共查询到20条相似文献,搜索用时 453 毫秒
1.
Jer-Shyong Lin 《Linear algebra and its applications》2010,432(1):14-23
Let A be a prime ring of characteristic not 2, with center Z(A) and with involution *. Let S be the set of symmetric elements of A. Suppose that f:S→A is an additive map such that [f(x),f(y)]=[x,y] for all x,y∈S. Then unless A is an order in a 4-dimensional central simple algebra, there exists an additive map μ:S→Z(A) such that f(x)=x+μ(x) for all x∈S or f(x)=-x+μ(x) for all x∈S. 相似文献
2.
Strong commutativity preserving maps on Lie ideals 总被引:2,自引:0,他引:2
Jer-Shyong Lin 《Linear algebra and its applications》2008,428(7):1601-1609
Let A be a prime ring and let R be a noncentral Lie ideal of A. An additive map f:R→A is called strong commutativity preserving (SCP) on R if [f(x),f(y)]=[x,y] for all x,y∈R. In this paper we show that if f is SCP on R, then there exist λ∈C, λ2=1 and an additive map μ:R→Z(A) such that f(x)=λx+μ(x) for all x∈R where C is the extended centroid of A, unless charA=2 and A satisfies the standard identity of degree 4. 相似文献
3.
Eliza Jab?ońska 《Journal of Mathematical Analysis and Applications》2011,381(2):565-572
Let X be a linear space over a commutative field K. We characterize a general solution f,g,h,k:X→K of the pexiderized Go?a?b-Schinzel equation f(x+g(x)y)=h(x)k(y), as well as real continuous solutions of the equation. 相似文献
4.
Shih Ping Tung 《Journal of Number Theory》2010,130(4):912-929
In this paper we study the maximum-minimum value of polynomials over the integer ring Z. In particular, we prove the following: Let F(x,y) be a polynomial over Z. Then, maxx∈Z(T)miny∈Z|F(x,y)|=o(T1/2) as T→∞ if and only if there is a positive integer B such that maxx∈Zminy∈Z|F(x,y)|?B. We then apply these results to exponential diophantine equations and obtain that: Let f(x,y), g(x,y) and G(x,y) be polynomials over Q, G(x,y)∈(Q[x,y]−Q[x])∪Q, and b a positive integer. For every α in Z, there is a y in Z such that f(α,y)+g(α,y)bG(α,y)=0 if and only if for every integer α there exists an h(x)∈Q[x] such that f(x,h(x))+g(x,h(x))bG(x,h(x))≡0, and h(α)∈Z. 相似文献
5.
C.E. Chidume 《Journal of Mathematical Analysis and Applications》2003,282(2):756-765
Let E be a real uniformly smooth Banach space. Let A:D(A)=E→2E be an accretive operator that satisfies the range condition and A−1(0)≠∅. Let {λn} and {θn} be two real sequences satisfying appropriate conditions, and for z∈E arbitrary, let the sequence {xn} be generated from arbitrary x0∈E by xn+1=xn−λn(un+θn(xn−z)), un∈Axn, n?0. Assume that {un} is bounded. It is proved that {xn} converges strongly to some x∗∈A−1(0). Furthermore, if K is a nonempty closed convex subset of E and T:K→K is a bounded continuous pseudocontractive map with F(T):={Tx=x}≠∅, it is proved that for arbitrary z∈K, the sequence {xn} generated from x0∈K by xn+1=xn−λn((I−T)xn+θn(xn−z)), n?0, where {λn} and {θn} are real sequences satisfying appropriate conditions, converges strongly to a fixed point of T. 相似文献
6.
Jian YuDingtao Peng Shuwen Xiang 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):6326-6332
Let X be a nonempty, convex and compact subset of normed linear space E (respectively, let X be a nonempty, bounded, closed and convex subset of Banach space E and A be a nonempty, convex and compact subset of X) and f:X×X→R be a given function, the uniqueness of equilibrium point for equilibrium problem which is to find x∗∈X (respectively, x∗∈A) such that f(x∗,y)≥0 for all y∈X (respectively, f(x∗,y)≥0 for all y∈A) is studied with varying f (respectively, with both varying f and varying A). The results show that most of equilibrium problems (in the sense of Baire category) have unique equilibrium point. 相似文献
7.
