共查询到20条相似文献,搜索用时 46 毫秒
1.
Umberto Cerruti 《Journal of Mathematical Analysis and Applications》1983,94(2):312-327
It is shown that the category of complete L-similarities on L-sets is a full reflective subcategory of (L) (L-fuzzy graphs); is equivalent to (L)(sheaves on L). Connections with other known “fuzzy” categories are also studied. 相似文献
2.
Fopke Klok 《Journal of Differential Equations》1984,55(1):101-134
A real-valued function L on the tangent bundle of n gives rise to variational problems as follows: for two points x0, x1 in n and a time interval [0, T] to determine a curve γ: [O,T] → n, connecting x0 with x1 which minimizes ∫0TL(γ(t), gg(t)) dt. We consider the associated Hamiltonian vectorfield on the cotangent bundle. If L is not convex on each fibre then the corresponding Hamiltonian vectorfield is not continuous. For homogeneous L and n = 2 restriction to an energy level gives an essentially three-dimensional vectorfield. In this case we list the possible discontinuities for generic L. Then we observe that there exits an open class of such variational problems, which admit no minimizing solution. 相似文献
3.
Siegfried Gottwald 《Fuzzy Sets and Systems》1980,3(2):181-192
Fuzzy logic ∞9 considered in connection with fuzzy sets theory, is a special theory, is a special many valued logic with truth-value sets [0, 1], which has been studied already by Lukasiewicz. We consider also his versions m for m ? 2 with finite truth-value sets. In all cases we add two further propositional connectives, one conjunction and one disjunction. For these logics we give a list of tautologies, consider relations between their sets of tautologies, prove their compactness, and mention some further results. 相似文献
4.
Let be a strongly equicontinuous Boolean algebra of projections on the quasi-complete locally convex space X and assume that the space L(X) of continuous linear operators on X is sequentially complete for the strong operator topology. Methods of integration with respect to spectral measures are used to show that the closed algebra generated by in L(X) consists precisely of those continuous linear operators on X which leave invariant each closed -invariant subspace of X. 相似文献
5.
The paper deals with the following: (I) If S is a subnormal operator on , then (S) = (S) = Alg Lat S. (II) If L ∈ ((S), σ-wot)1, then there exist vectors a and b in such that L(T) = 〈Ta, b〉 for every T in . (III) In addition to I the map i(T) = T is a homeomorphism from (, σ-wot) onto ((S), wot). (IV) If S is not a reductive normal operator, then there exists a cyclic invariant subspace for S that has an open set of bounded point evaluations. (This open set can be constructed to be as large as possible.) 相似文献
6.
John Palmer 《Journal of Functional Analysis》1978,27(3):308-336
In this paper a Cohen factorization theorem x = at · xt (t > 0) is proved for a Banach algebra A with a bounded approximate identity, where t ? at is a continuous one-parameter semigroup in A. This theorem is used to show that a separable Banach algebra B has a bounded approximate identity bounded by 1 if and only if there is a homomorphism θ from L1(+) into B such that ∥ θ ∥ = 1 and θ(L1(+)). B = B = B · θ(L1(+)). Another corollary is that a separable Banach algebra with bounded approximate identity has a commutative bounded approximate identity, which is bounded by 1 in an equivalent algebra norm. 相似文献
7.
