Recently clustering techniques have been used to automatically discover typical user profiles. In general, it is a challenging problem to design effective similarity measure between the session vectors which are usual...Recently clustering techniques have been used to automatically discover typical user profiles. In general, it is a challenging problem to design effective similarity measure between the session vectors which are usually high-dimensional and sparse. Two approaches for mining typical user profiles, based on matrix dimensionality reduction, are presented. In these approaches, non-negative matrix factorization is applied to reduce dimensionality of the session-URL matrix, and the projecting vectors of the user-session vectors are clustered into typical user-session profiles using the spherical k -means algorithm. The results show that two algorithms are successful in mining many typical user profiles in the user sessions.展开更多
An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local ...An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local model. Thus, the stability analysis method of the homogeneous fuzzy system can be used for reference. Stability conditions are derived in terms of linear matrix inequalities based on the fuzzy Lyapunov functions and the modified common Lyapunov functions, respectively. The results demonstrate that the stability result based on the fuzzy Lyapunov functions is less conservative than that based on the modified common Lyapunov functions via numerical examples. Compared with the method which does not expand the consequent part, the proposed method is simpler but its feasible region is reduced. Finally, in order to expand the application of the fuzzy Lyapunov functions, the piecewise fuzzy Lyapunov function is proposed, which can be used to analyze the stability for triangular or trapezoidal membership functions and obtain the stability conditions. A numerical example validates the effectiveness of the proposed approach.展开更多
It is a main form using the main beamwidth of the ambiguity function to judge the signal resolution, in which the range or Doppler resolution of the signals are investigated for the targets close to each other. Howeve...It is a main form using the main beamwidth of the ambiguity function to judge the signal resolution, in which the range or Doppler resolution of the signals are investigated for the targets close to each other. However, for the pulse signal with rectangular envelope, if the nominal range resolution is calculated from the classic definition, there exists the problem of infinite integral for the high power terms of sine function, and a definite result could not be obtained. Though a definite solution of the nominal velocity resolution can be calculated from the definition, the calculation for the signal consisting of multiple-pulse, especially several periods, is very complex. The paper begins with the physical meaning of nominal resolution rather than from the definition formula to solve the problem using the ambiguity matrix, and make the calculation simplified greatly.展开更多
The upper triangular matrix of Lie algebra is used to construct integrable couplings of discrete solition equations. Correspondingly, a feasible way to construct integrable couplings is presented. A nonlinear lattice ...The upper triangular matrix of Lie algebra is used to construct integrable couplings of discrete solition equations. Correspondingly, a feasible way to construct integrable couplings is presented. A nonlinear lattice soliton equation spectral problem is obtained and leads to a novel hierarchy of the nonlinear lattice equation hierarchy. It indicates that the study of integrable couplings using upper triangular matrix of Lie algebra is an important step towards constructing integrable systems.展开更多
This paper focuses graph theory method for the problem of decomposition w.r.t. outputs for Boolean control networks(BCNs). First, by resorting to the semi-tensor product of matrices and the matrix expression of BCNs, ...This paper focuses graph theory method for the problem of decomposition w.r.t. outputs for Boolean control networks(BCNs). First, by resorting to the semi-tensor product of matrices and the matrix expression of BCNs, the definition of decomposition w.r.t. outputs is introduced. Second, by referring to the graphical structure of BCNs, a necessary and sufficient condition for the decomposition w.r.t. outputs is obtained based on graph theory method. Third, an effective algorithm to realize the maximum decomposition w.r.t. outputs is proposed. Finally, some examples are addressed to validate the theoretical results.展开更多
This paper aims at developing a "local-global" approach for various types of finite dimensional algebras, especially those related to Hecke algebras. The eventual intention is to apply the methods and applic...This paper aims at developing a "local-global" approach for various types of finite dimensional algebras, especially those related to Hecke algebras. The eventual intention is to apply the methods and applications developed here to the cross-characteristic representation theory of finite groups of Lie type. We first review the notions of quasi-hereditary and stratified algebras over a Noetherian commutative ring. We prove that many global properties of these algebras hold if and only if they hold locally at every prime ideal. When the commutative ring is sufficiently good, it is often sufficient to check just the prime ideals of height at most one. These methods are applied to construct certain generalized q-Schur algebras, proving they are often quasi-hereditary(the "good" prime case) but always stratified. Finally, these results are used to prove a triangular decomposition matrix theorem for the modular representations of Hecke algebras at good primes. In the bad prime case, the generalized q-Schur algebras are at least stratified, and a block triangular analogue of the good prime case is proved, where the blocks correspond to Kazhdan-Lusztig cells.展开更多
