Gem-dinitro compounds in organic synthesis. 4. Use of the condensation product of glyoxal and dinitromethane in the synthesis of nitro-1,2,3-triazoles

The condensation of dinitromethane with glyoxal has been investigated and it has been demonstrated that 1,1,4,4-tetranitro-2,3-butandiol, -hydroxy-,-dinitropropionic acid or their mixture may be formed. Interaction of 1,1,4,4-tetranitro-2,3-butandiol or 1,4-dibromo-1,1,4,4-tetranitro-2,3-butanediol diacetates with sodium azide leads to bis(5-nitro-1,2,3-triazol-4-yl) via intermediate 1,1,4,4-tetranitro-1,3-butadiene.For communication 3, see [1].N. D. Zelinskii Institute of Organic Chemistry, Russian Academy of Sciences, 117913 Moscow. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 9, pp. 2123–2131, September, 1992.     

Decay rates of energy of the 1D damped original nonlinear wave equation

We consider the decay rate of energy of the 1D damped original nonlinear wave equation. We first construct a new energy function. Then, employing the perturbed energy method and the generalized Young’s inequality, we prove that, with a general growth assumption on the nonlinear damping force near the origin, the decay rate of energy is governed by a dissipative ordinary differential equation. This allows us to recover the classical exponential, polynomial, or logarithmic decay rate for the linear, polynomial or exponentially degenerating damping force near the origin, respectively. Unlike the linear wave equation, the exponential decay rate constant depends on the initial data, due to the nonlinearity.     

Limit cycles of a class of Liénard systems derived from state-dependent impulses

Discontinuous phenomena, in which objects may behave continuously and sometimes discretely are not only found in nature and under laboratory conditions but also in simple, familiar contexts. For example, this phenomenon is skillfully incorporated into the internal structure of mechanical wristwatches. Unless an extremely small amount of state-dependent impulse is applied intermittently, the reciprocating rotational movement of the balance and hairspring, which is the heart of the mechanical wristwatch, cannot be maintained. The small amount of state-dependent impulse, which is often overlooked, can make a significant difference; however, very few studies have examined this subject. This study assumes the underlying cause of discontinuous behaviors as impulses generated when an object reaches a particular state, assuming that the continuous behavior follows the Liénard system, which is widely studied in the field of electrical circuits. The main theorem provides the conditions under which the effect of the impulses causes a stable limit cycle in the Liénard system, even if no limit cycle exists when there are no impulses. The Poincaré–Bendixson theorem for discontinuous dynamical systems and phase plane analysis are used to prove the main theorem. Several examples and their simulations are provided to illustrate the main theorem.     

Stochastic phase lockings in a relaxation oscillator forced by a periodic input with additive noise: A first-passage-time approach

Noise effects on phase lockings in a system consisting of a piecewise-linear van der Pol relaxation oscillator driven by a periodic input are studied. The problem of finding the period of the oscillator is reduced to the first-passage-time problem of the Ornstein-Uhlenbeck process with time-varying boundary. The probability density functions of the first-passage time are used to define the operator which governs a transition of an input phase density after one cycle of the oscillator. Phase lockings in a stochastic sense are investigated on the basis of the density evolution by the operator.     

Preparation and characterization of a viscosity index improver for naphthenic and paraffinic base oils

Copolymers of -methyl styrene and 2-ethylhexyl acrylate were prepared in a benzene solution. The presence of the copolymers were confirmed by solubility, IR and NMR tests. The molecular weight and the polydispersity of the polymers were estimated by GPC. The copolymers obtained were blended with paraffinic and naphthenic base oils. The viscosity, the viscosity index (VI) the Q value as well as the stability to shear and oxidation were obtained for these blends. The results are compared with the results obtained with an oil blend containing a commonly used high temperature additive. Two of the copolymers obtained have shown to be good alternatives for specific applications.Presented at the Symposium, 76^th CSC Congress, Sherbrooke, Quebec, May 30–June 3, 1993, honoring Professor Donald Patterson on the occasion of his 65^th birthday.     

Stable σ-adducts of 4,6-dinitrotetrazolo[1,5-a]pyridine with alkoxide anions

The reaction of 2-chloro-3,5-dinitropyridine with two equivalents of KN₃ in the presence of ROH results in stable Meisenheimer-type -adducts of 4,6-dinitrotetra-zolo[1,5-a]pyridine with RO^– anions (R = H, Alk, Ph). The mechanism of -complex formation was suggested. The structure of the -adduct with R = Me was established by IR and NMR spectroscopy and by X-ray diffraction analysis.For the preliminary communication, see Ref. 1.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1278–1283, July, 1994.This work was supported by the Russian Foundation for Basic Research (project code 93-03-5329).