A variational formalism of tetrad gravitation theory is developed in the Weyl-Cartan space with independent variations in the tetrad coefficients, metric tensor components, and affine connectivity coefficients that considers the Weyl condition imposed on the nonmetricity based on the method of undetermined Lagrange multipliers. The gravitational field equations are derived for the Lagrangian comprising all possible quadratic convolutions of curvature, torsion, and nonmetricity tensors in addition to the linear component. Differential identities are obtained for the general gravitational Lagrangian in the Weyl-Cartan space.

The variational procedure for the nonlinear Langrangians is investigated for a tetrad description of an affine metric space. The equations of the gravitation field with a source in the form of matter with a dilatational charge are derived for the general Langrangian quadratically dependent on the curvature, torsion, and nonmetricity tensors. It is established that differential variational identities hold true for these equations.

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The results of investigation of the spectra of 2-butanol in CCl 4 , pure 2-butanol, and a 2-butanol-water mixture in the region of the second overtone of the stretching O-H vibration are presented. The assignment of the bands of the overtones is performed. The role of various associates in the processes of stratification in the 2-butanol-water system is discussed.Introduction. Characteristic of a 2-butanol-water mixture (just as of an n-butanol-water one) is the presence of the dependence of the stratification curves on the strength of the hydrogen bond (H-bond) between the molecules of water and alcohol [1][2][3][4]. The question of the formation of critical points and stratification curves in the case of association between the molecules of water and alcohol through the H-bond (including the 2-butanol-water system and n-butanol-water one) has been considered fairly thoroughly theoretically in [3,4].It is well known that alcohols and water are highly associated liquids [5]. Taking into consideration that the study of the overtone region of the spectra of alcohols and their associates with other liquids gives fairly complete structural information, we have investigated the spectra in the region <1 µm.Experimental. The spectra were registered by an SF-16 spectrophotometer (LOMO, USSR) with cylindrical cuvettes of length 5 cm (pure 2-butanol and a 2-butanol-water mixture) and 10 cm (2-butanol in CCl 4 ) [6]. For the analysis, analytical-grade alcohols and bidistilled water were used.Discussion of Results. Having studied the concentration dependence of the spectra of the O-H stretching vibration of 2-butanol in CCl 4 (Fig. 1), we have assigned the 0.96-µm band to a monomer, the 0.91 µm one -to dimers, and the 1.02-µm band -to polymer forms. According to [5], when an H-bond is formed, the frequency of the stretching vibration is usually shifted towards lower values, and a band that accounts for coupled O-H vibrations appears.It is well known that in highly diluted solutions only the bands of nonassociated O-H groups are observed. Therefore, the assignment of the 0.96-µm band to a monomer is related to the fact that at a concentration of 0.1 M of 2-butanol in CCl 4 it is just this band which is the most intense one. The relative intensity of this band is considerably decreased on increase in the concentration. Moreover, its width is smaller than that of other bands observed. In pure 2-butanol (Fig. 2), the intensity of the 0.96-µm band is very low, which fits in with the concept of alcohols as highly associated liquids.In accordance with the results of investigations of the overtones of methanol and butanol, the band of free O-H groups is found at 10,440 cm -1 (0.960 µm) for methanol and at 10,320 cm -1 (0.968 µm) for tert-butanol [7]. Pauling [8] points to the band of free O-H vibrations in methanol at 10,440 cm -1 and emphasizes its small width. There is an empirical formula (which may not, of course, be reckoned as universal) for the vibrational term [9]: