共查询到20条相似文献,搜索用时 828 毫秒
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2.
It was proved by R. Gomory and T. Hu in 1961 that, for every finite nonempty ultrametric space (X, d), the inequaliy \( \left| {\mathrm{Sp}(X)} \right|\leq \left| X \right|-1 \), where Sp(X) = {d(x, y) : x, y ∈ X, x ≠ y} , holds. We characterize the spaces X for which the equality is attained by the structural properties of some graphs and show that the set of isometric types of such X is dense in the Gromov–Hausdorff space of the isometric types of compact ultrametric spaces. 相似文献
3.
The paper studies the differential properties of functions of the form where x ∈ X (X is an open convex set from ? m ) and y ∈ Y (Y is a compact from ? n ). Apart from the conventional smoothness conditions imposed on f(x, y), the condition of the concavity of g(x) on X is also imposed.
The differentiability of function g(x) on X is proved.The results of the study facilitate the derivation of the conditions ensuring the sufficiency of Pontryagin’s maximum principle. 相似文献
$g(x) = \mathop {\max }\limits_{y \in Y} f(x,y),$
4.
Let G be a graph and k ≥ 2 a positive integer. Let h: E(G) → [0, 1] be a function. If \(\sum\limits_{e \mathrel\backepsilon x} {h(e) = k} \) holds for each x ∈ V (G), then we call G[Fh] a fractional k-factor of G with indicator function h where Fh = {e ∈ E(G): h(e) > 0}. A graph G is fractional independent-set-deletable k-factor-critical (in short, fractional ID-k-factor-critical), if G ? I has a fractional k-factor for every independent set I of G. In this paper, we prove that if n ≥ 9k ? 14 and for any subset X ? V (G) we have then G is fractional ID-k-factor-critical.
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$${N_G}(X) = V(G)if|X| \geqslant \left\lfloor {\frac{{kn}}{{3k - 1}}} \right\rfloor ;or|{N_G}(X)| \geqslant \frac{{3k - 1}}{k}|X|if|X| < \left\lfloor {\frac{{kn}}{{3k - 1}}} \right\rfloor ,$$
5.
O. A. Alekseeva A. S. Kondrat’ev 《Proceedings of the Steklov Institute of Mathematics》2009,266(1):10-23
It is proved that, if G is a finite group that has the same set of element orders as the simple group D p (q), where p is prime, p ≥ 5 and q ∈ {2, 3, 5}, then the commutator group of G/F(G) is isomorphic to D p (q), the subgroup F(G) is equal to 1 for q = 5 and to O q (G) for q ∈ {2, 3}, F(G) ≤ G′, and |G/G′| ≤ 2. 相似文献
6.
Let G be a simple algebraic group defined over an algebraically closed field of characteristic 0 or a good prime for G. Let U be a maximal unipotent subgroup of G and \( \mathfrak{u} \) its Lie algebra. We prove the separability of orbit maps and the connectedness of centralizers for the coadjoint action of U on (certain quotients of) the dual \( \mathfrak{u} \)* of \( \mathfrak{u} \). This leads to a method to give a parametrization of the coadjoint orbits in terms of so-called minimal representatives which form a disjoint union of quasi-affine varieties. Moreover, we obtain an algorithm to explicitly calculate this parametrization which has been used for G of rank at most 8, except E8.When G is defined and split over the field of q elements, for q the power of a good prime for G, this algorithmic parametrization is used to calculate the number k(U(q); \( \mathfrak{u} \)*(q)) of coadjoint orbits of U(q) on \( \mathfrak{u} \)*(q). Since k(U(q), \( \mathfrak{u} \)*(q)) coincides with the number k(U(q)) of conjugacy classes in U(q), these calculations can be viewed as an extension of the results obtained in [11]. In each case considered here there is a polynomial h(t) with integer coefficients such that for every such q we have k(U(q)) = h(q). We also explain implications of our results for a parametrization of the irreducible complex characters of U(q). 相似文献
7.
