Uniqueness of solutions of mixed problems and a Cauchy problem for parabolic equations of high order with unbounded coefficients

New uniqueness classes of generalized solutions (generalized Tacklind classes) of initial-boundary-value problems are found for linear and quasilinear divergent parabolic equations of high order with coefficients increasing at infinity.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 2, pp. 149–155, February, 1992.     

On the features of reactivity of 8-[(1E)-2-phenylethenyl]-substituted thebaine and codeinone derivatives

An improved method for the synthesis of 8-[(1E)-2-phenylethenyl]codeinone dimethyl ketal was described. The ability of [(1E)-2-phenylethenyl] substituent to stabilize effectively the π-system of the ring C is responsible for the essential difference in both the reactivity and the compositions of products formed in the reactions of the corresponding substituted and unsubstituted codeinone and thebaine derivatives.     

Initial propagation of support in thin-film flow

We study the behaviour for small time of interfaces connected with supports of strong solutions of one-dimensional thin-film equation with compactly supported initial functions. In some sense, sharp upper estimates of interfaces are obtained for initial functions with arbitrary asymptotic behaviour near the boundary of their supports.     

Molecular structure study of 1,2,3-trimethyldiaziridine by means of gas electron diffraction method

The molecular structure of 1,2,3-trimethyldiaziridine has been determined from the gas-phase electron diffraction data supplemented spectral and quantum chemical calculations. The configuration of studied compound incorporates trans-position of methyl groups attached to nitrogen atoms of diaziridine cycle. The following principal structural parameters were determined (r_h1 bond lengths in Å, bond angles in degrees with 3σ in parentheses): r(N–C), 1.489(9); r(N–N), 1.480(15); r(C–C), 1.503(15); ∠NCN, 61.5(9); ∠(H₃C)CN, 124.0(15). The obtained structural parameters of 1,2,3-trimethyldiaziridine were compared with those for structural analogues. The gaseous standard enthalpy of formation of 1,2,3-trimethyldiaziridine was estimated to be 176.2?±?5.0 kJ/mol.

     

Spectrally encoded miniature endoscopy

A method for performing miniature endoscopy with a high number of resolvable points is presented. This approach, spectrally encoded endoscopy (SEE), uses a broad-bandwidth light source and a diffraction grating to simultaneously detected the reflectivity at multiple points along a transverse line within the sample. As opposed to images from miniature optical fiber bundle endoscopes, the number of resolvable points in SEE images is dependent on the spectral width and the groove density of the diffraction grating. We acquired images of a human finger in vivo, using a 550-mu;m -diameter SEE system to demonstrate the feasibility of this technique.     

Effect of Time Delay of Support Propagation in Equations of Thin Films

We prove the existence of the effect of time delay of propagation of the support of strong solutions of the Cauchy problem for an equation of thin films and establish exact conditions on the behavior of an initial function near the free boundary that guarantee the appearance of this effect.     

Anisotropy of the faraday rotation in orthoferrites

Faraday rotation in plates of orthoferrites, cut normally to the optical axis, depends strongly on the polarization of the incident light in the vicinity of the absorption bands, where linear dichroism is large     

Microwave radiation in the electrical explosion of conductors

Moscow. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 1, pp. 3–5, January–February, 1995