共查询到20条相似文献,搜索用时 31 毫秒
1.
Daniel A. Klain 《Advances in Mathematics》2010,224(2):601-4601
For n?2 a construction is given for convex bodies K and L in Rn such that the orthogonal projection Lu onto the subspace u⊥ contains a translate of Ku for every direction u, while the volumes of K and L satisfy Vn(K)>Vn(L).A more general construction is then given for n-dimensional convex bodies K and L such that each orthogonal projection Lξ onto a k-dimensional subspace ξ contains a translate of Kξ, while the mth intrinsic volumes of K and L satisfy Vm(K)>Vm(L) for all m>k.For each k=1,…,n, we then define the collection Cn,k to be the closure (under the Hausdorff topology) of all Blaschke combinations of suitably defined cylinder sets (prisms).It is subsequently shown that, if L∈Cn,k, and if the orthogonal projection Lξ contains a translate of Kξ for every k-dimensional subspace ξ of Rn, then Vn(K)?Vn(L).The families Cn,k, called k-cylinder bodies of Rn, form a strictly increasing chain
Cn,1⊂Cn,2⊂?⊂Cn,n−1⊂Cn,n, 相似文献
2.
We study the existence of homoclinic orbits for the second order Hamiltonian system , where q∈Rn and V∈C1(R×Rn,R), V(t,q)=-K(t,q)+W(t,q) is T-periodic in t. A map K satisfies the “pinching” condition b1|q|2?K(t,q)?b2|q|2, W is superlinear at the infinity and f is sufficiently small in L2(R,Rn). A homoclinic orbit is obtained as a limit of 2kT-periodic solutions of a certain sequence of the second order differential equations. 相似文献
3.
Jiecheng Chen 《Journal of Mathematical Analysis and Applications》2008,337(2):1048-1052
We consider the singular integral operator T with kernel K(x)=Ω(x)/n|x| and prove its boundedness on the Triebel-Lizorkin spaces provided that Ω satisfies a size condition which contains the case Ω∈Lr(Sn−1), r>1. 相似文献
4.
Let N denote the set of positive integers. The asymptotic density of the set A⊆N is d(A)=limn→∞|A∩[1,n]|/n, if this limit exists. Let AD denote the set of all sets of positive integers that have asymptotic density, and let SN denote the set of all permutations of the positive integers N. The group L? consists of all permutations f∈SN such that A∈AD if and only if f(A)∈AD, and the group L* consists of all permutations f∈L? such that d(f(A))=d(A) for all A∈AD. Let be a one-to-one function such that d(f(N))=1 and, if A∈AD, then f(A)∈AD. It is proved that f must also preserve density, that is, d(f(A))=d(A) for all A∈AD. Thus, the groups L? and L* coincide. 相似文献
5.
R. Sakai 《Journal of Approximation Theory》1998,93(3):441-449
We consider the “Freud weight”W2Q(x)=exp(−Q(x)). let 1<p<∞, and letL*n(f) be a modified Lagrange interpolation polynomial to a measurable functionf∈{f; ess supx∈ |f(x)| WQ(x)(1+|x|)α<∞},α>0. Then we have limn→∞ ∫∞−∞ [|f(x)−L*n(f; x)| WQ(x)(1+|x|)−Δ]p dx=0, whereΔis a constant depending onpandα. 相似文献
6.
Janne Kauhanen 《Journal of Mathematical Analysis and Applications》2006,315(2):656-665
Let f∈W1,1(Ω,Rn) be a homeomorphism of finite distortion K. It is known that if K1/(n−1)∈L1(Ω), then the Jacobian Jf of f is positive almost everywhere in Ω. We will show that this integrability assumption on K is sharp in any Orlicz-scale: if α is increasing function (satisfying minor technical assumptions) such that limt→∞α(t)=∞, then there exists f such that K1/(n−1)/α(K)∈L1(Ω) and Jf vanishes in a set of positive measure. 相似文献
7.