O. P. Filatov 《Differential Equations》2008,44(3):349-363
We consider the system of differential inclusions , where F,G: D → Kυ (\(R^{m_1 } \)), Kυ (\(R^{m_2 } \)) are mappings into the sets of nonempty convex compact sets in the Euclidean spaces \(R^{m_1 } \) and \(R^{m_2 } \), respectively, D = R + × \(R^{m_1 } \) × \(R^{m_2 } \) × [0, a], a > 0, and µ is a small parameter. The functions F and G and the right-hand side of the averaged problem \(\dot u\) ∈ µF 0(u), u(0) = x 0, F 0(u) ∈ Kυ (\(R^{m_1 } \)), satisfy the one-sided Lipschitz condition with respect to the corresponding phase variables. Under these and some other conditions, we prove that, for each ? > 0, there exists a µ > 0 such that, for an arbitrary µ ∈ (0, µ0] and any solution x µ(·), y µ(·) of the original problem, there exists a solution u µ(·) of the averaged problem such that ∥x µ(t) ? y µ(t) ∥ ≤ ? for t ∈ [0, 1/µ]. Furthermore, for each solution u µ(·)of the averaged problem, there exists a solution x µ(·), y µ(·) of the original problem with the same estimate.
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$$\dot x \in \mu F(t, x, y, \mu ), x(0) = x_0 , \dot y \in G(t, x, y, \mu ), y(0) = y_0 $$
8.
Let G be a nonabelian group, and associate the noncommuting graph ?(G) with G as follows: the vertex set of ?(G) is G\Z(G) with two vertices x and y joined by an edge whenever the commutator of x and y is not the identity. Let S 4(q) be the projective symplectic simple group, where q is a prime power. We prove that if G is a group with ?(G) ? ?(S 4(q)) then G ? S 4(q). 相似文献
9.
Igor I. Skrypnik 《Israel Journal of Mathematics》2016,212(1):163-188
We study the well-posedness of the third-order degenerate differential equation \(\left( {{P_3}} \right):\alpha {\left( {Mu} \right)^{\prime \prime \prime }}\left( t \right) + {\left( {Mu} \right)^{\prime \prime }}\left( t \right) = \beta Au\left( t \right) + f\left( t \right)\), (t ∈ [0, 2p]) with periodic boundary conditions \(Mu\left( 0 \right) = Mu\left( {2\pi } \right),\;Mu'\left( 0 \right) = Mu'\left( {2\pi } \right),\;Mu''\left( 0 \right) = Mu''\left( {2\pi } \right)\), in periodic Lebesgue–Bochner spaces Lp(T,X), periodic Besov spaces Bp,qs(T,X) and periodic Triebel–Lizorkin spaces Fp,qs(T,X), where A, B and M are closed linear operators on a Banach space X satisfying D(A) \( \cap \)D(B) ? D(M) and α, β, γ ∈ R. Using known operator-valued Fourier multiplier theorems, we completely characterize the well-posedness of (P3) in the above three function spaces. 相似文献
10.
Let (X, μ) and (Y, ν) be standard measure spaces. A function \({\varphi\in L^\infty(X\times Y,\mu\times\nu)}\) is called a (measurable) Schur multiplier if the map S φ , defined on the space of Hilbert-Schmidt operators from L 2(X, μ) to L 2(Y, ν) by multiplying their integral kernels by φ, is bounded in the operator norm. The paper studies measurable functions φ for which S φ is closable in the norm topology or in the weak* topology. We obtain a characterisation of w*-closable multipliers and relate the question about norm closability to the theory of operator synthesis. We also study multipliers of two special types: if φ is of Toeplitz type, that is, if φ(x, y) = f(x ? y), \({x,y\in G}\), where G is a locally compact abelian group, then the closability of φ is related to the local inclusion of f in the Fourier algebra A(G) of G. If φ is a divided difference, that is, a function of the form (f(x) ? f(y))/(x ? y), then its closability is related to the “operator smoothness” of the function f. A number of examples of non-closable, norm closable and w*-closable multipliers are presented. 相似文献
11.
Let T X denote the full transformation semigroup on a set X. For an equivalence E on X, let Then T ?(X) is exactly the semigroup of mappings on the topological space X for which the collection of all E-classes is a basis. In this paper, we discuss regularity of elements and Green’s relations for T ?(X).
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$T_{\exists}(X)=\{\alpha\in T_X:\forall x,y\in X,(x\alpha,y\alpha)\in E\Rightarrow(x,y)\in E\}.$
12.
