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1.
We consider an infinite lower triangular matrix L=[?n,k]n,k∈N0 and a sequence Ω=(ωn)n∈N0 called the (a,b)-sequence such that every element ?n+1,k+1 except lying in column 0 can be expressed as
2.
In the space L 2 of real-valued measurable 2π-periodic functions that are square summable on the period [0, 2π], the Jackson-Stechkin inequality , is considered, where E n (f) is the value of the best approximation of the function f by trigonometric polynomials of order at most n and ω(δ, f) is the modulus of continuity of the function f in L 2 of order 1 or 2. The value is found at the points δ = 2π/m (where m ∈ ?) for m ≥ 3n 2 + 2 and ω = ω 1 as well as for m ≥ 11n 4/3 ? 1 and ω = ω 2.
相似文献
$$E_n (f) \leqslant \mathcal{K}_n (\delta ,\omega )\omega (\delta ,f), f \in L^2 $$
$$\mathcal{K}_n (\delta ,\omega ) = \sup \left\{ {\frac{{E_n (f)}}{{\omega (\delta ,f)}}:f \in L^2 } \right\}$$
3.
Hajnal and Juhász proved that under CH there is a hereditarily separable, hereditarily normal topological group without non-trivial convergent sequences that is countably compact and not Lindelöf. The example constructed is a topological subgroup H⊆ω12 that is an HFD with the following property
- (P)
- the projection of H onto every partial product I2 for I∈ω[ω1] is onto.
4.
For any real number β > 1, let S n (β) be the partial sum of the first n items of the β-expansion of 1. It was known that the approximation order of 1 by S n (β) is β ?n for Lebesgue almost all β > 1. We consider the size of the set of β > 1 for which 1 can be approximated with the other orders \({\beta^{-\varphi(n)}}\) , where \({\varphi}\) is a positive function defined on \({\mathbb N}\) . More precisely, the size of the setsandare determined, where \({\mathfrak{B}=\{ \beta>1:\beta \text{ is not a simple Parry number}\}}\) .
相似文献
$$\left\{\beta\in \mathfrak{B}:\limsup_{n\rightarrow\infty}\frac{\log_{\beta}(1-S_n(\beta))}{\varphi(n)}=-1\right\}$$
$$\left\{\beta\in \mathfrak{B}:\liminf_{n\rightarrow\infty}\frac{\log_{\beta}(1-S_n(\beta))}{\varphi(n)}=-1\right\}$$
5.
Let Ω⊂{0,1}N be a nonempty closed set with N={0,1,2,…}. For N={N0<N1<N2<?}⊂N and ω∈{0,1}N, define ω[N]∈{0,1}N by and
6.
Suppose β1 α1 ≥0,β2 α2 ≥ 0 and(k,j) ∈R2. In this paper, we mainly investigate the mapping properties of the operator T_αβf(x,y,z)=∫_Q~2f(x-t,y-s,z-t~ks~j)e~(-2πit-β1_s-β2)t~(-1-α1)s~(-1-α2)dtds on modulation spaces, where Q~2 = [0,1] x [0,1] is the unit square in two dimensions. 相似文献
7.
Hamiltonian cycles in Dirac graphs 总被引:1,自引:1,他引:0
We prove that for any n-vertex Dirac graph (graph with minimum degree at least n/2) G=(V,E), the number, Ψ(G), of Hamiltonian cycles in G is at least where h(G)=maxΣ e x e log(1/x e ), the maximum over x: E → ?+ satisfying Σ e?υ x e = 1 for each υ ∈ V, and log =log2. (A second paper will show that this bound is tight up to the o(n).)
We also show that for any (Dirac) G of minimum degree at least d, h(G) ≥ (n/2) logd, so that Ψ(G) > (d/(e + o(1))) n . In particular, this says that for any Dirac G we have Ψ(G) > n!/(2 + o(1)) n , confirming a conjecture of G. Sárközy, Selkow, and Szemerédi which was the original motivation for this work. 相似文献
$exp_2 [2h(G) - n\log e - o(n)],$
8.
In this paper, we consider the non-autonomous modified Korteweg-de Vries (mKdV) equation , where f(ωt) is real analytic and quasi-periodic in t with frequency vector ω = (ω1,ω2, · · ·; ω m ). Basing on an abstract infinite dimensional KAM theorem dealing with unbounded perturbation vector-field, we obtain the existence of Cantor families of smooth quasi-periodic solutions.
相似文献
$${u_t} = {u_{xxx}} - 6f\left( {\omega t} \right){u^2}{u_x},x \in \mathbb{R}/2\pi \mathbb{Z}$$
9.
Rafa? Kapica Janusz Morawiec 《Applied mathematics and computation》2011,217(21):8311-8317
Taking advantage of perpetuities and the asymptotic behavior of products of random matrices we obtain the direct form of the Fourier transform of an L1-solution of the following random matrix refinement type equation
f(x)=∫Ω|detL(ω)|C(ω)f(L(ω)x-M(ω))P(dω), 相似文献
10.
V. R. Fatalov 《Theoretical and Mathematical Physics》2018,195(2):641-657
We prove theorems on the exact asymptotic forms as u → ∞ of two functional integrals over the Bogoliubov measure μB of the forms for p = 4, 6, 8, 10 with p > p0, where p0 = 2+4π2/β2ω2 is the threshold value, β is the inverse temperature, ω is the eigenfrequency of the harmonic oscillator, and 0 < α < 2. As the method of study, we use the Laplace method in Hilbert functional spaces for distributions of almost surely continuous Gaussian processes.
