsets. The dependence between two attributes （binary） is determined based on the probabilities of their joint values that contribute to positive and negative classification decisions. If opposing sets of attribute values do not lead to opposing classification decisions （zero probability）, then the two attributes are considered independent of each other, otherwise dependent, and one of them can be removed and thus the number of attributes is reduced. The process must be repeated on all combinations of attributes. The paper also evaluates the approach by comparing it with existing feature selection algorithms over 8 datasets from University of California, Irvine （UCI） machine learning databases. The proposed method shows better results in terms of number of selected features, classification accuracy, and running time than most existing algorithms.展开更多
This paper deals with the bending problem of rectangular plates with two opposite edges simply supported. It is proved that there exists no normed symplectic orthogonal eigenfunction system for the associated infinite...This paper deals with the bending problem of rectangular plates with two opposite edges simply supported. It is proved that there exists no normed symplectic orthogonal eigenfunction system for the associated infinite-dimensional Hamiltonian operator H and that the two block operators belonging to Hamiltonian operator H possess two normed symplectic orthogonal eigenfunction systems in some space. It is demonstrated by using the properties of the block operators that the above bending problem can be solved by the symplectic eigenfunction expansion theorem, thereby obtaining analytical solutions of rectangular plates with two opposite edges simply supported and the other two edges supported in any manner.展开更多
This paper presents a formulation for solving three-dimensional moving punch problem. It proves that Galin's theorem holds for the punch. As an example, the study offers some results (including numerical data) of ...This paper presents a formulation for solving three-dimensional moving punch problem. It proves that Galin's theorem holds for the punch. As an example, the study offers some results (including numerical data) of dynamic displacement over an ellipse contact region.展开更多
Let k be a commutative ring with finite weak dimension and let G be a group. In this paper, we explore the criterion that a group G has finite Gorenstein homological dimension.It is shown that the finiteness of the Go...Let k be a commutative ring with finite weak dimension and let G be a group. In this paper, we explore the criterion that a group G has finite Gorenstein homological dimension.It is shown that the finiteness of the Gorenstein homological dimension of G coincides with the finiteness of the Gorenstein weak dimension of the group ring kG. Furthermore, we give a Gorenstein analogy of the Serre's theorem. Some well-known results for the Gorenstein homological dimension of G over the integer ring are also extended.展开更多
Some related problems of two n-dimensional simplices which are on an(n- 1)-dimensional hypersphere are investigated and a sine theorem of the k-dimensional mixed vertex angles which are defined in this paper is given....Some related problems of two n-dimensional simplices which are on an(n- 1)-dimensional hypersphere are investigated and a sine theorem of the k-dimensional mixed vertex angles which are defined in this paper is given. This result is a generalization of the sine theorem established. By using the generalized sine theorem, we present some new interesting geometric inequalities involving the k-dimensional vertex angles of each n-simplex and the k-dimensional mixed vertex angle of two n-simplices. These results can improve some recent results.展开更多
A time-harmonic plane acoustic wave is scattered by a piecewise homogeneous obstacle with a penetrable or impenetrable core. We construct in the close form an integral representation for the far field pattern in which...A time-harmonic plane acoustic wave is scattered by a piecewise homogeneous obstacle with a penetrable or impenetrable core. We construct in the close form an integral representation for the far field pattern in which we have incorporated the physical and geometrical characteristics of the scatterer. Through this representation, we obtain the far field pattern for this scatterer. We prove scattering relations between the far field patterns of two scattering problems due to two distinct incident waves on the same scatterer. In particular, we prove reciprocity and general scattering theorems. The optical theorem, connecting the total power that the scatterer extracts from the incident plane wave either by radiation or by absorption with the corresponding far field pattern of an incident plane wave, is recovered as a corollary of the general scattering theorem. Moreover, if we consider incident waves to be both a plane and a spherical, we derive a mixed reciprocity theorem. We define the corresponding far field operators and using these relations, we prove some properties that can be used for solving inverse scattering problems.展开更多
In this paper. based on large deviation formulas established in stronger topology generated by Hlder norm, we obtain the functional limit theorems for C-R increments of k-dimensional Brownian motion in Hlder norm
In this paper, we obtain functional limit theorems for d-dimensional FBM in HSlder norm via estimating large deviation probabilities for d-dimensional FBM in HSlder norm.