Peter Giesl 《Journal of Mathematical Analysis and Applications》2007,335(1):461-479
We consider the general nonlinear differential equation with x∈R2 and develop a method to determine the basin of attraction of a periodic orbit. Borg's criterion provides a method to prove existence, uniqueness and exponential stability of a periodic orbit and to determine a subset of its basin of attraction. In order to use the criterion one has to find a function W∈C1(R2,R) such that LW(x)=W′(x)+L(x) is negative for all x∈K, where K is a positively invariant set. Here, L(x) is a given function and W′(x) denotes the orbital derivative of W. In this paper we prove the existence and smoothness of a function W such that LW(x)=−μ‖f(x)‖. We approximate the function W, which satisfies the linear partial differential equation W′(x)=〈∇W(x),f(x)〉=−μ‖f(x)‖−L(x), using radial basis functions and obtain an approximation w such that Lw(x)<0. Using radial basis functions again, we determine a positively invariant set K so that we can apply Borg's criterion. As an example we apply the method to the Van-der-Pol equation. 相似文献
8.
Kamal Boussaf 《Bulletin des Sciences Mathématiques》2010,134(1):44
Let K be a complete ultrametric algebraically closed field. We investigate several properties of sequences (an)n∈N in a disk d(0,R−) with regards to bounded analytic functions in that disk: sequences of uniqueness (when f(an)=0∀n∈N implies f=0), identity sequences (when limn→+∞f(an)=0 implies f=0) and analytic boundaries (when lim supn→∞|f(an)|=‖f‖). Particularly, we show that identity sequences and analytic boundary sequences are two equivalent properties. For certain sequences, sequences of uniqueness and identity sequences are two equivalent properties. A connection with Blaschke sequences is made. Most of the properties shown on analytic functions have continuation to meromorphic functions. 相似文献
9.
Let ?n∈C∞(Rd?{0}) be a non-radial homogeneous distance function of degree n∈N satisfying ?n(tξ)=tn?n(ξ). For f∈S(Rd+1) and δ>0, we consider convolution operator associated with the smooth cone type multipliers defined by
10.
The existence of a -global attractor is proved for the p-Laplacian equation ut−div(|∇u|p−2∇u)+f(u)=g on a bounded domain Ω⊂Rn(n?3) with Dirichlet boundary condition, where p?2. The nonlinear term f is supposed to satisfy the polynomial growth condition of arbitrary order c1q|u|−k?f(u)u?c2q|u|+k and f′(u)?−l, where q?2 is arbitrary. There is no other restriction on p and q. The asymptotic compactness of the corresponding semigroup is proved by using a new a priori estimate method, called asymptotic a priori estimate. 相似文献
11.
We study certain hypersingular integrals TΩ,α,βf defined on all test functions f∈S(Rn), where the kernel of the operator TΩ,α,β has a strong singularity |y|−n−α(α>0) at the origin, an oscillating factor ei|y|−β(β>0) and a distribution Ω∈Hr(Sn−1), 0<r<1. We show that TΩ,α,β extends to a bounded linear operator from the Sobolev space to the Lebesgue space Lp for β/(β−α)<p<β/α, if the distribution Ω is in the Hardy space Hr(Sn−1) with 0<r=(n−1)/(n−1+γ)(0<γ?α) and β>2α>0. 相似文献
12.
We study oscillation in the prefix-free complexity of initial segments of 1-random reals. For upward oscillations, we prove that ∑n∈ω2−g(n) diverges iff (∃∞n)K(X?n)>n+g(n) for every 1-random X∈ω2. For downward oscillations, we characterize the functions g such that (∃∞n)K(X?n)<n+g(n) for almost every X∈ω2. The proof of this result uses an improvement of Chaitin's counting theorem—we give a tight upper bound on the number of strings σ∈n2 such that K(σ)<n+K(n)−m.The work on upward oscillations has applications to the K-degrees. Write XK?Y to mean that K(X?n)?K(Y?n)+O(1). The induced structure is called the K-degrees. We prove that there are comparable () 1-random K-degrees. We also prove that every lower cone and some upper cones in the 1-random K-degrees have size continuum.Finally, we show that it is independent of ZFC, even assuming that the Continuum Hypothesis fails, whether all chains of 1-random K-degrees of size less than ℵ02 have a lower bound in the 1-random K-degrees. 相似文献
13.
For n≥3 and p>1, the elliptic equation Δu+K(x)up+μf(x)=0 in possesses a continuum of positive entire solutions, provided that (i) locally Hölder continuous functions K and f vanish rapidly, for instance, K(x),f(x)=O(|x|l) near ∞ for some l<−2 and (ii) μ≥0 is sufficiently small. Especially, in the radial case with K(x)=k(|x|) and f(x)=g(|x|) for some appropriate functions k,g on [0,∞), there exist two intervals Iμ,1, Iμ,2 such that for each α∈Iμ,1 the equation has a positive entire solution uα with uα(0)=α which converges to l∈Iμ,2 at ∞, and uα1<uα2 for any α1<α2 in Iμ,1. Moreover, the map α to l is one-to-one and onto from Iμ,1 to Iμ,2. If K≥0, each solution regarded as a steady state for the corresponding parabolic equation is stable in the uniform norm; moreover, in the radial case the solutions are also weakly asymptotically stable in the weighted uniform norm with weight function |x|n−2. 相似文献
14.