Aleksander Grytczuk 《Journal of Number Theory》2010,130(7):1480-1487
Let Fn be a binary form with integral coefficients of degree n?2, let d denote the greatest common divisor of all non-zero coefficients of Fn, and let h?2 be an integer. We prove that if d=1 then the Thue equation (T) Fn(x,y)=h has relatively few solutions: if A is a subset of the set T(Fn,h) of all solutions to (T), with r:=card(A)?n+1, then
- (#)
- h divides the numberΔ(A):=∏1?k<l?rδ(ξk,ξl),
8.
For a set A let k[A] denote the family of all k-element subsets of A. A function f:k[A]→C is a local coloring if it maps disjoint sets of A into different elements of C. A family F⊆k[A] is called a flower if there exists E∈[A]k−1 so that |F∩F′|=E for all F,F′∈F, F≠F′. A flower is said to be colorful if f(F)≠f(F′) for any two F,F′∈F. In the paper we find the smallest cardinal γ such that there exists a local coloring of k[A] containing no colorful flower of size γ. As a consequence we answer a question raised by Pelant, Holický and Kalenda. We also discuss a few results and conjectures concerning a generalization of this problem. 相似文献
9.
G. Gripenberg 《Journal of Mathematical Analysis and Applications》2009,352(1):175-183
Sufficient conditions are given for the solutions to the (fully nonlinear, degenerate) elliptic equation F(x,u,Du,D2u)=0 in Ω to satisfy |u(x)−u(y)|?Cα|x−y| for some α∈(0,1) when x∈Ω and y∈∂Ω. 相似文献
10.
Chun-Gil Park 《Journal of Mathematical Analysis and Applications》2005,307(2):753-762
It is shown that every almost linear bijection of a unital C∗-algebra A onto a unital C∗-algebra B is a C∗-algebra isomorphism when h(n2uy)=h(n2u)h(y) for all unitaries u∈A, all y∈A, and n=0,1,2,…, and that almost linear continuous bijection of a unital C∗-algebra A of real rank zero onto a unital C∗-algebra B is a C∗-algebra isomorphism when h(n2uy)=h(n2u)h(y) for all , all y∈A, and n=0,1,2,…. Assume that X and Y are left normed modules over a unital C∗-algebra A. It is shown that every surjective isometry , satisfying T(0)=0 and T(ux)=uT(x) for all x∈X and all unitaries u∈A, is an A-linear isomorphism. This is applied to investigate C∗-algebra isomorphisms between unital C∗-algebras. 相似文献
11.
Mohammed Guedda 《Journal of Mathematical Analysis and Applications》2009,352(1):259-270
A multiplicity result for the singular ordinary differential equation y″+λx−2yσ=0, posed in the interval (0,1), with the boundary conditions y(0)=0 and y(1)=γ, where σ>1, λ>0 and γ?0 are real parameters, is presented. Using a logarithmic transformation and an integral equation method, we show that there exists Σ?∈(0,σ/2] such that a solution to the above problem is possible if and only if λγσ−1?Σ?. For 0<λγσ−1<Σ?, there are multiple positive solutions, while if γ=(λ−1Σ?)1/(σ−1) the problem has a unique positive solution which is monotonic increasing. The asymptotic behavior of y(x) as x→0+ is also given, which allows us to establish the absence of positive solution to the singular Dirichlet elliptic problem −Δu=d−2(x)uσ in Ω, where Ω⊂RN, N?2, is a smooth bounded domain and d(x)=dist(x,∂Ω). 相似文献
12.
Jacek Chudziak 《Journal of Mathematical Analysis and Applications》2008,339(1):454-460
Let X be a vector space over a field K of real or complex numbers, n∈N and λ∈K?{0}. We study the stability problem for the Go?a?b-Schinzel type functional equations
f(x+fn(x)y)=λf(x)f(y) 相似文献
13.
Ognjen Milatovic 《Differential Geometry and its Applications》2004,21(3):361-377
We consider a family of Schrödinger-type differential expressions L(κ)=D2+V+κV(1), where κ∈C, and D is the Dirac operator associated with a Clifford bundle (E,∇E) of bounded geometry over a manifold of bounded geometry (M,g) with metric g, and V and V(1) are self-adjoint locally integrable sections of EndE. We also consider the family I(κ)=*(∇F)∇F+V+κV(1), where κ∈C, and ∇F is a Hermitian connection on a Hermitian vector bundle F of bonded geometry over a manifold of bounded geometry (M,g), and V and V(1) are self-adjoint locally integrable sections of EndF. We give sufficient conditions for L(κ) and I(κ) to have a realization in L2(E) and L2(F), respectively, as self-adjoint holomorphic families of type (B). In the proofs we use Kato's inequality for Bochner Laplacian operator and Weitzenböck formula. 相似文献
14.
