共查询到20条相似文献,搜索用时 31 毫秒
1.
Charles M. Harris 《Archive for Mathematical Logic》2010,49(6):673-691
We investigate and extend the notion of a good approximation with respect to the enumeration ${({\mathcal D}_{\rm e})}We investigate and extend the notion of a good approximation with respect to the enumeration (De){({\mathcal D}_{\rm e})} and singleton (Ds){({\mathcal D}_{\rm s})} degrees. We refine two results by Griffith, on the inversion of the jump of sets with a good approximation, and we consider
the relation between the double jump and index sets, in the context of enumeration reducibility. We study partial order embeddings
is{\iota_s} and [^(i)]s{\hat{\iota}_s} of, respectively, De{{\mathcal D}_{\rm e}} and DT{{\mathcal D}_{\rm T}} (the Turing degrees) into Ds{{\mathcal D}_{\rm s}} , and we show that the image of DT{{\mathcal D}_{\rm T}} under [^(i)]s{\hat{\iota}_s} is precisely the class of retraceable singleton degrees. We define the notion of a good enumeration, or singleton, degree
to be the property of containing the set of good stages of some good approximation, and we show that is{\iota_s} preserves the latter, as also other naturally arising properties such as that of totality or of being G0n{\Gamma^0_n} , for G ? {S,P,D}{\Gamma \in \{\Sigma,\Pi,\Delta\}} and n > 0. We prove that the good enumeration and singleton degrees are immune and that the good S02{\Sigma^0_2} singleton degrees are hyperimmune. Finally we show that, for singleton degrees a
s < b
s such that b
s is good, any countable partial order can be embedded in the interval (a
s, b
s). 相似文献
2.
Pierre Maréchal 《Optimization Letters》2012,6(2):357-362
We generalize a well known convexity property of the multiplicative potential function. We prove that, given any convex function
g : \mathbbRm ? [0, ¥]{g : \mathbb{R}^m \rightarrow [{0}, {\infty}]}, the function ${({\rm \bf x},{\rm \bf y})\mapsto g({\rm \bf x})^{1+\alpha}{\bf y}^{-{\bf \beta}}, {\bf y}>{\bf 0}}${({\rm \bf x},{\rm \bf y})\mapsto g({\rm \bf x})^{1+\alpha}{\bf y}^{-{\bf \beta}}, {\bf y}>{\bf 0}}, is convex if β ≥ 0 and α ≥ β
1 + ··· + β
n
. We also provide further generalization to functions of the form (x,y1, . . . , yn)? g(x)1+af1(y1)-b1 ···fn(yn)-bn{({\rm \bf x},{\rm \bf y}_1, . . . , {y_n})\mapsto g({\rm \bf x})^{1+\alpha}f_1({\rm \bf y}_1)^{-\beta_1} \cdot \cdot \cdot f_n({\rm \bf y}_n)^{-\beta_n} } with the f
k
concave, positively homogeneous and nonnegative on their domains. 相似文献
3.
R. Abreu-Blaya J. Bory-Reyes F. Brackx H. De Schepper F. Sommen 《Complex Analysis and Operator Theory》2012,6(2):359-372
We consider H?lder continuous circulant (2 × 2) matrix functions G12{{\bf G}^1_2} defined on the fractal boundary Γ of a Jordan domain Ω in
\mathbbR2n{\mathbb{R}^{2n}}. The main goal is to establish a Hilbert transform for such functions, within the framework of Hermitian Clifford analysis.
This is a higher dimensional function theory centered around the simultaneous null solutions of two first order vector valued
differential operators, called Hermitian Dirac operators. In Brackx et al. (Bull Braz Math Soc 40(3): 395–416, 2009) a Hermitian Cauchy integral was constructed by means of a matrix approach using circulant (2 × 2) matrix functions, from
which a Hilbert transform was derived in Brackx et al. (J Math Anal Appl 344: 1068–1078, 2008) for the case of domains with smooth boundary. However, crucial parts of the method are not extendable to the case where
the boundary of the considered domain is fractal. At present we propose an alternative approach which will enable us to define
a new Hermitian Hilbert transform in that case. As a consequence, we give necessary and sufficient conditions for the Hermitian
monogenicity of a circulant matrix function G12{{\bf G}^1_2} in the interior and exterior of Ω, in terms of its boundary value g12=G12|G{{\bf g}^1_2={\bf G}^1_2|_\Gamma}, extending in this way also results of Abreu Blaya et al. (Bound. Value Probl. 2008: 2008) (article ID 425256), (article ID 385874), where Γ is required to be Ahlfors–David regular. 相似文献
4.