It is proved that if an entire function f: ? → ? satisfies an equation of the form α 1(x)β 1(y) + α 2(x)β 2(y) + α 3(x)β 3(y), x,y ∈ C, for some α j , β j : ? → ? and there exist no \({\widetilde \alpha _j}\) and ?\({\widetilde \beta _j}\) for which \(f\left( {x + y} \right)f\left( {x - y} \right) = {\overline \alpha _1}\left( x \right){\widetilde \beta _1}\left( y \right) + {\overline \alpha _2}\left( x \right){\widetilde \beta _2}\left( y \right)\), then f(z) = exp(Az 2 + Bz + C) ? σ Γ(z - z 1) ? σ Γ(z - z 2), where Γ is a lattice in ?; σ Γ is the Weierstrass sigma-function associated with Γ; A,B,C, z 1, z 2 ∈ ?; and \({z_1} - {z_2} \notin \left( {\frac{1}{2}\Gamma } \right)\backslash \Gamma \). 相似文献
13.
Let ?: E(G) → {1, 2, · · ·, k} be an edge coloring of a graph G. A proper edge-k-coloring of G is called neighbor sum distinguishing if \(\sum\limits_{e \mathrel\backepsilon u} {\phi \left( e \right)} \ne \sum\limits_{e \mathrel\backepsilon v} {\phi \left( e \right)} \) for each edge uv ∈ E(G). The smallest value k for which G has such a coloring is denoted by χ′Σ(G), which makes sense for graphs containing no isolated edge (we call such graphs normal). It was conjectured by Flandrin et al. that χ′Σ(G) ≤ Δ(G) + 2 for all normal graphs, except for C5. Let mad(G) = \(\max \left\{ {\frac{{2\left| {E\left( h \right)} \right|}}{{\left| {V\left( H \right)} \right|}}|H \subseteq G} \right\}\) be the maximum average degree of G. In this paper, we prove that if G is a normal graph with Δ(G) ≥ 5 and mad(G) < 3 ? \(\frac{2}{{\Delta \left( G \right)}}\), then χ′Σ(G) ≤ Δ(G) + 1. This improves the previous results and the bound Δ(G) + 1 is sharp. 相似文献
14.
I. V. Sadovnichaya 《Differential Equations》2009,45(4):520-525
In the space L 2(?), we consider the self-adjoint extension \(\mathcal{L}\) of the Sturm-Liouville operator ly = ?y″ + q(x)y whose potential q is uniformly locally integrable on ?, i.e., satisfies the condition . We study the problem on the equiconvergence rate of the spectral expansion associated with \(\mathcal{L}\) of a function f ∈ L 1(?) with the Fourier integral on the entire real line. We obtain uniform estimates of the equiconvergence rate under some additional conditions on f or q.
相似文献
$\omega _q (h) = \mathop {\sup }\limits_{x \in \mathbb{R}} \int\limits_x^{x + h} {\left| {q(t)} \right|dt < + \infty ,h > 0.} $
15.
Youri Davydov 《Lithuanian Mathematical Journal》2011,51(2):171-179
Let X i = {X i (t), t ∈ T} be i.i.d. copies of a centered Gaussian process X = {X(t), t ∈ T} with values in\( {\mathbb{R}^d} \) defined on a separable metric space T. It is supposed that X is bounded. We consider the asymptotic behavior of convex hullsand show that, with probability 1,(in the sense of Hausdorff distance), where the limit shape W is defined by the covariance structure of X: W = conv{K t , t ∈ T}, Kt being the concentration ellipsoid of X(t). We also study the asymptotic behavior of the mathematical expectations E f(W n ), where f is an homogeneous functional.
相似文献
$ {W_n} = {\text{conv}}\left\{ {{X_1}(t), \ldots, {X_n}(t),\,\,t \in T} \right\} $
$ \mathop {{\lim }}\limits_{n \to \infty } \frac{1}{{\sqrt {{2\ln n}} }}{W_n} = W $
16.
