共查询到20条相似文献,搜索用时 15 毫秒
1.
Ansten Mørch Klev 《Archive for Mathematical Logic》2009,48(7):691-703
Using infinite time Turing machines we define two successive extensions of Kleene’s O{\mathcal{O}} and characterize both their height and their complexity. Specifically, we first prove that the one extension—which we will
call O+{\mathcal{O}^{+}}—has height equal to the supremum of the writable ordinals, and that the other extension—which we will call O++{\mathcal{O}}^{++}—has height equal to the supremum of the eventually writable ordinals. Next we prove that O+{\mathcal{O}^+} is Turing computably isomorphic to the halting problem of infinite time Turing computability, and that O++{\mathcal{O}^{++}} is Turing computably isomorphic to the halting problem of eventual computability. 相似文献
2.
Tóth János T. Filip Ferdinánd Bukor József Zsilinszky László 《Periodica Mathematica Hungarica》2021,82(2):125-135
Periodica Mathematica Hungarica - Let $$\mathbb N$$ be the set of positive integers, and denote by $$\begin{aligned} \lambda (A)=\inf \{t>0:\sum _{a\in A} a^{-t}<\infty \}... 相似文献
3.
4.
Ukrainian Mathematical Journal - Over an arbitrary ring, a module M is said to be $$ {\mathcal{Z}}^{\ast } $$-semilocal if every submodule U of M has a $$ {\mathcal{Z}}^{\ast } $$ -supplement V in... 相似文献
5.
The Ramanujan Journal - An asymptotic classification for the linear homogeneous partition inequalities of the form $$sum nolimits _{i=1}^{r} p(n+x_i) leqslant sum nolimits _{i=1}^{s}... 相似文献
6.
WenMing Wu 《中国科学A辑(英文版)》2008,51(11):2081-2088
Given the hyperbolic measure dxdy/y
2 on the upper half plane ℍ, the rational actions of PSL2(ℝ) on ℍ induces a continuous unitary representation α of this group on the Hilbert space L
2(ℍ, dxdy/y
2). Supposing that = {M
f
: f ∈ L
∞ (ℍ, dxdy/y
2)}, we show that the crossed product is of type I. In fact, the crossed product is *-isomorphic to the von Neumann algebra , where is the abelian group von Neumann algebra generated by the left regular representation of K.
This work was supported by the Youth Foundation of Sichuan Education Department of China (Grant No. 2003B017) 相似文献
7.
The Aronszajn–Donoghue Theory for Rank One Perturbations of the
$$\mathcal{H}_{-2} {\text{-Class}}$$
A singular rank one perturbation
of a self-adjoint operator A in a Hilbert space
is considered, where
and
but
with
the usual A–scale of Hilbert spaces. A modified version of the Aronszajn-Krein formula is given. It has the form
where F denotes the regularized Borel transform of the scalar spectral measure of A associated with . Using this formula we develop a variant of the well known Aronszajn–Donoghue spectral theory for a general rank one perturbation of the
class.Submitted: March 14, 2002 Revised: December 15, 2002 相似文献
8.
María Martí Sánchez 《Geometriae Dedicata》2011,150(1):49-61
This note describes minimal surfaces S of general type satisfying p
g
≥ 5 and K
2 = 2p
g
. For p
g
≥ 8 the canonical map of such surfaces is generically finite of degree 2 and the bulk of the paper is a complete characterization
of such surfaces with non birational canonical map. It turns out that if p
g
≥ 13, S has always an (unique) genus 2 fibration, whose non 2-connected fibres can be characterized, whilst for p
g
≤ 12 there are two other classes of such surfaces with non birational canonical map. 相似文献
9.
10.
Violeta Petkova 《Integral Equations and Operator Theory》2007,59(3):355-378
A Wiener–Hopf operator on a Banach space of functions on is a bounded operator T such that P
+
S
−a
TS
a
= T, a ≥ 0, where S
a
is the operator of translation by a. We obtain a representation theorem for the Wiener–Hopf operators on a large class of functions on with values in a separable Hilbert space.
相似文献
11.
Let \(({{\mathcal {X}}},d,\mu )\) be an RD-space, \(H^1_{\rho }({{\mathcal {X}}})\), and \({\mathrm {BMO}}_{\rho }({{\mathcal {X}}})\) be, respectively, the local Hardy space and the local BMO space associated with an admissible function \(\rho \). Under an additional assumption that there exists a specific generalized approximation of the identity, the authors prove that the product \(f\times g\) of \(f\in H^1_{\rho }({{\mathcal {X}}})\) and \(g\in {\mathrm {BMO}}_{\rho }({{\mathcal {X}}})\), viewed as a distribution, can be written into a sum of two bounded bilinear operators, respectively, from \(H^1_{\rho }({{\mathcal {X}}})\times {\mathrm {BMO}}_{\rho } ({{\mathcal {X}}})\) into \(L^1({{\mathcal {X}}})\) and from \(H^1_{\rho }({{\mathcal {X}}}) \times {\mathrm {BMO}}_{\rho } ({{\mathcal {X}}})\) into \(H^{\log }({{\mathcal {X}}})\), which is of wide generality. The authors also give out four applications of this result to Schrödinger operators, respectively, over different underlying spaces, where three of these applications are new. 相似文献
12.
