Let A be a CSL subalgebra of a von Neumann algebra on a Hilbert space H.It is shown that a Jordan (α,β)-derivation on A is an (α,β)-derivation under a mild condition,where α,β are automorphisms on A.It is also shown that any Jordan (α,β)-derivation on a CSL algebra is an (α,β)-derivation with no additional conditions being assumed.We also investigate the n-th power (α,β)-maps on CSL subalgebras of von Neumann algebras.
For M-matrix,we prove that its H-compatible splitting is the regular splitting,but not vice versa.This indicates that the regular splittings of M-matrix contain all H-compatible splittings.For the linear complementarity problems with M-matrices,we establish two convergence theorems:one is that of the modulus-based multisplitting iteration method with regular splittings,the other is that of the modulus-based twostage multisplitting iteration method with regular splittings for outer iterations and weak regular splittings for inner iterations.
A new approach to the construction of mixed-level uniform designs under the wrap-around L2-discrepancy by permuting the levels of factors is proposed.Based on the relationship between average wrap-around L2-discrepancy and generalized wordlength pattern,we employ a less aberration design as the starting design,then conduct level permutations,calculate wrap-around L2-discrepancy,and finally obtain the uniform design.Two properties of the wrap-around L2-discrepancy are utilized to make the algorithm more efficient.Numerical results show that the designs constructed via this approach perform well under the wrap-around L2-discrepancy.Finally,conclusion and future work are summarized.
For a point configuration in general position in Rn,we define the notion of the r-th minimal convex hull distance and prove an optimal inequality between the minimal convex hull distance and the minimal point-hyperplane distance.A direct corollary of this result is that we can estimate from below the Gromov-Guth thickness of a k-dimensional simplicial complex K in Rn in terms of the minimal point-hyperplane distance of the vertex set of K.Moreover,we construct an example which shows that this lower bound is almost optimal in every dimension k.
We study the evolving behaviors of the first eigenvalue of the Laplace-Beltrami operator under the normalized Ricci flow of model geometries.In every Bianchi class,we estimate the derivative of the eigenvalue.Then we construct monotonic quantities under the Ricci flow and obtain upper and lower bounds for the eigenvalue.
We propose the concept of a diagonal quantum channel (DQC) by using the Kraus operators of a quantum channel and prove some properties of DQCs.It is proved that a quantum channel is a DQC if and only if it makes every diagonal matrix unchanged;all condensed matrices of a DQC have the same rank;a DQC is uncorrectable if and only if its condensed matrices are of full rank,and a DQC is correctable on the whole space if and only if its condensed matrices are of rank one.Finally,we give a constructing method of the code space of a DQC by using a concrete example.
We aimed to investigate tractability of the approximation problems of Sobolev classes of functions defined over the product of m copies of the simplex T d ⊂ Rd in the worst case setting.We obtained the matching necessary and sufficient conditions for some notions of tractability in terms of the parameters of the problem for the class Λall.It is a further study of the corresponding integral problems.
We study the block-sparse signal recovery under compressed sensing framework.We mainly establish an improved condition on the restricted isometry property in both noiseless and noisy cases for mixed l2/l1 norm minimization.Especially,we prove that under the condition δk+θk,k < 1 for measurement matrix,any block k-sparse signals can be exactly recovered in the noiseless case and robustly recovered in the noisy case by mixed l2/l1 minimization method.Finally,we further show that the obtained condition is clearly weaker than existing ones in the literature.
This paper deals with the existence of positive solutions of the second-order boundary value problem
,
where f:[0,1]×R+ → R+ is continuous.We present new eigenvalue criteria for the existence of positive solution to this problem,which improve some existent results.Our discussion is based on the theory of fixed point index in cones.
A mixed dominating set of a graph G=(V,E) is a set D ⊆ V ∪ E such that every vertex or edge not in D is adjacent or incident to at least one vertex or edge in D.The mixed domination problem is to determine a minimum mixed dominating set of G.This paper studies the complexity of mixed domination in graphs.We prove that the mixed domination problem remains NP-complete for undirected path graphs,and is solvable for block graphs.Both undirected path graphs and block graphs are subclasses of chordal graphs and superclasses of trees.
Using Nevanlinna theory of the value distribution of meromorphic functions,and maximum modulus principle,we investigate the problem of the existence of the algebroid solutions of a class of complex higher-order differential equations and the transcendental meromorphic solutions of a class of system of complex higher-order differential equations and obtain two results.Extensions of some results in references are presented.Examples show that our results are precise.
In this paper,using the estimate of the derivative of the function in Bloch type spaces,the properties of the analytic function and operator theory,the authors characterize the compactness of product-type operators between different Bloch type spaces by means of constructing some test functions.
We introduce a new hybrid projection algorithm for finding a common element of the set of common fixed points of two countable families of hemi-relatively nonexpansive mappings and the set of solutions of finite general equilibrium problems and the set of solutions of finite variational inequalities for relaxed cocoercive operators in the framework of uniformly smooth and 2-uniformly convex Banach spaces.The results obtained in this paper improve and extend the corresponding results announced by many others.
Let G be a residually finite minimax soluble group and α an automorphism of G.If the map φ:G → G defined by gφ=[g,α]is surjective,then the following hold:(1) When αp=1,G is (nilpotent of class at most h(p))-by-finite,where h(p) is a function depending only on p;(2) When α4=1,G contains a characteristic subgroup H of finite index such that the second derived subgroup H"is included in the centre of H and CH(α2) is abelian.Both CG(α2) and G/[G,α2]are abelian-by-finite.
We study the change of orbifold Gromov-Witten invariants of the form 〈α1,…,αm,[pt]〉g,AXof a compact symplectic orbifold groupoid (X,ω) under weighted blow-up along smooth points.Here[pt]∈HdR2n(X) is the generator,dim X=2n.We prove that for nonzero A∈H2(|X|,Z),
〈α1,…,αm,[pt]〉g,AX
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where .jpg){kind=small}
is the weight a=(a1,…,an) blow-up of X along a smooth point,and a1 ≥ ai,2 ≤ i ≤ n.
This note is to give such characterizations of the α-comparison property for non-simple C*-algebras:when each τ∈QT(A⊗K) is faithful,A has the α-comparison property,if and only if,for any 〈a〉,〈b〉∈Cu (A) with 〈a〉∝〈b〉,α·dτ(a)<dτ(b)(∀τ,∈QT(A⊗K)) implies 〈a〉 ≤ 〈b〉 in Cu (A);in general,when QT(A⊗K)≠0,A has the α-comparison property,if and only if,for any a〉,〈b〉∈Cu (A),if there is some η>0 such that dτ(a)≤(α-1-η)dτ(b)(∀τ,∈QT(A⊗K)),then 〈a〉 ≤ 〈b〉inCu (A).
