Let A be an m by n matrix of rank l, and let M and N be m by k and n by q matrices, respectively, where k is not necessarily equal to q or rank(M AN) < min(k, q). In this paper, we provide some necessary and suffic...Let A be an m by n matrix of rank l, and let M and N be m by k and n by q matrices, respectively, where k is not necessarily equal to q or rank(M AN) < min(k, q). In this paper, we provide some necessary and sufficient conditions for the validity of the rank subtractivity formula: rank(A-AN(M AN)-M A) = rank(A)-rank(AN(M AN)-M A)by applying the full rank decomposition of A = F G(F ∈ Rm×l, G ∈ Rl×n, rank(A) =rank(F) = rank(G) = l) and the product singular value decomposition of the matrix pair[F M, GN ]. This rank subtractivity formula along with the condition under which it holds is called the extended Wedderburn-Guttman theorem.展开更多
A class of normal-like derivatives for functions with low regularity defined on Lipschitz domains are introduced and studied.It is shown that the new normal-like derivatives,which are called the generalized normal der...A class of normal-like derivatives for functions with low regularity defined on Lipschitz domains are introduced and studied.It is shown that the new normal-like derivatives,which are called the generalized normal derivatives,preserve the major prop- erties of the existing standard normal derivatives.The generalized normal derivatives are then applied to analyze the convergence of domain decomposition methods (DDMs) with nonmatching grids and discontinuous Galerkin (DG) methods for second-order el- liptic problems.The approximate solutions generated by these methods still possess the optimal energy-norm error estimates,even if the exact solutions to the underlying elliptic problems admit very low regularities.展开更多
We show that the cuspidal component of the stable trace formula of a split special odd orthogonal group over a number field, satisfies a weak form of beyond endoscopic decomposition. We also study the r-stable trace f...We show that the cuspidal component of the stable trace formula of a split special odd orthogonal group over a number field, satisfies a weak form of beyond endoscopic decomposition. We also study the r-stable trace formula, when r is the standard or the second fundamental representation of the dual group, and show that they satisfy a similar kind of beyond endoscopic decomposition. The results are consequences of Arthur's works(2013) on endoscopic classification of automorphic representations, together with known results concerning a class of Langlands L-functions for special odd orthogonal groups.展开更多
Under investigation in this paper is the invariance properties of the time fractional Rosenau-Haynam equation, which can be used to describe the formation of patterns in liquid drops. By using the Lie group analysis m...Under investigation in this paper is the invariance properties of the time fractional Rosenau-Haynam equation, which can be used to describe the formation of patterns in liquid drops. By using the Lie group analysis method, the vector fields and symmetry reductions of the equation are derived, respectively. Moreover, based on the power series theory, a kind of explicit power series solutions for the equation are well constructed with a detailed derivation. Finally, by using the new conservation theorem, two kinds of conservation laws of the equation are well constructed with a detailed derivation.展开更多
The operator level proof of factorization theorem exhibited in [ar Xiv：hep-ph/1307.4194] is extended to the semi-inclusive deep inelastic scattering process（SIDIS）. Factorization theorem can be proved at operator l...The operator level proof of factorization theorem exhibited in [ar Xiv：hep-ph/1307.4194] is extended to the semi-inclusive deep inelastic scattering process（SIDIS）. Factorization theorem can be proved at operator level if there are not detected soft hadrons. The key point is that the initial one-nucleon state is the eigenstate of QCD.展开更多
An additive functor F:A→B between additive categories is said to be objective,provided any morphism f in A with F(f)=0 factors through an object K with F(K)=0.We concentrate on triangle functors between triangulated ...An additive functor F:A→B between additive categories is said to be objective,provided any morphism f in A with F(f)=0 factors through an object K with F(K)=0.We concentrate on triangle functors between triangulated categories.The first aim of this paper is to characterize objective triangle functors F in several ways.Second,we are interested in the corresponding Verdier quotient functors VF:A→A/Ker F,in particular we want to know under what conditions VF is full.The third question to be considered concerns the possibility to factorize a given triangle functor F=F2F1with F1a full and dense triangle functor and F2a faithful triangle functor.It turns out that the behavior of splitting monomorphisms and splitting epimorphisms plays a decisive role.展开更多
This paper presents new results for strong solutions and their coincidence sets of the obstacle problem for linear hyperbolic operators of first order. An inequality similar to the LewyStampacchia ones for elliptic an...This paper presents new results for strong solutions and their coincidence sets of the obstacle problem for linear hyperbolic operators of first order. An inequality similar to the LewyStampacchia ones for elliptic and parabolic problems is shown. Under nondegeneracy conditions the stability of the coincidence set is shown with respect to the variation of the data and with respect to approximation by semilinear hyperbolic problems. These results are applied to the asymptotic stability of the evolution problem with respect to the stationary coercive problem with obstacle.展开更多
文摘Let A be an m by n matrix of rank l, and let M and N be m by k and n by q matrices, respectively, where k is not necessarily equal to q or rank(M AN) < min(k, q). In this paper, we provide some necessary and sufficient conditions for the validity of the rank subtractivity formula: rank(A-AN(M AN)-M A) = rank(A)-rank(AN(M AN)-M A)by applying the full rank decomposition of A = F G(F ∈ Rm×l, G ∈ Rl×n, rank(A) =rank(F) = rank(G) = l) and the product singular value decomposition of the matrix pair[F M, GN ]. This rank subtractivity formula along with the condition under which it holds is called the extended Wedderburn-Guttman theorem.