Lisandro A. Parente Laura S. Aragone Pablo A. Lotito Gabriela F. Reyero 《PAMM》2007,7(1):1060401-1060402
We consider the problem which consists in finding an optimal Lipschitz extension to the domain Ω of functions that verify the restriction u = g on ∂Ω. This work deals with the numerical approximations of the problem in dimension two. Using a discretization procedure based on finite differences method we obtain a large scale non smooth convex minimization problem, which is solved via Variable Metric Hibrid Proximal Point Method. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
13.
We show that for every sequence \({(p_n)_{n\in\mathbb{N}}}\) with 1 ≤ p n ≤ 2 there exists an \({\mathcal{L}_1}\) -space with the Radon-Nikodým containing an isomorphic copy of \({\ell_1(\ell_{p_n})}\) . 相似文献
14.
In this paper we prove the existence of multi-bump solutions for a class of quasilinear Schrödinger equations of the form \({-\Delta{u} + (\lambda{V} (x) + Z(x))u - \Delta(u^{2})u = \beta{h}(u) + u^{22*-1}}\) in the whole space, where h is a continuous function, \({V, Z : \mathbb{R}^{N} \rightarrow \mathbb{R}}\) are continuous functions. We assume that V(x) is nonnegative and has a potential well \({\Omega : = {\rm int} V^{-1}(0)}\) consisting of k components \({\Omega_{1}, \ldots , \Omega{k}}\) such that the interior of Ω i is not empty and \({\partial\Omega_{i}}\) is smooth. By using a change of variables, the quasilinear equations are reduced to a semilinear one, whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem for suitable assumptions. We show that for any given non-empty subset. \({\Gamma \subset \{1, \ldots ,k\}}\), a bump solution is trapped in a neighborhood of \({\cup_{{j}\in\Gamma}\Omega_{j}}\) for\({\lambda > 0}\) large enough. 相似文献
15.
In this paper, we consider the Sturm–Liouville problem with spectral parameter in the boundary conditions. We associate this problem with a self-adjoint operator in the Pontryagin space \(\Pi _{2}\). Using this operator-theoretic formulation and analytic methods, we study the basis properties in the space \(L_{p} (0,1),\,1<p < \infty \), of systems of root functions of this problem. 相似文献
16.
Guido De Philippis Giovanni Franzina Aldo Pratelli 《Journal of Geometric Analysis》2017,27(2):1086-1105
In this paper, we consider the isoperimetric problem in the space \({\mathbb {R}}^N\) with a density. Our result states that, if the density f is lower semi-continuous and converges to a limit \(a>0\) at infinity, with \(f\le a\) far from the origin, then isoperimetric sets exist for all volumes. Several known results or counterexamples show that the present result is essentially sharp. The special case of our result for radial and increasing densities positively answers a conjecture of Morgan and Pratelli (Ann Glob Anal Geom 43(4):331–365, 2013. 相似文献
17.
Giovany M. Figueiredo Gaetano Siciliano 《NoDEA : Nonlinear Differential Equations and Applications》2016,23(2):12
In this work we study the following class of problems in \({\mathbb R^{N}, N > 2s}\) where \({0 < s < 1}\), \({(-\Delta)^{s}}\) is the fractional Laplacian, \({\varepsilon}\) is a positive parameter, the potential \({V : \mathbb{R}^N \to \mathbb{R}}\) and the nonlinearity \({f : \mathbb R \to \mathbb R}\) satisfy suitable assumptions; in particular it is assumed that \({V}\) achieves its positive minimum on some set \({M.}\) By using variational methods we prove existence and multiplicity of positive solutions when \({\varepsilon \to 0^{+}}\). In particular the multiplicity result is obtained by means of the Ljusternick-Schnirelmann and Morse theory, by exploiting the “topological complexity” of the set \({M}\).
相似文献
$$\varepsilon^{2s}(-\Delta)^{s}u + V(z)u = f(u), \,\,\,u(z) > 0$$
18.
Manfred G. Madritsch 《Mathematica Slovaca》2010,60(6):801-810
We present a generalization of a result due to Thuswaldner and Tichy to the ring of polynomials over a finite fields. In particular,
we want to show that every polynomial of sufficiently large degree can be represented as sum of kth powers, where the bases evaluated on additive functions meet certain congruence restrictions. 相似文献
19.
Journal of Theoretical Probability - It is well known that, on a purely algebraic level, a simplified version of the central limit theorem (CLT) can be proved in the framework of a non-commutative... 相似文献
20.
The Ramanujan Journal - Let $$\mathbb {Z}_{n}$$ be the additive group of residue classes modulo n. Let s(m, n) denote the total number of subgroups of the group $$\mathbb {Z}_{m} \times... 相似文献