Stokes constants of an oblate ellipsoid of revolution with equidensites homothetic to its surface

The theory of equilibrium figures was actively developed in the 19th century, when it was found that the observed massive celestial bodies (the Sun, planets, and satellites) had an almost ellipsoidal form. The existence of exactly ellipsoidal figures was also established. The gravitational potential of these figures is represented by a Laplace series with its coefficients (Stokes’ constants I _n ) determined by some integral operator. The general term of the series was found for a homogeneous ellipsoid of revolution and the first terms of the series were found for some other mass distributions. Here, we have obtained the general term of the series for an arbitrary mass distribution given that the equidensites (surfaces of equal density) are homothetic to the outer surface of the ellipsoid of revolution. Simple estimates and an asymptotics of I _n have also been obtained.     

Thermal stability and degradation of starch derivatives

Thermal behaviour of different starch derivatives, i.e. starch esters and ethers having degree of substitution (DS) in the range of 0.02–0.18 were studied. Potato, maize and wheat starches were used. Measurements were carried out by coupled thermal analysis/ mass spectrometry method (STA-MS) in air atmosphere. The major DTG peak during the investigation for starch derivatives is observed below 300°C. The mass loss up to a temperature of 300°C is about 50%. The most abundant ions found areH₂O⁺ and CO₂ ⁺. For the studied starch derivatives with a low degree of substitution (DS<0.18) no correlation was found between thermal stability and the level of substitution regardless of the nature of substitution.     

Nuclear reactions induced by stopped negative pions in133Cs,93Nb and45Sc

The energy and angular distributions ofp, d, t,³He and⁴He from the three targets Cu, Ag and Au were measured at five different angles for bremsstrahlung with peak energy 500MeV. The measurements were made using a telescope consisting of four surface-barrier detectors. The experimental data are compared with cascade-evaporation calculations. For the⁴He-distributions the calculations were extended to include the contribution from knock-out of surface alphas by the cascade nucleons. The comparison shows that the main contribution comes from evaporation but that there is a direct component of the order of 10%.     

Precise mass measurement of a double-stranded 500 base-pair (309 kDa) polymerase chain reaction product by negative ion electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry

Electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI-FTICRMS) has been used to determine the mass of a double-stranded 500 base-pair (bp) polymerase chain reaction (PCR) product with an average theoretical mass of the blunt-ended (i.e. unadenylated) species of 308 859.35 Da. The PCR product was generated from the linearized bacteriophage Lambda genome which is a double-stranded template. Utilization of ethanol precipitation in tandem with a rapid microdialysis step to purify and desalt the PCR product was crucial to obtain a precise mass measurement. The PCR product (0.8 pmol/μL) was electrosprayed from a solution containing 75% acetonitrile, 25 mM piperidine, and 25 mM imidazole and was infused at a rate of 200 nL/min. The average molecular mass and the corresponding precision were determined using the charge-states ranging from 172 to 235 net negative charges. The experimental mass and corresponding precision (reported as the 95% confidence interval of the mean) was 309 406 +/- 27 Da (87 ppm). The mass accuracy was compromised due to the fact that the PCR generates multiple products when using Taq polymerase due to the non-template directed 3'-adenylation. This results in a mixture of three PCR products with nearly identical mass (i.e. blunt-ended, mono-adenylated and di-adenylated) with unknown relative abundances that were not resolved in the spectrum. Thus, the experimental mass will be a weighted average of the three species which, under our experimental conditions, reflects a nearly equal concentration of the mono- and di-adenylated species. This report demonstrates that precise mass measurements of PCR products up to 309 kDa (500 bp) can be routinely obtained by ESI-FTICR requiring low femtomole amounts. Copyright 1999 John Wiley & Sons, Ltd.     

Bis(2‐but­yl‐N,N′‐diisopropyl­amidinato)dichloro­hafnium(IV)

The title compound, [Hf(C₁₁H₂₃N₂)₂Cl₂], is a monomeric hafnium(IV) complex containing two bidentate amidinate ligands and two cis Cl atoms. The crystals are triclinic (space group ) and there is one independent six‐coordinate monomer with a highly distorted octa­hedral geometry in the asymmetric unit. The reported structure is the first hafnium–amidinate complex to be characterized successfully by single‐crystal X‐ray diffraction.     