The cascade algorithm plays an important role in computer graphics and wavelet analysis.In this paper,we first investigate the convergence of cascade algorithms associated with a polynomially decaying mask and a gener...The cascade algorithm plays an important role in computer graphics and wavelet analysis.In this paper,we first investigate the convergence of cascade algorithms associated with a polynomially decaying mask and a general dilation matrix in L p (R s) (1 p ∞) spaces,and then we give an error estimate of the cascade algorithms associated with truncated masks.It is proved that under some appropriate conditions if the cascade algorithm associated with a polynomially decaying mask converges in the L p-norm,then the cascade algorithms associated with the truncated masks also converge in the L p-norm.Moreover,the error between the two resulting limit functions is estimated in terms of the masks.展开更多
In the framework of the NRQCD factorization formalism,we calculate the decay rate for the process Υ(1 S) → ccgg to the next-to-leading order(NLO) in the relative velocity v of the b quark in the bottomonium rest fra...In the framework of the NRQCD factorization formalism,we calculate the decay rate for the process Υ(1 S) → ccgg to the next-to-leading order(NLO) in the relative velocity v of the b quark in the bottomonium rest frame.We also study the momentum distributions of the charm quark and the charmed-hadron in the decay.The momentum distribution of the charmed-hadron is obtained by convolving the charm quark momentum distribution with a fragmentation function of the charm quark into the hadron.In addition,we fit the nonperturbative NRQCD matrix element v 2 Υ through comparing the theoretical prediction with the measurement from the BaBar collaboration for the decay rate of Υ(1 S) → D + X.In return,taking this matrix element as an input parameter,we predict the decay rates as well as the momentum distributions for a collection of charmed-hadrons in the process Υ(1S) → ccgg → hX.展开更多
We are concerned with the problem of characterizing the distribution of the maximum number of individuals alive during a fixed time interval in host-parasitoid models, which is shown to have a matrix exponential form....We are concerned with the problem of characterizing the distribution of the maximum number of individuals alive during a fixed time interval in host-parasitoid models, which is shown to have a matrix exponential form. We present simple conditions on the rates of change of population sizes for the matrix exponential solution to be explicit or algo- rithmically tractable. A particularly appealing feature of our solution based on splitting methods is that it allows us to obtain global error control.展开更多
文摘Recently clustering techniques have been used to automatically discover typical user profiles. In general, it is a challenging problem to design effective similarity measure between the session vectors which are usually high-dimensional and sparse. Two approaches for mining typical user profiles, based on matrix dimensionality reduction, are presented. In these approaches, non-negative matrix factorization is applied to reduce dimensionality of the session-URL matrix, and the projecting vectors of the user-session vectors are clustered into typical user-session profiles using the spherical k -means algorithm. The results show that two algorithms are successful in mining many typical user profiles in the user sessions.
基金Specialized Research Fund for the Doctoral Program of Higher Education ( No. 20090092110051)the Key Project of Chinese Ministry of Education ( No. 108060)the National Natural Science Foundation of China ( No. 51076027, 51036002, 51106024)
文摘An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local model. Thus, the stability analysis method of the homogeneous fuzzy system can be used for reference. Stability conditions are derived in terms of linear matrix inequalities based on the fuzzy Lyapunov functions and the modified common Lyapunov functions, respectively. The results demonstrate that the stability result based on the fuzzy Lyapunov functions is less conservative than that based on the modified common Lyapunov functions via numerical examples. Compared with the method which does not expand the consequent part, the proposed method is simpler but its feasible region is reduced. Finally, in order to expand the application of the fuzzy Lyapunov functions, the piecewise fuzzy Lyapunov function is proposed, which can be used to analyze the stability for triangular or trapezoidal membership functions and obtain the stability conditions. A numerical example validates the effectiveness of the proposed approach.
基金Supported by the National Natural Science Foundation of China(No.60232010)
文摘It is a main form using the main beamwidth of the ambiguity function to judge the signal resolution, in which the range or Doppler resolution of the signals are investigated for the targets close to each other. However, for the pulse signal with rectangular envelope, if the nominal range resolution is calculated from the classic definition, there exists the problem of infinite integral for the high power terms of sine function, and a definite result could not be obtained. Though a definite solution of the nominal velocity resolution can be calculated from the definition, the calculation for the signal consisting of multiple-pulse, especially several periods, is very complex. The paper begins with the physical meaning of nominal resolution rather than from the definition formula to solve the problem using the ambiguity matrix, and make the calculation simplified greatly.