Let X and Y be completely regular spaces and E and F be Hausdorff topological vector spaces. We call a linear map T from a subspace of C(X, E) into C(Y, F) a Banach–Stone map if it has the form T f (y) = S y (f (h(y))) for a family of linear operators S y : E → F, \({y \in Y}\) , and a function h: Y → X. In this paper, we consider maps having the property: where Z(f) = {f = 0}. We characterize linear bijections with property (Z) between spaces of continuous functions, respectively, spaces of differentiable functions (including C ∞), as Banach–Stone maps. In particular, we confirm a conjecture of Ercan and Önal: Suppose that X and Y are realcompact spaces and E and F are Hausdorff topological vector lattices (respectively, C *-algebras). Let T: C(X, E) → C(Y, F) be a vector lattice isomorphism (respectively, *-algebra isomorphism) such thatThen X is homeomorphic to Y and E is lattice isomorphic (respectively, C *-isomorphic) to F. Some results concerning the continuity of T are also obtained.
相似文献
$\bigcap^{k}_{i=1}Z(f_{i}) \neq\emptyset \iff \bigcap^{k}_{i=1}Z(Tf_{i})\neq\emptyset , \quad({\rm Z}) $
$ Z(f) \neq\emptyset\iff Z(Tf) \neq\emptyset. $
17.
V. F. Molchanov 《Functional Analysis and Its Applications》2005,39(4):284-295
For the hyperboloid \(X = G/H\), where G = SO0(p, q) and H = SO0(p, q ? 1), we define canonical representations Rλ,ν λ ∈ ?, ν = 0, 1, as the restrictions to G of representations \(\tilde R\lambda ,\nu\), associated with a cone, of the group \(\tilde G = \operatorname{SO} _0 (p + 1,q)\). They act on functions on the direct product Ω of two spheres of dimensions p ? 1 and q ? 1. The manifold Ω contains two copies of \(X\) as open G-orbits. We explicitly describe the interaction of the Lie operators of the group \({\tilde G}\) in \(\tilde R\lambda ,\nu\) with the Poisson and Fourier transforms associated with the canonical representations. These transforms are operators intertwining the representations Rλ,ν with representations of G associated with a cone. 相似文献
18.
E. S. Zhukovskiy 《Siberian Mathematical Journal》2018,59(6):1063-1072
The recent articles of Arutyunov and Greshnov extend the Banach and Hadler Fixed-Point Theorems and the Arutyunov Coincidence-Point Theorem to the mappings of (q1, q2)-quasimetric spaces. This article addresses similar questions for f-quasimetric spaces.Given a function f: R +2 → R+ with f(r1, r2) → 0 as (r1, r2) → (0, 0), an f-quasimetric space is a nonempty set X with a possibly asymmetric distance function ρ: X2 → R+ satisfying the f-triangle inequality: ρ(x, z) ≤ f(ρ(x, y), ρ(y, z)) for x, y, z ∈ X. We extend the Banach Contraction Mapping Principle, as well as Krasnoselskii’s and Browder’s Theorems on generalized contractions, to mappings of f-quasimetric spaces. 相似文献
19.
Let L be a Schrdinger operator of the form L =-? + V acting on L~2(R~n), n≥3, where the nonnegative potential V belongs to the reverse Hlder class B_q for some q≥n. Let BMO_L(R~n) denote the BMO space associated to the Schrdinger operator L on R~n. In this article, we show that for every f ∈ BMO_L(R~n) with compact support, then there exist g ∈ L~∞(R~n) and a finite Carleson measure μ such that f(x) = g(x) + S_(μ,P)(x) with ∥g∥∞ + |||μ|||c≤ C∥f∥BMO_L(R~n), where S_(μ,P)=∫(R_+~(n+1))Pt(x,y)dμ(y, t),and Pt(x, y) is the kernel of the Poisson semigroup {e-~(t(L)~(1/2))}t0 on L~2(R~n). Conversely, if μ is a Carleson measure, then S_(μ,P) belongs to the space BMO_L(R~n). This extends the result for the classical John-Nirenberg BMO space by Carleson(1976)(see also Garnett and Jones(1982), Uchiyama(1980) and Wilson(1988)) to the BMO setting associated to Schrdinger operators. 相似文献
20.
Let G be a digraph with n vertices, a arcs, c 2 directed closed walks of length 2. Let q1; q2;:::; q n be the eigenvalues of the signless Laplacian matrix of G. The signless Laplacian energy of a digraph G is defined as E SL (G) = \(\sum\limits_{i = 1}^n {\left| {{q_i} - \frac{a}{n}} \right|} \). In this paper, some lower and upper bounds are derived for the signless Laplacian energy of digraphs. 相似文献