Periodic solutions of second-order differential inclusions systems with p-Laplacian

Some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with p-Laplacian.     

On the environmental decoherence and spin interference in mesoscopic loop structures

Mechanisms of ‘environmental decoherence’ such as surface scattering, Elliot–Yafet process and precession mechanisms, as well as their influence on the spin phase relaxation are considered and compared. It is shown that the ‘spin ballistic’ regime is possible, when the phase relaxation length for the spin part of the wave function (L^(s)) is much greater than the phase relaxation length for the ‘orbital part’ (L^(e)). In the presence of an additional magnetic field, the spin part of the electron's wave function (WF) acquires a phase shift due to additional spin precession about that field. If the structure length L is chosen to be L^(s)>L>L^(e), it is possible to ‘wash out’ the quantum interference related to the phase coherence of the ‘orbital part’ of the WF, retaining at the same time that related to the phase coherence of the spin part and, hence, to reveal corresponding conductance oscillations.     

Nonlinear and chaotic oscillations of a constrained cantilevered pipe conveying fluid: A full nonlinear analysis

In this paper, the planar dynamics of a nonlinearly constrained pipe conveying fluid is examined numerically, by considering the full nonlinear equation of motions and a refined trilinear-spring model for the impact constraints—completing the circle of several studies on the subject. The effect of varying system parameters is investigated for the two-degree-of-freedom (N=2) model of the system, followed by less extensive similar investigations forN=3 and 4. Phase portraits, bifurcation diagrams, power spectra and Lyapunov exponents are presented for a selected set of system parameters, showing some rather interesting, and sometimes unexpected, results. The numerical results are compared with experimental ones obtained previously. It is found that in the parameter space that includesN, there exists a subspace wherein excellent qualitative, and reasonably good (N=2) to excellent (N=4) quantitative agreement with experiment. In the latter case, excellent agreement is not only obtained in the threshold flow velocities (u) for the key bifurcations, but the inclusion of the nonlinear terms improves agreement with experiment in terms of amplitudes of motion and by capturing features of behaviour not hitherto predicted by theory.     

On matrices with operator entries

In this paper we consider certain matrix equations in the field of Mikusiński operators, and construct a method for obtaining an approximate solution which allows working with numerical constants instead of operators. The theory of diagonally dominant matrices is applied for the analysis, existence and character of the obtained solutions. We introduce a method for determining approximate solutions of a discrete analogue for operational differential equations and give conditions for their existence. The error of the approximation is estimated.     

Transition metal complexes with Girard reagent-based ligands

The ligand, salicylaldehyde Girard-T hydrazonium chloride, [H₂SalGT]Cl (1), and two complexes [Cu(HSalGT)X₂]·H₂O (X = Br(2); Cl(3)) were synthesized and their crystal structures were determined by single-crystal X-ray analysis. In the two isostructural complexes, the Cu(II) is located in a square-pyramidal environment, with the chelating ligand and one halogen atom in the basal plane and the second halogen in the apical position. The most apparent structural difference between the 1 and its complexes 2 and 3 is the orientation of the N(CH₃)₃ group: in 1, it is practically coplanar to the rest of the molecule, while in 2 and 3 it is oriented to the side of the axially bonded halogen, which can be explained by the C–H…X intramolecular interactions. The compounds were characterized by elemental analysis, molar conductivity, magnetic susceptibility and electronic absorption spectra.     

Path integrals on half-line

In the framework of path integrals we present a solution to the Schrödinger equation for a free particle confined to the half-linex > 0. A solution in question corresponds to the boundary condition (/x) (0,t)= (0,t) where is a real constant.     

Synthesis of peptides based onβ-(N1-uracilyl)-α-alanine

The synthesis of peptides which include a DL--(N₁-uracilyl)--alanine (DL-willardiine) residue as an N-terminal or C-terminal group was investigated, dipeptides of DL-willardiine with glycine and L-tyrosine were obtained, and DL-willardiyl-DL-willardiine was synthesized; the latter is the simplest representative of the family of monotonic homopeptides which contain, as a repeating side substituent, a natural nucleic base capable of participation in intermolecular interactions of the complementary type.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, pp. 404–408, March, 1971.     

Hydrogenation and double bond isomerization of hexenes over EUROPT-1

Hexenes give large amounts of hexane and isomeric hexenes over EUROPT-1. A constant hydrocarbon coverage can be assumed in the steady-state period of the reaction; the direction of reactions of these surface species depends on the hydrogen excess and also on the structure of starting hydrocarbon.

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EUROPT-1 , . , . , .

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Based on the diploma work of Mr. M. Räth and Ms. B. Brose.     

Synthesis and properties of 1-(5-halo-1-uracilyl)-β-D-glucofuranuronic acids

1-(5-Halo-1-uracilyl)-2, 5-di-O-acetyl--D-glucofuranurono-6,3-lactones were obtained by condensation of 2,4-bis(trimethylsilyl)-5-halouracils with 1,2,5-tri-O-acetyl--D-glucofuranurono;-6, 3-lactone. The chemical transformations of these compounds were studied. The structure of the glucuronides was proved by the IR, UV, circular dichroism, and NMR spectra.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 11, pp. 1532–1537, November, 1981.