Let X be the solution of the SDE:dX_t=σ(X_t)dB_t+b(X_t)dt,with σ and b ∈C_B~∞(R) such that σ≥λ>0 for some constant λ,and B a real Brownian motion.Let μ be the law of X on E=C([0,1],R)and k ∈E~*-{0},where ...Let X be the solution of the SDE:dX_t=σ(X_t)dB_t+b(X_t)dt,with σ and b ∈C_B~∞(R) such that σ≥λ>0 for some constant λ,and B a real Brownian motion.Let μ be the law of X on E=C([0,1],R)and k ∈E~*-{0},where E~* is the topological dual space of E.Consider the classical form:where u and v are smooth functions on E.We prove that,if is closable for any k in a dense subset of E~* and if the smooth functions are contained in the domain of the generator of the closure of ε_k,σ must be a constant function.展开更多
Thek-dimensional Piatetski-Shapiro prime number problem fork?3 is studied. Let π(x 1 c 1,?,c k ) denote the number of primesp withp?x, $p = [n_1^{c_1 } ] = \cdots [n_k^{c_k } ]$ , where 1<c 1<?<c k are fixed...Thek-dimensional Piatetski-Shapiro prime number problem fork?3 is studied. Let π(x 1 c 1,?,c k ) denote the number of primesp withp?x, $p = [n_1^{c_1 } ] = \cdots [n_k^{c_k } ]$ , where 1<c 1<?<c k are fixed constants. It is proved that π(x;c 1,?,c k ) has an asymptotic formula ifc 1 ?1 +?+c k ?1 >k?k/(4k 2+2).展开更多
基金supported by the Natural Science Foundation of China under Grant Nos.60804008,61174048and 11071263the Fundamental Research Funds for the Central Universities and Guangdong Province Key Laboratory of Computational Science at Sun Yat-Sen University
文摘In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. By the criterion algorithm, the global controllability can be determined in finite steps of arithmetic operations. The algorithm is imposed on the coefficients of the polynomials only and the analysis technique is based on Sturm Theorem in real algebraic geometry and its modern progress. Finally, the authors will give some examples to show the application of our results.
文摘As per Hawking and Bekenstein’s work on black holes, information resides on the surface and there is a limit on it amounting to a bit for every Planck area. It would seem therefore that extra dimensions would logically lead to a hyper-surface for a black hole and consequently a reduction of the corresponding information density due to the dilution effect of these additional dimensions. The present paper argues that the counterintuitive opposite of the above is what should be expected. This surprising result is a consequence of a well known theorem on measure concentration due to I. Dvoretzky.
文摘In this article, I consider the right triangle as the simplex in the Euclidean plane, and extend this definition to higher dimensions. The n-dimensional simplex has one hypotenuse and (n−1)legs (catheti). The (n−1)legs define an orthogonal path of edges in the solid with perpendicular adjacent edges along the path. The length of the hypotenuse and the volume of the solid can be calculated without the Cayley-Menger determinant, by direct extension of the corresponding right triangle formulas. I give a proof of the existence of these shapes, describe the distribution of right angles in them, give an algebraic proof of the Coxeter trisection of a right tetrahedron into three smaller right tetrahedra, and generalize this construction to n-dimensional spaces. Finally, I investigate the connection between the Coxeter partition and the Hadwiger conjecture on the partition of the simplex into orthoschemes, which I call Pythagorean simplexes.
文摘This paper proposes one method of feature selection by using Bayes＇ theorem. The purpose of the proposed method is to reduce the computational complexity and increase the classification accuracy of the selected feature subsets. The dependence between two attributes （binary） is determined based on the probabilities of their joint values that contribute to positive and negative classification decisions. If opposing sets of attribute values do not lead to opposing classification decisions （zero probability）, then the two attributes are considered independent of each other, otherwise dependent, and one of them can be removed and thus the number of attributes is reduced. The process must be repeated on all combinations of attributes. The paper also evaluates the approach by comparing it with existing feature selection algorithms over 8 datasets from University of California, Irvine （UCI） machine learning databases. The proposed method shows better results in terms of number of selected features, classification accuracy, and running time than most existing algorithms.
基金supported by the National Natural Science Foundation of China(Grant No 10562002)the Natural Science Foundation of Inner Mongolia,China(Grants No 200508010103 and 200711020106)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No 20070126002)
文摘This paper deals with the bending problem of rectangular plates with two opposite edges simply supported. It is proved that there exists no normed symplectic orthogonal eigenfunction system for the associated infinite-dimensional Hamiltonian operator H and that the two block operators belonging to Hamiltonian operator H possess two normed symplectic orthogonal eigenfunction systems in some space. It is demonstrated by using the properties of the block operators that the above bending problem can be solved by the symplectic eigenfunction expansion theorem, thereby obtaining analytical solutions of rectangular plates with two opposite edges simply supported and the other two edges supported in any manner.
