共查询到20条相似文献,搜索用时 62 毫秒
1.
Russell Merris 《Discrete Mathematics》1982,39(2):167-169
Suppose λ and χ are different irreducible characters of the symmetric group Sm. If the partition of m to which λ corresponds majorizes the partition to which χ corresponds, then , where τ is a transposition and e is the identity. 相似文献
2.
A Ghosh 《Journal of Number Theory》1983,17(1):93-102
Asymptotic formulae for the mean values of |S(t)|λ, where λ is any nonnegative number are proved,. These are then used with λ ∈ , to obtain information of the distribution of |S(t)|. 相似文献
3.
Hermann König 《Journal of Functional Analysis》1977,24(1):32-51
For an open set Ω ? N, 1 ? p ? ∞ and λ ∈ +, let denote the Sobolev-Slobodetzkij space obtained by completing in the usual Sobolev-Slobodetzkij norm (cf. A. Pietsch, “r-nukleare Sobol. Einbett. Oper., Ellipt. Dgln. II,” Akademie-Verlag, Berlin, 1971, pp. 203–215). Choose a Banach ideal of operators , 1 ? p, q ? ∞ and a quasibounded domain Ω ? N. Theorem 1 of the note gives sufficient conditions on λ such that the Sobolev-imbedding map exists and belongs to the given Banach ideal : Assume the quasibounded domain fulfills condition Ckl for some l > 0 and 1 ? k ? N. Roughly this means that the distance of any to the boundary ?Ω tends to zero as for , and that the boundary consists of sufficiently smooth ?(N ? k)-dimensional manifolds. Take, furthermore, 1 ? p, q ? ∞, p > k. Then, if μ, ν are real positive numbers with λ = μ + v ∈ , μ > λ S(; p,q:N) and v > N/l · λD(;p,q), one has that belongs to the Banach ideal . Here λD(;p,q;N)∈+ and λS(;p,q;N)∈+ are the D-limit order and S-limit order of the ideal , introduced by Pietsch in the above mentioned paper. These limit orders may be computed by estimating the ideal norms of the identity mappings lpn → lqn for n → ∞. Theorem 1 in this way generalizes results of R. A. Adams and C. Clark for the ideals of compact resp. Hilbert-Schmidt operators (p = q = 2) as well as results on imbeddings over bounded domains.Similar results over general unbounded domains are indicated for weighted Sobolev spaces.As an application, in Theorem 2 an estimate is given for the rate of growth of the eigenvalues of formally selfadjoint, uniformly strongly elliptic differential operators with Dirichlet boundary conditions in , where Ω fulfills condition C1l.For an open set Ω in N, let denote the Sobolev-Slobodetzkij space obtained by completing in the usual Sobolev-Slobodetzkij norm, see below. Taking a fixed Banach ideal of operators and 1 ? p, q ? ∞, we consider quasibounded domains Ω in N and give sufficient conditions on λ such that the Sobolev imbedding operator exists and belongs to the Banach ideal. This generalizes results of C. Clark and R. A. Adams for compact, respectively, Hilbert-Schmidt operators (p = q = 2) to general Banach ideals of operators, as well as results on imbeddings over bounded domains. Similar results over general unbounded domains may be proved for weighted Sobolev spaces. As an application, we give an estimate for the rate of growth of the eigenvalues of formally selfadjoint, uniformly strongly elliptic differential operators with Dirichlet boundary conditions in , where Ω is a quasibounded open set in N. 相似文献
4.