相似文献
$$\int_{C[0,\beta ]} {[\int_0^\beta {|x(t){|^p}dt{]^u}d{\mu _B}(x)} } ,\;\int_{C(0,\beta )} {\exp \left\{ {\mu {{(\int_0^\beta {|x(t){|^p}dt} )}^{a/p}}} \right\}d{\mu _B}(x)} $$
11.
Timo S. Hänninen 《Israel Journal of Mathematics》2017,219(1):71-114
We study the operator-valued positive dyadic operator where the coefficients {λ Q : C → D} Q∈D are positive operators from a Banach lattice C to a Banach lattice D. We assume that the Banach lattices C and D* each have the Hardy–Littlewood property. An example of a Banach lattice with the Hardy–Littlewood property is a Lebesgue space.
$${T_\lambda }\left( {f\sigma } \right): = \sum\limits_{Q \in D} {{\lambda _Q}} \int_Q {fd\sigma 1Q}, $$
In the two-weight case, we prove that the L C p (σ) → L D q (ω) boundedness of the operator T λ( · σ) is characterized by the direct and the dual L ∞ testing conditions: , .
Here L C p (σ) and L D q (ω) denote the Lebesgue–Bochner spaces associated with exponents 1 < p ≤ q < ∞, and locally finite Borel measures σ and ω.$$\left\| {{1_Q}{T_\lambda }} \right\|{\left( {{1_Q}f\sigma } \right)||_{L_D^q\left( \omega \right)}} \lesssim {\left\| f \right\|_{L_C^\infty \left( {Q,\sigma } \right)}}\sigma {\left( Q \right)^{1/p}}$$
$${\left\| {{1_Q}{T_\lambda }*\left( {{1_{Qg\omega }}} \right)} \right\|_{L_{C*}^{p'}\left( \sigma \right)}} \lesssim {\left\| g \right\|_{L_{D*}^\infty \left( {Q,\omega } \right)}}\omega {\left( Q \right)^{1/q'}}$$
In the unweighted case, we show that the L C p (μ) → L D p (μ) boundedness of the operator T λ( · μ) is equivalent to the end-point direct L ∞ testing condition: .
This condition is manifestly independent of the exponent p. By specializing this to particular cases, we recover some earlier results in a unified way. 相似文献
$${\left\| {{1_Q}{T_\lambda }\left( {{1_Q}f\mu } \right)} \right\|_{L_D^1\left( \mu \right)}} \lesssim {\left\| f \right\|_{L_C^\infty \left( {Q,\mu } \right)}}\left( {Q,\mu } \right)\mu \left( Q \right)$$
12.
Ian Melbourne 《Journal of Differential Equations》2004,199(1):22-46
For αβ>−1, stable time periodic solutions A(X,T)=AqeiqX+iωqT are the locally preferred planform for the complex Ginzburg-Landau equation
13.
Let −Dω(·,z)D+q be a differential operator in L2(0,∞) whose leading coefficient contains the eigenvalue parameter z. For the case that ω(·,z) has the particular form
14.
A. V. Harutyunyan G. Marinescu 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2018,53(2):77-87
Let S be the space of functions of regular variation and let ω = (ω1,..., ωn), ωj ∈ S. The weighted Besov space of holomorphic functions on polydisks, denoted by B p (ω) (0 < p < +∞), is defined to be the class of all holomorphic functions f defined on the polydisk U n such that \(||f||_{{B_{P(\omega )}}}^P = \int_{{U^n}} {|Df(z){|^p}\prod\limits_{j = 1}^n {{\omega _j}{{(1 - |{z_j}{|^2})}^{P - 2}}dm{a_{2n}}(z) < \infty } } \), where dm2n(z) is the 2ndimensional Lebesgue measure on U n and D stands for a special fractional derivative of f.We prove some theorems concerning boundedness of the generalized little Hankel and Berezin type operators on the spaces B p (ω) and L p (ω) (the weighted L p -space). 相似文献
15.
R. Nair 《Indagationes Mathematicae》2004,15(3):373-381
Given a subset S of Z and a sequence I = (In)n=1∞ of intervals of increasing length contained in Z, let
16.
It is a longstanding problem in Algebraic Geometry to determine whether the syzygy bundle Ed1,…,dn on PN defined as the kernel of a general epimorphism
17.
Let {Q n (α,β) (x)} n=0 ∞ denote the sequence of polynomials orthogonal with respect to the non-discrete Sobolev inner product where λ>0 and d μ α,β(x)=(x?a)(1?x)α?1(1+x)β?1 dx, d ν α,β(x)=(1?x) α (1+x) β dx with a1, α,β>0. Their inner strong asymptotics on (?1,1), a Mehler-Heine type formula as well as some estimates of the Sobolev norms of Q n (α,β) are obtained.
相似文献
$\langle f,g\rangle=\int_{-1}^{1}f(x)g(x)d\mu_{\alpha,\beta}(x)+\lambda\int_{-1}^{1}f'(x)g'(x)d\nu_{\alpha,\beta}(x)$
18.
19.
E. N. Pavlovskii 《Siberian Mathematical Journal》2008,49(3):512-523
We estimate the algorithmic complexity of the index set of some natural classes of computable models: finite computable models (Σ 2 0 -complete), computable models with ω-categorical theories (Δ ω 0 -complex Π ω+2 0 -set), prime models (Δ ω 0 -complex Π ω+2 0 -set), models with ω 1-categorical theories (Δ ω 0 -complex Σ ω+1 0 -set. We obtain a universal lower bound for the model-theoretic properties preserved by Marker’s extensions (Δ ω 0 . 相似文献
20.
Thierry Huillet 《Journal of Computational and Applied Mathematics》2010,233(10):2449-2467
We consider the random walk on Z+={0,1,…}, with up and down transition probabilities given the chain is in state x∈{1,2,…}:
(1) 相似文献