文摘This paper presents a formulation for solving three-dimensional moving punch problem. It proves that Galin's theorem holds for the punch. As an example, the study offers some results (including numerical data) of dynamic displacement over an ellipse contact region.
基金Supported by the Natural Science Foundation of Hunan Province (Grant No. 2021JJ30536)the Scientific Research Foundation of Hunan Provincial Education Department (Grant No. 21A0493)。
文摘Let k be a commutative ring with finite weak dimension and let G be a group. In this paper, we explore the criterion that a group G has finite Gorenstein homological dimension.It is shown that the finiteness of the Gorenstein homological dimension of G coincides with the finiteness of the Gorenstein weak dimension of the group ring kG. Furthermore, we give a Gorenstein analogy of the Serre's theorem. Some well-known results for the Gorenstein homological dimension of G over the integer ring are also extended.
基金Supported by the Doctoral Programs Foundation of Education Ministry of China（2011 3401110009） Supported by the Universities Natural Science Foundation of Anhui Province（KJ2013A220） Supported by the Natural Science Research Project of Hefei Normal University（2012kj11）
文摘Some related problems of two n-dimensional simplices which are on an(n- 1)-dimensional hypersphere are investigated and a sine theorem of the k-dimensional mixed vertex angles which are defined in this paper is given. This result is a generalization of the sine theorem established. By using the generalized sine theorem, we present some new interesting geometric inequalities involving the k-dimensional vertex angles of each n-simplex and the k-dimensional mixed vertex angle of two n-simplices. These results can improve some recent results.
文摘A time-harmonic plane acoustic wave is scattered by a piecewise homogeneous obstacle with a penetrable or impenetrable core. We construct in the close form an integral representation for the far field pattern in which we have incorporated the physical and geometrical characteristics of the scatterer. Through this representation, we obtain the far field pattern for this scatterer. We prove scattering relations between the far field patterns of two scattering problems due to two distinct incident waves on the same scatterer. In particular, we prove reciprocity and general scattering theorems. The optical theorem, connecting the total power that the scatterer extracts from the incident plane wave either by radiation or by absorption with the corresponding far field pattern of an incident plane wave, is recovered as a corollary of the general scattering theorem. Moreover, if we consider incident waves to be both a plane and a spherical, we derive a mixed reciprocity theorem. We define the corresponding far field operators and using these relations, we prove some properties that can be used for solving inverse scattering problems.
文摘In this paper. based on large deviation formulas established in stronger topology generated by Hlder norm, we obtain the functional limit theorems for C-R increments of k-dimensional Brownian motion in Hlder norm
基金1)This work is supported by NSFC(10571159),SRFDP(2002335090)and KRF(D00008)2)This work is supported by NSFC(10401037)and China Postdoctoral Science Foundation3)This work is supported by the Brain Korea 21 Project in 2005
文摘In this paper, we obtain functional limit theorems for d-dimensional FBM in HSlder norm via estimating large deviation probabilities for d-dimensional FBM in HSlder norm.
文摘Let X be the solution of the SDE:dX_t=σ(X_t)dB_t+b(X_t)dt,with σ and b ∈C_B~∞(R) such that σ≥λ>0 for some constant λ,and B a real Brownian motion.Let μ be the law of X on E=C([0,1],R)and k ∈E~*-{0},where E~* is the topological dual space of E.Consider the classical form:where u and v are smooth functions on E.We prove that,if is closable for any k in a dense subset of E~* and if the smooth functions are contained in the domain of the generator of the closure of ε_k,σ must be a constant function.
基金Project supported by the National Natural Science Foundation of China (Grant No. 19801021)the Natural Science Foundation of Shandong Province (Grant No. Q98A02110).
文摘Thek-dimensional Piatetski-Shapiro prime number problem fork?3 is studied. Let π(x 1 c 1,?,c k ) denote the number of primesp withp?x, $p = [n_1^{c_1 } ] = \cdots [n_k^{c_k } ]$ , where 1<c 1<?<c k are fixed constants. It is proved that π(x;c 1,?,c k ) has an asymptotic formula ifc 1 ?1 +?+c k ?1 >k?k/(4k 2+2).
