Potential constants and mean amplitudes of vibrations of N-methyl acetamide

A normal co-ordinate treatment based on general quadratic forcefield has been applied to N-methyl acetamide molecule. In these calculations, the structure parameters of N-methyl acetamide, as given recently by Katzet al., and the Raman and infra-red data obtained by the authors are used and the potential constants have been obtained. The potential energy distribution among the various symmetry co-ordinates of each normal vibration and the mean amplitudes of vibrations have been calculated.     

Vibrational spectra and normal vibrations of acetanilide and N-deuterated acetanilide

The Raman and infra-red spectra of acetanilide and N-methylacetamide and of their N-deuterated compounds have been recorded. The vibrational frequencies of acetanilide have been assigned and the nature of the Amide I, II and III bands in acetanilide and N-methylacetamide has been investigated by the study of the changes in the frequencies of these bands in the spectra of their deuterated compounds. Acetanilide and deuterated acetanilide molecules have been subjected to normal co-ordinate treatment and the mixing up of the skeletal frequencies arising out of the in-plane vibrations has been determined. These results indicate that as in secondary amides, the amide II and amide III bands in acetanilide are due to the combined contribution ofδ (NH) andν (C-N) vibrations, but the contribution ofν (C-N) to the amide II band is less in acetanilide and deuterated acetanilide than in cases of N-methylacetamide and deuterated N-methylacetamide.     

Raman and infrared spectra and normal vibrations of N-methylpropionamide and N-deuterated N-methyl propionamide

Raman and infrared spectra of N-methyl-propionamide and N-deuterated N-methyl-propionamide were recorded in various states of aggregation—pure amide, in solution and vapour state—and the frequency changes of the functional groups were studied. The implane skeletal vibrations of N-methyl-propionamide and its deuterated compound were calculated treating these molecules as six-body problems. The distribution of potential energy of each normal mode among various symmetry co-ordinates was calculated and the nature of the amide I, II and III bands and the mixing up of the inplane vibrational frequencies of N-methyl-propionamide and the deuterated amide are discussed on a quantitative basis.     

Vibrational spectra,force constants and mean amplitudes of vibrations of urea and deuterated urea

The vibrational spectra of urea and deuterated urea have been recorded. Using a most general potential function, the force constants and the mean amplitudes of vibration have been calculated.     

Infrared and Raman spectra and normal vibrations of N,N-dimethylthioformamide and N,N-dimethylthioacetamide

The Raman and infrared spectra of N, N-dimethylthioformamide and N, N-dimethylthioacetamide were recorded and the vibrational frequencies are assigned. The normal co-ordinate treatment of these molecules has been carried out and the potential energy distributions calculated in order to clarify the nature of normal vibrations and investigate the magnitude of mixing up of various skeletal frequencies. The results in regard to the nature of the C-N and C=S stretching frequencies in these thioamides are compared with those of primary and secondary thioamides on the one hand and those of the corresponding ordinary tertiary amides on the other. It has been shown that the force constants of the general quadratic force field type are transferable in the series of molecules of tertiary amides and tertiary thioamides. The lowest frequency in the region of 150 cm.^?1 to 160 cm.^?1 has been recorded by the authors in the Raman spectra of the two tertiary thioamides under consideration. In the normal vibrational analysis of related molecules, the earlier workers only calculated this frequency, but did not record it.     

In-plane normal vibrations of 1,2,5-oxa-, thia- and selena-diazoles, 1,3,4-oxa- and thia-diazoles and 1,2,3,4-thiatriazoles

In-plane vibration modes of 1,2,5- and 1,3,4-oxa- and thia-diazoles, and 1,2,5-selenadiazole have been assigned on the basis of detailed normal coordinate analysis employing data on several deuterated species. In-plane vibration frequencies of two 1,2,3,4-thiatriazole derivatives have been calculated and compared with observed values.     

