On (4p~2q~(2b),2p~2q~(2b)-pq~b,p~2q~(2b)-pq~b) Menon Difference Sets

Ｏｎ（４ｐ２ｑ２ｂ，２ｐ２ｑ２ｂ－ｐｑｂ，ｐ２ｑ２ｂ－ｐｑｂ）ＭｅｎｏｎＤｉｆｅｒｅｎｃｅＳｅｔｓＷａｎＺｈａｏｚｅ（万兆泽）（ＣｏｌｅｇｅｏｆＭａｔｈｅｍａｔｉｃＳｃｉｅｎｃｅ，ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ，１００８７１）Ａｂｓ...     

A VIEW OF THE CHI-SQUARE STATISTIC

Statistical analysis of contingency tables is essentially a discrete multivariate problem. To test independence in a two-way contingency table, one can use different principles such as general class of distance or Mahalanobis distance to derive test statistic. Most of them result in the chi-square statistic, which is a simple test statistic. The disadvantage of the chi-square test is discussed from a multivariate point of view. A new test statistic is proposed for testing independence. This statistic is more sensitive to dependence than the chi-square statistic.     

S-PLUS code for simple and multiple correspondence analysis

An exploration of the application of S-PLUS code designed to perform classical correspondence analysis is made in this paper. This code allows for the “classical” analysis to be performed on categorical data consisting of two or more variables. For multi-way contingency tables, correspondence analysis can be performed by considering either the indicator matrix or the Burt matrix. The code also allows the user to incorporate into the analysis confidence circles (to identify categorical responses that deviate from the hypothesis of independence) and for an asymmetrical analysis to be performed. The function includes various warnings and stoppages to help the user properly analyse their data.     

Strong Endomorphism Monoid of Graph Union

ＳｔｒｏｎｇＥｎｄｏｍｏｒｐｈｉｓｍＭｏｎｏｉｄｏｆＧｒａｐｈＵｎｉｏｎ＊）ＬｉＷｅｉｍｉｎ（李为民）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｈａｎｇｈａｉＪｉａｏｔｏｎｇＵｎｉｖｅｒｓｉｔｙ，２００２４０）ＡｂｓｔｒａｃｔＴｈｅｓｔｒｏ...     

Some Reducibilities of Heegaard Splittings

ＳｏｍｅＲｅｄｕｃｉｂｉｌｉｔｉｅｓｏｆＨｅｅｇａａｒｄＳｐｌｉｔｉｎｇｓ＊）ＬｅｉＦｅｎｇｃｈｕｎ（雷逢春）ａｎｄＺｈａｎｇＹｉｎｇ（张影）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇｃｈｕｎ，１３０...     

K-Convergent Sequences in Topological Vector Spaces with a Basis

Ｋ┐ＣｏｎｖｅｒｇｅｎｔＳｅｑｕｅｎｃｅｓｉｎＴｏｐｏｌｏｇｉｃａｌＶｅｃｔｏｒＳｐａｃｅｓｗｉｔｈａＢａｓｉｓ＊）ＷｕＪｕｎｄｅ（武俊德）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＤａｑｉｎｇＰｅｔｒｏｌｅｕｍＩｎｓｔｉｔｕｔｅ，Ａｎｄａ，...     

Almost Flat Theorem for Complete Open Riemannian Manifolds with Nonnegative Ricci Curvature

ＡｌｍｏｓｔＦｌａｔＴｈｅｏｒｅｍｆｏｒＣｏｍｐｌｅｔｅＯｐｅｎＲｉｅｍａｎｎｉａｎＭａｎｉｆｏｌｄｓｗｉｔｈＮｏｎｎｅｇａｔｉｖｅＲｉｃｃｉＣｕｒｖａｔｕｒｅ＊）ＭｅｉＪｉａｑｉａｎｇ（梅加强）ＸｕＳｅｎｌｉｎ（徐森林）（ＤｅｐａｒｔｍｅｎｔｏｆＭ...     

Fixed Point Theorems on a Non-convex Set

ＦｉｘｅｄＰｏｉｎｔＴｈｅｏｒｅｍｓｏｎａＮｏｎ－ｃｏｎｖｅｘＳｅｔ￥ＺｈａｏＸｉａｏｑｕａｎ（赵晓全）ａｎｄＳｕｎＸｕｅｓｉ（孙学思）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃａ，ＨａｒｂｉｎＩｎｓｔｉｔｕｔｅｏｆＥｌｅｃｔｒｉｃａｌＴｅｃｈｎ...     

Spectral Geometry of Closed Minimal Real Hypersurfaces in CP~(n+1) and QP~(n+1)

ＳｐｅｃｔｒａｌＧｅｏｍｅｔｒｙｏｆＣｌｏｓｅｄＭｉｎｉｍａｌＲｅａｌＨｙｐｅｒｓｕｒｆａｃｅｓｉｎＣＰｎ＋１ａｎｄＱＰｎ＋１＊）ＱｕＣｈｅｎｇｑｉｎ（瞿成勤）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮａｎｊｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｎａ...     

Representation Formulas for Analytic Function Non－exponential in a Half Plane

ＲｅｐｒｅｓｅｎｔａｔｉｏｎＦｏｒｍｕｌａｓｆｏｒＡｎａｌｙｔｉｃＦｕｎｃｔｉｏｎＮｏｎ－ｅｘｐｏｎｅｎｔｉａｌｉｎａＨａｌｆＰｌａｎｅＤｅｎｇＧｕａｎｔｉｅ（邓冠铁）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｕａｚｈｏｎｇＵｎｉｖｅｒｓｉ...     