Palle E.T. Jørgensen 《Advances in Mathematics》1982,44(2):105-120
Let Ω be an arbitrary open subset of n of finite positive measure, and assume the existence of a subset Λ ? n such that the exponential functions eλ = exp i(λ1x1 + … + λnxn), λ = (λ1,…, λn) ∈ Λ, form an orthonormal basis for with normalized measure. Assume 0 ∈ Λ and define subgroups K and A of (n, +) by K = Λ0 = {γ ∈ n:γ·λ ∈ 2π}, A = {a ∈ n:Ua U1a = }, where Ut is the unitary representation of n on given by Ute = eitλeλ, t ∈ n, λ ∈ Λ, and where is the multiplication algebra of on L2. Assume that A is discrete. Then there is a discrete subgroup D ? A of dimension n, a fundamental domain for D, and finite sets of representers RΛ, RΓ, , each containing 0, RΛ for in K0, and for in A such that Ω is disjoint union of translates of : Ω = ∪a∈RΩ (a + ), neglecting null sets, and Λ = RΛ ⊕ D0. If RΓ is a set of representers for in D, then Γ = RΓ ⊕ K is a translation set for Ω, i.e., Ω ⊕ Γ = n, direct sum, (neglecting null sets). The case A = n corresponds to Ω = , Λ = D0 and Γ = K. This last case corresponds in turn to a function theoretic assumption of Forelli. 相似文献
8.
George Hutchinson 《Journal of Pure and Applied Algebra》1977,10(2):115-119
Let R be a ring with 1, Rop the opposite ring, and R-Mod the category of left unitary R-modules and R-linear maps. A characterization of well-powered abelian categories such that there exists an exact embedding functor →R-Mod is given. Using this characterization and abelian category duality, the following duality principles can be established.Theorem. There exists an exact embedding functor →R-Mod if and only if there exists an exact embedding functor op→Rop-Mod.Corollary. If R-Mod has a specified diagram-chasing property, then Rop-Mod has the dual property.A lattice L is representable by R-modules if it is embeddable in the lattice of submodules of some unitary left R-module; (R) denotes the quasivariety of all lattices representable by R-modules.Theorem. A lattice L is representable by R-modules if and only if its order dual L1 is representable by Rop-modules. That is, .If is a commutative ring with 1 and a specified diagram-chasing result is satisfied in R-Mod, then the dual result is also satisfied in R-Mod. Furthermore, is self-dual: 相似文献
9.
Ronald E Bruck 《Journal of Mathematical Analysis and Applications》1980,76(1):159-173
We show that if u is a bounded solution on + of u″(t) ?Au(t) + f(t), where A is a maximal monotone operator on a real Hilbert space H and f∈Lloc2(+;H) is periodic, then there exists a periodic solution ω of the differential equation such that u(t) ? ω(t) 0 and u′(t) ? ω′(t) → 0 as t → ∞. We also show that the two-point boundary value problem for this equation has a unique solution for boundary values in and that a smoothing effect takes place. 相似文献
10.
Robert S Strichartz 《Journal of Functional Analysis》1973,12(4):341-383
The regular representation of O(n, N) acting on is decomposed into a direct integral of irreducible representations. The homogeneous space is realized as the Hyperboloid . The problem is essentially equivalent to finding the spectral resolution of a certain self-adjoint invariant differential operator □h on H, which is the tangential part of the operator □ = Δx ? Δt on Rn + N. The spectrum of □h contains a discrete part (except when N = 1) with eigenfunctions generated by restricting to H solutions of □u = 0 which vanish in the region , and a continuous part ?. As a representation of O(n, N), ? ⊕ ? is unitarily equivalent to the regular representation on L2 of the cone , and the intertwining operator is obtained by solving the equation □u = 0 with given boundary values on the cone. Explicit formulas are given for the spectral decomposition. The special case n = N = 2 gives the Plancherel formula for SL(2, R). 相似文献
11.
James G. Hooton 《Journal of Mathematical Analysis and Applications》1981,83(2):570-581
We provide conditions on a finite measure μ on n which insure that the imbeddings Wk, p(ndμ)?Lp(ndμ) are compact, where 1 ? p < ∞ and k is a positive integer. The conditions involve uniform decay of the measure μ for large ¦x¦ and are satisfied, for example, by . 相似文献
12.
A weighted translation semigroup {St} on L2(+) is defined by for x ? t and 0 otherwise, where φ is a continuous nonzero scalar-valued function on +. It is shown that {St} is subnormal if and only if φ2 is the product of an exponential function and the Laplace-Stieltjes transform of an increasing function of total variation one. A necessary and sufficient condition for similarity of weighted translation semigroups is developed. 相似文献
13.
