Azimuthal wave motions on the surface of a rotating fluid cylinder

Wave motions in a fluid cylinder rotating about the axis are investigated within the framework of the linear theory. The cylinder is assumed to be fairly long. This makes it possible to restrict attention to the study of the plane oscillation pattern. The fluid is assumed to be ideal and incompressible. The models in which the fluid particles are confined by gravitational (body) or/and capillary forces (surface stress forces) are considered. A mode analysis is carried out and the dispersion relations are constructed. Traveling and steady-state waves on the surface of the fluid cylinder are investigated; qualitative effects ("wave inertia") are established. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 128–133, May–June, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00221). An erratum to this article is available at .     

Determination of Natural Frequencies of Internal Waves in an Essentially Inhomogeneous Fluid

The two-dimensional problem of the natural wave motions of a heavy inhomogeneous fluid confined between two absolutely rigid plane-parallel boundary surfaces is investigated. It is assumed that the fluid is stably and continuously stratified in the vertical. The motions are considered in the class of waves moving in the horizontal direction. An efficient numerical-analytic method of solving and analyzing the corresponding Sturm-Liouville problem for a coordinate function depending on the depth is proposed. A technique for constructing high-accuracy two-sided estimates of the natural frequencies of the traveling waves is developed. A recurrent accelerated-convergence scheme for the refinement of the eigenvalues (natural frequencies) and eigenfunctions (forms) of the wave motion of the fluid is proposed and tested. Two examples of stratification are calculated and the dispersion curves and the oscillation shapes are constructed.     

Dual Functioning Thieno‐Pyrrole Fused BODIPY Dyes for NIR Optical Imaging and Photodynamic Therapy: Singlet Oxygen Generation without Heavy Halogen Atom Assistance

We discovered a rare phenomenon wherein a thieno‐pyrrole fused BODIPY dye (SBDPiR690) generates singlet oxygen without heavy halogen atom substituents. SBDPiR690 generates both singlet oxygen and fluorescence. To our knowledge, this is the first example of such a finding. To establish a structure–photophysical property relationship, we prepared SBDPiR analogs with electron‐withdrawing groups at the para‐position of the phenyl groups. The electron‐withdrawing groups increased the HOMO–LUMO energy gap and singlet oxygen generation. Among the analogs, SBDPiR688, a CF₃ analog, had an excellent dual functionality of brightness (82290 m ^?1 cm^?1) and phototoxic power (99170 m ^?1 cm^?1) comparable to those of Pc 4, due to a high extinction coefficient (211 000 m ^?1 cm^?1) and balanced decay (Φ_flu=0.39 and Φ_Δ=0.47). The dual functionality of the lead compound SBDPiR690 was successfully applied to preclinical optical imaging and for PDT to effectively control a subcutaneous tumor.     

Standard enthalpies of formation of 4-methylbiphenyl and 4,4′-dimethylbiphenyl

The energies of combustion of 4-methylbiphenyl and 4,4′-dimethylbiphenyl in the crystal state were measured in a precision calorimeter equipped with a self-sealing bomb at 298.15 K. The enthalpies of vaporization of these substances were measured in an isothermal heat-conducting Calvet microcalorimeter. Standard enthalpies of formation were calculated for 4-methylbiphenyl and 4,4′-dimethylbiphenyl in the crystal, liquid, and gas states.     

Thermodynamic properties of nitro derivatives of diphenyl ether and biphenyl

The heat capacity of 4,4′-dinitrodiphenyl ether and 4-nitro-4′-biphenylcarboxylic acid were measured by adiabatic calorimetry (AC) in temperature ranges of 8–372 K and 10–372 K, respectively. The heat capacity of 4,4′-dinitrodiphenyl ether in the temperature range 323–500 K, the thermodynamic properties of fusion, and the purity of the ether were measured by differential scanning calorimetry (DSC). The main thermodynamic functions in the temperature range 5–370 K were calculated for both compounds using the heat capacities of adiabatic calorimetry. Related thermodynamic functions of 4,4′-dinitrodiphenyl ether in the temperature range 370–500 K were calculated on the basis of DSC data.     

