Absolute potassium cation affinities (PCAs) in the gas phase

The potassium cation affinities (PCAs) of 136 ligands (20 classes) in the gas phase were established by hybrid density functional theory calculations (B3-LYP with the 6-311+G(3df,2p) basis set). For these 136 ligands, 70 experimental values are available for comparison. Except for five specific PCA values-those of phenylalanine, cytosine, guanine, adenine (kinetic-method measurement), and Me(2)SO (by high-pressure mass spectrometric equilibrium measurement)-our theoretical estimates and the experimental affinities are in excellent agreement (mean absolute deviation (MAD) of 4.5 kJ mol(-1)). Comparisons with previously reported theoretical PCAs are also made. The effect of substituents on the modes of binding and the PCAs of unsubstituted parent ligands are discussed. Linear relations between Li+/Na+ and K+ affinities suggest that for the wide range of ligands studied here, the nature of binding between the cations and a given ligand is similar, and this allows the estimation of PCAs from known Li+ and/or Na+ affinities. Furthermore, empirical equations relating the PCAs of ligands with their dipole moments, polarizabilities (or molecular weights), and the number of binding sites were established. Such equations offer a simple method for estimating the PCAs of ligands not included in the present study.     

Protonation and bromination of an osmabenzyne: reactions leading to the formation of new metallabenzynes

The reactivities of benzynes and metal-carbyne complexes are normally associated with the triple bond units. However, we have now found that electrophiles do not attack the formal osmium-carbon triple bond of osmabenzyne complex 1. Instead, 1 undergoes electrophilic substitution reactions-the typical reactions of aromatic systems.     

Templating and supersaturation-driven anti-templating: principles of biomineral architecture

The structural synergy between biominerals (CaCO(3), hydroxyapatite) and biosubstrates were examined for the first time. The templating effect of substrate and a newly identified supersaturation-driven interfacial structure mismatch effect were identified in the context of a new nucleation model. It follows that the heterogeneous nucleation which corresponds to a good structural match and synergy between biominerals and substrates will promote an ordered, compact, and tough complex biomineral structure, and occur only at low supersaturations, whereas at high supersaturations the heterogeneous nucleation associated with a poor structural match and synergy between biominerals and substrates will become dominant due to supersaturation-driven interfacial structural mismatch. The latter normally results in a disordered and porous structure. A phenomenon, so-called microgravity-driven homogeneous nucleation, was also examined. It turns out that microgravity will suppress convection and consequently promote homogeneous-like nucleation during biomineralization. This could be responsible for microgravity-induced osteoporousis.     

A new copper acetate-bis(oxazoline)-catalyzed, enantioselective Henry reaction

A highly enantioselective, nitroaldol reaction catalyzed by a chiral Cu(II) bis(oxazoline) complex has been developed. The reaction scope includes both aromatic and aliphatic aldehydes (15 examples) affording products in good yields and enantioselectivities (87-94% ee). An X-ray structure of the catalyst has been provided along with a rationalization of the sense of asymmetric induction.     

On Some Three-Color Ramsey Numbers

 In this paper we study three-color Ramsey numbers. Let K _i,j denote a complete i by j bipartite graph. We shall show that (i) for any connected graphs G ₁, G ₂ and G ₃, if r(G ₁, G ₂)≥s(G ₃), then r(G ₁, G ₂, G ₃)≥(r(G ₁, G ₂)−1)(χ(G ₃)−1)+s(G ₃), where s(G ₃) is the chromatic surplus of G ₃; (ii) (k+m−2)(n−1)+1≤r(K _1,k , K _1,m , K _n )≤ (k+m−1)(n−1)+1, and if k or m is odd, the second inequality becomes an equality; (iii) for any fixed m≥k≥2, there is a constant c such that r(K _k,m , K _k,m , K _n )≤c(n/logn), and r(C _2m , C _2m , K _n )≤c(n/logn) ^m/(m−1) for sufficiently large n. Received: July 25, 2000 Final version received: July 30, 2002 RID="*" ID="*" Partially supported by RGC, Hong Kong; FRG, Hong Kong Baptist University; and by NSFC, the scientific foundations of education ministry of China, and the foundations of Jiangsu Province Acknowledgments. The authors are grateful to the referee for his valuable comments. AMS 2000 MSC: 05C55     

Multivariate Polynomial Minimization and Its Application in Signal Processing

We make a conjecture that the number of isolated local minimum points of a 2n-degree or (2n+1)-degree r-variable polynomial is not greater than n ^r when n 2. We show that this conjecture is the minimal estimate, and is true in several cases. In particular, we show that a cubic polynomial of r variables may have at most one local minimum point though it may have 2^r critical points. We then study the global minimization problem of an even-degree multivariate polynomial whose leading order coefficient tensor is positive definite. We call such a multivariate polynomial a normal multivariate polynomial. By giving a one-variable polynomial majored below a normal multivariate polynomial, we show the existence of a global minimum of a normal multivariate polynomial, and give an upper bound of the norm of the global minimum and a lower bound of the global minimization value. We show that the quartic multivariate polynomial arising from broad-band antenna array signal processing, is a normal polynomial, and give a computable upper bound of the norm of the global minimum and a computable lower bound of the global minimization value of this normal quartic multivariate polynomial. We give some sufficient and necessary conditions for an even order tensor to be positive definite. Several challenging questions remain open.     

Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit

Classical optical lithography is diffraction limited to writing features of a size lambda/2 or greater, where lambda is the optical wavelength. Using nonclassical photon-number states, entangled N at a time, we show that it is possible to write features of minimum size lambda/(2N) in an N-photon absorbing substrate. This result allows one to write a factor of N2 more elements on a semiconductor chip. A factor of N = 2 can be achieved easily with entangled photon pairs generated from optical parametric down-conversion. It is shown how to write arbitrary 2D patterns by using this method.     

Investigation of excited states of11B and7Li by means of thermal neutron capture on10B nuclei

Theγ-radiation from the¹⁰B(n,γ) reaction is studied using an unpolarized target. More accurate values for energies of transitions in¹¹B could be determined. No new levels have been found. TheQ value of this reaction: 11,454.1 (2)keV, is in agreement with earlier experiments. Also a new value for the cross section could be derived: 0.29 (4) barn, which is a factor 5 more accurate than earlier experiments. The¹⁰B(n, α)⁷ Li reaction, leading to the 478 keV state in⁷Li, is studied by means of polarized¹⁰B nuclei and polarized neutrons. The resulting anisotropy in the directional distribution of the⁷Li particles manifests itself in the Doppler broadening of the 478 keV line. Analysis of the line shape directly yields the conclusion, that the reaction proceeds for more than 96% through theJ=7/2 channel of¹¹B in case of destructive channel interference of theJ=5/2 channel. Constructive channel interference is only possible if the reaction proceeds for more than 99.5% through theJ=7/2 channel. It appeared that the outcomingα and⁷Li particles are emitted predominantly in directions perpendicular to the nuclear orientation axis.