Behavior of zirconium and hafnium ions in ultramicroconcentrations investigated by horizontal zone electrophoresis in free electrolyte*

The electrophoresis of zirconium and hafnium ions in aqueous solutions was investigated. No-carrier-added ⁸⁸Zr and ¹⁷⁵Hf have been used in microconcentrations (10^-11M). The complexation of zirconium and hafnium with DTPA has been investigated in a large pH interval. The stability constants of the Zr-DTPA and Hf-DTPA complexes were determined for the first time by the method of horizontal zone electrophoresis in free electrolyte. The electrophoretic behavior of Zr(IV) and Hf(IV) ions in nitric acid solutions has also been studied.     

Electromigration of carrier-free radionuclides

Dependences of La(III) overall ion mobilities on concentrations of ox^2– and tart^2– anions of oxalic and tartaric acid in aqueous solutions of 0.01 overall ionic strength and temperature 298.1 K were obtained by direct measurements of electromigration of carrierfree¹⁴⁰La-lanthanum(III). Concentration stability constants K_n and individual ion mobilities u _i ^o of oxalate and tartrate complexes of La(III) have been calculated for nitrate and perchlorate electrolytes, respectively: [La(ox)]⁺, lg K₁=5.63(9), u⁰[La(ox)]⁺=1.95(15)·10^–4 cm²·s^–1·V^–1; [la(ox)₂]^–, lg K₂=4.05(19) u⁰[La(ox)₂]^–=–1.76(20)·10^–4 cm²·s^–1·V^–1; [La(tart)]⁺, lg K₁=4.40(5), u⁰[La(tart)]⁺=+1.99(18)·10^–4 cm²·s^–1·V^–1.Results are compared with literature data. Additional, limiting individual La³⁺ ion mobility was calculated: =+6.9(1)·10^–4 cm²·s^–1·V^–1 for pure water at 298.1 K.     

Guanidinate-stabilized monomeric hafnium amide complexes as promising precursors for MOCVD of HfO2

Novel guanidinato complexes of hafnium [Hf{eta2-(iPrN)2CNR2}2(NR2)2] (R2 = Et2, 1; Et, Me, 2; Me2, 3), synthesized by insertion reactions of N,N'-diisopropylcarbodiimide into the M-N bonds of homologous hafnium amide complexes 1-3 and {[mu2-NC(NMe2)2][NC(NMe2)2]2HfCl}2 (4) using a salt metathesis reaction, are reported. Single-crystal X-ray diffraction analysis revealed that compounds 1-3 were monomers, while compound 4 was found to be a dimer. The observed fluxional behavior of compounds 1-3 was studied in detail using variable-temperature and two-dimensional NMR techniques. The thermal characteristics of compounds 1-3 seem promising for HfO2 thin films by vapor deposition techniques. Metal-organic chemical vapor deposition experiments with compound 2 as the precursor resulted in smooth, uniform, and stoichiometric HfO2 thin films at relatively low deposition temperatures. The basic properties of HfO2 thin films were characterized in some detail.     

Soliton equations,vertex operators,and simple singularities

We prove the equivalence of two hierarchies of soliton equations associated to a simply-laced finite Dynkin diagram. The first was defined by Kac and Wakimoto (Proc. Symp. Pure Math. 48:138–177, 1989) using the principal realization of the basic representations of the corresponding affine Kac–Moody algebra. The second was defined in Givental and Milanov (The Breadth of Symplectic and Poisson Geometry, Progress in Mathematics, vol. 232, pp. 173–201, Birkhäuser, Basel, 2005) using the Frobenius structure on the local ring of the corresponding simple singularity. We also obtain a deformation of the principal realization of the basic representation over the space of miniversal deformations of the corresponding singularity. As a by-product, we compute the operator product expansions of pairs of vertex operators defined in terms of Picard–Lefschetz periods for more general singularities. Thus, we establish a surprising link between twisted vertex operators and deformation theory of singularities.