Angular asymptotics of the spectra of operators,close to normal ones

For two classes of non-self-adjoint operators, close to normal ones, one establishes a formula for the asymptotic behavior of the eigenvalues situated in a fixed angle of the complex plane. One considers elliptic pseudodifferential operators, acting in the sections of a vector bundle over a manifold without boundary, the operators of elliptic boundary-value problems for pseudodifferential operators. The closeness of the operator to a normal one is defined by the smallness of the commutator of the operator and of its adjoint.Translated from Problemy Matematicheskogo Analiza, No. 10, pp. 180–195, 1986.     

Molecular vibrations of HCOF and DCOF

The harmonic wave numbers for HCOF and DCOF have been calculated using the observed fundamentals and the force constants have been evaluated on the basis of the general quadratic and Urey-Bradley force fields. The out-of-plane fundamental in HCOF, which has not been reported so far, is calculated. The thermodynamic properties of HCOF and DCOF have been calculated for fourteen temperatures ranging from 200° K. to 1500° K. for the ideal gaseous state at one atmosphere pressure and for a rigid rotor, harmonic oscillator approximation.     

Non-linear vibrations of beams and membranes

Summary Non-linear vibrations of beams and membranes are considered using a modified perturbation method based on the Linstedt-Poincare technique, which avoids the secular terms.

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Zusammenfassung Mittels einer abgeänderten Störungsmethode, welche auf der Linstedt-Poincaré-Technik basiert und die säkularen Glieder vermeidet, werden nichtlineare Schwingungen von Trägern und Membranen untersucht.

     

Vibrational stabilization and the Brockett problem

The present paper deals with the exposition of methods for solving the Brockett problem on the stabilization of linear control systems by a nonstationary feedback. The paper consists of two parts. We consider continuous linear control systems in the first part and discrete systems in the second part. In the first part, we consider two approaches to the solution of the Brockett problem. The first approach permits one to obtain low-frequency stabilization, and the second part deals with high-frequency stabilization. Both approaches permit one to derive necessary and sufficient stabilization conditions for two-dimensional (and three-dimensional, for the first approach) linear systems with scalar inputs and outputs. In the second part, we consider an analog of the Brockett problem for discrete linear control systems. Sufficient conditions for low-frequency stabilization of linear discrete systems are obtained with the use of a piecewise constant periodic feedback with sufficiently large period. We obtain necessary and sufficient conditions for the stabilization of two-dimensional discrete systems. In the second part, we also consider the control problem for the spectrum (the pole assignment problem) of the monodromy matrix for discrete systems with a periodic feedback.     

Mathematical Modeling of Vibrational Combustion

Doklady Mathematics - A new model of laminar vibrational combustion is constructed relying on a thermodynamic analysis of the combustion process. Two combustion modes, detonation and deflagration,...     

Vibrational creep of polymeric materials

An experimental study of the effect of vibration on the creep process has been carried out in the case of the rigid porous polyurethane PPU-3, as a function of the magnitude of the vibrational loading and the level of basic static stresses. It has been shown that with increase in the velocity amplitude of the dynamic stresses, the creep process is accelerated, without being accompanied thereupon by vibrational heating of the material. The possibility has been established of approximating vibrational creep curves by the integral equation of Volterra, using a discrete series of relaxation times transformed by the vibro-time analogy method.For Communication No. 3, see [1].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 223–232, March–April, 1970.     

Browder spectra and essential spectra of operator matrices

Let Mc = （ A0CB ） be a 2 × 2 upper triangular operator matrix acting on the Banach space X × Y. We prove that
σr（A） ∪ σr（ B）= σr （Mc） ∪ W ,
where W is the union of certain of the holes in σr（Mc） which happen to be subsets of σr（A） ∩ σr（B）, and σr（A）, σr（B）, σr（Mc） can be equal to the Browder or essential spectra of A, B, Mc, respectively. We also show that the above result isn＇t true for the Kato spectrum, left （right） essential spectrum and left （right） spectrum.