We consider nonlinear elliptic eigenvalue problems on unbounded domains G?n. Using an extended Ljusternik-Schnirelman theory we prove the existence of infinitely many eigenfunctions on every sphere in L2(G). Moreover, we establish that the infimum λ1 of the spectrum of the linearized problem L is always a bifurcation point. In addition, there is an infinity of branches emanating at λ1 from the trivial line of solutions if λ1 belongs to the essential spectrum of L. 相似文献
14.
Hans G Kaper 《Journal of Mathematical Analysis and Applications》1978,63(3):691-718
In this article we discuss the solution of boundary value problems which are described by the linear integrodifferential equation , where t∈J?, x∈. We interpret the equation in functional form as an ordinary differential equation for the mapping u:J→L2(R,μ), where L2(R,μ) is a weighted L2-space. Emphasis is on the constructive aspects of the solution and on finding representations of the relevant isomorphisms. 相似文献
15.
Matania Ben Artzi 《Journal of Differential Equations》1984,52(3):327-341
Let be a Schrödinger operator in Rn. Here is an “exploding” radially symmetric potential which is at least C2 monotone nonincreasing and O(r2) as r → ∞. V is a general potential which is short range with respect to VE. In particular, VE 0 leads to the “classical” short-range case (V being an Agmon potential). Let Λ = limr → ∞VE(r) and R(z) = (H ? z)?1, 0 < Im z, Λ < Re z < ∞. It is shown that R(z) can be extended continuously to Im z = 0, except possibly for a discrete subset ?(Λ, ∞), in a suitable operator topology . And L ? L2(Rn) is a weighted L2-space; H is then absolutely continuous over (Λ, ∞), except possibly for a discrete set of eigenvalues. The corresponding eigenfunctions are shown to be rapidly decreasing. 相似文献
16.
17.
Nonlinear partial differential operators having the form G(u) = g(u, D1u,…, DNu), with g?C(R × RN), are here shown to be precisely those operators which are local, (locally) uniformly continuous on, , and (roughly speaking) translation invariant. It is also shown that all such partial differential operators are necessarily bounded and continuous with respect to the norm topologies of . 相似文献
18.
To say that a commutative ring with unit is coherent amounts to saying, in case has no divisors of zero, that the intersection of two finitely generated ideals in is finitely generated. We prove that the ring H∞ of bounded analytic functions in the unit disc is coherent, while the disc algebra A is not coherent. For any positive measure μ, L∞(μ) is coherent. 相似文献
19.
Bent Fuglede 《Journal of Functional Analysis》1974,16(1):101-121
In Rn let Ω denote a Nikodym region (= a connected open set on which every distribution of finite Dirichlet integral is itself in . The existence of n commuting self-adjoint operators such that each Hj is a restriction of (acting in the distribution sense) is shown to be equivalent to the existence of a set Λ ?Rn such that the restrictions to Ω of the functions exp i ∑ λjxj form a total orthogonal family in . If it is required, in addition, that the unitary groups generated by H1,…, Hn act multiplicatively on , then this is shown to correspond to the requirement that Λ can be chosen as a subgroup of the additive group Rn. The measurable sets Ω ?Rn (of finite Lebesgue measure) for which there exists a subgroup Λ ?Rn as stated are precisely those measurable sets which (after a correction by a null set) form a system of representatives for the quotient of Rn by some subgroup Γ (essentially the dual of Λ). 相似文献
20.
《Mathematical Social Sciences》1988,15(2):179-188
The Euclidean distance technique of Arrow and Hahn is used to construct an upper semicontinuous order homomorphism (partial utility function) from (X, ≻) to (, >), where X is a closed, convex subset of N and ≻ is a continuous strict partial order on X. It is also shown that the order homomorphism is upper semicontinuous as a function on , where is the set of continuous strict partial orders on X, taken with the topology of closed convergence. 相似文献