Test spaces,dacey spaces,and completeness of inner product spaces

We show that a test space consisting of the unit sphere of a real or complex inner product spaceS and of the set all maximal orthonormal systems inS, is algebraic iffS is Dacey or, equivalently, iffS is complete. In addition, we present another completeness criterion.This research is supported by the grant G-368 of the Slovak Academy of Sciences, Slovakia.     

High resolution study of24Mg(p,d)23Mg for the Ne-E problem

Nuclear levels of²³Mg near and above the proton threshold were investigated with high resolution. A new level has been identified at 7.643 MeV (66 keV above the proton threshold) with a possible J=(3/2, 5/2)⁺. Some other spin-parity and excitation-energy assignments are also made. These results enable the reaction rate estimate of²²Na(p,)²³Mg with much smaller uncertainties, which is critical for the Ne-E problem in nuclear astrophysics.     

Sharp Inequalities for the Product of Polynomials

Let f₁(z),..., f_m(z) be polynomials with complex coefficients,and let their product be of degree n. For any polynomial, let||f|| be the maximum of |f(z)| on the unit circle. We determineconstants C_m < 2 for which for any n. The inequalities are asymptotically sharp as n .This improves earlier results of Gel'fond and Mahler, who gavethe constants e and 2 respectively. If f₁,..., f_m have realcoefficients, we show that for all m 2 and that this is asymptotically sharp. That is,in the real case, the best constant does not depend upon m form 2.     

Difference posets and the histories approach to quantum theories

Direct limits and tensor products of difference posets are studied. In the spirit of a recent paper by Isham, a potential model for an unsharp histories approach to quantum theory based on difference posets as abstract models for the set of effects is considered. It is shown that the set of all histories in this approach has an algebraic structure of a difference poset.     

Decay properties of the key resonant states in8Li(α, n)11B for primordial nucleosynthesis

The particle decay property of the key resonant states in the reaction⁸Li(,n)¹¹B for the inhomogeneous big bang models was studied experimentally. The sum of the branching ratios of the 10.572 MeV state for the neutron decays to the excited states in¹¹B is as large as for the ground state, indicating that the neutron decays to excited states are crucial and enhance the reaction rate for heavy element synthesis considerably.     

Key resonant states in the8Li(α,n)11B reaction in the inhomogeneous big bang models

The resonant states in the key reaction⁸Li(,n)¹¹B for the inhomogeneous Big Bang Models were studied experimentally through the⁹Be(,p)¹²B reaction at 64 MeV. This reaction is found to excite all the resonances of interest in¹²B. The most crucial resonant state at 10.572 MeV in¹²B (0.572 MeV above the threshold) was found to have _tot20±10 keV and J=(1^–), suggesting that the S-factor of the (,n) process should be larger than that obtained before.     

Absolute configuration, conformation, and circular dichroism of monocyclic arene dihydrodiol metabolites: it is all due to the heteroatom substituents

Absolute configurations and conformations of selected cis-1,2-dihydrodiols, isolated from bacterial enzyme-catalyzed arene dihydroxylation, have been examined by comparison of experimental and DFT-calculated CD spectra and confrontation with the results of X-ray diffraction studies in the crystalline phase. The equilibrium between the diene P and M conformers in cis-dihydrodiols is strongly dependent on the intramolecular OH-OH, OH-pi, and OH-F hydrogen bonding pattern and is crucial in determining the sign and magnitude of the long-wavelength diene pi-pi transition Cotton effect. The differences originate from a dominant contribution of either P-helical (1b, X=Me) or M-helical conformers (1d, X=F), or are due to M and P low-energy conformers, both contributing a positive rotational strength (1c, X=Br). Computations show that cis-dihydrodiol 1e (X=CF3) has only one M conformer stabilized by an intramolecular O-H...F hydrogen bond. cis-Dihydrodiol 1f (X=CN) shows a Cotton effect of the sign opposite to the sense of helicity of the dominating conformer. The results of the computations highlight the inadequacy of the Diene Helicity Rule and the Allylic Chirality Rule to correlate observed Cotton effects with dihydrodiol absolute configuration. A reliable model is presented to predict the absolute configuration of substituted benzene dihydrodiol derivatives from CD spectra, based on the confrontation of DFT-computed and experimental CD spectra. For 3-alkyl derivatives, a simple noncomputational model is offered, which is based on the contributions of the allylic hydroxy groups and the diene core in P and M conformers.     

cis-Dihydrodiol, arene oxide and phenol metabolites of dictamnine: key intermediates in the biodegradation and biosynthesis of furoquinoline alkaloids

Biotransformation of the parent furoquinoline alkaloid dictamnine and its 4-chlorofuroquinoline precursor, using the B8/36 bacterial mutant strain of Sphingomonas yanoikuyae, yielded, via biphenyl dioxygenase-catalysed dihydroxylation, the first isolable alkaloid cis-dihydrodiol metabolites; these metabolites were used in the chemoenzymatic synthesis of postulated arene oxide and phenol intermediates, and a range of derived furoquinoline alkaloids.