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991.
Chemical kinetics of benzonitrile nitration with mixed acid is investigated in the temperature range 283–299 K. Pseudo-first-order rate constants are evaluated by means of rate experiments on homogeneous reacting mixtures having large stoichiometric excesses of nitric acid. The second-order kinetic constants for nitronium ion attack to the aromatic substrate are derived on the basis of the assessed nitration mechanism. An activation energy of 604 ± 37 kJ mol?1 is calculated for this reaction step. © 1993 John Wiley & Sons, Inc. 相似文献
992.
The nonlinear Schrödinger-type equations invariant with respect to the extended Galilean group are described. We study the conditional symmetry of such equations, realize the reduction procedure, and construct the classes of exact solutions.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 4, pp. 539–551, April, 1993. 相似文献
993.
V. G. Osmolovski 《Journal of Mathematical Sciences》1997,84(1):898-910
An existence theorem for the variational problem for the two-phase medium energy functional is proved. Dependence of the solution
on the surface tension coefficient and on the temperature is investigated. Bibliography: 7 titles.
Dedicated to V. A. Solonnikov on his sixtieth anniversary
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 213, 1994, pp. 131–150.
Translated by S. Yu. Pilyugin. 相似文献
994.
An iterative method from the class of completely implicit methods (CIM) is proposed for solving the equation of the velocity
potential of elliptical-hyperbolic type. The advantage of the proposed method compared to other CIM schemes is demonstrated
in application to mixed perfect gas flows in a nozzle of a given shape. Accuracy issues, rate of convergence, and various
techniques of ensuring stability in the hyperbolic region are discussed.
Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996, pp. 39–51. 相似文献
995.
996.
A self-avoiding polygon (SAP) on a graph is an elementary cycle. Counting SAPs on the hypercubic lattice ℤ
d
withd≥2, is a well-known unsolved problem, which is studied both for its combinatorial and probabilistic interest and its connections
with statistical mechanics. Of course, polygons on ℤ
d
are defined up to a translation, and the relevant statistic is their perimeter.
A SAP on ℤ
d
is said to beconvex if its perimeter is “minimal”, that is, is exactly twice the sum of the side lengths of the smallest hyper-rectangle containing
it. In 1984, Delest and Viennot enumerated convex SAPs on the square lattice [6], but no result was available in a higher
dimension.
We present an elementar approach to enumerate convex SAPs in any dimension. We first obtain a new proof of Delest and Viennot's
result, which explains combinatorially the form of the generating function. We then compute the generating function for convex
SAPs on the cubic lattice. In a dimension larger than 3, the details of the calculations become very cumbersome. However,
our method suggests that the generating function for convex SAPs on ℤ
d
is always a quotient ofdifferentiably finite power series. 相似文献
997.
998.
D. V. Peregoudov 《Theoretical and Mathematical Physics》1997,113(1):1331-1341
The effective potential method, used in quantum field theory to study spontaneous symmetry violation, is discussed from the
point of view of Bogoliubov’s quasi-averaging procedure. It is shown that the effective potential method is a disguised type
of this procedure. The catastrophe theory approach to the study of phase transitions is discussed and the existence of the
potentials used in that approach is proved from the statistical point of view. It is shown that in the case of broken symmetry,
the nonconvex effective potential is not a Legendre transform of the generating functional for connected Green’s functions.
Instead, it is a part of the potential used in catastrophe theory. The relationship between the effective potential and the
Legendre transform of the generating functional for connected Green’s functions is given by Maxwell’s rule. A rigorous rule
for evaluating quasi-averaged quantities within the framework of the effective potential method is established.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 113, No. 1, pp. 149–161, October, 1997. 相似文献
999.
Fe(II)--Fe(III) hydroxy-chloride, -sulphate and -carbonate were prepared by oxidation of a ferrous hydroxide precipitate in anion-containing aqueous solutions. The compounds are characterized by monitoring the redox potential Eh and the pH of stochiometric suspension vs time with the appropriate concentration ratios. X-ray diffraction allows us to characterize the crystal structure by distinguishing “green rust one” (GR1) from “green rust two” (GR2). Since green rusts (GRs) are of a pyroaurite-sjögrenite-like structure, i.e., consisting of intercalated foreign anions and water molecules in the interlayers between the brucite-like layers of Fe(OH)2, their chemical formulae can be determined from the Mössbauer spectra. Three quadrupole doublets are observed: D1 and D2 correspond to a ferrous state with isomershift IS of about 1.27 mm s-1 and quadrupole splittings QS of about 2.85 and 2.60 mm s-1, respectively, whereas D3 corresponds to a ferric state with IS and QS of about 0.4 mm s-1. The hyperfine parameters of these doublets are similar from one green rust to another but their intensity ratios vary considerably. Finally, Eh and pH equilibrium diagrams of the Fe species in the presence of chloride, sulphate and carbonate anions contained within the water solution are drawn and the thermodynamic conditions of existence and degrees of oxidation of green rusts are discussed. 相似文献
1000.