共查询到20条相似文献,搜索用时 15 毫秒
1.
C. Richter 《Discrete and Computational Geometry》2001,25(1):65-83
The paradox of Banach, Tarski, and Hausdorff shows that any two bounded sets M,N subseteq E 3 with non-empty interior are equidecomposable. The result remains true if M and N are replaced by collections of sets. We present quantified versions of the paradox by giving estimates for the minimal number of pieces in such decompositions. The emphasis is on replications of sets M , i.e., on the equidecomposability of M with k copies of M , k ≥ 2 . In particular, we discuss the problem of replicating the cube. Received January 21, 1999, and in revised form March 23, 2000. Online publication October 10, 2000. 相似文献
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3.
《Journal of computational and graphical statistics》2013,22(2):299-319
Online auctions have been the subject of many empirical research efforts in the fields of economics and information systems. These research efforts are often based on analyzing data from Web sites such as eBay.com which provide public information about sequences of bids in closed auctions, typically in the form of tables on HTML pages. The existing literature on online auctions focuses on tools like summary statistics and more formal statistical methods such as regression models. However, there is a clear void in this growing body of literature in developing appropriate visualization tools. This is quite surprising, given that the sheer amount of data that can be found on sites such as eBay.com is overwhelming and can often not be displayed informatively using standard statistical graphics. In this article we introduce graphical methods for visualizing online auction data in ways that are informative and relevant to the types of research questions that are of interest. We start by using profile plots that reveal aspects of an auction such as bid values, bidding intensity, and bidder strategies. We then introduce the concept of statistical zooming (STAT-zoom) which can scale up to be used for visualizing large amounts of auctions. STAT-zoom adds the capability of looking at data summaries at various time scales interactively. Finally, we develop auction calendars and auction scene visualizations for viewing a set of many concurrent auctions. The different visualization methods are demonstrated using data on multiple auctions collected from eBay.com. 相似文献
4.
Martin Theus Stephan R. W. Lauer 《Journal of computational and graphical statistics》2013,22(3):396-412
Abstract We consider visual methods based on mosaic plots for interpreting and modeling categorical data. Categorical data are most often modeled using loglinear models. For certain loglinear models, mosaic plots have unique shapes that do not depend on the actual data being modeled. These shapes reflect the structure of a model, defined by the presence and absence of particular model coefficients. Displaying the expected values of a loglinear model allows one to incorporate the residuals of the model graphically and to visually judge the adequacy of the loglinear fit. This procedure leads to stepwise interactive graphical modeling of loglinear models. We show that it often results in a deeper understanding of the structure of the data. Linking mosaic plots to other interactive displays offers additional power that allows the investigation of more complex dependence models than provided by static displays. 相似文献
5.
John Donnelly 《Semigroup Forum》2007,75(1):160-172
Ore's condition states that a cancellative semigroup S which has common right multiples embeds into a group G such that certain
properties are satisfied by S and G. We show that G is nonamenable if and only if the semigroup S-1 is G-paradoxical with respect to right multiplication by elements of S. We explore certain properties of this decomposition
of S-1. 相似文献
6.
We characterize the boundary ∂Σ
p
of the solution set Σ
p
of a parametric linear system A(p)x=b(p) where the elements of the n×n matrix and the right-hand side vector depend on a number of parameters p varying within interval bounds. The characterization of ∂Σ
p
is by means of pieces of parametric hypersurfaces, the latter represented by their coordinate functions depending on corresponding
subsets of n-1 parameters. The presented approach has a direct application for efficient visualization of parametric solution sets by
utilizing some plotting functions supported by Mathematica and Maple.
Electronic supplementary material The online version of this article (doi: ) contains supplementary material, which is available to authorized users.
AMS subject classification (2000) 15A06, 65G99, 65S05, 68U05 相似文献
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Yuri Bilu 《Combinatorica》1998,18(4):449-459
A of integers is sum-free if . Cameron conjectured that the number of sum-free sets is . As a step towards this conjecture, we prove that the number of sets satisfying
is .
Received: 22 July, 1996 相似文献
9.
Wolfgang M. Schmidt 《Monatshefte für Mathematik》2003,138(1):61-71
Subsets 𝒜, 𝒮 of an additive group G are complementary if 𝒜 + 𝒮 = G. When 𝒜 is of finite cardinality ∣𝒜∣, and G is ℤ or ℝ, we give sufficient conditions for the existence of a complementary set 𝒮 with “density” not much larger than
1/∣𝒜∣.
Supported in part by NSF DMS-0074531.
Received February 14, 2002; in revised form July 18, 2002
RID="a"
ID="a" Dedicated to Professor Edmund Hlawka on the occasion of his 85th birthday 相似文献
10.
Wolfgang M. Schmidt 《Monatshefte für Mathematik》2003,43(2):61-71
Subsets 𝒜, 𝒮 of an additive group G are complementary if 𝒜 + 𝒮 = G. When 𝒜 is of finite cardinality ∣𝒜∣, and G is ℤ or ℝ, we give sufficient conditions for the existence of a complementary set 𝒮 with “density” not much larger than
1/∣𝒜∣. 相似文献
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Shiva Mittal Niraj K. Shukla Nadya A. S. Atlouba 《Numerical Functional Analysis & Optimization》2016,37(2):253-276
In this article, we study the theory of nonuniform minimally supported frequency multiwavelets and nonuniform multiscaling sets. A characterization of nonuniform multiwavelet sets is obtained which generalizes a result of Yu and Gabardo. After introducing a notion of generalized nonuniform scaling set, we obtain a characterization of nonuniform multiscaling sets associated with nonuniform multiresolution analysis having finite multiplicity. In addition, we provide a geometric construction to find families of symmetric nonuniform multiwavelet sets. 相似文献
13.
