Positons of the modified Korteweg de Vries equation

The concept of positons, i.e. certain multiparametric solutions of the Korteweg de Vries equation with new properties, is extended to the modified Korteweg de Vries equation. It is shown that the essential features of positons carry over to this case; the collision of positons, the solitary-wave-positon interaction and simple generalizations are discussed in detail. Suggestions for future research and possible applications of the present work are sketched.     

The Ansatz Method for Analyzing Schrödinger’s Equation with Three Anharmonic Potentials in D Dimensions

In this letter, by applying a suitable ansatz to the wave functions, the solutions of the D-dimensional radial Schrödinger equation with some anharmonic potentials are obtained.     

Dynamical algebras for Pöschl-Teller Hamiltonian hierarchies

The dynamical algebras of the trigonometric and hyperbolic symmetric Pöschl-Teller Hamiltonian hierarchies are obtained. A kind of discrete-differential realizations of these algebras are found which are isomorphic to so(3, 2) Lie algebras. In order to get them, first the relation between ladder and factor operators is investigated. In particular, the action of the ladder operators on normalized eigenfunctions is found explicitly. Then, the whole dynamical algebras are generated in a straightforward way.     

Development of sound measurement systems for auditory functional magnetic resonance imaging

Auditory functional magnetic resonance imaging (fMRI) requires quantification of sound stimuli in the magnetic environment and adequate isolation of background noise. We report the development of two novel sound measurement systems that accurately measure the sound intensity inside the ear, which can simultaneously provide the similar or greater amount of scanner- noise protection than ear-muffs. First, we placed a 2.6 x 2.6-mm microphone in an insert phone that was connected to a headphone [microphone-integrated, foam-tipped insert-phone with a headphone (MIHP)]. This attenuated scanner noise by 37.8+/-4.6 dB, a level better than the reference amount obtained using earmuffs. The nonmetallic optical microphone was integrated with a headphone [optical microphone in a headphone (OMHP)] and it effectively detected the change of sound intensity caused by variable compression on the cushions of the headphone. Wearing the OMHP reduced the noise by 28.5+/-5.9 dB and did not affect echoplanar magnetic resonance images. We also performed an auditory fMRI study using the MIHP system and presented increase in the auditory cortical activation following 10-dB increment in the intensity of sound stimulation. These two newly developed sound measurement systems successfully achieved the accurate quantification of sound stimuli with maintaining the similar level of noise protection of wearing earmuffs in the auditory fMRI experiment.     

Redox properties of hydrogenated quinoline derivatives — inhibitors in oxidation processes of hydrocarbons

Half-wave potentials of the one-electron electrochemical oxidation (E _1/2 ^ox) of hydroquinolines with different degrees of heterocycle hydrogenization as well as containing substituents of various natures in the benzene ring and heterocycle have been measured. Linear correlations betweenE _1/2 ^ox and the values of the Hammett polar -constants form- andp-substituents in dihydroquinolines and related sulfur-containing dithiolthiones were established. The character of the variation ofE _1/2 ^ox in the series of hydroquinolines was found to correlate with the characteristic features of the inhibiting action of these compounds in the liquid-phase oxidation of various hydrocarbons. However, in contrast to phenolic antioxidants for hydroquinolines, there is no dependence of the retardation period onE _1/2 ^oxin the oxidation of hydrocarbons at temperatures higher than 100 °C.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 610–613, April, 1994.     

A comparative quantum-chemical analysis of electronic structures and spectroscopic parameters of cycloalkanes and cyclopolysilanes

A comparative quantum-chemical analysis of the electronic structures and spectroscopic parameters of the cycloalkanes C₃H₆, C₄H₈, C₅H₁₀, and C₆H₁₂ and their silicon analogs Si₃H₆, Si₄H₈, Si₅H₁₀ and Si₆H₁₂ was performed in the framework of the SCF MO LCAO method in the INDO approximation. Qualitative interpretation of “abnormal” ionization potentials and energies of electronic absorption spectra of cyclopolysilanes has been given. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1105–1108, June, 1997.     

Anab initio investigation of Cu2Se and Cu4Se2

Summary Experimentally known copper selenium clusters show extraordinary geometrical features, especially short Cu-Cu distances. We report the first theoretical investigation of Cu₂Se and Cu₄Se₂. Various quantum chemical methods (SCF, MP2, CPF, CCSD, CCSD(T), LDF) are applied to determine the importance of dynamic electron correlation. We find that inclusion of correlation does not essentially change the electronic structure of the clusters but has a strong influence on geometries. To reduce the computational effort we apply effective core potentials (ECPs) in combination with small, but carefully optimized basis sets. The applicability of simple modellings of correlation energies for approximate inclusion of correlation effects in SCF geometry optimizations is tested.     

pH,Definition and measurement at high temperatures

In this review paper, the NBS scale and its limitations are briefly discussed. The magnitude of liquid junction potentials and some calculated values are presented. The use of a molality scale for hydrogen electrode concentration cells at high temperatures is described, and results from measurements on ionization equilibria are summarized. Use of this scale is also recommended for certain circumstances with cells without liquid junction. As an alternative activity scale, use of the Pitzer ion-interaction treatment for ions is recommended for special cases. Finally, reference data are presented for _±HCl in HCl(aq) to 350°C and (HCl+NaCl)(aq) to 200°C that were derived by use of the Pitzer ion-interaction treatment.Presented at the Second International Symposium on Chemistry in High Temperature Water, Provo, UT, August 1991.     

Calculation of Vertical Ionization Potentials of Oxygen Difluoride,Difluoramine, and Difluoromethane by Local Density Approximation

The vertical ionization potentials of OF₂, HNF₂, and CH₂F₂ were computed by the deMon density functional program. The results are compared with earlier calculations and with experiment. The average absolute deviation of the 21 computed ionization potentials of the outer valence electrons from experiment is 0.44 eV, which compares well with 0.37 eV for frozen-orbital configuration-interaction calculations. Although this performance is not as good as perturbation corrections to Koopmans' theorem, the computation requirements are much less demanding.