Bounded imaginary powers of differential operators on manifolds with conical singularities

 We study the minimal and maximal closed extension of a differential operator A on a manifold B with conical singularities, when A acts as an unbounded operator on weighted L _p -spaces over B, 1<p<∞. Under suitable ellipticity assumptions we can define a family of complex powers A ^z , zℂ. We also obtain sufficient information on the resolvent of A to show the boundedness of the purely imaginary powers. Examples concern unique solvability and maximal regularity for the solution of the Cauchy problem for the Laplacian on conical manifolds as well as certain quasilinear diffusion equations. Received: 12 June 2001; in final form: 3 June 2002 / Published online: 1 April 2003 Mathematics Subject Classification (2000): 35J70, 47A10, 35K57     

Reaction of aroyl- and hetaroyltrifluoroacetones with acylhydrazines: Regioselectivity and tautomerism of the condensation products

Acylhydrazines react with 1,3-diketones of the general formula CF₃COCH₂COR (where R is an aryl or hetaryl group) at both carbonyl groups. The reaction at the trifluoroacetyl group is favored by donor substituents in the aromatic ring of the 1,3-diketone or by the 2-furyl and, especially, 2-thienyl group as a hetaryl substituent, as well as by elevated temperature. The condensation products at the carbonyl group contiguous to the aryl or hetaryl ring have the structure of 5-hydroxy-4,5-dihydropyrazoles and do not undergo tautomeric transformations in solution. The condensation products at the trifluoroacetyl group have either 5-hydroxy-4,5-dihydropyrazole or hydrazone structure and give rise to ring-chain tautomeric equilibrium in solution. Electron-withdrawing substituents in the aromatic ring of the 1,3-dicarbonyl fragment and CDCl₃ as solvent favor formation of the cyclic tautomer. The state of the tautomeric equilibrium is weakly sensitive to structural variations in the hydrazine component.     

Ultraviolet photoemission spectroscopy of hydrogen complex deactivation on InP:Zn(1 0 0) surfaces

Ultraviolet photoemission spectroscopy is used to study the kinetics of the H-Zn complex deactivation in Zn doped InP(1 0 0). Hydrogen injected into the material electronically passivates the local carrier concentration. Reverse-biased anneals of the InP under ultra-high vacuum show a dramatic change in the work function of the material with increasing temperature. Spectral features are also shown to be sensitive to sample temperature. To our knowledge, we show the first view of hydrogen retrapping at the surface using photoemission spectroscopy. A simple photoelectron threshold energy analysis shows the state of charge compensation of the material.     

Spectroscopic studies of biologically active organotin(IV) derivatives of 2-[N-(2,4,6-tribromophenylamido]propanoic acid

Herein we describe the synthesis and characterization of compounds having the formulae R₂SnL₂ and R₃SnL, where R = Me, n-Bu, Ph and n-Oct and L = 2-[N-(2,4,6-tribromophenylamido]propanoic acid. All the complexes have been characterized by various spectroscopic methods (IR and ¹H, ¹³C, ¹¹⁹Sn NMR), elemental analysis, mass spectrometry and physical data. These compounds were also screened for their biological activity and found some encouraging results.     

Theoretical study of hydrolysis mechanism of khellin

This paper describes khellin hydrolysis mechanism using semiemperical PM3 implemented in Gaussian 03 package. The calculations show that in the presence of an acidic media, an enolate molecular ion leads directly to ω-acetokhellinone while in the basic media it leads to khellinone.     

Specific features of the formation of submicron inclusion in Ti:sapphire

Specific features of the formation of submicron (70–300 nm) inclusions in Ti:sapphire (Al₂O₃:Ti) grown in a carbon-containing medium have been investigated. These inclusions are caused by deviation from the melt stoichiometry and are formed during the melt-crystal phase transition. These defects are submicropores containing excess aluminum and its suboxides; they can be destroyed by thermal loading of a crystal.     

Numerical study of the influence of boundary conditions on the dynamic behavior of a cylindrical shell conveying a fluid

We consider a finite element algorithm intended to study the dynamic behavior of an elastic cylindrical shell filled with an immovable or flowing fluid. To describe the fluid, we use the perturbed velocity potential whose equations with the corresponding boundary conditions are solved by the Bubnov-Galerkin method. To describe the shell, we use the variation principle, which includes the linearized Bernoulli equation for calculating the hydrodynamic pressure acting on the shell on the side of the fluid. Solving the problem is reduced to calculating and analyzing the eigenvalues of the coupled system of equations obtained as a result of combining the equations for the perturbed velocity potential and the shell displacements. We consider several test problems in which, along with the comparison of the computational results with the earlier published experimental, analytic, and numerical data, we also study the dynamic behavior of the “shell-fluid” system for various boundary conditions for the perturbed velocity potential.     

Feedback stabilization of snap-through buckling in a preloaded two-bar linkage with hysteresis

We study a linearly damped preloaded two-bar linkage that exhibits hysteresis due to the presence of multiple attracting equilibria. The dynamics at the unstable equilibrium, through which a snap-through buckle occurs, are not linearizable due to a solution-dependent singularity. We stabilize the unstable equilibrium using two distinct non-linear controllers. The feedback-linearization controller requires knowledge of the linkage parameters, whereas the robust version of the intrinsic non-linear proportional-derivative controller requires only an upper bound on the stiffness.     

Identification of nonstationary axisymmetric load distributed along a cylindrical shell

The paper outlines a procedure to identify the space-and time-dependent external nonstationary load acting on a closed circular cylindrical shell of medium thickness. Time-dependent deflections at several points of the shell are used as input data to solve the inverse problem. Examples of numerical identification of various nonstationary loads, including moving ones are presented. The relationship between the external load and the stress-strain state of the shell is described by the Volterra equation of the first kind. The identification problem is solved using Tikhonov's regularization method and Apartsin's h-regularization method __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 7, pp. 91–100, July 2008.