基金＊The project supported by the National Key Basic Research Development of China under Grant No. N1998030600 and National Natural Science Foundation of China under Grant No. 10072013
文摘The upper triangular matrix of Lie algebra is used to construct integrable couplings of discrete solition equations. Correspondingly, a feasible way to construct integrable couplings is presented. A nonlinear lattice soliton equation spectral problem is obtained and leads to a novel hierarchy of the nonlinear lattice equation hierarchy. It indicates that the study of integrable couplings using upper triangular matrix of Lie algebra is an important step towards constructing integrable systems.
基金supported in part by the National Natural Science Foundation of China under Grant Nos.61673012,11271194a Project on the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)
文摘This paper focuses graph theory method for the problem of decomposition w.r.t. outputs for Boolean control networks(BCNs). First, by resorting to the semi-tensor product of matrices and the matrix expression of BCNs, the definition of decomposition w.r.t. outputs is introduced. Second, by referring to the graphical structure of BCNs, a necessary and sufficient condition for the decomposition w.r.t. outputs is obtained based on graph theory method. Third, an effective algorithm to realize the maximum decomposition w.r.t. outputs is proposed. Finally, some examples are addressed to validate the theoretical results.
基金supported by a 2017 University of New South Wales Science Goldstar Grant(Jie Du)the Simons Foundation(Grant Nos. #359360(Brian Parshall) and #359363 (Leonard Scott))
文摘This paper aims at developing a "local-global" approach for various types of finite dimensional algebras, especially those related to Hecke algebras. The eventual intention is to apply the methods and applications developed here to the cross-characteristic representation theory of finite groups of Lie type. We first review the notions of quasi-hereditary and stratified algebras over a Noetherian commutative ring. We prove that many global properties of these algebras hold if and only if they hold locally at every prime ideal. When the commutative ring is sufficiently good, it is often sufficient to check just the prime ideals of height at most one. These methods are applied to construct certain generalized q-Schur algebras, proving they are often quasi-hereditary(the "good" prime case) but always stratified. Finally, these results are used to prove a triangular decomposition matrix theorem for the modular representations of Hecke algebras at good primes. In the bad prime case, the generalized q-Schur algebras are at least stratified, and a block triangular analogue of the good prime case is proved, where the blocks correspond to Kazhdan-Lusztig cells.
基金supported by National Natural Science Foundation of China (GrantNos. 11101120,11001247)the Natural Science Foundation of Hohai University (Grant No. 2011B10714)+1 种基金supported by National Natural Science Foundation of China (Grant Nos. 11171299,10971189)the Natural Science Foundation of Zhejiang Province of China (Grant No. Y6090091)
文摘The cascade algorithm plays an important role in computer graphics and wavelet analysis.In this paper,we first investigate the convergence of cascade algorithms associated with a polynomially decaying mask and a general dilation matrix in L p (R s) (1 p ∞) spaces,and then we give an error estimate of the cascade algorithms associated with truncated masks.It is proved that under some appropriate conditions if the cascade algorithm associated with a polynomially decaying mask converges in the L p-norm,then the cascade algorithms associated with the truncated masks also converge in the L p-norm.Moreover,the error between the two resulting limit functions is estimated in terms of the masks.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10875130,10935012,and 10875156
文摘In the framework of the NRQCD factorization formalism,we calculate the decay rate for the process Υ(1 S) → ccgg to the next-to-leading order(NLO) in the relative velocity v of the b quark in the bottomonium rest frame.We also study the momentum distributions of the charm quark and the charmed-hadron in the decay.The momentum distribution of the charmed-hadron is obtained by convolving the charm quark momentum distribution with a fragmentation function of the charm quark into the hadron.In addition,we fit the nonperturbative NRQCD matrix element v 2 Υ through comparing the theoretical prediction with the measurement from the BaBar collaboration for the decay rate of Υ(1 S) → D + X.In return,taking this matrix element as an input parameter,we predict the decay rates as well as the momentum distributions for a collection of charmed-hadrons in the process Υ(1S) → ccgg → hX.
文摘We are concerned with the problem of characterizing the distribution of the maximum number of individuals alive during a fixed time interval in host-parasitoid models, which is shown to have a matrix exponential form. We present simple conditions on the rates of change of population sizes for the matrix exponential solution to be explicit or algo- rithmically tractable. A particularly appealing feature of our solution based on splitting methods is that it allows us to obtain global error control.
