共查询到20条相似文献,搜索用时 46 毫秒
1.
S. Yu. Podzorov 《Algebra and Logic》2005,44(2):82-94
We deal in specific features of the algebraic structure of Rogers semilattices of n
0-computable numberings, for n 2. It is proved that any Lachlan semilattice is embeddable (as an ideal) in such every semilattice, and that over an arbitrary non 0-principal element of such a lattice, any Lachlan semilattice is embeddable (as an interval) in it.Supported by INTAS grant No. 00-499, by FP Universities of Russia grant UR.04.01.013, and by the Grant Center for Fundamental Research (GCFR), project PD02-1.1-475.__________Translated from Algebra i Logika, Vol. 44, No. 2, pp. 148–172, March–April, 2005. 相似文献
2.
The partial ordering of Medvedev reducibility restricted to the family of 01 classes is shown to be dense. For two disjoint computably enumerable sets, the class of separating sets is an important example of a 01 class, which we call a ``c.e. separating class'. We show that there are no non-trivial meets for c.e. separating classes, but that the density theorem holds in the sublattice generated by the c.e. separating classes.
Mathematics Subject Classification (2000): 03D30, 03D25 相似文献
3.
Stable rational cohomology groups of spaces of non-resultant homogeneous polynomial systems of growing degree in ?n are calculated. 相似文献
4.
D. V. Trushchin 《Moscow University Mathematics Bulletin》2009,64(2):87-90
A problem of realization of Boolean functions by α-formulas is considered. These formulas are such that each subformula contains not more than one nontrivial principal subformula. The depth is considered as a complexity measure of a formula. Upper and lower polynomial estimates of Shannon functions for α-completions of finite systems of Boolean functions are obtained. 相似文献
5.
We define a family of differential operators indexed with fixed point free partitions. When these differential operators act on normalized power sum symmetric functions q(x), the coefficients in the decomposition of this action in the basis q(x) are precisely those of the decomposition of products of corresponding conjugacy classes of the symmetric group Sn. The existence of such operators provides a rigorous definition of Katriels elementary operator representation of conjugacy classes and allows to prove the conjectures he made on their properties.Work partially supported by a grant from the Natural Sciences and Engineering Research Council of Canada.Work partially supported by ECs Research Training Network Algebraic Combinatorics in Europe (grant HPRN-CT-2001-00272). 相似文献
6.
This paper is a sequel to our [7]. In that paper we constructed a 10 tree of avoidable points. Here we construct a 10 tree of shadow points. This tree is a tree of sharp filters, where a sharp filter is a nested sequence of basic open sets converging to a point. In the construction we assign to each basic open set on the tree an address in 2<. One interesting fact is that while our 10 tree of sharp filters (a subtree of <) is isomorphic to the tree of addresses (a subtree of 2<), the tree of addresses is recursively enumerable but not recursive. To achieve this end we use a finite injury priority argument.Mathematics Subject Classification (2000): 03D45, 03D80, 03C57, 54A20 相似文献
7.
K. V. Kostousov 《Siberian Mathematical Journal》2007,48(3):489-499
We study the limits of the finite graphs that admit some vertex-primitive group of automorphisms with a regular abelian normal subgroup. It was shown in [1] that these limits are Cayley graphs of the groups ?d. In this article we prove that for each d > 1 the set of Cayley graphs of ?d presenting the limits of finite graphs with vertex-primitive and edge-transitive groups of automorphisms is countable (in fact, we explicitly give countable subsets of these limit graphs). In addition, for d < 4 we list all Cayley graphs of ?d that are limits of minimal vertex-primitive graphs. The proofs rely on a connection of the automorphism groups of Cayley graphs of ?d with crystallographic groups. 相似文献
8.
We use a distortion to define the dual complex of a cubical subdivision of ℝ
n
as an n-dimensional subcomplex of the nerve of the set of n-cubes. Motivated by the topological analysis of high-dimensional digital image data, we consider such subdivisions defined
by generalizations of quad- and oct-trees to n dimensions. Assuming the subdivision is balanced, we show that mapping each vertex to the center of the corresponding n-cube gives a geometric realization of the dual complex in ℝ
n
. 相似文献
9.
E. L. Shishkina 《Journal of Mathematical Sciences》2009,160(1):95-102
In [3], the inversion of an integral operator of potential type with constant characteristic generated by the many-dimensional
generalized shift was obtained. In this paper, the author obtains a generalization of the results from [3] to the case of a shift of mixed type, i.e., on a part of the variable generalized shifts of integral nature adopted to deal
with the Bessel singular differential operator act, whereas on the other part, the ordinary shift act. Also, it should be
noted that in contrast to [3], the integral of B-potential type with homogeneous characteristic is considered in this paper. This generalization is attained
by introducing general hypersingular integrals of the general form [8].
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 57, Suzdal
Conference–2006, Part 3, 2008. 相似文献
10.
S. V. Konyagin A. A. Kuleshov 《Proceedings of the Steklov Institute of Mathematics》2016,293(1):186-193
Necessary conditions are established for the continuity of finite sums of ridge functions defined on convex subsets E of the space Rn. It is shown that under some constraints imposed on the summed functions ?i, in the case when E is open, the continuity of the sum implies the continuity of all ?i. In the case when E is a convex body with nonsmooth boundary, a logarithmic estimate is obtained for the growth of the functions ?i in the neighborhoods of the boundary points of their domains of definition. In addition, an example is constructed that demonstrates the accuracy of the estimate obtained. 相似文献
11.
