ISSN:0025-5793    

DOI:10.1112/S0025579300013218

出版商:London Mathematical Society    

年代:1987

数据来源: WILEY

摘要:

AbstractThe Minkowski‐Hlawka bound implies that there exist lattice packings ofn‐dimensional “superballs” |x1|σ+ … + |xn|σ≤ 1 (σ = 1,2,…) having density Δ satisfying log2Δ ≥ −n(l +o(l)) asn→ ∞. For eachn=pσ(pan odd prime) we exhibit a finite set of lattices, constructed from codes overGF(p), that contain packings of superballs having log2Δ ≥ −cn(l +o(l)), wherec=1+2e−2π2log2 e+…=1.000000007719…for σ = 2 (the classical sphere packing problem), worse than but surprisingly close to the Minkowski‐Hlawka bound, andc= 0·8226 … for σ = 3,c= 0·6742 … for σ = 4, etc., improving on that bound.

ISSN:0025-5793    

DOI:10.1112/S0025579300013231

出版商:London Mathematical Society    

年代:1987

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300013243

出版商:London Mathematical Society    

年代:1987

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300013255

出版商:London Mathematical Society    

年代:1987

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300013267

出版商:London Mathematical Society    

年代:1987

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300013279

出版商:London Mathematical Society    

年代:1987

数据来源: WILEY

摘要:

AbstractWe prove that, if (fn)n∈ω is aΔ11sequence of continuous functions on some recursively presentable Polish space, such that any pointwise cluster point of (fn)n∈ω is a Borel function, then there exists aΔ11‐subsequence of (fn)n∈ω which is pointwise convergent. This is an effective version of a well known result of Bourgain, Fremlin and Talagrand.

ISSN:0025-5793    

DOI:10.1112/S0025579300013280

出版商:London Mathematical Society    

年代:1987

数据来源: WILEY

摘要:

AbstractWe construct a universal function φ on the real line such that, for every continuously differentiable functionfthe range off– φ has measure zero. We then apply this to obtain results on curve packing that generalize the Besicovitch set. In particular, we show that given a continuously differentiable family of measurable curves, there exists a plane set of measure zero containing a translate of each curve in the family. Examples are given to show that the differentiability hypothesis cannot be weakened to a Lipschitz condition of order α for any 0<α<1.

ISSN:0025-5793    

DOI:10.1112/S0025579300013292

出版商:London Mathematical Society    

年代:1987

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300013309

出版商:London Mathematical Society    

年代:1987

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300013310

出版商:London Mathematical Society    

年代:1987

数据来源: WILEY