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1.
Let ? be a ring containing a nontrivial idempotent. In this article, under a mild condition on ?, we prove that if δ is a Lie triple derivable mapping from ? into ?, then there exists a Z A, B (depending on A and B) in its centre 𝒵(?) such that δ(A + B) = δ(A) + δ(B) + Z A, B . In particular, let ? be a prime ring of characteristic not 2 containing a nontrivial idempotent. It is shown that, under some mild conditions on ?, if δ is a Lie triple derivable mapping from ? into ?, then δ = D + τ, where D is an additive derivation from ? into its central closure T and τ is a mapping from ? into its extended centroid 𝒞 such that τ(A + B) = τ(A) + τ(B) + Z A, B and τ([[A, B], C]) = 0 for all A, B, C ∈ ?.  相似文献   

2.

Let G be a non-elementary subgroup of SL(2,Г n ) containing hyperbolic elements. We show that G is the extension of a subgroup of SL(2,C) if and only if that G is conjugate in SL(2,Г n ) to a group G' with the following properties: (1) There are g 0, h ? G', where g 0 and h are hyperbolic, such that fix(g 0) = {0,∞}, fix(h)∩fix(g 0) =  and fix(h) ∩ C ≠ ; (2) tr(g) ? C for each g ? G'. As an application, we show that if G contains only hyperbolic elements and uniformly parabolic elements, then G is the extension of a subgroup of SL(2,C), which also yields the discreteness of G.  相似文献   

3.
Xiaofei Qi 《代数通讯》2013,41(10):3824-3835
Let ? be a unital prime ring with characteristic not 2 and containing a nontrivial idempotent P. It is shown that, under some mild conditions, an additive map L on ? satisfies L([A, B]) = [L(A), B] + [A, L(B)] whenever AB = 0 (resp., AB = P) if and only if it has the form L(A) = ?(A) + h(A) for all A ∈ ?, where ? is an additive derivation on ? and h is an additive map into its center.  相似文献   

4.
Let Rbe a principal ideal ringRn the ring of n× nmatrices over R, and dk (A) the kth determinantal divisor of Afor 1 ? k? n, where Ais any element of Rn , It is shown that if A,BεRn , det(A) det(B:) ≠ 0, then dk (AB) ≡ 0 mod dk (A) dk (B). If in addition (det(A), det(B)) = 1, then it is also shown that dk (AB) = dk (A) dk (B). This provides a new proof of the multiplicativity of the Smith normal form for matrices with relatively prime determinants.  相似文献   

5.
This paper deals with the generalized vector quasivariational inclusion Problem (P1) (resp. Problem (P2)) of finding a point (z 0,x 0) of a set E×K such that (z 0,x 0)∈B(z 0,x 0A(z 0,x 0) and, for all ηA(z 0,x 0),
lF(z0,x0,h) ì G(z0,x0,x0)+C(z0,x0) [resp.F(z0,x0,x0) ì G(z0,x0,h)+C(z0,x0)],\begin{array}{l}F(z_0,x_0,\eta)\subset G(z_0,x_0,x_0)+C(z_0,x_0)\cr \mathrm{[resp.}F(z_0,x_0,x_0)\subset G(z_0,x_0,\eta)+C(z_0,x_0)],\end{array}  相似文献   

6.
The linear equation Δ2u = 1 for the infinitesimal buckling under uniform unit load of a thin elastic plate over ?2 has the particularly interesting nonlinear generalization Δg2u = 1, where Δg = e?2u Δ is the Laplace‐Beltrami operator for the metric g = e2ug0, with g0 the standard Euclidean metric on ?2. This conformal elliptic PDE of fourth order is equivalent to the nonlinear system of elliptic PDEs of second order Δu(x)+Kg(x) exp(2u(x)) = 0 and Δ Kg(x) + exp(2u(x)) = 0, with x ∈ ?2, describing a conformally flat surface with a Gauss curvature function Kg that is generated self‐consistently through the metric's conformal factor. We study this conformal plate buckling equation under the hypotheses of finite integral curvature ∫ Kg exp(2u)dx = κ, finite area ∫ exp(2u)dx = α, and the mild compactness condition K+L1(B1(y)), uniformly w.r.t. y ∈ ?2. We show that asymptotically for |x|→∞ all solutions behave like u(x) = ?(κ/2π)ln |x| + C + o(1) and K(x) = ?(α/2π) ln|x| + C + o(1), with κ ∈ (2π, 4π) and . We also show that for each κ ∈ (2π, 4π) there exists a K* and a radially symmetric solution pair u, K, satisfying K(u) = κ and maxK = K*, which is unique modulo translation of the origin, and scaling of x coupled with a translation of u. © 2001 John Wiley & Sons, Inc.  相似文献   