N-Centralizing Mappings in Semiprime Rings

Ｎ┐ＣｅｎｔｒａｌｉｚｉｎｇＭａｐｐｉｎｇｓｉｎＳｅｍｉｐｒｉｍｅＲｉｎｇｓＭａｊｅｅｄ，Ａ．Ｈ．ａｎｄＮｉｕＦｅｎｇｗｅｎ（牛凤文）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇｃｈｕｎ，１３００２３）...     

On Some Linear Maps from an Algebra into Its Bimodules

ＯｎＳｏｍｅＬｉｎｅａｒＭａｐｓｆｒｏｍａｎＡｌｇｅｂｒａｉｎｔｏＩｔｓＢｉｍｏｄｕｌｅｓＸｕＢｅｎｌｏｎｇ（徐本龙）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＱｕｆｕＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｑｕｆｕ，Ｓｈａｎｄｏｎｇ，２７３１６５...     

Boundary Element Approximation of Steklov Eigenvalue Problem for Helmholtz Equation in Three Dimensions

ＢｏｕｎｄａｒｙＥｌｅｍｅｎｔＡｐｐｒｏｘｉｍａｔｉｏｎｏｆＳｔｅｋｌｏｖＥｉｇｅｎｖａｌｕｅＰｒｏｂｌｅｍｆｏｒＨｅｌｍｈｏｌｔｚＥｑｕａｔｉｏｎｉｎＴｈｒｅｅＤｉｍｅｎｓｉｏｎｓＴａｎｇＷｅｉｊｕｎ（唐维军）（ＬａｂｏｒａｔｏｒｙｏｆＣｏｍｐｕｔ...     

A Remark on the Weak Topology and the Degree

ＡＲｅｍａｒｋｏｎｔｈｅＷｅａｋＴｏｐｏｌｏｇｙａｎｄｔｈｅＤｅｇｒｅｅＬｏｔｆｉＬａｓｓｏｕｅｄ（Ｌａｂｏｒａｔｏｉｒｅｄ＇ＡｎａｌｙｓｅＮｕｍéｒｉｑｕｅＵｎｉｖｅｒｓｉｔéＰｉｅｒｒｅｅｔＭａｒｉｅＣｕｒｉｅ４，ｐｌａｃｅＪｕｓｉｅｕ，７５２５...     

On p-Radical Groups

Ｏｎｐ－ＲａｄｉｃａｌＧｒｏｕｐｓ￥ＺｈｏｕＹｏｎｇｘｉｎ（周永新）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｅｂｅｉＴｅａｃｈｅｒｓＵｎｉｖｅｒｓｉｔｙ，Ｓｈｉｊｉａｚｈｕａｎｇ，Ｈｅｂｅｉ，０５００１６）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐ...     

OSCILLATION FOR NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS

ＯＳＣＩＬＬＡＴＩＯＮＦＯＲＮＯＮＬＩＮＥＡＲＮＥＵＴＲＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ（申建华）（王志成）湖南大学，邮编：４１００８２ＳｈｅｎＪｉａｎｈｕａ；ＷａｎｇＺｈｉｃｈｅｎｇ（ＨｕｎａｎＵｎｉｖｅｒｓｉｔｙ，）Ａｂｓｔｒａｃｔ...     

On Joint Relations between the Two Subsets D_0 and D_1 in Affine Weyl Group W_a（A_n－1）

ＯｎＪｏｉｎｔＲｅｌａｔｉｏｎｓｂｅｔｗｅｅｎｔｈｅＴｗｏＳｕｂｓｅｔｓＤ_０ａｎｄＤ_１ｉｎＡｆｆｉｎｅＷｅｙｌＧｒｏｕｐＷ_ａ（Ａ_ｎ－１）￥ＲｕｉＨｅｂｉｎｇ（芮和兵）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＥａｓｔＣｈｉｎａＮｏｒｍａｌ...     

Rings over which Invertible Modulesare Free

ＲｉｎｇｓｏｖｅｒｗｈｉｃｈＩｎｖｅｒｔｉｂｌｅＭｏｄｕｌｅｓａｒｅＦｒｅｅＣｈｅｎＨｕａｎｙｉｎ（陈焕艮）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｕｎａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇｓｈａ，４１０００６）Ａｂｓｔｒａｃｔ...     

A high dimensional Open Coloring Axiom

We prove a partition theorem for analytic sets, namely, if X is an analytic set in a Polish space and [X]ⁿ = K₀ ∪ K₁ with K₀ open in the relative topology, and the partition satisfies a finitary condition, then either there is a perfect K₀‐homogeneous subset or X is a countable union of K₁‐homogeneous subsets. We also prove a partition theorem for analytic sets in the three‐dimensional case. Finally, we give some applications of the theorems. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Free Weakly Hamilitonian Lattice-Ordered Groups

ＦｒｅｅＷｅａｋｌｙＨａｍｉｌｉｔｏｎｉａｎＬａｔｔｉｃｅ－ＯｒｄｅｒｅｄＧｒｏｕｐｓ￥ＴｏｎｇＤａｏｒｏｎｇ（仝道荣）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｅｈａｉＵｎｉｖｅｒｓｉｔｙ．Ｎａｎｉｊｎｇ，２１００２４）Ａｂｓｔｒａｃｔ：...