Z4-Kerdock Codes, Orthogonal Spreads, and Extremal Euclidean Line-Sets

When m is odd, spreads in an orthogonal vector space of type⁺(2m + 2,2) are related to binary Kerdock codes and extremalline-sets in 2^{m + 1} with prescribed angles. Spreads in a 2m-dimensionalbinary symplectic vector space are related to Kerdock codesover Z₄ and extremal line-sets in with prescribed angles. These connections involve binary, realand complex geometry associated with extraspecial 2-groups.A geometric map from symplectic to orthogonal spreads is shownto induce the Gray map from a corresponding Z₄-Kerdock codeto its binary image. These geometric considerations lead tothe construction, for any odd composite m, of large numbersof Z₄-Kerdock codes. They also produce new Z₄-linear Kerdockand Preparata codes. 1991 Mathematics Subject Classification:primary 94B60; secondary 51M15, 20C99.     

Application of Combinatorial Procedures in the Search for Serine-Protease-Like Activity with Focus on the Acyl Transfer Step

Recursive deconvolution of a 729-membered peptide library has identified three active sequences, in which both Ser and His are present in one of the two tripeptidic chains generated on a steroidal scaffold (see structural formula), for the cleavage of an activated p-nitrophenyl ester. This combinatorial approach aims at searching for serine-protease-like activity.     

Self-assembled polynuclear clusters derived from some flexible polydentate dihydrazide ligands

Polynuclear manganese(II), cobalt(II)/(III), iron(II)/(III) and nickel(II) complexes of a group of flexible polydentate dihydrazone ligands, based on pyridine-2,6-dipicolinic (A), oxalic (B) and malonic (C) subunits are described. Structural details are reported for the linear dinuclear complexes [Ni2(2poap)2(H2O)2](NO3)4 . 2CH3OH . 2.5H2O (1), [Mn2(pttp)(NO3)2(CH3OH)2(H2O)2](NO3)2 . H2O (2) and [Mn2(mapttp)2(NO3)2(H2O)2](NO3)2 . 10H2O (3), a square tetranuclear complex [Co4(pttp)4]Br6 . 9H2O (4), a tetranuclear tetrahedral complex [Ni4(pttp)6](BF4)6F2 . 14H2O (7), and a mixed spin state tetranuclear Ni(II) complex [(2pyoap)2Ni4(CH3OH)4] . 1.5CH3OH (10), with a diamond-like arrangement of metal ions. The paramagnetic metal centers are well separated in each case, leading to weak antiferromagnetic coupling or non-existent spin exchange.     

Structural investigations of a lead(IV) tetraacetate-pyridine complex

A 1 : 1 crystalline complex of lead(IV) tetraacetate and pyridine (LTA-py) has been prepared. The single-crystal X-ray structure, at 296 and 150 K, establishes the presence of a relatively short Pb-N bond (2.307 A) within an intriguing seven-coordinate lead inner sphere consisting of the pyridine ligand and two bidentate and two monodentate acetate ligands. The pyridine occupies a surprising amount of the available coordination space and has induced a dramatic change in coordination compared to the four chelating acetate ligands found in lead tetraacetate (LTA). Thermal measurements (TGA/DSC) indicate the de-coordination of pyridine and its loss from the solid between 360 and 380 K. (207)Pb CP/MAS NMR spectroscopy also demonstrates the existence of the Pb-N bond through observation of (1)J((207)Pb,(14)N)= 63 Hz and a (207)Pb-(14)N dipolar coupling constant, of 149 Hz. The solid-state (207)Pb NMR parameters are used to give insight into the coordination environment of Pb(iv) in LTA-py. In solution, ligand exchange is rapid on chemical shift and J-coupling time scales. A (207)Pb NMR study of the titration of an LTA solution by pyridine yields a stability constant for LTA-py of K = 1.5 M(-1) and predicts it to have a (207)Pb NMR chemical shift essentially identical to that observed by CP/MAS NMR in the solid state. This correlation between the solid state and solution indicates that the seven-coordinate LTA-py structure found in the crystalline state does persist in solution, and this could further explain why the addition of pyridine has such profound effects on lead(IV) carboxylate-mediated organic reactions. Simulations of exchange-broadened line shapes of (13)C CP/MAS NMR spectra in the temperature regime above 280 K indicate local motion of the pyridine rings in the form of 180 degrees jumps (activation energy 72.5 kJ mol(-1)); these are first such ring flips reported for a coordinated pyridine ligand.     

