Nondurable K-Theory Equivalence and Bousfield Localization*

In this paper we consider what happens when Adams self maps are modified by adding certain unstable maps. The unstable maps which are added are trivial after a single suspension. We can choose the modification so that the maps are still K-theory equivalences but the loops on the map are no longer K-theory equivalences. As a corollary we note that the maps are K-theory equivalences but not v ₁-periodic equivalences. Another consequence is the behavior of the cobar spectral sequences for generalized homology theories. Tamaki shows that in certain cases a cobar-type spectral sequence for generalized homology theories is well behaved. The maps we construct give an example where despite the connectivity of the spaces the cobar spectral sequence is still poorly behaved. Finally we use our maps to construct spaces whose Bousfield class is distinct from the cofiber of the Adams map but which becomes the same after one suspension.     

A geometric theory of harmonic and semi-conformal maps

We describe for any Riemannian manifold M a certain scheme M _L , lying in between the first and second neighbourhood of the diagonal of M. Semi-conformal maps between Riemannian manifolds are then analyzed as those maps that preserve M _L ; harmonic maps are analyzed as those that preserve the (Levi-Civita-) mirror image formation inside M _L .     

<Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>-mixed intersection bodies

In this paper the author first introduce a new concept of L _p -dual mixed volumes of star bodies which extends the classical dual mixed volumes. Moreover, we extend the notions of L _p intersection body to L _p -mixed intersection body. Inequalities for L _p -dual mixed volumes of L _p -mixed intersection bodies are established and the results established here provide new estimates for these type of inequalities. This work was supported by the Natural Science Foundation of Zhejiang Province of China (Grant No. Y605065) and the Foundation of the Education Department of Zhejiang Province of China (Grant No. 20050392)     

Codes with the Same Weight Distributions as the Goethals Codes and the Delsarte-Goethals Codes

The Goethals code is a binary nonlinear code of length 2^m+1 which has codewords and minimum Hamming distance 8 for any odd . Recently, Hammons et. al. showed that codes with the same weight distribution can be obtained via the Gray map from a linear code over Z ₄of length 2^m and Lee distance 8. The Gray map of the dual of the corresponding Z ₄ code is a Delsarte-Goethals code. We construct codes over Z ₄ such that their Gray maps lead to codes with the same weight distribution as the Goethals codes and the Delsarte-Goethals codes.     

Bolzano’s intermediate-value theorem for quasi-holomorphic maps

We extend Bolzano’s intermediate-value theorem to quasi-holomorphic maps of the space of continuous linear functionals from l _p into the scalar field, (0< p<1). This space is isomorphic to l _∞.     

The decomposition of Kv into K2×K5''''s

The decomposition of the complete graph Kv into Kr×Kc's, the products of Kr and Kc,is originated from the use of DNA library screening. In this paper, we consider the case where r=2 and c = 5, and show that such a decomposition exists if and only if v ≡ 1 (mod 25).     

Weak Equality and Exact Sequences in H v -modules

The largest class of multivalued systems satisfying the module-like axioms is the H_v-module. H_v-modules first were introduced by Vougiouklis. In this paper we define weak equality between two subsets of an H_v-module and introduced the notion of exact sequences of H_v-modules. Also some results on the weak equality and exact sequences are given.     

The L p -curvature images of convex bodies and L p -projection bodies

Associated with the L _p -curvature image defined by Lutwak, some inequalities for extended mixed p-affine surface areas of convex bodies and the support functions of L _p -projection bodies are established. As a natural extension of a result due to Lutwak, an L _p -type affine isoperimetric inequality, whose special cases are L _p -Busemann-Petty centroid inequality and L _p -affine projection inequality, respectively, is established. Some L _p -mixed volume inequalities involving L _p -projection bodies are also established.     

Some complete metrics on spaces of fuzzy subsets

The classes of the L_p,∞- and L_p-metrics play an important role to develop a probability theory in fuzzy sample spaces. All of these metrics are known to be separable, but not complete. The classes are closely related as for each L_p,∞-metric there exists some L_p-metric which induces the same topology. This paper deals with the completion of the L_p,∞- and L_p-metrics. We can also show that the relationship between the classes of L_p,∞- and L_p-metrics still holds for the obtained respective classes of their completions.     

A new multivariable <Subscript><Emphasis Type="BoldItalic">6</Emphasis></Subscript><Emphasis Type="BoldItalic">ψ</Emphasis><Subscript><Emphasis Type="BoldItalic">6</Emphasis></Subscript> summation formula

By multidimensional matrix inversion, combined with an A _r extension of Jackson’s ₈ φ ₇ summation formula by Milne, a new multivariable ₈ φ ₇ summation is derived. By a polynomial argument this ₈ φ ₇ summation is transformed to another multivariable ₈ φ ₇ summation which, by taking a suitable limit, is reduced to a new multivariable extension of the nonterminating ₆ φ ₅ summation. The latter is then extended, by analytic continuation, to a new multivariable extension of Bailey’s very-well-poised ₆ ψ ₆ summation formula. Partly supported by FWF Austrian Science Fund grants P17563-N13, and S9607 (the second is part of the Austrian National Research Network “Analytic Combinatorics and Probabilistic Number Theory”).     

