Energy spectra for decaying 2D turbulence in a bounded domain

We use results derived in the framework of the replica approach to study the liquid-glass thermodynamic transition. The main results are derived without using replicas and applied to the study of the Lennard-Jones binary mixture introduced by Kob and Andersen. We find that there is a phase transition due to the entropy crisis. We compute both analytically and numerically the value of the phase transition point T(K) and the specific heat in the low temperature phase.     

Analysis of the Gerber-Shiu function and dividend barrier problems for a risk process with two classes of claims

In this paper we consider a risk model with two independent classes of insurance risks. We assume that the two independent claim counting processes are, respectively, the Poisson and the generalized Erlang(2) process. We prove that the Gerber-Shiu function satisfies some defective renewal equations. Exact representations for the solutions of these equations are derived through an associated compound geometric distribution and an analytic expression for this quantity is given when the claim severities have rationally distributed Laplace transforms. Further, the same risk model is considered in the presence of a constant dividend barrier. A system of integro-differential equations with certain boundary conditions for the Gerber-Shiu function is derived and solved. Using systems of integro-differential equations for the moment-generating function as well as for the arbitrary moments of the discounted sum of the dividend payments until ruin, a matrix version of the dividends-penalty is derived. An extension to a risk model when the two independent claim counting processes are Poisson and generalized Erlang(ν), respectively, is considered, generalizing the aforementioned results.     

Divergences without probability vectors and their applications

In general, divergences and measures of information are defined for probability vectors. However, in some cases, divergences are ‘informally’ used to measure the discrepancy between vectors, which are not necessarily probability vectors. In this paper we examine whether divergences with nonprobability vectors in their arguments share the properties of probabilistic or information theoretic divergences. The results indicate that divergences with nonprobability vectors share, under some conditions, some of the properties of probabilistic or information theoretic divergences and therefore can be considered and used as information measures. We then use these divergences in the problem of actuarial graduation of mortality rates. Copyright © 2009 John Wiley & Sons, Ltd.     

Model Investigations for Vanadium-Protein Interactions. Synthetic, Structural, and Physical Studies of Vanadium(III) and Oxovanadium(IV/V) Complexes with Amidate Ligands

Reaction of the amide ligand N-[2-((2-pyridylmethylene)amino)phenyl]pyridine-2-carboxamide (Hcapca) with VCl(3) affords the compound trans-[VCl(2)(capca)] (1), the first example of a vanadium(III) complex containing a vanadium-deprotonated amide nitrogen bond, while reaction of bis(pentane-2,4-dionato)oxovanadium(IV) with the related ligands N-[2-((2-phenolylmethylene)amino)phenyl]pyridine-2-carboxamide (H(2)phepca), 1-(2-hydroxybenzamido)-2-(2-pyridinecarboxamido)benzene (H(3)hypyb), and 1,2-bis(2-hydroxybenzamido)benzene (H(4)hybeb) yields the complexes [VO(phepca)] (2), Na[VO(hypyb)].2CH(3)OH (4.2CH(3)OH), and Na(2)[VO(hybeb)].3CH(3)OH (5.3CH(3)OH) respectively. The preparation of the complex {N-[2-((2-thiophenoylmethylene)amino)phenyl]pyridine-2-carboxamido}oxovanadium(IV) (3) has been achieved by reaction of N-(2-aminophenyl)pyridine-2-carboxamide and 2-mercaptobenzaldehyde with [VO(CH(3)COO)(2)](x)(). Oxidation of complex 5.3CH(3)OH with silver nitrate gives its vanadium(V) analogue (8.CH(3)OH), which is readily converted to its corresponding tetraethylammonium salt (10.CH(2)Cl(2)) by a reaction with Et(4)NCl. The crystal structures of the octahedral 1.CH(3)CN, and the square-pyramidal complexes 3, 4.CH(3)CN, 5.2CH(3)OH, and 10 were demonstrated by X-ray diffraction analysis. Crystal data are as follows: 1.CH(3)CN, C(18)H(13)Cl(2)N(4)OV.CH(3)CN M(r) = 464.23, monoclinic, P2(1)/n, a = 10.5991(7) ?, b = 13.9981(7) ?, c = 14.4021(7) ?, beta = 98.649(2)(o), V = 2112.5(3) A(3), Z = 4, R = 0.0323, and R(w) 0.0335; 3, C(19)H(13)N(3)O(2)SV, M(r) = 398.34, monoclinic, P2(1)/n, a = 12.1108(10) ?, b = 19.4439(18) ?, c = 7.2351(7) ?, beta = 103.012(3) degrees, V = 1660.0(4) ?(3), Z = 4, R = 0.0355, and R(w) = 0.0376; 4.CH(3)CN, C(19)H(12)N(3)O(4)VNa.CH(3)CN, M(r) = 461.31, monoclinic, P2(1)/c, a = 11.528(1) ?, b = 11.209(1) ?, c = 16.512(2) ?, beta = 103.928(4)(o), V = 2071.0(5) ?(3), Z = 4, R = 0.0649, and R(w) = 0.0806; 5.2CH(3)OH, C(20)H(10)N(2)O(5)VNa(2).2CH(3)OH, M(r) = 519.31, triclinic, P1, a = 12.839(1) ?, b = 8.334(1) ?, c = 12.201(1) ?, alpha = 106.492(2) degrees, beta = 105.408(2) degrees, gamma = 73.465(2) degrees, V = 1175.6(3) ?(3), Z = 2, R = 0.0894, and R(w) = 0.1043; 10, C(28)H(32)N(3)O(5)V M(r) = 541.52, monoclinic, P2(1)/c, a = 11.711(3) ?, b = 18.554(5) ?, c = 12.335(3) ?, beta = 95.947(9) degrees, V = 2666(2) ?(3), Z = 4, R = 0.0904, and R(w) = 0.0879. In addition to the synthesis and crystallographic studies, we report the optical, infrared, magnetic, and electrochemical properties of these complexes. Electron paramagnetic resonance [of oxovanadium(IV) species] and (1)H, (13)C{(1)H}, and (51)V nuclear magnetic resonance [of oxovanadium(V) complex] properties are reported as well. This study represents the first systematic study of vanadium(III), V(IV)O(2+), and V(V)O(3+) species containing a vanadium-deprotonated amide nitrogen bond.     

