Explicit Traveling Wave Solutions and Their Dynamical Behaviors for the Coupled Higgs Field Equation

In this paper, we focus on the traveling wave solutions of the coupled Higgs field equation from the perspective of dynamical systems. Through the phase portraits, in addition to periodic wave solutions and solitary wave solutions, we also obtain explicit periodic singular wave solutions, singular wave solutions and kink wave solutions, which were not found in the previous works. The dynamical behavior of these solutions and their internal relations are revealed through asymptotic analysis. The results will help supplement the study of field equation.     

Preparation and characterization of theβ-cyclodextrin inclusion complex with sulfafurazole

The 1 : 1 inclusion complex involving sulfafurazole (SF) and-cyclodextrin (-CD) is prepared by the freeze-drying method and characterized on the basis of its chemical analysis, thermal behavior, infrared spectrum, X-ray powder pattern and¹³C NMR spectrum in DMSO-d₆ solution. The stability constant of the inclusion complex was determined by the solubility method. The effect of cyclodextrin on the UV absorption spectrum of sulfafurazole was also observed.     

Salt effects and the mechanism of electrophilic mercuration of unsaturated compounds

The reaction of Hg(OAc)₂ with bornylene in THF-H₂O and CH₃CN-H₂O mixed solvents (75 25, v/v) was studied. The effects of the addition of NaOAc on the reaction rate and the composition of products were investigated. In the CH₃CN-H₂O mixture, the addition of NaOAc decreases the amount of the rearranged product, fundamentally changes the ratio between the regioisomeric solvoadducts, and promotes the formation of products of Hg(OAc)₂ addition. The reaction proceedsvia an ion pair and free mercurinium ion; the cation of the ion pair and the free mercurinium ion have dissimilar structures.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 544–548, March, 1995.     

A public-key cryptosystem utilizing cyclotomic fields

While it is well-known that the RSA public-key cryptosystem can be broken if its modulusN can be factored, it is not known whether there are other ways of breaking RSA. This paper presents a public-key scheme which necessarily requires knowledge of the factorization of its modulus in order to be broken. Rabin introduced the first system whose security is equivalent to the difficulty of factoring the modulus. His scheme is based on squaring (cubing) for encryption and extracting square (cube) roots for decryption. This introduces a 14 (19) ambiguity in the decryption. Various schemes which overcome this problem have been introduced for both the quadratic and cubic case. We generalize the ideas of Williams' cubic system to larger prime exponents. The cases of higher prime order introduce a number of problems not encountered in the quadratic and cubic cases, namely the existence of fundamental units in the underlying cyclotomic field, the evaluation of higher power residue symbols, and the increased difficulty of Euclidean division in the field.     

Non-abelian electrodynamics and the vacuumB (3)

By using an 0(3) gauge group, a non-Abelian theory of vacuum electrodynamics is developed in which the newly discovered longitudinal vacuum fieldsB ⁽³⁾ andi E ⁽³⁾ appear self-consistently with the usual plane wavesB ⁽¹⁾,B ⁽²⁾,E ⁽¹⁾, andE ⁽²⁾ in the circular basis (1), (2), (3), a complex representation of space. Using the charge quantization condition the vacuum Maxwell equations are given in the non-Abelian representation.     

Lyotropic effect in surface charge,electrokinetics, and coagulation of a rutile dispersion

Potentiometric, electrokinetic, and coagulation experiments with a rutile dispersion in the pH region above the point of zero charge exhibit an inverse lyotropic sequence for counterions: Li⁺>K⁺>Cs⁺. The potentiometric and electrokinetic data were interpreted by a surface complexation model assuming the Stern-Gouy-Chapman structure of the interfacial layer, which yielded the values of inner layer capacitances,C, and the intrinsic equilibrium constants,K _ass ⁰ , characterizing the specificity of each counterion. These parameters were used to explain the order of lyotropic sequences in the adsorption, coagulation, and electrokinetic phenomena.     

Ein Beitrag über Ba3Pt4HgO11: Das erste Erdkalimetall-Oxoplatinat(II,V)/Oxomercurat

A Contribution on Ba₃Pt₄HgO₁₁: The First Alkaline-Earth Oxoplatinate(II,V)/Oxomercurate Single crystals of Ba₃Pt₄HgO₁₁ were prepared by oxygen high pressure technique (4 200–3 600 bar) and investigated by X-ray methods. It crystallizes with hexagonal symmetry, space group D? P6 2c, a = 6.021, c = 17.374 Å, Z = 2. Ba₃Pt₄HgO₁₁ represents a new structure type, showing structural relationships to Ba₂Hg₃Pd₇O₁₄ and to the precious metal 6L-perovskites. The Hg²⁺ ions show dumb-bell like coordination, Pt²⁺ a square-planar surrounding and Pt⁵⁺ face shared double octahedra.     

CdHgO2: Ein Oxomercurat mit Verwandtschaft zur Crednerit-Struktur

CdHgO₂: An Oxomercurate related to the Crednerite Structure Single crystals of CdHgO₂ were prepared by oxygen high pressure technique (600°C, 3900 bar) and investigated by X-ray technique. It crystallizes with monoclinic symmetry, space group C–C2/m; a = 5.933, b = 3.452, c = 5.875 Å, β = 91.26°; Z = 2. The Hg²⁺ ions show dumb-bell like coordination, Cd²⁺ an octahedral one. CdHgO₂ shows strong relationship to the Crednerite structure. The orientation of the O? Hg? O dump-bells to the CdO₆ octahedra layers is discussed with respect to related oxomercurates.     

Kinetics and mechanisms of halide ion catalysis of CO substitution reactions in Os3(CO)12 and Ru3(CO)12 metal carbonyl clusters

The results of kinetic studies on ligand substitution in [M₃(CO)₁₁X]^– complexes (M = Ru, Os; X = Cl, Br, I) are summarized. The [Os₃(CO)₁₁X]^– complexes react with PPh₃ under mild conditions to initially yield monosubstituted products [Os₃(CO)₁₀(PPh₃)X]^–. The rate of CO substitution obeys a first-order equation with respect to the concentration of the complex and does not depend on the ligand concentration. The rates of the reactions decrease in the order Cl > Br > I withH values increasing from 15 to 18 kcal mol^–1 and S values varying from –19 to –13 cal mol^–1 K^–1. The enhanced reactivities of these complexes as well as the low activation energies and negative activation entropies are discussed in terms of the effects of -X bridge formation on the transition state of the reaction. Reactions of PPN[Ru₃(CO)_11–x (Cl)] (PPN is the bis(triphenylphosphine)iminium cation;x=0, 1) and PPN[Ru₃(CO)₉(₃-I)] with alkynes are also reported. The reactivities of alkynes follow the order BuCCH PhCCH EtCCEt PhCCPh. The higher rates of the reactions of monosubstituted acetylenes compared with those of their disubstituted analogs are explained by agostic interaction between the metal atom and the C-H bond in the reaction transition state and by steric effects. The results obtained attest that the reaction with alkynes occursvia intermediates containing halide bridges and that ₃-halide complexes are more reactive than ₂-halide complexes.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1540–1545, September, 1994.This work was supported by a Presidential Grant from Northwestern University. One of the authors (F. Basolo) wishes to thank Academician M. E. Vol'pin for the invitation to participate in the Workshop The Modern Problems of Organometallic Chemistry (INEOS-94) and Academician O. M. Nefedov for the invitation to publish a review in theRussian Chemical Bulletin.