Common supports as fixed points

A family S of sets in R ^d is sundered if for each way of choosing a point from rd+1 members of S, the chosen points form the vertex-set of an (r–1)-simplex. Bisztriczky proved that for each sundered family S of d convex bodies in R ^d , and for each partition (S , S ), of S, there are exactly two hyperplanes each of which supports all the members of S and separates the members of S from the members of S . This note provides an alternate proof by obtaining each of the desired supports as (in effect) a fixed point of a continuous self-mapping of the cartesian product of the bodies.     

Synthesis and DNA cross-linking of a phototriggered FR900482 mitosene progenitor

[reaction: see text] The synthesis and biochemical reactivity of the first photoactivated mitosene-based DNA interstrand cross-linking agent is described.     

A one-step synthesis of γ-pyrones

The potassium enolate of 4-methoxy-3-buten-2-one reacts with acid chlorides anhydrides and acylimidazoles by C-acylation and $\text{in situ}$ cyclization to afford 2-substituted γ-pyrones directly.     

Semiempirical local spin: Theory and implementation of the ZILSH method for predicting Heisenberg exchange constants of polynuclear transition metal complexes

The local spin formalism ( 3 ) for computing expectation values 〈S_A · S_B〉 that appear in the Heisenberg spin model has been extended to semiempirical single determinant wave functions. An alternative derivation of expectation values in restricted and unrestricted cases is given that takes advantage of the zero differential overlap (ZDO) approximation. A formal connection between single determinant wave functions (which are not in general spin eigenfunctions) and the Heisenberg spin model was established by demonstrating that energies of single determinants that are eigenfunctions of the local spin operators with eigenvalues corresponding to high‐spin radical centers are given by the same Heisenberg coupling constants {J_AB} that describe the true spin states of the system. Unrestricted single determinant wave functions for transition metal complexes are good approximations of local spin eigenfunctions when the metal d orbitals are local in character and all unpaired electrons on each metal have the same spin (although spins on different metals might be reversed). Good approximations of the coupling constants can then be extracted from local spin expectation values 〈S_A · S_B〉 energies of the single determinant wave functions. Once the coupling constants are obtained, diagonalization of the Heisenberg spin Hamiltonian provides predictions of the energies and compositions of the spin states. A computational method is presented for obtaining coupling constants and spin‐state energies in this way for polynuclear transition metal complexes using the intermediate neglect of differential overlap Hamiltonian parameterized for optical spectroscopy (INDO/S) in the ZINDO program. This method is referred to as ZILSH, derived from ZINDO, Davidson's local spin formalism, and the Heisenberg spin model. Coupling constants and spin ground states obtained for 10 iron complexes containing from 2 to 6 metals are found to agree well with experimental results in most cases. In the case of the complex [Fe₆O₃(OAc)₉(OEt)₂(bpy)₂]⁺, a priori predictions of the coupling constants yield a ground‐state spin of zero, in agreement with variable‐temperature magnetization data, and corroborate spin alignments proposed earlier on the basis of structural considerations. This demonstrates the potential of the ZILSH method to aid in understanding magnetic interactions in polynuclear transition metal complexes. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

A concise total synthesis of (+)-FR900482 and (+)-FR66979

The concise, enantioselective total synthesis of the potent antitumor antibiotics (+)-FR900482 and (+)-FR66979 are described. Sharpless asymmetric epoxidation technology has been deployed to construct the optically active aziridine-containing fragment that is joined to the aromatic moiety in a highly convergent manner. Dimethyldioxirane effects the remarkable one-step deprotection/oxidative cyclization of an eight-membered ring amino-ketone to the unique hydroxylamine hemiketal ring system that is a distinctive structural motif of FR900482. This reaction has been exploited in a concise 33-step enantioselective total synthesis of FR900482.     

EFFECT OF CHLORIDE AND BENZOATE ANIONS ON THE DELAYED LIGHT EMISSION IN DCMU-TREATED SPINACH CHLOROPLASTS

Abstract —Chloride anions, when added to DCMU [3-(3,4-dichlorophenyl)-1,1-dimethylurea]-treated spinach chloroplasts, change the rate of decay of the delayed light emission in the seconds region but do not change the shape or the temperature dependence of the decay. Benzoate anions, on the other hand, change both the rate and the shape of the decay of the delayed light emission. These results are consistent with a model in which the membrane potential and the structure of the reaction center affect the decay kinetics of the delayed light emission in the seconds region.     

Determination of glucosamine in raw materials and dietary supplements containing glucosamine sulfate and/or glucosamine hydrochloride by high-performance liquid chromatography with FMOC-Su derivatization: collaborative study

A collaborative study was conducted for determination of glucosamine in raw materials and dietary supplements containing glucosamine sulfate and/or glucosamine hydrochloride by high-performance liquid chromatography (HPLC) with N-(9-fluorenyl-methoxycarbonyloxy) succinimide (FMOC-Su) derivatization. Thirteen blind materials, one pair of which were duplicates, were tested by 12 collaborating laboratories. The test samples consisted of various commercial products, including tablets, capsules, drink mix, and liquids as well as raw materials, blanks, and those for spike recovery analyses. The tests with blank products and products spiked with glucosamine showed good specificity of the method. The average recoveries at spike levels of 100 and 150% of the declared amount were 99.0% with a relative standard deviation (RSD) of 2.1%, and 101% with an RSD of 2.3%, respectively. The test results between laboratories on each commercial product were reproducible with RSD values of no more than 4.0%, and the results were repeatable in the same laboratory with an average RSD of 0.7%. HorRat values ranged from 0.5 to 1.7 on both tests of spike recovery and reproducibility between laboratories on commercial products. The average determination coefficient of the calibration curves from the laboratories was 0.9995 with an RSD of 0.03%. All of the 12 collaborating laboratories succeeded in the study and none of their reported test results were outliers, partly indicating the robustness of the method. It is recommended that the method be accepted by AOAC INTERNATIONAL as Official First Action.     

Production of Organometallic Polymers by the Interfacial Technique. XXXII. Reaction Variables in the Synthesis of Oligomeric Tin Poly(cobalticinium Esters) and Thermal Properties of the Products

The synthesis of oligomeric tin poly(cobalticinium esters) is presented as a function of the particular reaction variables stirring rate, pH and amount of added base, mole ratio of reactants, concentration of reactants, and volume of organic phase. Factors which decrease the solubility of the stannane apparently act to increase the yield of polyester. The thermal characterization of I was carried out via DSC and TGA. The products generally exhibit endotherms below 150 to 200[ddot]C which may be related to T_g. Above 200[ddot]C, degradation occurs in air by an oxidative mode.     

Could we use a million cores to solve an integer program?

Given the steady increase in cores per CPU, it is only a matter of time before supercomputers will have a million or more cores. In this article, we investigate the opportunities and challenges that will arise when trying to utilize this vast computing power to solve a single integer linear optimization problem. We also raise the question of whether best practices in sequential solution of ILPs will be effective in massively parallel environments.