Simultaneous attainment of high electron and ion temperatures in discharges with internal transport barriers in ASDEX upgrade

Internal transport barriers have been demonstrated to exist also under conditions with T(e) approximately T(i) approximately 10 keV and predominant electron heating of the tokamak core region. Central electron cyclotron heating was added to neutral beam injection-heated ASDEX Upgrade discharges with a preexisting internal transport barrier, established through programmed current ramping leading to shear reversal. Compared to a reference internal transport barrier discharge without electron cyclotron resonance heating, the electron heat conductivity in the barrier region was found not to increase, in spite of a fivefold increase in electron heat flux, and also angular momentum and ion energy transport did not deteriorate.     

Solid phases of cyclopentane: combined experimental and simulation study

The phase diagram of cyclopentane has been studied by powder neutron diffraction, providing diffraction patterns for phases I, II, and III, over a range of temperatures and pressures. The putative phase IV was not observed. The structure of the ordered phase III has been solved by single-crystal diffraction. Computational modeling reveals that there are many equienergetic ordered structures for cyclopentane within a small energy range. Molecular dynamics simulations reproduce the structures and diffraction patterns for phases I and III and also show an intermediate disordered phase, which is used to interpret phase II.     

Skew Boolean algebras derived from generalized Boolean algebras

Every skew Boolean algebra S has a maximal generalized Boolean algebra image given by S/ where is the Green’s relation defined initially on semigroups. In this paper we study skew Boolean algebras constructed from generalized Boolean algebras B by a twisted product construction for which . In particular we study the congruence lattice of with an eye to viewing as a minimal skew Boolean cover of B. This construction is the object part of a functor from the category GB of generalized Boolean algebras to the category LSB of left-handed skew Boolean algebras. Thus we also look at its left adjoint functor . This paper was written while the second author was a Visiting Professor in the Department of Education at the University of Cagliari. The facilities and assistance provided by the University and by the Department are gratefully acknowledged.     

Patterning of PLZT and PSZT thin films by excimer laser

The patterning of lanthanum-doped lead zirconate titanate (PLZT) and strontium-doped lead zirconate titanate (PSZT) thin films has been examined using a 5-ns pulsed excimer laser. Both types of film were deposited by rf magnetron sputtering with in situ heating and a controlled cooling rate in order to obtain the perovskite-structured films. The depth of laser ablation in both PSZT and PLZT films showed a logarithmic dependence on fluence. The ablation rate of PLZT films was slightly higher than that of PSZT films over the range of fluence (10–150 J/cm²) and increased linearly with number of pulses. The threshold fluence required to initiate ablation was ∼ 1.25 J/cm² for PLZT and ∼ 1.87 J/cm² for PSZT films. Individual squares were patterned with areas ranging from 10×10 μm² up to 30×30 μm² using single and multiple pulses. The morphology of the etched surfaces comprised globules which had diameters of 200–250 nm in PLZT and 1400 nm in PSZT films. The diameter of the globules has been shown to increase with fluence until reaching an approximately constant size at ≤ 20 J/cm² in both types of film. The composition of the films following ablation has been compared using X-ray photoelectron spectroscopy and energy-dispersive X-ray spectroscopy. PACS 79.20.Ds; 82.80.Pv; 82.80.Ej     

Perspectives from above and beyond the proton drip-line

This paper will review the dramatic increase in our knowledge of one and two proton unbound nuclei [1] such as recoil decay tagging [2] are revealing unique insights into the structure of nuclei beyond the proton drip-line. These studies of excited states provide complementary information to proton radioactivity studies, particularly regarding the role of deformation [3]. Radioactive beams are being used to study two-proton unbound resonances and to study explosive nuclear astrophysical reactions in the region of the proton drip-line.