A t-spread set [1] is a set of (t + 1) × (t + 1) matrices over GF(q) such that ∥C∥ = qt+1, 0 ? C, I?C, and det(X ? Y) ≠ 0 if X and Y are distinct elements of . The amount of computation involved in constructing t-spread sets is considerable, and the following construction technique reduces somewhat this computation. Construction: Let be a subgroup of GL(t + 1, q), (the non-singular (t + 1) × (t + 1) matrices over GF(q)), such that ∥G∥|at+1, and det (G ? H) ≠ 0 if G and H are distinct elements of . Let A1, A2, …, An?GL(t + 1, q) such that det(Ai ? G) ≠ 0 for i = 1, …, n and all G?G, and det(Ai ? AjG) ≠ 0 for i > j and all G?G. Let , and ∥C∥ = qt+1. Then is a t-spread set. A t-spread set can be used to define a left V ? W system over V(t + 1, q) as follows: x + y is the vector sum; let e?V(t + 1, q), then xoy = yM(x) where M(x) is the unique element of with x = eM(x). Theorem: Letbe a t-spread set and F the associatedV ? Wsystem; the left nucleus = {y | CM(y) = C}, and the middle nucleus = }y | M(y)C = C}. Theorem: Forconstructed as aboveG ? {M(x) | x?Nλ}. This construction technique has been applied to construct a V ? W system of order 25 with ∥Nλ∥ = 6, and ∥Nμ∥ = 4. This system coordinatizes a new projective plane. 相似文献
5.
Woody Lichtenstein 《Journal of Functional Analysis》1979,34(3):433-455
For a symmetric space of compact type, the highest-weight vectors for representations of G occurring in become heavily concentrated near certain submanifolds of as the highest weight goes to infinity. This fact is applied to obtain estimates for the spectral measures of the operators qλ = PλqPλ, where is an orthogonal projection onto a G-irreducible summand, and q: G/K → is a continuous function acting on by multiplication. 相似文献
6.
Given an embedding f: G →2 of a graph G in the two-dimensional lattice, let |f| be the maximum L1 distance between points f(x) and f(y) where xy is an edge of G. Let B2(G) be the minimum |f| over all embeddings f. It is shown that the determination of B2(G) for arbitrary G is NP-complete. Essentially the same proof can be used in showing the NP-completeness of minimizing |f| over all embeddings f: G → n of G into the n-dimensional integer lattice for any fixed n ≥ 2. 相似文献
7.
Robert Chen 《Journal of multivariate analysis》1978,8(2):328-333
Let {Xn}n≥1 be a sequence of independent and identically distributed random variables. For each integer n ≥ 1 and positive constants r, t, and ?, let Sn = Σj=1nXj and . In this paper, we prove that (1) lim?→0+?α(r?1)E{N∞(r, t, ?)} = K(r, t) if E(X1) = 0, Var(X1) = 1, and E(| X1 |t) < ∞, where 2 ≤ t < 2r ≤ 2t, , and ; (2) if 2 < t < 4, E(X1) = 0, Var(X1) > 0, and E(|X1|t) < ∞, where G(t, ?) = E{N∞(t, t, ?)} = Σn=1∞nt?2P{| Sn | > ?n} → ∞ as ? → 0+ and , i.e., H(t, ?) goes to infinity much faster than G(t, ?) as ? → 0+ if 2 < t < 4, E(X1) = 0, Var(X1) > 0, and E(| X1 |t) < ∞. Our results provide us with a much better and deeper understanding of the tail probability of a distribution. 相似文献
8.
Hansjörg Kielhöfer 《Journal of Functional Analysis》1980,38(3):416-441
Let X and Y be Banach spaces, Y ?X, and let V be a neighborhood of zero in Y. We consider the equation G(λ, u) ≡ A(λ)u + F(λ, u) = 0, where G: [?d1, d1] × V → X, G(λ, 0) = 0, and A(λ) is the Fréchet derivative of G with respect to u at (λ, 0). Furthermore, we assume that G is analytic with respect to λ and u. Bifurcation at a simple eigenvalue means that zero is a simple eigenvalue of A (0). Let μ(λ) be the simple eigenvalue of the perturbed operator A(λ) for λ near zero. Let . Under the nondegeneracy condition m = 1 the existence of a unique curve of solutions intersecting the trivial solution (λ, 0) at (0, 0) is well known. Furthermore the “Principle of Exchange of Stability” was established in this case. We show that in the degenerate case (m > 1) up to m bifurcating curves of solutions can exist and that at least one nontrivial curve exists if m is odd. Our approach supplies all curves of solutions near (0, 0) together with their direction of bifurcation and their linearized stability. The decisive fact is that Am is also the leading term of the bifurcation equation. A consequence is a “Generalized Principle of Exchange of Stability”, which means that adjacent solutions for the same λ have opposite stability properties in a weakened sense. For practical use we give a criterion for asymptotic stability or instability which follows from the construction of the curves of solutions themselves. 相似文献
9.