关于L_p球的几个新不等式和性质(英文)

本文研究了L_p球的相关问题.利用对偶混合体积、球面Radon变换和Fourier变换的方法,获得了关于L_p球的几个新不等式和性质,其中一个不等式与著名的最大切片猜想有关.     

<Emphasis Type="Italic">∂</Emphasis>-operations and <Emphasis Type="Italic">H</Emphasis><Subscript><Emphasis Type="Italic">V</Emphasis></Subscript>-fields

The hyperoperations, called theta-operations （δ）, are motivated from the usual property, which the derivative has on the derivation of a product of functions. Using any map on a set, one can define δ-operations. In this paper, we continue our study on the δ-operations on groupoids, rings, fields and vector spaces or on the corresponding hyperstructures. Using δ-operations one obtains, mainly, Hwstructures, which form the largest class of the hyperstructures. For representation theory of hyperstructures, by hypermatrices, one needs special Hv-rings or Hy-fields, so these hyperstructures can be used. Moreover, we study the relation of these δ-structures with other classes of hyperstructures, especially with the Hv-structures.     

Localization of <Emphasis Type="Italic">LM</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>-algebras

The aim of this paper is to define the localization LM _n -algebra of an LM _n —algebra L with respect to a topology F on L; in Section 5 we prove that the maximal LM _n -algebra of fractions (defined in [3]) and the LM _n -algebra of fractions relative to an Λ—closed system (defined in Section 2) are LM _n -algebras of localization.     

Characterizations of spaces in the unit ball of

Let B denote the unit ball of . For 0<p<∞, the holomorphic function spaces Q_p and Q_p,0 on the unit ball of are defined as

and

In this paper, we give some derivative-free, mixture and oscillation characterizations for Q_p and Q_p,0 spaces in the unit ball of .     

The Smallest Degree Sum That Yields Potentially Kr＋1 - K3-Graphic Sequences

Let a（Kr,＋1 - K3,n） be the smallest even integer such that each n-term graphic sequence п= （d1,d2,…dn） with term sum σ（п） = d1 ＋ d2 ＋…＋ dn 〉 σ（Kr＋1 -K3,n） has a realization containing Kr＋1 - K3 as a subgraph, where Kr＋1 -K3 is a graph obtained from a complete graph Kr＋1 by deleting three edges which form a triangle. In this paper, we determine the value σ（Kr＋1 - K3,n） for r ≥ 3 and n ≥ 3r＋ 5.     

Absolute summability of infinite series

It is shown in [4] that if a normal matrix,A satisfies some conditions then |C,1| _k summability implies |A| _k summability wherek≥1. In the present paper, we consider the converse implication.     

A Variation of an Extremal Theorem Due to Woodall

We consider a variation of an extremal theorem due to Woodall [12, or 1, Chapter 3] as follows: Determine the smallest even integer (₃C₁,n), such that every n-term graphic sequence = (d₁, d₂,..., d_n) with term sum () = d₁ + d₂ + ... + d_n (₃C₁,n) has a realization G containing a cycle of length r for each r = 3,4,...,l. In this paper, the values of (₃C_l,n) are determined for l = 2m – 1,n 3m – 4 and for l = 2m,n 5m – 7, where m 4.AMS Mathematics subject classification (1991) 05C35Project supported by the National Natural Science Foundation of China (Grant No. 19971086) and the Doctoral Program Foundation of National Education Department of China     

Lp-Lq DECAY ESTIMATES FOR HYPERBOLIC EQUATIONS WITH OSCILLATIONS IN COEFFICIENTS

This work is concerned with the proof of Lp -Lq decay estimates for solutions of the Cauchy problem for utt -λ2(t)b2(t)/Δu =0. The coefficient consists of an increasing smooth function λ and an oscillating smooth and bounded function b which are uniformly separated from zero. The authors‘ main interest is devoted to the critical case where one has an interesting interplay between the growing and the oscillating part.     

The Coordinatewise Uniformly Kadec–Klee Property in Some Banach Spaces

We introduce a new property UKK _c for a Banach space and show for an Orlicz sequence space the following: UKK _c H _{c 2}.     

F_2+vF_2上的循环码

本文研究了环F_2+vF_2上的循环码.利用标准形生成元集刻画了环F_2+vF_2上的循环码的代数结构,证明了环F_2+vF_2上的每一个非零的循环码均有唯一的标准形生成元集,进而得到了每一个循环码均是由一个多项式生成的.