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Let F be an algebraically closed field. Let V be a vector space equipped with a non-degenerate symmetric or symplectic bilinear form B over F. Suppose the characteristic of F is sufficiently large , i.e. either zero or greater than the dimension of V. Let I(V,B) denote the group of isometries. Using the Jacobson–Morozov lemma we give a new and simple proof of the fact that two elements in I(V,B) are conjugate if and only if they have the same elementary divisors. 相似文献
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An ACI-matrix over a field F is a matrix whose entries are polynomials with coefficients on F, the degree of these polynomials is at most one in a number of indeterminates, and where no indeterminate appears in two different columns. In 2011 Huang and Zhan characterized the m×n ACI-matrices such that all its completions have rank equal to min{m,n} whenever |F|?max{m,n+1}. We will give a characterization for arbitrary fields by introducing two classes of ACI-matrices: the maximal and the minimal full rank ACI-matrices. 相似文献
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Given an arbitrarily weak notion of left-〈f〉-porosity and an arbitrarily strong notion of right-〈g〉-porosity, we construct an example of closed subset of R which is not σ -left-〈f〉-porous and is right-〈g〉-porous. We also briefly summarize the relations between three different definitions of porosity controlled by a function; we then observe that our construction gives the example for any combination of these definitions of left-porosity and right-porosity. 相似文献
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In this paper we propose the R-K type Landweber iteration and investigate the convergence of the method for nonlinear ill-posed problem F(x)=y where F:H→H is a nonlinear operator between Hilbert space H . Moreover, for perturbed data with noise level δ we prove that the convergence rate is O(δ2/3) under appropriate conditions. Finally, the numerical performance of this R-K type Landweber iteration for a nonlinear convolution equation is compared with the Landweber iteration. 相似文献
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Let F be an infinite field with characteristic not equal to two. For a graph G=(V,E) with V={1,…,n}, let S(G;F) be the set of all symmetric n×n matrices A=[ai,j] over F with ai,j≠0, i≠j if and only if ij∈E. We show that if G is the complement of a partial k -tree and m?k+2, then for all nonsingular symmetric m×m matrices K over F, there exists an m×n matrix U such that UTKU∈S(G;F). As a corollary we obtain that, if k+2?m?n and G is the complement of a partial k-tree, then for any two nonnegative integers p and q with p+q=m, there exists a matrix in S(G;R) with p positive and q negative eigenvalues. 相似文献
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This paper is devoted to a problem of finding the smallest positive integer s(m,n,k) such that (m+1) generic skew-symmetric (k+1)-forms in (n+1) variables as linear combinations of the same s(m,n,k) decomposable skew-symmetric (k+1)-forms. 相似文献
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M. Gürdal 《Expositiones Mathematicae》2009,27(2):153-160
In the present paper we consider the Volterra integration operator V on the Wiener algebra W(D) of analytic functions on the unit disc D of the complex plane C. A complex number λ is called an extended eigenvalue of V if there exists a nonzero operator A satisfying the equation AV=λVA. We prove that the set of all extended eigenvalues of V is precisely the set C?{0}, and describe in terms of Duhamel operators and composition operators the set of corresponding extended eigenvectors of V. The similar result for some weighted shift operator on ?p spaces is also obtained. 相似文献
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Let K be a closed convex subset of a q-uniformly smooth separable Banach space, T:K→K a strictly pseudocontractive mapping, and f:K→K an L-Lispschitzian strongly pseudocontractive mapping. For any t∈(0,1), let xt be the unique fixed point of tf+(1-t)T. We prove that if T has a fixed point, then {xt} converges to a fixed point of T as t approaches to 0. 相似文献
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For a non-degenerate convex subset Y of the n -dimensional Euclidean space Rn, let F(Y) be the family of all fuzzy sets of Rn which are upper semicontinuous, fuzzy convex and normal with compact supports contained in Y . We show that the space F(Y) with the topology of sendograph metric is homeomorphic to the separable Hilbert space ?2 if Y is compact; and the space F(Rn) is also homeomorphic to ?2. 相似文献
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Given a metric continuum X, we consider the following hyperspaces of X : 2X, Cn(X) and Fn(X) (n∈N). Let F1(X)={{x}:x∈X}. A hyperspace K(X) of X is said to be rigid provided that for every homeomorphism h:K(X)→K(X) we have that h(F1(X))=F1(X). In this paper we study under which conditions a continuum X has a rigid hyperspace Fn(X). 相似文献
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We present a regularity result for weak solutions of the 2D quasi-geostrophic equation with supercritical (α<1/2) dissipation α(−Δ): If a Leray–Hopf weak solution is Hölder continuous θ∈Cδ(R2) with δ>1−2α on the time interval [t0,t], then it is actually a classical solution on (t0,t]. 相似文献
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The subconstituents of the orthogonal graph O(2ν+δ,q), where ν?2 and δ∈{1,2}, over a finite field of odd characteristic are shown to be quasi-strongly regular. Furthermore, the first subconstituent is shown to be co-edge regular, and when ν?3 its automorphism group is determined. The second subconstituent is shown to be edge regular, and when ν?2 its automorphism group is determined. Their parameters and chromatic numbers are also determined. 相似文献