Let ${\mathbb {F}}Let
\mathbb F{\mathbb {F}} a finite field. We show that the universal characteristic factor for the Gowers–Host–Kra uniformity seminorm U
k
(X) for an ergodic action
(Tg)g ? \mathbb Fw{(T_{g})_{{g} \in \mathbb {F}^{\omega}}} of the infinite abelian group
\mathbb Fw{\mathbb {F}^{\omega}} on a probability space X = (X, B, m){X = (X, \mathcal {B}, \mu)} is generated by phase polynomials f: X ? S1{\phi : X \to S^{1}} of degree less than C(k) on X, where C(k) depends only on k. In the case where
k £ char(\mathbb F){k \leq {\rm char}(\mathbb {F})} we obtain the sharp result C(k) = k. This is a finite field counterpart of an analogous result for
\mathbb Z{\mathbb {Z}} by Host and Kra [HK]. In a companion paper [TZ] to this paper, we shall combine this result with a correspondence principle
to establish the inverse theorem for the Gowers norm in finite fields in the high characteristic case
k £ char(\mathbb F){k \leq {\rm char}(\mathbb {F})} , with a partial result in low characteristic. 相似文献
5.
Iterating the triple construction applied consecutively to n Boolean algebras, we introduce two finitely axiomatizable subclasses SAin{{\bf SA}^{\rm i}_n} and SAsn{{\bf SA}^{\rm s}_n} of the class SA
n
of all Stone algebras of degree n with all the structure homomorphisms in their P-product representation injective or surjective, respectively. Then the class
of all Post algebras of degree n is definitionally equivalent to the intersection SAin ?SAsn{{\bf SA}^{\rm i}_{n} \cap {\bf SA}^{\rm s}_{n}}. We show that for each n ≥ 2 the class SAin{{\bf SA}^{\rm i}_n} is hereditarily undecidable while SAsn{{\bf SA}^{\rm s}_{n}} is decidable. As a consequence we obtain several (un)decidability results for various axiomatic classes of Stone algebras:
among them the decidability of the class of all Stone algebras of degree n which are dually pseudocomplemented and form a dual Stone algebra under the operation of dual pseudocomplement, and undecidability
of the class of all Stone algebras with Boolean dense set. On the other hand, the class of all finite members in SA
n
is decidable. 相似文献
6.
Igor V. Protasov 《Algebra Universalis》2009,62(4):339-343
Let ${\mathbb{A}}Let
\mathbbA{\mathbb{A}} be a universal algebra of signature Ω, and let I{\mathcal{I}} be an ideal in the Boolean algebra
P\mathbbA{\mathcal{P}_{\mathbb{A}}} of all subsets of
\mathbbA{\mathbb{A}} . We say that I{\mathcal{I}} is an Ω-ideal if I{\mathcal{I}} contains all finite subsets of
\mathbbA{\mathbb{A}} and f(An) ? I{f(A^{n}) \in \mathcal{I}} for every n-ary operation f ? W{f \in \Omega} and every A ? I{A \in \mathcal{I}} . We prove that there are 22à0{2^{2^{\aleph_0}}} Ω-ideals in
P\mathbbA{\mathcal{P}_{\mathbb{A}}} provided that
\mathbbA{\mathbb{A}} is countably infinite and Ω is countable. 相似文献
7.
A class Uk1 (J){\mathcal{U}}_{\kappa 1} (J) of generalized J-inner mvf’s (matrix valued functions) W(λ) which appear as resolvent matrices for bitangential interpolation problems in the generalized Schur class of p ×q mvf¢s Skp ×qp \times q \, {\rm mvf's}\, {\mathcal{S}}_{\kappa}^{p \times q} and some associated reproducing kernel Pontryagin spaces are studied. These spaces are used to describe the range of the
linear fractional transformation TW based on W and applied to Sk2p ×q{\mathcal{S}}_{\kappa 2}^{p \times q}. Factorization formulas for mvf’s W in a subclass U°k1 (J) of Uk1(J){\mathcal{U}^{\circ}_{\kappa 1}} (J)\, {\rm of}\, {\mathcal{U}}_{\kappa 1}(J) found and then used to parametrize the set Sk1+k2p ×q ?TW [ Sk2p ×q ]{\mathcal{S}}_{{\kappa 1}+{\kappa 2}}^{p \times q} \cap T_{W} \left[ {\mathcal{S}}_{\kappa 2}^{p \times q} \right]. Applications to bitangential interpolation problems in the class Sk1+k2p ×q{\mathcal{S}}_{{\kappa 1}+{\kappa 2}}^{p \times q} will be presented elsewhere. 相似文献
8.
Christopher Hammond 《Mathematische Zeitschrift》2010,266(2):285-288
Let Ω be a domain in ${\mathbb{C}^{2}}Let Ω be a domain in
\mathbbC2{\mathbb{C}^{2}}, and let
p: [(W)\tilde]? \mathbbC2{\pi: \tilde{\Omega}\rightarrow \mathbb{C}^{2}} be its envelope of holomorphy. Also let W¢=p([(W)\tilde]){\Omega'=\pi(\tilde{\Omega})} with
i: W\hookrightarrow W¢{i: \Omega \hookrightarrow \Omega'} the inclusion. We prove the following: if the induced map on fundamental groups i*:p1(W) ? p1(W¢){i_{*}:\pi_{1}(\Omega) \rightarrow \pi_{1}(\Omega')} is a surjection, and if π is a covering map, then Ω has a schlicht envelope of holomorphy. We then relate this to earlier
work of Fornaess and Zame. 相似文献
9.
