Approximate momentum conservation for spatial semidiscretizations of semilinear wave equations

Summary. We prove that a standard second order finite difference uniform space discretization of the semilinear wave equation with periodic boundary conditions, analytic nonlinearity, and analytic initial data conserves momentum up to an error which is exponentially small in the stepsize. Our estimates are valid for as long as the trajectories of the full semilinear wave equation remain real analytic. The method of proof is that of backward error analysis, whereby we construct a modified equation which is itself Lagrangian and translation invariant, and therefore also conserves momentum. This modified equation interpolates the semidiscrete system for all time, and we prove that it remains exponentially close to the trigonometric interpolation of the semidiscrete system. These properties directly imply approximate momentum conservation for the semidiscrete system. We also consider discretizations that are not variational as well as discretizations on non-uniform grids. Through numerical example as well as arguments from geometric mechanics and perturbation theory we show that such methods generically do not approximately preserve momentum.Mathematics Subject Classification (2000): 65M20, 58J70, 70H33     

Suspension and fall of heavy particles in random two-dimensional flow

We investigate the settling of heavy particles in a steady, two-dimensional random velocity field, and find instances in which particle suspension occurs. This leads to a bimodal velocity distribution that may explain some apparently conflicting results reported in the literature. The bimodal distribution is typically smeared out by a time dependence of the ambient flow but, if the time variation is slow, the settling rates of some particles will be as well. The resulting broadbanded velocity distribution of the settling particles will have significance for processes such as rain drop formation, in which the spread of particle velocities affects the statistics of particle collisions.     

Synthetic peptides in the diagnosis of HIV infection

Peptide-based enzyme-linked immunosorbent assays have been found to be enough sensitive and specific for the diagnosis of human immunodeficiency virus specific antibodies in acquired immunodeficiency syndrome patients. This review provides an overview of the most important peptides developed for use as synthetic antigens in immunodiagnosis of HIV-infected patients. In particular, many studies have been devoted to discriminate between the two retroviruses HIV-1 and HIV-2, as well as different subtypes.     

Structural and magnetic properties of carboxylato-bridged manganese(II) complexes involving tetradentate ligands: discrete complex and 1D polymers. Dependence of J on the nature of the carboxylato bridge

The crystal structure of an inorganic linear polymer consisting of Mn(II) and an N-centered tripodal ligand N,N-bis(2-(6-methyl)pyridylmethyl)glycinate is presented (1, C(16)H(20)N(3)O(3)F(6)P(1)Mn(1), a = 9.993(2) A, b = 13.285(3) A, c = 16.040(3) A, orthorhombic, Pnam, Z = 4). The polymeric structure is ensured by carboxylato ligands connecting two Mn(II) in a rather rare syn-anti geometry. The magnetic properties of this infinite chain have been investigated, together with the magnetic properties of a dimeric Mn(II) compound (3) from a closely related ligand [N,N-bis[(1-methylimidazol-2-yl)-methyl)glycinate] involving an unusual bis(monatomic-carboxylato) bridge. The inorganic polymer 1 shows a pseudo-2D magnetic structure, with a major interaction pathway along the chain (J/k = -0.172 +/- 0.005 K) and an interchain minor one (zJ'/k = -0.006 +/- 0.004 K). These properties are reminiscent of those from a closely related previously reported inorganic Mn(II) polymer (2 obtained from manganese(II) and N,N-(2-pyridylmethyl)((1-methylimidazol-2-yl)methyl)glycinate). The dimer 3 shows a small antiferromagnetic coupling of J/k = -0.693 +/- 0.016 K. To address the influence of the carboxylato bridging mode on the magnetic properties, these complexes are compared to a series of compounds involving carboxylato bridges of several geometries between Mn(II) ions. Carboxylato bridges induce usually antiferromagnetic coupling, with the magnitude of the interaction (/J/) increasing with the number of bridges. The J value is dependent on the bridging mode. The syn-syn bridge is an efficient pathway, even by comparison with the monatomic [(mu-eta(1)-carboxylato)] bridge.     

Cu(II) complexes with heterocyclic substituted thiosemicarbazones: the case of 5-formyluracil. Synthesis,characterization, x-ray structures,DNA interaction studies,and biological activity

Two new 5-formyluracil thiosemicarbazone (H(3)ut) derivatives, Me-H(3)ut (1) and Me(2)-H(3)ut (2), were synthesized by reacting thiosemicarbazides, mono- and dimethylated on the aminic nitrogen, with 5-formyluracil and were subsequently characterized. These ligands, treated with copper chloride and nitrate, afforded three complexes: [Cu(Me-H(3)ut)Cl(2)].H(2)O (3), [Cu(Me(2)-H(3)ut)Cl(2)].H(2)O (4), and [Cu(Me-H(3)ut)(NO(3))(OH(2))(2)]NO(3) (5). The crystal structures of these complexes have been determined by single-crystal X-ray diffraction. In 3 and 4, a similar pentacoordination is present; the copper atom is surrounded by the ligand SNO donor atoms and by two chloride ions. The structure of 5 consists of [Cu(Me-H(3)ut)(NO(3))(OH(2))(2)](+) cations and nitrate anions. The copper coordination (4 + 2) involves the SNO ligand atoms and a water oxygen in the basal plane; the apical positions are occupied by a second water oxygen and by an oxygen of a monodentate nitrate group. Two biochemical techniques, namely DNA titration in the UV-vis region and thermal denaturation, have been employed to probe the details of DNA binding of these compounds. Analysis of the results suggests that our compounds are able to interact with DNA by electrostatic and groove binding but not by intercalation. The compounds have been also tested in vitro on human leukemic cell line U937, but they are not able to inhibit significantly cell proliferation.     

