Local complexity of Delone sets and crystallinity

This paper characterizes when a Delone set X in R-n is an ideal crystal in terms of restrictions on the number of its local patches of a given size or on the heterogeneity of their distribution. For a Delone set X, let N-X (T) count the number of translation-inequivalent patches of radius T in X and let M-X (T) be the minimum radius such that every closed ball of radius M-X(T) contains the center of a patch of every one of these kinds. We show that for each of these functions there is a gap in the spectrum of possible growth rates between being bounded and having linear growth, and that having sufficiently slow linear growth is equivalent to X being an ideal crystal. Explicitly, for N-X (T), if R is the covering radius of X then either N-X (T) is bounded or N-X (T) greater than or equal to T/2R for all T > 0. The constant 1/2R in this bound is best possible in all dimensions. For M-X(T), either M-X(T) is bounded or M-X(T) greater than or equal to T/3 for all T > 0. Examples show that the constant 1/3 in this bound cannot be replaced by any number exceeding 1/2. We also show that every aperiodic Delone set X has M-X(T) greater than or equal to c(n)T for all T > 0, for a certain constant c(n) which depends on the dimension n of X and is > 1/3 when n > 1.

Doubling and Tripling Constructions for Defining Sets in Steiner Triple Systems

A minimal defining set of a Steiner triple system on a points (STS(v)) is a partial Steiner triple system contained in only this STS(v), and such that any of its proper subsets is contained in at least two distinct STS(v)s. We consider the standard doubling and tripling constructions for STS(2v + 1) and STS(3v) from STS(v) and show how minimal defining sets of an STS(v) gives rise to minimal defining sets in the larger systems. We use this to construct some new families of defining sets. For example, for Steiner triple systems on, 3" points; we construct minimal defining sets of volumes varying by as much as 7(n-/-).

Synthesis, structure and magnetism of the oxalato-bridged chromium(III) complex [NBu4n](4)[Cr-2(ox)(5)]center dot 2CHCl(3)

The binuclear complex [NBu4n](4)[Cr-2(ox)(5)]. 2CHCl(3) has been prepared by an ion-exchange procedure employing Dowex 50WX2 cation-exchange resin in the n-butylammonium form and potassium tris(oxalato)chromate(III). The dimeric complex was characterised by a crystal structure determination: monoclinic, space group C2/c, a = 29.241(7), b = 15.192(2), c = 22.026(5) Angstrom, beta = 94.07(1)degrees, Z = 4. The magnetic susceptibility (300-4.2 K) indicated that the chromium(III) sites were antiferromagnetically coupled (J = -3.1 cm(-1)).

Effect of oral creatine supplementation on near-maximal strength and repeated sets of high-intensity bench press exercise

This study examined the effects of 26 days of oral creatine monohydrate (Cr) supplementation on near-maximal muscular strength, high-intensity bench press performance, and body composition. Eighteen male powerlifters with at least 2 years resistance training experience took part in this 28-day experiment. Pre and postmeasurements (Days 1 and 28) were taken of near-maximal muscular strength, body mass, and % body fat. There were two periods of supplementation Days 2 to 6 and Days 7 to 27. ANOVA and t-tests revealed that Cr supplementation significantly increased body mass and lean body mass with no changes in % body fat. Significant increases in 3-RM strength occurred in both groups, both absolute and relative to body mass; the increases were greater in the Cr group. The change in total repetitions also increased significantly with Cr supplementation both in absolute terms and relative to body mass, while no significant change was seen in the placebo (P) group. Creatine supplementation caused significant changes in the number of BP reps in Sets 1, 4, and 5. No changes occurred in the P group. It appears that 26 days of Cr supplementation significantly improves muscular strength and repeated near-maximal BP performance, and induces changes in body composition.

Critical sets for families of Latin squares

In this paper I give details of new constructions for critical sets in latin squares. These latin squares, of order n, are such that they can be partitioned into four subsquares each of which is based on the addition table of the integers module n/2, an isotopism of this or a conjugate.

Interference pattern with a dark center from two atoms driven by a coherent laser field

In a recent paper Meyer and Yeoman [Phys. Rev. Lett. 79, 2650 (1997)] have shown that the resonance fluorescence from two atoms placed in a cavity and driven by an incoherent field can produce an interference pattern with a dark center. We study the fluorescence from two coherently driven atoms in free space and show that this system can also produce an interference pattern with a dark center. This happens when the atoms are in nonequivalent positions in the driving: field, i.e., the atoms experience different intensities and phases of the driving field. We discuss the role of the interatomic interactions in this process and find that the interference pattern with a dark center results from the participation of the antisymmetric state in the dynamics of the driven two-atom system.

