Orthogonality in Classes

 Let denote the von Neumann–Schatten class, its norm and let be an elementary operator defined by . We shall characterize those operators which are orthogonal to the range of in the sense that for all . The main results of this paper are: If and (i) if A, C, respectively B, D are commuting normal operators with , or (ii) if A, B are contractions and , then is orthogonal to the range of if and only of S is in the kernel of . Furthermore, in both cases, the algebraic direct sum satisfies . (Received 9 February 2000; in revised form 21 February, 2001)     

Preparation by different methods and analytical characterization of gadolinium-doped ceria

The present work reports the influence of chemical synthesis on structural, morphological and optical properties of gadolinium-doped ceria (GDC) with analytical characterization of synthesized specimens. GDC powders with Gd content of 10, 15 and 20 mol% were synthesized by aqueous sol–gel and sol–gel combustion methods using glycerol as complexing agent and fuel. The phase purity and structural features of obtained powders were evaluated using X-ray diffraction analysis and Raman spectroscopy. These studies confirmed that crystallization of GDC occurs into cubic fluorite-type crystal structure. Morphological features as well as optical properties of GDC powders were determined to be strongly dependent on the synthesis method. To confirm chemical composition of prepared samples, spectrophotometric approach for the determination of Ce and Gd in GDC samples was suggested. Relative standard deviation values for Ce and Gd were in the range of 1.5–4.1 and 2.0–5.6%, respectively. The obtained results demonstrated that the suggested analytical procedure can be successfully used for the analysis of GDC specimens with high accuracy.     

Similarity solutions of the equations of a boundary layer in a nonuniform external flow

Similarity solutions of the equations of a laminar incompressible boundary layer, formed in a rotational external flow, are investigated. Such problems arise in the analysis of the flow in a boundary layer when there is an abrupt change in the boundary conditions (for example, in the case of a discrete inflation of the boundary layer, in hypersonic flow about blunt bodies, etc.). Various approaches to their solution have been proposed earlier in [1–4]. Solved below is the so-called inverse problem of boundary layer theory (see [3], p. 200), where the contour of the body that causes a given flow outside the boundary layer is unknown beforehand and is found during the course of solution of the problem in connection with the coupling of the longitudinal and transverse velocity components. The cases of a parabolic (u_e ~ y²) and a linear (u_e=a(x)+b(x)y) variation in the velocity of the external flow with distance along the transverse direction are considered in detail. The latter includes an investigation of the flow in the neighborhood of the critical point of a blunt body, taking account of the vorticity of the flow in the shock layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 78–83, March–April, 1971.     

Determination of the parameters of the boundary layer on rotating axisymmetric cones

A method is proposed for solving the three-dimensional equations of laminar and turbulent boundary layers on a pointed rotating axisym-metric cone flying at an angle of attack . New properties of the obtained solutions are found, and a comparison is made with the results of other authors.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 34–39, May–June, 1984.     

Nonlinear effects in the dynamics of concentrated polymer solutions and melts

The dependence of the environmental characteristics on the induced anisotropy is found by means of self-consistency for large velocity gradients. It is shown that this method of taking the anisotropy into account is consistent with the model previously employed [11–13] and leads to results similar to those obtained in [14, 15]. Steady shear flow and steady uniaxial stretching are considered on the basis of the equations of state obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 88–96, July–August, 1990.     

Approximate relationships for the determination of the pressure on the surface of a sphere or cylinder with an arbitrary mach number in the free stream

Numerical calculations have been made [1–4] of the pressure distribution over the surface of a sphere or cylinder during transverse flow in the range 0 /2, where is the angle reckoned from the stagnation point along the meridional plane, and on the basis of these results simple analytical equations have been proposed in order to determine the pressure for arbitrary Mach numbers M in the free stream. The gas is assumed to be ideal and perfect.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 185–188, March–April, 1985.     

Carbamidocyclophanes F and G with anti-Mycobacterium tuberculosis activity from the cultured freshwater cyanobacterium Nostoc sp.

Two new (1 and 2) and three known (3–5) carbamidocyclophanes were isolated from a cultured freshwater cyanobacterium Nostoc sp. (UIC 10274) obtained from a sample collected at Des Plaines, Illinois. Their planar structures and stereoconfigurations were determined by extensive spectroscopic analysis including 1D/2D NMR experiments, HRESIMS as well as CD spectroscopy. Carbamidocyclophane F (1) showed potent anti-Mycobacterium tuberculosis activity in the microplate Alamar blue assay and low-oxygen-recovery assay with MIC values of 0.8 and 5.4 μM, respectively. Carbamidocyclophane F (1) also displayed antimicrobial activities against the gram positive bacteria Staphylococcus aureus and Enterococcus faecalis with MIC values of 0.1 and 0.2 μM, respectively. Carbamidocyclophane F (1) and Carbamidocyclophane G (2) both showed antiproliferative activity against MDA-MB-435 and HT-29 human cancer cell lines with IC₅₀ values in the range from 0.5 to 0.7 μM.     

Behavior of serine proteases thrombin,trypsin, and chymotrypsin under conditions of MALDI-TOF-Mass spectrometry

Features of ion formation under the influence of laser emission under the conditions of MALDI-TOF mass spectrometry in the glycosylated protein thrombin and the related proteases trypsin and chymotrypsin were studied for the first time. It was shown that trypsin and chymotrypsin are ionized in the form of molecular ions with masses 23800 and 25660 Da respectively. The molecular ion of thrombin was not detected; three main fragment ions with masses 9951, 10230, and 11982 Da were detected in the mass spectrum of thrombin. It was suggested that these fragments relate to peptide and glycopeptides fragment ions formed as a result of bond cleavage in the region of Asn60G during exposure to laser emission under the conditions of MALDI-TOF mass spectrometry. __________ Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 44, No. 2, pp. 74–78, March–April, 2008.