Inert site in a protein zinc cluster: isotope exchange by high resolution mass spectrometry

Using electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry, we show that one Zn2+ ion in the Zn4 cluster of cyanobacterial metallothionein is inert to exchange with 67Zn2+. We suggest that this is zinc in site A, which together with the surrounding alpha and beta secondary structure forms a zinc-finger fold.     

Introduction of 4(S)-oxazolidineacetic acid, 2-oxo (D-Oxac) motif in a polypeptide chain: synthesis and conformational analysis

A four step synthesis of 4(S)-oxazolidineacetic acid, 2-oxo benzyl ester (D-Oxac-OBn) from L-Asp-OH in 45% overall yield is reported. The formation of by-products is completely avoided, by microwave irradiation and by the use of caesium carbonate as base. Moreover the synthesis and IR and 1H NMR conformational analysis of the tetramers Boc-L-Val-D-Oxac-L-Ala-OBn and Boc-L-Val-D-Oxac-Aib-L-Ala-OBn in solution is reported.     

Easy Access to Phosphido-Selenido Clusters. Reaction of [Ru3(CO)12] with Ph2(pyth)PSe {pyth=5-(2-Pyridyl)-2-Thienyl} and Crystal Structure of [Ru3(μ3-Se)(μ-PPh2)(μ-pyth)(CO)6{P(pyth)Ph2}]

The reaction of [Ru₃(CO)₁₂] with Ph₂(pyth)PSe (pyth=5-(2-pyridyl)-2-thienyl) allows to obtain two novel clusters [Ru₃(₃-Se)₂(CO)₇{P(pyth)Ph₂}₂] 1 and [Ru₃(₃-Se)(-PPh₂)(-pyth)(CO)₆{P(pyth)Ph₂}] 2 in satisfactory yields. The first one exhibits the well-known bicapped, open triangular, 50-electron nido-core, whereas 2, whose crystal structure has been determined, shows the rather rare Ru₃Se tetrahedron with the Ph₂P and pyth fragments as side-bridging ligands. Morever cluster 2 belongs to the exiguous family of selenido-phosphido clusters not easily achievable by other routes.     

Core of projective dimension one modules

The core of a projective dimension one module is computed explicitly in terms of Fitting ideals. In particular, our formula recovers previous work by R. Mohan on integrally closed torsionfree modules over a two-dimensional regular local ring. The first author was partially supported by a Faculty Research Fellowship from the University of Kentucky. The second and third authors gratefully acknowledge partial support from the NSF.Mathematics Subject Classification (2000):Primary 13A30, 13B21; Secondary 13C99     

Magnetic response of microbially synthesized transition metal- and lanthanide-substituted nano-sized magnetites

The magnetic susceptibility (κ_RT) and saturation magnetization (M_S) of microbially synthesized magnetites were systematically examined. Transition metal (Cr, Mn, Co, Ni and Zn)- and lanthanide (Nd, Gd, Tb, Ho and Er)-substituted magnetites were microbially synthesized by the incubation of transition metal (TM)- and lanthanide (L)-mixed magnetite precursors with either thermophilic (TOR-39) or psychrotolerant (PV-4) metal-reducing bacteria (MRB). Zinc incorporated congruently into both the precursor and substituted magnetite, while Ni and Er predominantly did not. Microbially synthesized Mn- and Zn-substituted magnetites had higher κ_RT than pure biomagnetite depending on bacterial species and they exhibited a maximum κ_RT at 0.2 cationic mole fraction (CMF). Other TMs’ substitution linearly decreased the κ_RT with increasing substitution amount. Based on the M_S values of TM- and L-substituted magnetite at 0.1 and 0.02 CMF, respectively, Zn (90.7 emu/g for TOR-39 and 93.2 emu/g for PV-4)- and Mn (88.3 emu/g by PV-4)-substituted magnetite exhibited higher M_S than standard chemical magnetite (84.7 emu/g) or pure biomagnetite without metal substitution (76.6 emu/g for TOR-39 and 80.3 emu/g for PV-4). Lanthanides tended to decrease M_S, with Gd- and Ho-substituted magnetites having the highest magnetization. The higher magnetization of microbially synthesized TM-substituted magnetites by the psychrotroph, PV-4 may be explained by the magnetite formation taking place at low temperatures slowing mechanics, which may alter the magnetic properties compared to the thermophile, through suppression of the random distribution of substituted cations.