W. B. Gearhart 《Journal of Optimization Theory and Applications》1989,62(2):321-332
LetF be a family of real-valued maps onR
n, and letY be a subset ofR
n. Denote byS(Y|F) the set of ally* Y such that, for somef F,f(y)f(y*) for ally inY. Let us say thatF is a scalarization family if, for any subsetY,S(Y|F) is equal to the set of properly efficient points inY. General conditions forF to be a scalarization family were given in Ref. 1. However, scalarization families must contain nondifferentiable functions. In this note, it is shown that, if the condition of Ref. 1 which forces nondifferentiability is dropped, thenS(Y|F) is dense in the set of properly efficient points. 相似文献
15.
Michela Eleuteri 《Journal of Mathematical Analysis and Applications》2008,344(2):1120-1142
We prove regularity results for minimizers of functionals in the class , where is a fixed function and f is quasiconvex and fulfills a growth condition of the type
L−1|z|p(x)?f(x,ξ,z)?L(1+|z|p(x)), 相似文献
16.
Let f be a 1-periodic C1-function whose Fourier coefficientssatisfy the condition n|n|3|f(n|2 < . For every R\Q andm Z\{0}, we consider the Anzai skew product T(x, y) = (x +, y + mx + f(x)) acting on the 2-torus. It is shown that T hasinfinite Lebesgue spectrum on the orthocomplement L2(dx) ofthe space of functions depending only on the first variable.This extends some earlier results of Kushnirenko, Choe, Lemaczyk,Rudolph, and the author. 1991 Mathematics Subject Classification28D05. 相似文献
17.
Bengt-Olov Eriksson 《Journal of Approximation Theory》1998,94(3):420-454
An additive form of the Landau inequality forf∈Wn∞[−1, 1],is proved for 0<c?(cos(π/2n))−2, 1?m?n−1, with equality forf(x)=Tn(1+(x−1)/c), 1?c?(cos(π/2n))−2, whereTnis the Chebyshev polynomial. From this follows a sharp multiplicative inequality,for ‖f(n)‖?σ ‖f‖, 2n−1n! cos2n(π/2n)?σ?2n−1n!, 1?m?n−1. For these values ofσ, the result confirms Karlin's conjecture on the Landau inequality for intermediate derivatives on a finite interval. For the proof of the additive inequality a Duffin and Schaeffer-type inequality for polynomials is shown. 相似文献
18.
Results on the existence and non-existence of nontrivial
\mathbb L1{\mathbb L^1}-solutions of the refinement equation
f(x)=òW|detK(w)|f(K(w)x-L(w))dP(w)f(x)={\int\limits_{\Omega}}|\det K(\omega)|f(K(\omega)x-L(\omega))dP(\omega) 相似文献
19.
Let (x,t)y (x,t),x[0, 1],t[0,T], be the solution of the diffusion equation in one spatial variable corresponding to zero initial conditions and boundary controluL
2(0,T). GivenfL
2(0, 1), it is not possible, in general, to find a controlu such thaty(·,T)=f. We extend the space of controls in such a manner thatL
2(0,T) can be considered to be a subset of a new spaceS of control elements; this space contains elements which do provide a solution to the problem of moments associated with the problem of makingy(·,T)=f inL
2(0, 1). We show then that the action of the elements ofS can be approximated by that of control functions inL
2(0,T) in a suitable manner. 相似文献
20.
Given an r×r complex matrix T, if T=U|T| is the polar decomposition of T, then, the Aluthge transform is defined byΔ(T)=|T|1/2U|T|1/2. Let Δn(T) denote the n-times iterated Aluthge transform of T, i.e., Δ0(T)=T and Δn(T)=Δ(Δn−1(T)), n∈N. We prove that the sequence {Δn(T)}n∈N converges for every r×r matrix T. This result was conjectured by Jung, Ko and Pearcy in 2003. We also analyze the regularity of the limit function. 相似文献
|