Bromopyridazinedione-mediated protein and peptide bioconjugation

Bromopyridazinedione-mediated bioconjugation to a cysteine containing protein and a disulfide containing peptide is described. The conjugates are cleavable in an excess of thiol, including cytoplasmically-relevant concentrations of glutathione, and show a high level of hydrolytic stability. The constructs have the potential for four points of chemical attachment.     

Phosphonium-mediated cyclization of N-(2-aminophenyl)thioureas: efficient synthesis of 2-aminobenzimidazoles

BOP efficiently promoted the phosphonium-mediated cyclization of thioureas, leading to a convenient synthesis of 2-aminobenzimidazoles. Compared to conventional methods, the reactions were complete at room temperature with times ranging from a few minutes to 1 h in near quantitative yields. This method is also applicable to the synthesis of more challenging structures such as 2-akylaminobenzimidazoles and 2-(N-acyl)-aminobenzimidazoles. The methodology described herein represents a mild and efficient route to a variety of 2-aminobenzimidazoles.     

Correlation of dielectric properties,Raman spectra and calorimetric measurements of β-cyclodextrin-polyiodide complexes (β-cyclodextrin)2 ·BaI7 ·11H2O and (β-cyclodextrin)2 ·CdI7·15H2O

The frequency and temperature dependence of real and imaginary parts of the dielectric constant (ε′,?ε″), the phase shift (?) and the ac-conductivity (σ) of polycrystalline complexes (β-CD)₂·BaI₇·11H₂O and (β-CD)₂·CdI₇·15H₂O (β-CD?=?β-cyclodextrin) has been investigated over the frequency and temperature ranges 0–100?kHz and 140–420?K in combination with their Raman spectra, DSC traces and XRD patterns. The ε′(T), ε″(T) and ?(T) values at frequency 300?Hz in the range T<330?K show two sigmoids, two bell-shaped curves and two minima respectively revealing the existence of two kinds of water molecule, the tightly bound and the easily movable. Both complexes show the transition of normal hydrogen bonds to flip-flop type at 201?K. In the β-Ba complex most of the eleven water molecules remain tightly bound and only a small number of them are easily movable. On the contrary, in the β-Cd case the tightly bound water molecules are transformed gradually to easily movable. Their DSC traces show endothermic peaks with onset temperatures 118°C, 128°C for β-Ba and 106°C, 123°C, 131°C for β-Cd. The peaks 118°C, 106°C, 123°C are related to the easily movable and the tightly bound water molecules, while the peaks at 128°C, 131°C are caused by the sublimation of iodine. The activation energy of Ba²⁺ ions is 0.52?eV when all the water molecules exist in the sample and 0.99?eV when the easily movable water molecules have been removed. In the case of β-Cd the corresponding activation energies are 0.57?eV and 0.33?eV. The Raman peaks at 179?cm^?1, 170?cm^?1 and 165–166?cm^?1 are due to the charge transfer interactions in the polyiodide chains.     

Evidence of holes in the Arnold tongues of flow past two oscillating cylinders

The wake of two oscillating cylinders in a tandem arrangement is a nonlinear system that displays Arnold tongues. We show by numerical simulations that their geometry depends on the phase difference theta between the two oscillating cylinders. At theta = 0 there may be holes inside these intraresonance regions unlike the solid Arnold tongues encountered in single-cylinder oscillations. This implies that, surprisingly, self-excitation of the system may be suppressed inside these holes, at conditions close to its natural frequency.