基金supported by The Key Project of Natural Science Foundation of China G10531080National Basic Research Program of China No.2005CB321702Natural Science Foundation of China G10771178.
文摘A class of normal-like derivatives for functions with low regularity defined on Lipschitz domains are introduced and studied.It is shown that the new normal-like derivatives,which are called the generalized normal derivatives,preserve the major prop- erties of the existing standard normal derivatives.The generalized normal derivatives are then applied to analyze the convergence of domain decomposition methods (DDMs) with nonmatching grids and discontinuous Galerkin (DG) methods for second-order el- liptic problems.The approximate solutions generated by these methods still possess the optimal energy-norm error estimates,even if the exact solutions to the underlying elliptic problems admit very low regularities.
文摘We show that the cuspidal component of the stable trace formula of a split special odd orthogonal group over a number field, satisfies a weak form of beyond endoscopic decomposition. We also study the r-stable trace formula, when r is the standard or the second fundamental representation of the dual group, and show that they satisfy a similar kind of beyond endoscopic decomposition. The results are consequences of Arthur's works(2013) on endoscopic classification of automorphic representations, together with known results concerning a class of Langlands L-functions for special odd orthogonal groups.
基金Supported by the Fundamental Research Fund for Talents Cultivation Project of the China University of Mining and Technology under Grant No.YC150003
文摘Under investigation in this paper is the invariance properties of the time fractional Rosenau-Haynam equation, which can be used to describe the formation of patterns in liquid drops. By using the Lie group analysis method, the vector fields and symmetry reductions of the equation are derived, respectively. Moreover, based on the power series theory, a kind of explicit power series solutions for the equation are well constructed with a detailed derivation. Finally, by using the new conservation theorem, two kinds of conservation laws of the equation are well constructed with a detailed derivation.
基金Supported by the National Nature Science Foundation of China under Grant No.11275242
文摘The operator level proof of factorization theorem exhibited in [ar Xiv：hep-ph/1307.4194] is extended to the semi-inclusive deep inelastic scattering process（SIDIS）. Factorization theorem can be proved at operator level if there are not detected soft hadrons. The key point is that the initial one-nucleon state is the eigenstate of QCD.
基金supported by National Natural Science Foundation of China(Grant Nos.11271251 and 11431010)Specialized Research Fund for the Doctoral Program of Higher Education(GrantNo.20120073110058)
文摘An additive functor F:A→B between additive categories is said to be objective,provided any morphism f in A with F(f)=0 factors through an object K with F(K)=0.We concentrate on triangle functors between triangulated categories.The first aim of this paper is to characterize objective triangle functors F in several ways.Second,we are interested in the corresponding Verdier quotient functors VF:A→A/Ker F,in particular we want to know under what conditions VF is full.The third question to be considered concerns the possibility to factorize a given triangle functor F=F2F1with F1a full and dense triangle functor and F2a faithful triangle functor.It turns out that the behavior of splitting monomorphisms and splitting epimorphisms plays a decisive role.
基金Partially supported by the Project FCT-POCTI/34471/MAT/2000
文摘This paper presents new results for strong solutions and their coincidence sets of the obstacle problem for linear hyperbolic operators of first order. An inequality similar to the LewyStampacchia ones for elliptic and parabolic problems is shown. Under nondegeneracy conditions the stability of the coincidence set is shown with respect to the variation of the data and with respect to approximation by semilinear hyperbolic problems. These results are applied to the asymptotic stability of the evolution problem with respect to the stationary coercive problem with obstacle.