7.
Mahdi Boukrouche  Ionel Ciuperca 《PAMM》2007,7(1):4080023-4080024
Let (m, n) ∈ ℕ2, Ω an open bounded domain in ℝm , Y = [0, 1]m ; uε in (L2(Ω))n which is two-scale converges to some u in (L2(Ω × Y))n . Let φ: Ω × ℝm × ℝn → ℝ such that: φ(x, ·, ·) is continuous a.e. x ∈ Ω φ(·, y, z) is measurable for all (y, z) in ℝm × ℝn , φ(x, ·, z) is 1-periodic in y, φ(x, y, ·) is convex in z. Assume that there exist a constant C1 > 0 and a function C2L2(Ω) such that

  相似文献   


8.
Let I = [0, 1], let Y be a real normed linear space, C a convex cone in Y and Z a real Banach space. Denote by clb(Z) the set of all nonempty, convex, closed and bounded subsets of Z. If a superposition operator N generated by a set-valued function F : I × Cclb(Z) maps the set H α (I, C) of all Hölder functions ${\varphi : I \to C}Let I = [0, 1], let Y be a real normed linear space, C a convex cone in Y and Z a real Banach space. Denote by clb(Z) the set of all nonempty, convex, closed and bounded subsets of Z. If a superposition operator N generated by a set-valued function F : I × Cclb(Z) maps the set H α (I, C) of all H?lder functions j: I ? C{\varphi : I \to C} into the set H β (I, clb(Z)) of all H?lder set-valued functions f: I ? clb(Z){\phi : I \to clb(Z)} and is uniformly continuous, then
F(x,y)=A(x,y) \text+* B(x),       x ? I, y ? CF(x,y)=A(x,y) \stackrel{*}{\text{+}} B(x),\qquad x \in I, y \in C  相似文献   

9.
Let X, Y be Banach modules over a C *‐algebra. We prove the Hyers–Ulam–Rassias stability of the following functional equation in Banach modules over a unital C *‐algebra: It is shown that a mapping f: XY satisfies the above functional equation and f (0) = 0 if and only if the mapping f: XY is Cauchy additive. As an application, we show that every almost linear bijection h: AB of a unital C *‐algebra A onto a unital C *‐algebra B is a C *‐algebra isomorphism when h (2d uy) = h (2d u) h (y) for all unitaries uA, all yA, and all d ∈ Z . (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

10.
Let X be a real Banach space, ω : [0, +∞) → ? be an increasing continuous function such that ω(0) = 0 and ω(t + s) ≤ ω(t) + ω(s) for all t, s ∈ [0, +∞). According to the infinite dimensional analog of the Osgood theorem if ∫10 (ω(t))?1 dt = ∞, then for any (t0, x0) ∈ ?×X and any continuous map f : ?×XX such that ∥f(t, x) – f(t, y)∥ ≤ ω(∥xy∥) for all t ∈ ?, x, yX, the Cauchy problem (t) = f(t, x(t)), x(t0) = x0 has a unique solution in a neighborhood of t0. We prove that if X has a complemented subspace with an unconditional Schauder basis and ∫10 (ω(t))?1 dt < ∞ then there exists a continuous map f : ? × XX such that ∥f(t, x) – f(t, y)∥ ≤ ω(∥xy∥) for all (t, x, y) ∈ ? × X × X and the Cauchy problem (t) = f(t, x(t)), x(t0) = x0 has no solutions in any interval of the real line.  相似文献   

11.
We provide a universal axiom system for plane hyperbolic geometry in a firstorder language with two sorts of individual variables, ‘points’ (upper‐case) and ‘lines’ (lowercase), containing three individual constants, A0, A1, A2, standing for three non‐collinear points, two binary operation symbols, φ and ι, with φ(A, B) = l to be interpreted as ‘𝓁 is the line joining A and B’ (provided that AB, an arbitrary line, otherwise), and ι(g, h) = P to be interpreted as 𝓁P is the point of intersection of g and h (provided that g and h are distinct and have a point of intersection, an arbitrary point, otherwise), and two binary operation symbols, π1(P, 𝓁) and 2(P, 𝓁), with πi(P, 𝓁) = g (for i = 1, 2) to be interpreted as ‘g is one of the two limiting paralle lines from P to 𝓁 (provided that P is not on 𝓁, an arbitrary line, otherwise).  相似文献   