Tao Feng 《Designs, Codes and Cryptography》2012,62(3):253-258
In 1976, Helleseth conjectured that two binary m-sequences of length 2
m
− 1 can not have a three-valued crosscorrelation function when m is a power of 2. We show that this conjecture is true when −1 is a correlation value. In other words, if C1,k{{\mathcal{C}}_{1,k}} is the cyclic code of length 2
m
− 1 with two zeros α, α
k
, where α is a primitive element of
\mathbbF2m{{\mathbb{F}}_{2^m}} and gcd(k, 2
m
− 1) = 1, then its dual C1,k^{{\mathcal{C}}_{1,k}^{\perp}} can not have three weights when m is a power of 2. 相似文献
10.
Let ${\mathcal{P}_{d,n}}Let Pd,n{\mathcal{P}_{d,n}} denote the space of all real polynomials of degree at most d on
\mathbbRn{\mathbb{R}^n} . We prove a new estimate for the logarithmic measure of the sublevel set of a polynomial P ? Pd,1{P\in \mathcal{P}_{d,1}} . Using this estimate, we prove that
supP ? Pd,n| p.v.ò\mathbbRneiP(x)\fracW(x/|x|)|x|ndx| £ c log d (||W||L logL(Sn-1)+1),\mathop{\rm sup}\limits_ {P \in \mathcal{P}_{d,n}}\left| p.v.\int_{\mathbb{R}^{n}}{e^{iP(x)}}{\frac{\Omega(x/|x|)}{|x|^n}dx}\right | \leq c\,{\rm log}\,d\,(||\Omega||_L \log L(S^{n-1})+1), 相似文献
11.
Let
H2\mathbb F{{\bf H}^{\bf 2}_{\mathbb F}} denote the two dimensional hyperbolic space over
\mathbb F{\mathbb F} , where
\mathbb F{\mathbb F} is either the complex numbers
\mathbb C{\mathbb C} or the quaternions
\mathbb H{\mathbb H} . It is of interest to characterize algebraically the dynamical types of isometries of
H2\mathbb F{{\bf H}^{\bf 2}_{\mathbb F}} . For
\mathbb F=\mathbb C{\mathbb F=\mathbb C} , such a characterization is known from the work of Giraud–Goldman. In this paper, we offer an algebraic characterization
of isometries of
H2\mathbb H{{\bf H}^{\bf 2}_{\mathbb H}} . Our result restricts to the case
\mathbb F=\mathbb C{\mathbb F=\mathbb C} and provides another characterization of the isometries of
H2\mathbb C{{\bf H}^{\bf 2}_{\mathbb C}} , which is different from the characterization due to Giraud–Goldman. Two elements in a group G are said to be in the same z-class if their centralizers are conjugate in G. The z-classes provide a finite partition of the isometry group. In this paper, we describe the centralizers of isometries of
H2\mathbb F{{\bf H}^{\bf 2}_{\mathbb F}} and determine the z-classes. 相似文献
12.
Local and Global Existence of Solutions to Initial Value Problems of Nonlinear Kaup-Kupershmidt Equations 总被引:6,自引:0,他引:6
Shuang Ping TAO Shang Bin CUI 《数学学报(英文版)》2005,21(4):881-892
This paper is devoted to studying the initial value problems of the nonlinear Kaup Kupershmidt equations δu/δt + α1 uδ^2u/δx^2 + βδ^3u/δx^3 + γδ^5u/δx^5 = 0, (x,t)∈ E R^2, and δu/δt + α2 δu/δx δ^2u/δx^2 + βδ^3u/δx^3 + γδ^5u/δx^5 = 0, (x, t) ∈R^2. Several important Strichartz type estimates for the fundamental solution of the corresponding linear problem are established. Then we apply such estimates to prove the local and global existence of solutions for the initial value problems of the nonlinear Kaup- Kupershmidt equations. The results show that a local solution exists if the initial function u0(x) ∈ H^s(R), and s ≥ 5/4 for the first equation and s≥301/108 for the second equation. 相似文献
13.
Lin-Feng Wang 《Annals of Global Analysis and Geometry》2010,37(4):393-402
Let M be an n-dimensional complete non-compact Riemannian manifold, dμ = e
h
(x)dV(x) be the weighted measure and
\trianglem{\triangle_{\mu}} be the weighted Laplacian. In this article, we prove that when the m-dimensional Bakry–émery curvature is bounded from below by Ric
m
≥ −(m − 1)K, K ≥ 0, then the bottom of the Lm2{{\rm L}_{\mu}^2} spectrum λ1(M) is bounded by
|