Ola Bratteli Frederick M Goodman Palle E.T Jørgensen 《Journal of Functional Analysis》1985,61(3):247-289
Let G be a compact abelian group, and τ an action of G on a C1-algebra , such that τ(γ)τ(γ)1 = τ(0) τ for all , where τ(γ) is the spectral subspace of corresponding to the character γ on G. Derivations δ which are defined on the algebra F of G-finite elements are considered. In the special case δ¦τ = 0 these derivations are characterized by a cocycle on with values in the relative commutant of τ in the multiplier algebra of , and these derivations are inner if and only if the cocycles are coboundaries and bounded if and only if the cocycles are bounded. Under various restrictions on G and τ properties of the cocycle are deduced which again give characterizations of δ in terms of decompositions into generators of one-parameter subgroups of τ(G) and approximately inner derivations. Finally, a perturbation technique is devised to reduce the case δ(F) ? F to the case δ(F) ? F and δ¦τ = 0. This is used to show that any derivation δ with D(δ) = F is wellbehaved and, if furthermore G = T1 and δ(F) ? F the closure of δ generates a one-parameter group of 1-automorphisms of . In the case G = Td, d = 2, 3,… (finite), and δ(F) ? F it is shown that δ extends to a generator of a group of 1-automorphisms of the σ-weak closure of in any G-covariant representation. 相似文献
10.
J.J.A.M Brands 《Journal of Mathematical Analysis and Applications》1978,63(1):54-64
This paper presents some comparison theorems on the oscillatory behavior of solutions of second-order functional differential equations. Here we state one of the main results in a simplified form: Let q, τ1, τ2 be nonnegative continuous functions on (0, ∞) such that τ1 ? τ2 is a bounded function on [1, ∞) and t ? τ1(t) → ∞ if t → ∞. Then is oscillatory if and only if is oscillatory. 相似文献
11.
Stephen Bancroft 《Journal of Mathematical Analysis and Applications》1975,50(2):384-414
In this paper we discuss the problem of determining a T-periodic solution of the differential equation x = A(t)x + f(t, x, λ) + b(t), where the perturbation parameter λ is a vector in a parameter-space Rk. The customary approach assumes that λ = λ(?), ??R. One then establishes the existence of an ?0 > 0 such that the differential equation has a T-periodic solution for all ? satisfying 0 < ? < ?0. More specifically it is usually assumed that λ(?) has the form λ(?) = ?λ0 where λ0 is a fixed vector in Rk. This means that attention is confined in the perturbation procedure to examining the dependence of on λ as λ varies along a line segment terminating at the origin in the parameter-space Rk. The results established here generalize this previous work by allowing one to study the dependence of on λ as λ varies through a “conical-horn” whose vertex rests at the origin in Rk. In the process an implicit-function formula is developed which is of some interest in its own right. 相似文献
12.
Hui-Hsiung Kuo 《Journal of Functional Analysis》1976,21(1):63-75
Some parallel results of Gross' paper (Potential theory on Hilbert space, J. Functional Analysis1 (1967), 123–181) are obtained for Uhlenbeck-Ornstein process U(t) in an abstract Wiener space (H, B, i). Generalized number operator is defined by f(x) = ?lim∈←0{E[f((τ∈ξ))] ? f(x)}/E[τ∈ξ, where τx? is the first exit time of U(t) starting at x from the ball of radius ? with center x. It is shown that f(x) = ?trace D2f(x)+〈Df(x),x〉 for a large class of functions f. Let rt(x, dy) be the transition probabilities of U(t). The λ-potential Gλf, λ > 0, and normalized potential Rf of f are defined by Gλf(X) = ∫0∞e?λtrtf(x) dt and Rf(x) = ∫0∞ [rtf(x) ? rtf(0)] dt. It is shown that if f is a bounded Lip-1 function then trace D2Gλf(x) ? 〈DGλf(x), x〉 = ?f(x) + λGλf(x) and trace D2Rf(x) ? 〈DRf(x), x〉 = ?f(x) + ∫Bf(y)p1(dy), where p1 is the Wiener measure in B with parameter 1. Some approximation theorems are also proved. 相似文献
13.