Electrophile affinity and positional selectivity in electrophilic substitution reactions of N-substituted pyrroles

In terms of the density functional theory (DFT) using B3LYP/6-31G(d) method with full geometry optimization, gas-phase quantum chemical calculations were performed for ??-complexes formed upon the attack of electrophiles E (E = H⁺, Me⁺, Me³Si⁺, Br⁺, NO₂ ⁺, MeCO⁺, SO₃) on ??- and ??-positions of furan, thiophene, selenophene, pyrrole, and N-substituted pyrroles (NR-pyrroles, R = Me, Bu^t, SiMe₃, SiPrⁱ ₃, C₆H₄NO₂-p, SO₂Ph, CHO, COOMe) and for respective ??- and ??-substituted electrophilic substitution products. The energy differences between the ??- and ??-isomers of the ??-complexes characterize the preferred direction of the electrophilic attack, while the energy differences between the isomeric products make it possible to estimate the energy preference of a particular product. An analysis of the results obtained demonstrates the effect of the structure of heterocycle, the nature of electrophile, and thermodynamic and steric factors on the positional selectivity (??/?? ratio) in electrophilic substitution reactions of ??-electron rich five-membered heteroaromatics.     

Heterometallic Cu/Co and Cu/Co/Zn complexes bearing rare asymmetric tetranuclear cores: synthesis, structures, and magnetic and catalytic properties toward the peroxidative oxidation of cycloalkanes

The three novel heterometallic complexes [CuCo(III)Co(II)(2)(MeDea)(3)Cl(3)(CH(3)OH)(0.55)(H(2)O)(0.45)](H(2)O)(0.45) (1), [CuCo(III)Zn(2)(MeDea)(3)Cl(3)(CH(3)OH)(0.74)(H(2)O)(0.26)](H(2)O)(0.26) (2), and [CuCo(III)Zn(2)(MeDea)(3)Cl(3)(DMF)] (3) have been prepared using a one-pot reaction of copper powder with cobalt chloride (1) and zinc nitrate (2, 3) in a methanol (1, 2) or dimethylformamide (3) solution of N-methyldiethanolamine. A search of the Cambridge Structural Database shows that the tetranuclear asymmetric cores M(4)(μ(3)-X)(μ-X)(5) of 1-3 represent an extremely rare case of M(4)X(6) arrays. The magnetic investigations of 1 disclose antiferromagnetic coupling in a Co(II)-Cu(II)-Co(II) exchange fragment with J(Co-Cu)/hc = -4.76 cm(-1), J(Co-Co)/hc = -2.76 cm(-1), and D(Co)/hc = +34.3 cm(-1). Compounds 1-3 act as precursors for the mild peroxidative oxidation of cyclohexane to cyclohexanol and cyclohexanone with overall yields up to 23%. The synthetic and structural features as well as the thermogravimetric behavior and electrospray ionization mass spectrometry data are discussed.     

Method for detection of ground objects and recognition of their types from radar images of the earth surface

A method for detection of ground objects and recognition of their types against the background of the earth surface from objects’ radar images (RIs) is proposed. The method is based on a priori formation of template RIs of the objects in free space and scanning the RI of the earth surface with two types of rectangular windows. The dimensions of the window of the first type take into account the shadows of the objects, and the dimensions of the windows of the second type take into account only the outer dimensions of the objects. The results of the simulation of the detection characteristics and of the parameters of recognition of a KAMAZ truck and the control station mounted on the same chassis, which were located on a standard earth surface, are presented.     

A Zn4O-containing doubly interpenetrated porous metal-organic framework for photocatalytic decomposition of methyl orange

A doubly interpenetrated semiconducting MOF Zn(4)O(2,6-NDC)(3)(DMF)(1.5)(H(2)O)(0.5)·4DMF·7.5H(2)O (UTSA-38) of a cubic net has been constructed, which exhibits photocatalytic activity for the degradation of methyl orange in aqueous solution.     

Minimizing Uniformly Convex Functions by Cubic Regularization of Newton Method

Journal of Optimization Theory and Applications - In this paper, we study the iteration complexity of cubic regularization of Newton method for solving composite minimization problems with...