Limits of Gaudin Algebras,Quantization of Bending Flows,Jucys–Murphy Elements and Gelfand–Tsetlin Bases

Gaudin algebras form a family of maximal commutative subalgebras in the tensor product of n copies of the universal enveloping algebra \({U(\mathfrak {g})}\) of a semisimple Lie algebra \({\mathfrak {g}}\). This family is parameterized by collections of pairwise distinct complex numbers z ₁, . . . , z _n . We obtain some new commutative subalgebras in \({U(\mathfrak {g})^{\otimes n}}\) as limit cases of Gaudin subalgebras. These commutative subalgebras turn to be related to the Hamiltonians of bending flows and to the Gelfand–Tsetlin bases. We use this to prove the simplicity of spectrum in the Gaudin model for some new cases.     

Structure,thermal behavior,and chemical durability of lead–calcium–phosphate glasses

ABSTRACT

Structure and physical properties of 25CaO–xPbO–(75–x)P₂O₅ (0≤x≤35) glasses are investigated in this paper. Substitution of PbO for P₂O₅ in the binary 25CaO–75P₂O₅ glass was found to increase the density and to decrease the molar volume. Fourier transform infrared (FTIR) and Raman spectroscopies show the evolution of the phosphate skeleton when the PbO content increases: Q³ to Q² species (0<x≤25) and Q² phosphate network (x = 25) to short phosphate groups (x > 25) such as (P₄O₁₃^6?) (x = 35). The glass transition temperature first decreases with x, then increases for x values larger than 10%. The evolution of the glass transition temperatures is interpreted from the structural data: the minimum point observed in T_g is attributed to the transition of the ultraphosphate network from the network containing the modifying cations at isolated sites to a network with modifier sub-structure sharing terminal oxygens. At higher PbO content, the large increase in T_g is due to the reticulation of the phosphate network by PbO₄ groups.     

Role of kaon physics,present–future

The main issue for kaon physics in the next decade is a systematic study of the rare decay modes to test the unitarity of the quark flavour mixing matrix, the global symmetries of the Standard Model and new physics with the highest possible precision.     

Atomic structure of the Zr–He,Zr–vac,and Zr–vac–He systems: First-principles calculation

The ab initio investigations have been performed for the atomic structure of the Zr–He, Zr–vac, and Zr–vac–He systems with concentrations of helium atoms and vacancies (vac) of ~6 at %. A heliuminduced instability of the zirconia lattice has been revealed in the Zr–He system, which disappears with the formation of vacancies. The most preferred positions of impurities in the metal lattice have been determined. The energy of helium dissolution and the excess volume introduced by helium have been calculated. It has been established that the presence of helium in the Zr lattice leads to a significant decrease in the energy of vacancy formation.     

Influence of Chemical-Heat Treatment on Thermal Stability of Microstructure,Mechanical Properties and Fracture of V–Cr–Ta–Zr Alloy

Russian Physics Journal - A study of the features of structural-phase state, thermal stability, characteristics of mechanical properties and fracture behavior of V–Cr–Ta–Zr alloy...     

Franck–Condon Factors and r‐Centroids for the B–, C–, F–, and G–X Band Systems of YF Molecule

The Franck–Condon factors and r‐centroids, which are very closely related to relative transition probabilities, have been evaluated by a more reliable numerical integration procedure for the B¹π–X¹Σ⁺, C¹Σ⁺–X¹Σ⁺, F¹Σ⁺–X¹Σ⁺, and G¹π–X¹Σ⁺ band systems of the YF molecule, using suitable potentials.     

ICEMS study of isothermal oxidation of Fe–Mn–Al–C–Cr–Si–Mo, Fe–Mn–Al–C–Cr–Si and Fe–9Cr–1Mo alloys

The purpose of this paper is to investigate the isothermal behavior of Fe–27.3Mn–7.6Al–C–6.5Cr–0.25Si–0.88Mo (Mo(0)) and Fe–27.3Mn–7.6Al–1.0C–6.5Cr–0.25Si (Mo(1)) alloys and compare it against Fe–9Cr–1Mo (FCR) commercial alloy. The experiments were carried out at 600°C, 700°C, 750°C and 850°C, each one during 72 h in static air. The oxidation kinetics was measured as a function of time using a Thermogravimetry analyzer (TGA). The structure and composition of the oxide scale were characterized by X-ray diffraction (XRD) and Integral Conversion Electron Mössbauer Spectroscopy (CEMS). The TGA results show that at all oxidation temperatures the sample FCR exhibit the lowest kinetic corrosion and the lowest weight gain, whereas Mo(0) the highest. By CEMS technique it were found a broad magnetic sextet, which has been fit by one hyperfine field distribution with mean hyperfine field characteristic to ferritic/martensite phase, one Fe^3?+? doublet and one singlet for the Mo(0) and Mo(1) alloys. Samples oxidized at highest temperatures exhibit a strong paramagnetic line, probably due that the Cr or Mn oxides may be enriched on the surface. Then, the magnetic phase can be converted partially into austenite phase at highest temperatures.     

Calculation and analysis of vibrational spectra of adenine–thymine,guanine–cytosine,and adenine–uracil complementary pairs in the condensed state

We have calculated the frequencies of the normal vibrations of the complementary nucleic acid base pairs adenine–thymine, guanine–cytosine, adenine–uracil, corresponding to the Watson–Crick structure, and the adenine–uracil pair, corresponding to the Hoogsteen structure, in condensed states and we interpret the spectra. We determine the contributions of hydrogen bonds to the vibrational modes of the complementary pairs. We have analyzed the nature of the relative displacements of the nucleic acid bases as integral molecular units along the hydrogen bonds. We show the role of hydrogen bonds in tautomeric interconversions of complementary nucleic acid base pairs. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 1, pp. 84–92, January–February, 2009.     

Rotational Spectra of CH3CCH–NH3, NCCCH–NH3, and NCCCH–OH2

Microwave spectra of NCCCH–NH₃, CH₃CCH–NH₃, and NCCCH–OH₂have been recorded using a pulsed-nozzle Fourier-transform microwave spectrometer. The complexes NCCCH–NH₃and CH₃CCH–NH₃are found to have symmetric-top structures with the acetylenic proton hydrogen bonded to the nitrogen of the NH₃. The data for CH₃CCH–NH₃are further consistent with free or nearly free internal rotation of the methyl top against the ammonia top. For NCCCH–OH₂, the acetylenic proton is hydrogen bonded to the oxygen of the water. The complex has a dynamicalC_2vstructure, as evidenced by the presence of two nuclear-spin modifications of the complex. The hydrogen bond lengths and hydrogen-bond stretching force constants are 2.212 Å and 10.8 N/m, 2.322 Å and 6.0 N/m, and 2.125 Å and 9.6 N/m for NCCCH–NH₃, CH₃CCH–NH₃, and NCCCH–OH₂, respectively. For the cyanoacetylene complexes, these bond lengths and force constants lie between the values for the related hydrogen cyanide and acetylene complexes of NH₃and H₂O. The NH₃bending and weak-bond stretching force constants for CH₃CCH–NH₃are less than those found in NCCCH–NH₃, NCH–NH₃, and HCCH–NH₃, suggesting that the hydrogen bonding interaction is particularly weak in CH₃CCH–NH₃. The weakness of this hydrogen bond is partially a consequence of the orientation of the monomer electric dipole moments in the complex. In CH₃CCH–NH₃the antialigned monomer dipole moments lead to a repulsive dipole–dipole interaction energy, while in NCH–NH₃and NCCCH–NH₃the aligned dipoles give an attraction interaction.     

Internal-friction study of the interstitial–substitutional effect on the deformation behaviour of Nb–O,Nb–Ta–O and Nb–Mo–O single crystals

To investigate the interstitial-substitutional interaction in dislocations, the effect of 0 on the temperature, frequency and amplitude dependence of the internal friction Q ^?1 in Nb–O, Nb-20 mol% Ta–O and Nb-20 mol% Mo–O single crystals has been studied (f = 1.55–8.2 Hz) in the temperature range from 298 to 1473 K. In our previous study, Nb–Mo and Nb–Ta single crystals were found to be strengthened by solute O. It was also suggested that the interstitial–substitutional interaction in dislocations contributes to the increase in their critical resolved shear stress (CRSS). In this study, Snoek-type relaxation peaks due to O are observed between 500 and 700 K in all the single crystals. The Snoek peak of Nb-20mol% Mo–O consisting of several peaks is analysed. The activation energy of the Snoek peak in Nb-20mol% Mo–O is higher than that of Nb–O. These results are attributable to the existence of the interstitial–substitutional complexes. The amplitude dependence of Q ^?1 at intermediate and high temperatures decreases as the O content increases. Moreover, the breakaway stress of Nb-20 mol% Mo–O still has a high value at 1200K and does not decrease much even at 1473 K. This suggests that the formation of Mo–O complexes reduces the dislocation mobility at high temperatures. From the results, the effect of the interstitial-substitutional interaction on the CRSS was discussed.     

Analysis of the common characteristics of the Hartmann,Ronchi, and Shack–Hartmann tests

An overview of the settings of the planes for the filters and observed patterns in the Hartmann and Ronchi tests is presented. Also a new set of filters for both test were developed. In a similar way, it is easy to extend this analysis to the Shack–Hartmann test, and to propose a new Null Shack–Hartmann filter.     

Correlation study of structural,electrical and mechanical properties of quenched tin–zinc–cadmium solder alloys

It is important, for electronic application, to decrease the melting point of SnZn₉ solder alloy because it is too high as compared with the most popular eutectic Pb–Sn solder alloy. Adding Cd causes structural changes such as phase transformations, dissolution of atoms and formation of Cd crystals in the quenched SnZn₉ alloy, and its physical properties are affected by this change. For example, the melting point is decreased towards the melting point of the Pb–Sn eutectic alloy, or even much less. The structure, electrical and mechanical properties of quenched Sn_{91? x} Zn₉Cd _x (x?=?0 or x?≥?5) alloys have been investigated. Adding Cd to a quenched SnZn₉ alloy increases its electrical resistivity and decreases its elastic modulus and internal friction. The Sn₇₁Zn₉Cd₂₀ alloy has the lowest melting point (162 °C) and electrical and internal frictions as compared with commercial Pb–Sn solder alloys.     

Electronic Structure of Immunoactive Molecules of 8–Azagona–12,17–Dione

Using the semiempirical method of partial neglect of differential overlap (PNDO), we have calculated the wave functions, energies, orbital configurations of electronic states, oscillator strengths of transitions, electronic density distributions, and dipole moments for the molecule of biologically active 8–azagona–12,17–dione, containing a conformationally rigid –acyl––aminovinylcarbonyl fragment. It has been established that as to their orbital nature the excited lower and higher singlet electronic states of this molecule are of the n^*– and ^* type respectively. The results of the theoretical analysis are in good qualitative agreement with the spectral data on absorption and luminescence. The calculations of the intermolecular interaction of the compound under consideration with a medium show that the molecular systems under consideration can possess a dynamic multicenter structure.     

Mutual transformations between the P–Q,Q–P,and generalized Weyl ordering of operators

Based on the generalized Weyl quantization scheme, which relies on the generalized Wigner operator Ok （p, q） with a real k parameter and can unify the P-Q, Q-P, and Weyl ordering of operators in k = 1, - 1,0, respectively, we find the mutual transformations between 6 （p - P） （q - Q）, （q - Q） 3 （p - P）, and （p, q）, which are, respectively, the integration kernels of the P-Q, Q-P, and generalized Weyl quantization schemes. The mutual transformations provide us with a new approach to deriving the Wigner function of quantum states. The - and - ordered forms of （p, q） are also derived, which helps us to put the operators into their - and - ordering, respectively.     

Stability,electronic structures,and mechanical properties of Fe–Mn–Al system from first-principles calculations

The stability, electronic structures, and mechanical properties of the Fe–Mn–Al system were determined by firstprinciples calculations. The formation enthalpy and cohesive energy of these Fe–Mn–Al alloys are negative and show that the alloys are thermodynamically stable. Fe_3Al, with the lowest formation enthalpy, is the most stable compound in the Fe–Mn–Al system. The partial density of states, total density of states, and electron density distribution maps of the Fe–Mn–Al alloys were analyzed. The bonding characteristics of these Fe–Mn–Al alloys are mainly combinations of covalent bonding and metallic bonds. The stress-strain method and Voigt–Reuss–Hill approximation were used to calculate the elastic constants and moduli, respectively. Fe_(2.5)Mn_(0.5)Al has the highest bulk modulus, 234.5 GPa. Fe_(1.5)Mn_(1.5)Al has the highest shear modulus and Young's modulus, with values of 98.8 GPa and 259.2 GPa, respectively. These Fe–Mn–Al alloys display disparate anisotropies due to the calculated different shape of the three-dimensional curved surface of the Young's modulus and anisotropic index. Moreover, the anisotropic sound velocities and Debye temperatures of these Fe–Mn–Al alloys were explored.     

Ricci flow,Courant algebroids,and renormalization of Poisson–Lie T-duality

We use a generalized Ricci tensor, defined for generalized metrics in Courant algebroids, to show that Poisson–Lie T-duality is compatible with the 1-loop renormalization group flow.     

Hume-Rothery electron concentration rule across a whole solid solution range in a series of gamma-brasses in Cu–Zn,Cu–Cd,Cu–Al,Cu–Ga,Ni–Zn and Co–Zn alloy systems

The aim of the present work is to examine if the Hume-Rothery stabilisation mechanism holds across whole solid solution ranges in a series of gamma-brasses with especial attention to the role of vacancies introduced into the large unit cell. The concentration dependence of the number of atoms in the unit cell, N, for gamma-brasses in the Cu–Zn, Cu–Cd, Cu–Al, Cu–Ga, Ni–Zn and Co–Zn alloy systems was determined by measuring the density and lattice constants at room temperature. The number of itinerant electrons in the unit cell, e/uc, is evaluated by taking a product of N and the number of itinerant electrons per atom, e/a, for the transition metal element deduced earlier from the full-potential linearised augmented plane wave (FLAPW)-Fourier analysis. The results are discussed within the rigid-band model using as a host the density of states (DOS) derived earlier from the FLAPW band calculations for the stoichiometric gamma-brasses Cu₅Zn₈, Cu₉Al₄ and TM₂Zn₁₁ (TM = Co and Ni). A solid solution range of gamma-brasses in Cu–Zn, Cu–Cd, Cu–Al, Cu–Ga and Ni–Zn alloy systems is found to fall inside the existing pseudogap at the Fermi level. This is taken as confirmation of the validity of the Hume-Rothery stability mechanism for a whole solute concentration range of these gamma-brasses. An exception to this behaviour was found in the Co–Zn gamma-brasses, where orbital hybridisation effects are claimed to play a crucial role in stabilisation.     

The Study of Aggregation Processes in Colloidal Solutions of Magnetite–Silica Nanoparticles by NMR Relaxometry,AFM, and UV–Vis-Spectroscopy

Colloidal solutions of magnetic nanoparticles were studied as a promising magnetic resonance imaging (MRI) contrast agent. The problem of aggregative stability of solutions is considered. Sol-gel synthesis of magnetite colloidal solutions stabilized by silica is described. Transmittance spectra were measured to analyze sedimentation of nanoparticles in magnetite–silica solutions of different compositions and concentrations. It is shown that the synthesized nanoparticles can be used as MRI contrast agents. The surface morphology and particle size of Fe₃O₄/SiO₂ layers were estimated by atomic force mictroscopy (AFM) technique. The mechanism of magnetic-field-induced aggregation of Fe₃O₄/SiO₂ nanoparticles into chain-like and fractal structures is described.     

Surface tension and density of liquid Bi–Pb,Bi–Sn and Bi–Pb–Sn eutectic alloys

Surface tension and density measurement of liquid Bi₅₆Pb₄₄, Bi₄₃Sn₅₇ and Bi₄₆Pb₂₉Sn₂₅ eutectic alloys was carried out by using the large drop method over the temperature range of 380–750 K. The regular solution model has been used in conjunction with Butler's equation to calculate the surface tension of binary and ternary alloys of the Bi–Pb–Sn system, while the surface tension of ternary alloys has also been predicted by using geometric models. The new experimental results were compared with the calculated values of the surface tension as well as with the data available in the literature.