Clasine van Winter 《Journal of Mathematical Analysis and Applications》1975,49(1):88-123
The quantum mechanics of n particles interacting through analytic two-body interactions can be formulated as a problem of functional analysis on a Hilbert space consisting of analytic functions. On , there is an Hamiltonian H with resolvent R(λ). These quantities are associated with families of operators H(?) and R(λ, ?) on , the case ? = 0 corresponding to standard quantum mechanics. The spectrum of H(?) consists of possible isolated points, plus a number of half-lines starting at the thresholds of scattering channels and making an angle 2? with the real axis.Assuming that the two-body interactions are in the Schmidt class on the two-particle space , this paper studies the resolvent R(λ, ?) in the case ? ≠ 0. It is shown that a well known Fredholm equation for R(λ, ?) can be solved by the Neumann series whenever ¦λ¦ is sufficiently large and λ is not on a singular half-line. Owing to this, R(λ, ?) can be integrated around the various half-lines to yield bounded idempotent operators Pp(?) (p = 1, 2,…) on . The range of Pp(?) is an invariant subspace of H(?). As ? varies, the family of operators Pp(?) generates a bounded idempotent operator Pp on a space . The range of this is an invariant subspace of H. The relevance of this result to the problem of asymptotic completeness is indicated. 相似文献
14.
If X is a point random field on d then convergence in distribution of the renormalization Cλ|Xλ ? αλ| as λ → ∞ to generalized random fields is examined, where Cλ > 0, αλ are real numbers for λ > 0, and Xλ(f) = λ?dX(fλ) for . If such a scaling limit exists then Cλ = λθg(λ), where g is a slowly varying function, and the scaling limit is self-similar with exponent θ. The classical case occurs when and the limit process is a Gaussian white noise. Scaling limits of subordinated Poisson (doubly stochastic) point random fields are calculated in terms of the scaling limit of the environment (driving random field). If the exponent of the scaling limit is then the limit is an independent sum of the scaling limit of the environment and a Gaussian white noise. If the scaling limit coincides with that of the environment while if the limit is Gaussian white noise. Analogous results are derived for cluster processes as well. 相似文献
15.
If A∈T(m, N), the real-valued N-linear functions on Em, and σ∈SN, the symmetric group on {…,N}, then we define the permutation operator Pσ: T(m, N) → T(m, N) such that Pσ(A)(x1,x2,…,xN = A(xσ(1),xσ(2),…, xσ(N)). Suppose Σqi=1ni = N, where the ni are positive integers. In this paper we present a condition on σ that is sufficient to guarantee that 〈Pσ(A1?A2???Aq),A1?A2?? ? Aq〉 ? 0 for Ai∈S(m, ni), where S(m, ni) denotes the subspace of T(m, ni) consisting of all the fully symmetric members of T(m, ni). Also we present a broad generalization of the Neuberger identity which is sometimes useful in answering questions of the type described below. Suppose G and H are subgroups of SN. We let TG(m, N) denote all A∈T(m, N) such that Pσ(A) = A for all σ∈G. We define the symmetrizer G: T(m, N)→TG(m,N) such that . Suppose H is a subgroup of G and A∈TH(m, N). Clearly We are interested in the reverse type of comparison. In particular, if D is a suitably chosen subset of TH(m,N), then can we explicitly present a constant C>0 such that for all A∈D? 相似文献
16.
