Stochastic modeling of a billiard in a gravitational field: Power law behavior of Lyapunov exponents

We consider the motion of a point particle (billiard) in a uniform gravitational field constrained to move in a symmetric wedge-shaped region. The billiard is reflected at the wedge boundary. The phase space of the system naturally divides itself into two regions in which the tangent maps are respectively parabolic and hyperbolic. It is known that the system is integrable for two values of the wedge half-angle ₁ and ₂ and chaotic for ₁<< ₂. We study the system at three levels of approximation: first, where the deterministic dynamics is replaced by a random evolution; second, where, in addition, the tangent map in each region is, replaced by its average; and third, where the tangent map is replaced by a single global average. We show that at all three levels the Lyapunov exponent exhibits power law behavior near ₁ and ₂ with exponents 1/2 and 1, respectively. We indicate the origin of the exponent 1, which has not been observed in unaccelerated billiards.     

Fermi and Coulomb correlations in the 21 S state of the helium isoelectronic sequence

The Fermi and Coulomb holes of the 2¹ S state of the helium isoelectronic sequence are investigated. Several interesting differences between the results obtained and those which might be expected on the basis of the corresponding 2³ S state are pointed out and discussed.     

Structure and properties of the ion pair charge-transfer complex of octacyanotungstate(IV) with the 2,2′-bipyridinium dication

The X-ray crystal structure of (bpyH2)2[W(CN)8]·4H2 O (bpyH2=2,2-bipyridinium) is described. The [W(CN)8]4– anion has an approximately square antiprismatic (D4d) conformation, seemingly imposed by strong anion–water–cation hydrogen-bonding interactions. Bond distances in the anion are: WC 2.150(5), 2.163(5); CN 1.128(6), 1.145(6)Å and the angles WCN are 177.6(5), 178.3(5)°. The dihydrate and the anhydrous salt are both intensely black solids, exhibiting ion-pair charge-transfer interaction between cation and anion. E.s.r. spectra indicate that 30% of the tungsten is present as WV in the solid state, but that in solution only the WIV complex is present. The electron withdrawing effect of the cation is discussed and compared with that in a series of salts with different bipyridinium cations.     

Calculation of Siegert eigenvalues for molecular systems: results for He(21,3S)+ H

The variational calculation of Siegert eigenvalues has previously been shown to provide reliable positions and widths for atomic resonances. This approach is herein extended to molecular problems, and the first such calculations for a molecular autoionizing system, He(2^1,3S)+H→ He+H⁺+e^?, are reported.     

Synthesis of novel tetracyclic chromenes through carbanion chemistry of 4-methyl coumarins

Various substituents were introduced onto the methyl group in 4-methyl coumarins through lithiation, followed by reactions with a wide range of electrophiles. The presence of an alkoxy group on 6′-phenyl ring was found to be pivotal for the success of this reaction. This procedure provided a convenient synthetic pathway to elaborate the methyl group of 4-methylcoumarins. Application of this methodology was showcased with the synthesis of biologically important novel tetracyclic chromene ring systems (n = 1-3).     

Modeling the reaction mechanisms for redox regulation of protein tyrosine phosphatase 1B activity

Protein tyrosine phosphatase 1B (PTP1B) functions by removing the phosphoryl group from tyrosinephosphorylated proteins in insulin signaling and metabolism. The regeneration of the active site involves a sulphenylamide intermediate derived from the intrastrand cross-linking between the catalytic serine and the neighboring backbone nitrogen. Two mechanisms have been proposed for the formation of the sulphenylamide intermediate and the subsequent reactivation of the catalytic site. In the current work, the proposed mechanisms have been investigated by the use of density functional theory calculations. Our results suggest that these two mechanisms have similar overall energy barriers and that the preferred route will be determined by the availability of hydrogen peroxide or other oxidizing reagents.     

Evaluation of parameters critical to observing proteins inside living Escherichia coli by in-cell NMR spectroscopy

Our recently developed in-cell NMR procedure now enables one to observe protein conformations inside living cells. Optimization of the technique demonstrates that distinguishing the signals produced by a single protein species depends critically on protein overexpression levels and the correlation time in the cytoplasm. Less relevant is the selective incorporation of (15)N. Poorly expressed proteins, insoluble proteins, and proteins that cannot tumble freely due to associations within the cell cannot yet be observed. We show in-cell NMR spectra of bacterial NmerA and human calmodulin and discuss limitations of the technique as well as prospects for future applications.     

Liquid chromatographic determination of 4,4'-dinitrocarbanilide, the active component of the infertility agent nicarbazin, in chicken, duck, goose, and snake eggs

4,4'-Dinitrocarbanilide (DNC) was extracted from chicken, duck, goose, and snake eggs and isolated by reversed-phase liquid chromatography. DNC was detected by ultraviolet absorbance at 347 nm and quantitated by comparison with a calibration standard. Recoveries of DNC from fortified control chicken, duck, goose, and snake egg samples were determined for DNC levels of 0.16, 10, and 16 microg/g. The mean recoveries from chicken, duck, goose, and snake eggs were 92 +/- 4, 88 +/- 9, 87 +/- 7, and 95 +/- 6%, respectively. The method limits of detection for DNC in chicken, duck, goose, and snake eggs ranged from 0.015 to 0.035 microg/g. The reported method is much simpler than and equally efficient as previous methods developed for the determination of DNC residues in egg contents.