On G 2 Continuous Spline Interpolation of Curves in ℝ d

In this paper the problem of G ² continuous interpolation of curves in ^d by polynomial splines of degree n is studied. The interpolation of the data points and two tangent directions at the boundary is considered. The case n = r + 2 = d, where r is the number of interior points interpolated by each segment of the spline curve, is studied in detail. It is shown that the problem is uniquely solvable asymptotically, e., when the data points are sampled regularly and sufficiently dense, and lie on a regular, convex parametric curve in ^d . In this case the optimal approximation order is also determined.     

Surface integral and Gauss-Ostrogradskij theorem from the viewpoint of applications

Making use of a surface integral defined without use of the partition of unity, trace theorems and the Gauss-Ostrogradskij theorem are proved in the case of three-dimensional domains with a Lipschitz-continuous boundary for functions belonging to the Sobolev spaces H ^1,p () (1 p < ). The paper is a generalization of the previous author's paper which is devoted to the line integral.     

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Exciton system heating in ZnSe single crystals under laser excitation

The way to determine the effective temperature of the excitonic system from the study of the edge luminescence high energy region is motivated. Experimental data on the exciton heating in ZnSe single crystals under laser excitation are presented. The effective temperature of excitons T_x has reached 158 K at the lattice temperature T_L = 77 and the peak excitation intensity 2.7 MW cm^?2 (hv₀ = 3.50), while the excess temperature of the excitons (T_x ? T_L) increases as a square root of the pump intensity. Exciton-hot-electron, exciton-hot-photon, exciton-exciton interactions and excitonic Auger process are considered as possible causes of the exciton system heating.     

17O NQR study of the ferroelectric phase transition in PbHPO4

The temperature dependence of the ¹⁷O NQR spectra of the O-H---O bonded oxygens in PbHPO₄ have been studied using a proton-¹⁷O double resonance technique. The results show that the protons move between two off-centre sites above T_c and freeze into one of the possible equilibrium sites below T_c.     

Membrane switch hypothesis. 1. Cell density influences lateral domain structure of tumor cell membranes

The domain structure of human cancer cells membranes was investigated by electron paramagnetic resonance (EPR) in different phases of cell growth, and the results were compared to those obtained for nonmalignant cells. On the basis of computer simulation of the EPR spectra using a newly developed GHOST condensation routine it was suggested that plasma membranes of cancer cells have less lateral lipid domain types at confluent conditions than in the exponential growing phase, while in nonmalignant cells the domain structure does not change significantly during cell growth. In accordance to our experimental data we propose a membrane switch hypothesis: disappearance of certain membrane domain types might act as a switch promoting the clustering of membrane constituents into the active units in a common lipid membrane domain and thus influencing the physiology of cells.     

Mappings of Ruled Surfaces in Simply Isotropic Space <Emphasis Type="Italic">I</Emphasis><Subscript>3</Subscript><Superscript>1</Superscript> that Preserve the Generators

In this paper we study some mappings of skew ruled surfaces in simply isotropic space which preserve the generators. We study isometries, conformal mappings and mappings which preserve the area. Furthermore, we study mappings of surfaces in I ₃ ¹ which preserve the asymptotic lines.Received December 18, 2001; in revised form July 12, 2002 Published online April 4, 2003