We introduce the concept of paradoxical decomposition for semigroups. We show that a semigroup S admits a left paradoxical
decomposition if and only if S is not left amenable. Also Rosenbelatt and Willis introduced the configuration concept for
groups and showed that amenability of groups is equivalent with existence of normalised solution for any system of configuration
equations. We generalise it for semigroups. 相似文献
14.
Central subsets of a discrete semigroup S have very strong combinatorial properties which are a consequence of the Central Sets Theorem . We investigate here the class of semigroups that have a subset with zero Følner density which satisfies the conclusion of the Central Sets Theorem. We show that this class includes any direct sum of countably many finite abelian groups as well as any subsemigroup of (?,+) which contains ?. We also show that if S and T are in this class and either both are left cancellative or T has a left identity, then S×T is in this class. We also extend a theorem proved in (Beiglböck et al. in Topology Appl., to appear), which states that, if p is an idempotent in β? whose members have positive density, then every member of p satisfies the Central Sets Theorem. We show that this holds for all commutative semigroups. Finally, we provide a simple elementary proof of the fact that any commutative semigroup satisfies the Strong Følner Condition. 相似文献
15.
Let X be a reflexive Banach space, and let C X be a closed,convex and bounded set with empty interior. Then, for every > 0, there is a nonempty finite set F X with an arbitrarilysmall diameter, such that C contains at most .|F| points ofany translation of F. As a corollary, a separable Banach spaceX is reflexive if and only if every closed convex subset ofX with empty interior is Haar null. 2000 Mathematics SubjectClassification 46B20 (primary), 28C20 (secondary). 相似文献
16.
Summary This paper presents a graphical display for the parameters resulting from loglinear models. Loglinear models provide a method
for analyzing associations between two or several categorical variables and have become widely accepted as a tool for researchers
during the last two decades. An important part of the output of any computer program focused on loglinear models is that devoted
to estimation of parameters in the model. Traditionally, this output has been presented using tables that indicate the values
of the coefficients, the associated standard errors and other related information. Evaluation of these tables can be rather
tedious because of the number of values shown as well as their rather complicated structure, mainly when the analyst needs
to consider several models before reaching a model with a good fit. Therefore, a graphical display summarizing tables of parameters
could be of great help in this situation. In this paper we put forward an interactive dynamic graphical display that could
be used in such fashion. 相似文献
17.
Rob J. Hyndman David M. Bashtannyk Gary K. Grunwald 《Journal of computational and graphical statistics》2013,22(4):315-336
Abstract We consider the kernel estimator of conditional density and derive its asymptotic bias, variance, and mean-square error. Optimal bandwidths (with respect to integrated mean-square error) are found and it is shown that the convergence rate of the density estimator is order n –2/3. We also note that the conditional mean function obtained from the estimator is equivalent to a kernel smoother. Given the undesirable bias properties of kernel smoothers, we seek a modified conditional density estimator that has mean equivalent to some other nonparametric regression smoother with better bias properties. It is also shown that our modified estimator has smaller mean square error than the standard estimator in some commonly occurring situations. Finally, three graphical methods for visualizing conditional density estimators are discussed and applied to a data set consisting of maximum daily temperatures in Melbourne, Australia. 相似文献
18.
在拓扑空间中, 在$G$方法意义下以$G$壳与$G$核为基础, 引入$G$壳闭集,$G$核开集,$G$核邻域与$G$核导集的概念, 讨论其相应的一些性质. 特别的, 定义了点式$G$方法, 提供了在此方法下$G$闭集与$G$壳闭集, $G$开集与$G$核开集, $G$邻域与$G$核邻域, $G$导集与$G$核导集的一致性, 丰富了拓扑空间中关于$G$闭集, $G$开集, $G$内部, $G$邻域和$G$导集的一些结果. 同时, 提出一些问题以供进一步研究. 相似文献
19.
This paper addresses Gabor analysis on a discrete periodic set. Such a scenario can potentially find its applications in signal processing where signals may present on a union of disconnected discrete index sets. We focus on the Gabor systems generated by characteristic functions. A sufficient and necessary condition for a set to be a tight Gabor set in discrete periodic sets is obtained; discrete periodic sets admitting a tight Gabor set are also characterized; the perturbation of tight Gabor sets is investigated; an algorithm to determine whether a set is a tight Gabor set is presented. Furthermore, we prove that an arbitrary Gabor frame set can be represented as the union of a tight Gabor set and a Gabor Bessel set. 相似文献
20.
Zi-hong Tian Qing-de Kang 《应用数学学报(英文版)》2007,23(1):123-132
There are six types of triangles:undirected triangle,cyclic triangle,transitive triangle,mixed-1triangle,mixed-2 triangle and mixed-3 triangle.The triangle-decompositions for the six types of triangles havealready been solved.For the first three types of triangles,their large sets have already been solved,and theiroverlarge sets have been investigated.In this paper,we establish the spectrum of LT_i(v,λ),OLT_i(v)(i=1,2),and give the existence of LT_3(v,λ)and OLT_3(v,λ)with λ even. 相似文献