In this paper, we consider a general quasi-differential expressions t1,t2 Tn, each of order n with complex coefficients and their formal adjoints are t1＋,t2＋- x＋ on [0, b） respectively. We show in the direct sum s...In this paper, we consider a general quasi-differential expressions t1,t2 Tn, each of order n with complex coefficients and their formal adjoints are t1＋,t2＋- x＋ on [0, b） respectively. We show in the direct sum spaces LZ（Ip）, p = 1,2 N of functions defined on each of the separate intervals with the case of one singular end-points and under suitable conditions on the function F that all solutions of the product quasi-integro differential equations are bounded and LZw -bounded on [0,b）.展开更多
If a 3-tuple (A:H_1→H_1,B:H_2→H_1,C:H_2→H_2) of operators on Hilbert spaces is given,we proved that the operator A:= on H=H_1⊕H_2 is≥0 if and only if A≥0,R(B) R(A1/2)and C≥B~* A^+ B, where A^+ is the generalize...If a 3-tuple (A:H_1→H_1,B:H_2→H_1,C:H_2→H_2) of operators on Hilbert spaces is given,we proved that the operator A:= on H=H_1⊕H_2 is≥0 if and only if A≥0,R(B) R(A1/2)and C≥B~* A^+ B, where A^+ is the generalized inverse of A. In general,A^+ is a closed operator,but since R(B) R(A1/2),B~* A^+ B is bounded yet.展开更多
We give a strategy for nonlocal unambiguous discrimination (UD) among N linearly independent nonorthogonal qudit states lying in a higher-dimensional Hilbert space. The procedure we use is a nonlocal positive operator...We give a strategy for nonlocal unambiguous discrimination (UD) among N linearly independent nonorthogonal qudit states lying in a higher-dimensional Hilbert space. The procedure we use is a nonlocal positive operator valued measurement (POVM) in a direct sum space. This scheme is designed for obtaining the conclusive nonlocal measurement results with a finite probability of success. We construct a quantum network for realizing the nonlocal UD with a set of two-level remote rotations, and thus provide a feasible physical means to realize the nonlocal UD.展开更多
If a linear time-invariant system is uncontrollable,then the state space can be decomposed as a direct sum of a controllable subspace and an uncontrollable subspace.In this paper,for a class of discrete-time bilinear ...If a linear time-invariant system is uncontrollable,then the state space can be decomposed as a direct sum of a controllable subspace and an uncontrollable subspace.In this paper,for a class of discrete-time bilinear systems which are uncontrollable but can be nearly controllable,by studying the nearly-controllable subspaces and defining the near-controllability index,the controllability properties of the systems are fully characterized.Examples are provided to illustrate the conceptions and results of the paper.展开更多
Let V be a linear space over a field F with finite dimension,L(V) the semigroup,under composition,of all linear transformations from V into itself.Suppose that V = V1⊕V2⊕···⊕Vm is a direct sum decomp...Let V be a linear space over a field F with finite dimension,L(V) the semigroup,under composition,of all linear transformations from V into itself.Suppose that V = V1⊕V2⊕···⊕Vm is a direct sum decomposition of V,where V1,V2,...,Vm are subspaces of V with the same dimension.A linear transformation f ∈ L(V) is said to be sum-preserving,if for each i(1 ≤ i ≤ m),there exists some j(1 ≤ j ≤ m) such that f(Vi) ■Vj.It is easy to verify that all sum-preserving linear transformations form a subsemigroup of L(V) which is denoted by L⊕(V).In this paper,we first describe Green's relations on the semigroup L⊕(V).Then we consider the regularity of elements and give a condition for an element in L⊕(V) to be regular.Finally,Green's equivalences for regular elements are also characterized.展开更多
文摘In this paper, we consider a general quasi-differential expressions t1,t2 Tn, each of order n with complex coefficients and their formal adjoints are t1＋,t2＋- x＋ on [0, b） respectively. We show in the direct sum spaces LZ（Ip）, p = 1,2 N of functions defined on each of the separate intervals with the case of one singular end-points and under suitable conditions on the function F that all solutions of the product quasi-integro differential equations are bounded and LZw -bounded on [0,b）.
文摘If a 3-tuple (A:H_1→H_1,B:H_2→H_1,C:H_2→H_2) of operators on Hilbert spaces is given,we proved that the operator A:= on H=H_1⊕H_2 is≥0 if and only if A≥0,R(B) R(A1/2)and C≥B~* A^+ B, where A^+ is the generalized inverse of A. In general,A^+ is a closed operator,but since R(B) R(A1/2),B~* A^+ B is bounded yet.
基金supported by the Natural Science Foundation of Guangdong Province, China (Grant No. 06029431)
文摘We give a strategy for nonlocal unambiguous discrimination (UD) among N linearly independent nonorthogonal qudit states lying in a higher-dimensional Hilbert space. The procedure we use is a nonlocal positive operator valued measurement (POVM) in a direct sum space. This scheme is designed for obtaining the conclusive nonlocal measurement results with a finite probability of success. We construct a quantum network for realizing the nonlocal UD with a set of two-level remote rotations, and thus provide a feasible physical means to realize the nonlocal UD.
基金supported by the China Postdoctoral Science Foundation funded project under Grant Nos.2011M500216,2012T50035the National Nature Science Foundation of China under Grant Nos.61203231,61273141
文摘If a linear time-invariant system is uncontrollable,then the state space can be decomposed as a direct sum of a controllable subspace and an uncontrollable subspace.In this paper,for a class of discrete-time bilinear systems which are uncontrollable but can be nearly controllable,by studying the nearly-controllable subspaces and defining the near-controllability index,the controllability properties of the systems are fully characterized.Examples are provided to illustrate the conceptions and results of the paper.
文摘Let V be a linear space over a field F with finite dimension,L(V) the semigroup,under composition,of all linear transformations from V into itself.Suppose that V = V1⊕V2⊕···⊕Vm is a direct sum decomposition of V,where V1,V2,...,Vm are subspaces of V with the same dimension.A linear transformation f ∈ L(V) is said to be sum-preserving,if for each i(1 ≤ i ≤ m),there exists some j(1 ≤ j ≤ m) such that f(Vi) ■Vj.It is easy to verify that all sum-preserving linear transformations form a subsemigroup of L(V) which is denoted by L⊕(V).In this paper,we first describe Green's relations on the semigroup L⊕(V).Then we consider the regularity of elements and give a condition for an element in L⊕(V) to be regular.Finally,Green's equivalences for regular elements are also characterized.