12.
Let F m × n be the set of all m × n matrices over the field F = C or R Denote by Un (F) the group of all n × n unitary or orthogonal matrices according as F = C or F-R. A norm N() on F m ×n, is unitarily invariant if N(UAV) = N(A): for all AF m×n UU m (F). and VUn (F). We characterize those linear operators T F m × n F m × n which satisfy N (T(A)) = N(A)for all AF m × n

for a given unitarily invariant norm N(). It is shown that the problem is equivalent to characterizing those operators which preserve certain subsets in F m × n To develop the theory we prove some results concerning unitary operators on F m × n which are of independent interest.  相似文献   

13.
In this paper, the unboundedness of solutions for the following planar Hamilton system Ju ′ = ?H (u) + h (t) is discussed, where the function H (u) ∈ C2(R2, R) is positive for u ≠ 0 and is positively (q, p)‐quasihomogeneous of quasi‐degree pq, where p > 1 and + = 1, h: S1R2 with hL(0, 2π) is 2π ‐periodic and J is the standard symplectic matrix. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

14.
The main goal of this note is to study for certain o‐minimal structures the following propriety: for each definable C function g0: [0, 1] → ? there is a definable C function g: [–ε, 1] → ?, for some ε > 0, such that g (x) = g0(x) for all x ∈ [0, 1] (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

15.
Chenggong Hao  Ping Jin   《Journal of Algebra》2008,320(12):4092-4101
Let π(G,A):IrrA(G)→Irr(CG(A)) be the Glauberman–Isaacs correspondence, where G and A are finite groups with coprime orders and A acts on G by automorphisms. Let B be a subgroup of A. In this setting, we give some new conditions for the fixed-point subgroups CG(A) and CG(B) such that χπ(G,A) is an irreducible constituent of the restriction of χπ(G,B) to CG(A) for all χIrrA(G).  相似文献   

16.
17.
Let A be a commutative ring with nonzero identity, 1 ≤ n < ∞ be an integer, and R = A × A × … ×A (n times). The total dot product graph of R is the (undirected) graph TD(R) with vertices R* = R?{(0, 0,…, 0)}, and two distinct vertices x and y are adjacent if and only if x·y = 0 ∈ A (where x·y denote the normal dot product of x and y). Let Z(R) denote the set of all zero-divisors of R. Then the zero-divisor dot product graph of R is the induced subgraph ZD(R) of TD(R) with vertices Z(R)* = Z(R)?{(0, 0,…, 0)}. It follows that each edge (path) of the classical zero-divisor graph Γ(R) is an edge (path) of ZD(R). We observe that if n = 1, then TD(R) is a disconnected graph and ZD(R) is identical to the well-known zero-divisor graph of R in the sense of Beck–Anderson–Livingston, and hence it is connected. In this paper, we study both graphs TD(R) and ZD(R). For a commutative ring A and n ≥ 3, we show that TD(R) (ZD(R)) is connected with diameter two (at most three) and with girth three. Among other things, for n ≥ 2, we show that ZD(R) is identical to the zero-divisor graph of R if and only if either n = 2 and A is an integral domain or R is ring-isomorphic to ?2 × ?2 × ?2.  相似文献   

18.
Let T t : XX be a C 0-semigroup with generator A. We prove that if the abscissa of uniform boundedness of the resolvent s 0(A) is greater than zero then for each nondecreasing function h(s): ?+R + there are x′X′ and xX satisfying ∫ 0 h(|〈x′, T x x〉|)dt = ∞. If i? ∩ Sp(A) ≠ Ø then such x may be taken in D(A ).  相似文献   

19.
《代数通讯》2013,41(2):769-779
Let A, BGL(n, F) be diagonal non-scalar n × n matrices over any field F. It will be discussed under which conditions the product of conjugacy classes of A and B contains all cyclic matrices C with det C = det A det B. A sufficient condition depending on the number of pairwise different eigenvalues of A and B will be formulated.

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20.
Let 〈h n 〉 denote a sequence of positive real numbers. We show that for every set A ? ? there exists a function f: ? → ω such that A = {x ∈ ?: (∈〈h n 〉)[h n ↘ 0 & (? n ∈ ?)(f(x ? h n ) = f(x + h n ) = f(x))]}. This solves a problem of K. Ciesielski, K. Muthuvel and A. Nowik.  相似文献   

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