P Hanlon 《Journal of Combinatorial Theory, Series B》1985,38(3):226-239
We investigate the chromatic polynomial χ(G, λ) of an unlabeled graph G. It is shown that , where g is any labeled version of G, A(g) is the automorphism group of g and χ(g, π, λ) is the chromatic polynomial for colorings of g fixed by π. The above expression shows that χ(G, λ) is a rational polynomial of degree n = |V(G)| with leading coefficient . Though χ(G, λ) does not satisfy chromatic reduction, each polynomial χ(g, π, λ) does, thus yielding a simple method for computing χ(G, λ). We also show that the number N(G) of acyclic orientations of G is related to the argument λ = ?1 by the formula , where s(π) is the number of cycles of π. This information is used to derive Robinson's (“Combinatorial Mathematics V” (Proc. 5th Austral. Conf. 1976), Lecture Notes in Math. Vol. 622, pp. 28–43, Springer-Verlag, New York/Berlin, 1977) cycle index sum equations for counting unlabeled acyclic digraphs. 相似文献
17.
Let G be a simple graph with least eigenvalue λ and let S be a set of vertices in G which induce a subgraph with mean degree k. We use a quadratic programming technique in conjunction with the main angles of G to establish an upper bound of the form |S|?inf{(k+t)qG(t):t>-λ} where qG is a rational function determined by the spectra of G and its complement. In the case k=0 we obtain improved bounds for the independence number of various benchmark graphs. 相似文献
18.
Jean-Bernard Baillon 《Journal of Functional Analysis》1978,29(2):199-213
Let C be a closed convex subset of a uniformly smooth Banach space. Let S(t) : C → C be a semigroup of type ω. Then the generator A0 of S(t) has a dense domain in C. Moreover there is is an operator A such that: (i) A0 ? A and accretive, (iii) R(I + λA) ? C for λ > 0 and ωλ < 1, (iv) for every x?C. 相似文献
19.
Agnes Hui Chan 《Discrete Mathematics》1981,37(1):29-33
Let be a class of subsets of a finite set X. Elements of are called blocks. Let υ, t, λ and k be nonnegative integers such that υ?k?t?0. A pair (X, ) is called a (υ, k, λ) t-design, denoted by Sλ(t, k, υ), if (1) |X| = υ, (2) every t-subset of X is contained in exactly λ blocks and (3) for every block A in , |A| = k. A Möbius plane M is an S1(3, q+1, q2+1) where q is a positive integer. Let ∞ be a fixed point in M. If ∞ is deleted from M, together with all the blocks containing ∞, then we obtain a point-residual design M*. It can be easily checked that M* is an Sq(2, q+1, q2). Any Sq(2, q+1, q2) is called a pseudo-point-residual design of order q, abbreviated by PPRD(q). Let A and B be two blocks in a PPRD(q)M*. A and B are said to be tangent to each other at z if and only if A∩B={z}. M* is said to have the Tangency Property if for any block A in M*, and points x and y such that x?A and y?A, there exists at most one block containing y and tangent to A at x. This paper proves that any PPRD(q)M* is uniquely embeddable into a Möbius plane if and only if M* satisfies the Tangency Property. 相似文献
20.
Alan P Sprague 《Journal of Combinatorial Theory, Series B》1978,24(3):294-300
We denote the distance between vertices x and y of a graph by d(x, y), and pij(x, y) = ∥ {z : d(x, z) = i, d(y, z) = j} ∥. The (s, q, d)-projective graph is the graph having the s-dimensional subspaces of a d-dimensional vector space over GF(q) as vertex set, and two vertices x, y adjacent iff . These graphs are regular graphs. Also, there exist integers λ and μ > 4 so that μ is a perfect square, p11(x, y) = λ whenever d(x, y) = 1, and p11(x, y) = μ whenever d(x, y) = 2. The (s, q, d)-projective graphs where and , are characterized by the above conditions together with the property that there exists an integer r satisfying certain inequalities. 相似文献