Interference pattern with a dark center in resonance fluorescence from two atoms driven by a squeezed vacuum field

We study the resonance fluorescence from two interacting atoms driven by a squeezed vacuum field and show that this system produces an interference pattern with a dark center. We discuss the role of the interatomic interactions in this process and find that the interference pattern results from an unequal population of the symmetric and antisymmetric states of the two-atom system. We also identify intrinsically nonclassical effects versus classical squeezed field effects, (C) 1998 Elsevier Science B.V. All rights reserved.

Nickel complexes with tris(2-aminoethyl)amine (tren): [Ni-3(tren)(4)(H2O)(2)][Cr(ox)(3)](2)center dot 6H(2)O (ox = oxalate), {[Ni-2(tren)(3)][ClO4](4)center dot H2O}(n), and [Ni-2(tren)(2)(aepd)][ClO4](4)center dot 2H(2)O (aepd = N-(2-aminoethyl)pyrrolidi

Reaction of K-3[Cr(ox)(3)] (ox = oxalate) with nickel(II) and tris(2-aminoethyl)amine (tren) in aqueous solution resulted in isolation of the bimetallic assembly [Ni-3(tren)(4)(H2O)(2)][Cr(ox)(3)](2). 6H(2)O. The polymeric complex {[Ni-2(tren)(3)][ClO4](4). H2O}(n) has been prepared by reaction of nickel(II) perchlorate and tren in aqueous solution. From the same reaction mixture the complex [Ni-2(tren)(2)(aepd)][ClO4](4). 2H(2)O (aepd = N-(2-aminoethyl)pyrrolidine-3,4-diamine), in which a bridging tren ligand contains a carbon-carbon bond between two arms forming a substituted pyrrolidine, has been isolated. The complexes have been characterized by X-ray crystallography. The magnetic susceptibility (300-4.2 K) and magnetization data (2, 4 K, H = 0-5 T) for {[Ni-2(tren)(3)][ClO4](4). H2O}(n) (300 K , 4.23 mu(B)) exhibit evidence of weak antiferromagnetic coupling and zero field splitting (2J = -1.8 cm(-1); \ D\ = 2 cm(-1)) at low temperature. For [Ni-3(tren)(4)(H2O)(2)][Cr(ox)(3)](2). 6H(2)O the susceptibility data at 300 K are indicative of uncoupled nickel(II) and chromium(III) sites with zero-field splitting and intramolecular antiferromagnetic coupling predicted at low temperature.

Maximal sets of Hamilton cycles in Kn,n

In this article, we prove that there exists a maximal set of m Hamilton cycles in K-n,K-n if and only if n/4 < m less than or equal to n/2. (C) 2000 John Wiley & Sons, Inc.

Slant or occlusion: global factors resolve stereoscopic ambiguity in sets of horizontal lines

Perceived slant was measured for horizontal lines aligned on one side and of varying lengths whose length disparity was either a constant linear amount for all lines (consistent with uniocular occlusion) or proportional to line length (consistent with global slant). Although the disparity of any line was ambiguous with respect to these two possibilities, slant of individual lines did not occur in the former case, but a subjective contour in depth was reported along the alignment. For proportional disparity of the set, global slant was seen. Adding a constant length to each line on the invalid eye for occlusion resulted in multiple slants. Smooth uniocular variations in alignment shape elicited subjective contours slanting or curving in depth. Global context can disambiguate the depth status of individual disparate lines. (C) 2004 Elsevier Ltd. All rights reserved.

Critical sets in direct products of back circulant Latin squares

To date very Few families of critical sets for latin squares are known. The only previously known method for constructing critical sets involves taking a critical set which is known to satisfy certain strong initial conditions and using a doubling construction. This construction can be applied to the known critical sets in back circulant latin squares of even order. However, the doubling construction cannot be applied to critical sets in back circulant latin squares of odd order. In this paper a family of critical sets is identified for latin squares which are the product of the latin square of order 2 with a back circulant latin square of odd order. The proof that each element of the critical set is an essential part of the reconstruction process relies on the proof of the existence of a large number of latin interchanges.