Given E ? ? d , d ≥ 2, define to be the set of directions determined by E. We prove that if the Hausdorff dimension of E is greater than d ? 1, then σ(D(E)) > 0, where σ denotes the surface measure on S d?1. In the process, we prove some tight upper and lower bounds for the maximal function associated with the Radon-Nikodym derivative of the natural measure on D. This result is sharp, since the conclusion fails to hold if E is a (d ? 1)-dimensional hyper-plane. This result can be viewed as a continuous analog of a recent result of Pach, Pinchasi, and Sharir ([22, 23]) on directions determined by finite subsets of ? d . We also discuss the case when the Hausdorff dimension of E is precisely d ? 1, where some interesting counter-examples have been obtained by Simon and Solomyak ([25]) in the planar case. In response to the conjecture stated in this paper, T. Orponen and T. Sahlsten ([20]) have recently proved that if the Hausdorff dimension of E equals d ? 1 and E is rectifiable and is not contained in a hyper-pane, the Lebesgue measure of the set of directions is still positive. Finally, we show that our continuous results can be used to recover and, in some cases, improve the exponents for the corresponding results in the discrete setting for large classes of finite point sets. In particular, we prove that a finite point set P ? ? d , d ≥ 3, satisfying a certain discrete energy condition (Definition 3.1) determines ? #P distinct directions.
相似文献
$D(E) \equiv \left\{ {{{x - y} \over {\left| {x - y} \right|}}:x,y \in E} \right\} \subset {S^{d - 1}}$
12.
S. M. Umarkhadzhiev 《Mathematical Notes》2018,104(3-4):454-464
The Riesz potentials Laf, 0 < α < ∞, are considered in the framework of a grand Lebesgue space Lap),θ, 1 < p < ∞, θ > 0, on Rn with grandizers a ∈ L1(?n), which are understood in the case α ≥ n/p in terms of distributions on test functions in the Lizorkin space. The images under Iα of functions in a subspace of the grand space which satisfy the so-called vanishing condition is studied. Under certain assumptions on the grandizer, this image is described in terms of the convergence of truncated hypersingular integrals of order α in this subspace. 相似文献
13.
14.
T. O. Kononovych 《Ukrainian Mathematical Journal》2004,56(9):1403-1416
We obtain upper bounds in terms of Fourier coefficients for the best approximation by an angle and for norms in the metric of L
p
for functions of two variables defined by trigonometric series with coefficients such that
as l
1 + l
2 and
for a certain p, 1 < p < .__________Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 9, pp. 1182–1192, September, 2004. 相似文献
16.
Yemon Choi 《Semigroup Forum》2007,75(2):253-271
We show that if L is a semilattice then the ℓ1-convolution algebra of L is biflat precisely when L is "uniformly locally finite". Our proof technique shows in passing
that if this convolution algebra is biflat then it is isomorphic as a Banach algebra to the Banach space ℓ1(L) equipped with pointwise multiplication. At the end we sketch how these techniques may be extended to prove an analogous
characterisation of biflatness for Clifford semigroup algebras. 相似文献
17.
E. I. Berezhnoi 《Mathematical Notes》2018,104(5-6):628-635
The norm on the sum of Lorentz spaces endowed with norms equal to the products of the classical norm by some numbers is exactly calculated. The obtained result makes it possible to prove an extrapolation theorem for collections of Lorentz, Lebesgue, and Marcinkiewicz spaces with a sharp constant. 相似文献
18.
A. Kh. Khachatryan Kh. A. Khachatryan 《P-Adic Numbers, Ultrametric Analysis, and Applications》2018,10(2):90-99
In the present work the existence of continuous and bounded solutions for a class of nonlinear pseudo-differential equations on ? n is proved. The monotonicity, asymptotic behavior and other properties for obtained solutions are also presented. Mentioned class of equations arises in p-adic string theory. 相似文献
19.
In this paper, we find a bridge connecting a class of vector fields in ℝ3 with the planar vector fields and give a criterion of the existence of closed orbits, heteroclinic orbits and homoclinic
orbits of a class of vector fields in ℝ3. All the possible nonwandering sets of this class of vector fields fall into three classes: (i) singularities; (ii) closed
orbits; (iii) graphs of unions of singularities and the trajectories connecting them. The necessary and sufficient conditions
for the boundedness of the vector fields are also obtained. 相似文献
20.
Riddhipratim Basu Bhaswar B. Bhattacharya Tanmoy Talukdar 《Discrete and Computational Geometry》2012,47(2):329-346
The projection median of a finite set of points in ℝ2 was introduced by Durocher and Kirkpatrick [Computational Geometry: Theory and Applications, Vol. 42 (5), 364–375, 2009]. They proved that the projection median in ℝ2 provides a better approximation of the two-dimensional Euclidean median than the center of mass or the rectilinear median,
while maintaining a fixed degree of stability. In this paper we study the projection median of a set of points in ℝ
d
for d≥2. Using results from geometric measure theory we show that the d-dimensional projection median provides a (d/π)B(d/2,1/2)-approximation to the d-dimensional Euclidean median, where B(α,β) denotes the Beta function. We also show that the stability of the d-dimensional projection median is at least
\frac1(d/p)B(d/2, 1/2)\frac{1}{(d/\pi)B(d/2, 1/2)}, and its breakdown point is 1/2. Based on the stability bound and the breakdown point, we compare the d-dimensional projection median with the rectilinear median and the center of mass, as a candidate for approximating the d-dimensional Euclidean median. For the special case of d=3, our results imply that the three-dimensional projection median is a (3/2)-approximation of the three-dimensional Euclidean
median, which settles a conjecture posed by Durocher. 相似文献