L. Zhao 《Journal of Mathematical Analysis and Applications》2006,314(2):689-700
Let Φ:A→B be an additive surjective map between some operator algebras such that AB+BA=0 implies Φ(A)Φ(B)+Φ(B)Φ(A)=0. We show that, under some mild conditions, Φ is a Jordan homomorphism multiplied by a central element. Such operator algebras include von Neumann algebras, C∗-algebras and standard operator algebras, etc. Particularly, if H and K are infinite-dimensional (real or complex) Hilbert spaces and A=B(H) and B=B(K), then there exists a nonzero scalar c and an invertible linear or conjugate-linear operator U:H→K such that either Φ(A)=cUAU−1 for all A∈B(H), or Φ(A)=cUA∗U−1 for all A∈B(H). 相似文献
15.
Harris Kwong 《Discrete Mathematics》2008,308(23):5522-5532
Let G be a graph with vertex set V and edge set E, and let A be an abelian group. A labeling f:V→A induces an edge labeling f∗:E→A defined by f∗(xy)=f(x)+f(y). For i∈A, let vf(i)=card{v∈V:f(v)=i} and ef(i)=card{e∈E:f∗(e)=i}. A labeling f is said to be A-friendly if |vf(i)−vf(j)|≤1 for all (i,j)∈A×A, and A-cordial if we also have |ef(i)−ef(j)|≤1 for all (i,j)∈A×A. When A=Z2, the friendly index set of the graph G is defined as {|ef(1)−ef(0)|:the vertex labelingf is Z2-friendly}. In this paper we completely determine the friendly index sets of 2-regular graphs. In particular, we show that a 2-regular graph of order n is cordial if and only if n?2 (mod 4). 相似文献
16.
Let E be a real normed linear space, K be a nonempty subset of E and be a uniformly continuous generalized Φ-hemi-contractive mapping, i.e., , and there exist x∗∈F(T) and a strictly increasing function , Φ(0)=0 such that for all x∈K, there exists j(x−x∗)∈J(x−x∗) such that
〈Tx−x∗,j(x−x∗)〉?‖x−x∗‖2−Φ(‖x−x∗‖). 相似文献
17.
Vladimir Umanskiy 《Advances in Mathematics》2003,180(1):176-186
Given p≠0 and a positive continuous function g, with g(x+T)=g(x), for some 0<T<1 and all real x, it is shown that for suitable choice of a constant C>0 the functional has a minimizer in the class of positive functions u∈C1(R) for which u(x+T)=u(x) for all x∈R. This minimizer is used to prove the existence of a positive periodic solution y∈C2(R) of two-dimensional Lp-Minkowski problem y1−p(x)(y″(x)+y(x))=g(x), where p∉{0,2}. 相似文献
18.
19.
Wolfgang Arendt 《Journal of Functional Analysis》2006,238(1):340-352
Let A be the generator of a cosine function on a Banach space X. In many cases, for example if X is a UMD-space, A+B generates a cosine function for each B∈L(D((ω−A)1/2),X). If A is unbounded and , then we show that there exists a rank-1 operator B∈L(D(γ(ω−A)),X) such that A+B does not generate a cosine function. The proof depends on a modification of a Baire argument due to Desch and Schappacher. It also allows us to prove the following. If A+B generates a distribution semigroup for each operator B∈L(D(A),X) of rank-1, then A generates a holomorphic C0-semigroup. If A+B generates a C0-semigroup for each operator B∈L(D(γ(ω−A)),X) of rank-1 where 0<γ<1, then the semigroup T generated by A is differentiable and ‖T′(t)‖=O(t−α) as t↓0 for any α>1/γ. This is an approximate converse of a perturbation theorem for this class of semigroups. 相似文献
20.
Ioan Tomescu 《Discrete Applied Mathematics》2010,158(15):1714-1717
The concept of degree distance of a connected graph G is a variation of the well-known Wiener index, in which the degrees of vertices are also involved. It is defined by D′(G)=∑x∈V(G)d(x)∑y∈V(G)d(x,y), where d(x) and d(x,y) are the degree of x and the distance between x and y, respectively. In this paper it is proved that connected graphs of order n≥4 having the smallest degree distances are K1,n−1,BS(n−3,1) and K1,n−1+e (in this order), where BS(n−3,1) denotes the bistar consisting of vertex disjoint stars K1,n−3 and K1,1 with central vertices joined by an edge. 相似文献