THE RELATIONSHIP BETWEEN PROJECTIVE GEOMETRIC AND RATIONAL QUADRATIC B-SPLINE CURVES

For two rational quadratic B-spline curves with same control vertexes, the cross ratio of four eollinear points are represented; which are any one of the vertexes, and the two points that the ray initialing from the vertex intersects with the corresponding segments of the twocurves, and the point the ray intersecting with the connecting line between the two neighboring vertexes. Different from rational quadratic Beeier curves, the value is generally related with the loeation of the ray, and the necessary and sufficient condition o5 the ratio being independent of the ray‘s loeation is showed. Alsn another cross ratio o5 the following four collinear points are suggested, i.e. one vertex, the points that the ray from the initlal vertex intersects respectivdy with the curve segmentt the line connecting the segments end points, and the line connecting the two neighboring vertexes. This cross ratio is concerned only whh the ray‘s location, butnot with the weights of the curve. Furthermore, the cross ratio is projective invariant under the projective transformation between the two segments.     

与q形变玻色算符逆算符相关的相干态及其量子统计性质

讨论了ｑ形变玻色算符的广义逆算符作用于ｑ－相干态所得到的两类量子态的数学及量子统计性质。结果表明，ｑ－相干态的光子激发态不存在压缩但呈现反聚束效应，而ｑ－相干态的光子湮灭态却存在压缩但不呈现反聚束效应。     

Low-temperature specific heat of crystalline and amorphous Eu2(MoO4)3

The specific heat C _total of crystalline and amorphous Eu₂(MoO₄)₃ is measured in the temperature interval 4.5–30 K. The amorphous state is obtained by applying pressure ∼7 GPa at room temperature. It is found that the specific heat of the crystal at T⩽7.5 K is described by a cubic function of temperature, while the specific heat of the amorphous sample has a strongly non-Debye character in the entire experimental temperature interval. The curve of C _total for amorphous europium molybdate is analyzed in a model of soft atomic potentials, and it is shown that it agrees well with universal low-temperature anomalies of the specific heat of classical glasses obtained by quenching from the liquid. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 8, 623–627 (25 October 1998)     

Microencapsulation of DNA Within alginate microspheres and crosslinked chitosan membranes for in vivo application

Calf thymus DNA was microencapsulated within crosslinked chitosan membranes, or immobilized within chitosan-coated alginate microspheres. Microcapsules were prepared by interfacial polymerization of chitosan, and alginate microspheres formed by emulsification/ internal gelation. Diameters ranged from 20 to 500 Μm, depending on the formulation conditions. Encapsulated DNA was quantifiedin situ by direct spectrophotometry (260 nm) and ethidium bromide fluorimetry, and compared to DNA measurements on the fractions following disruption and dissolution of the microspheres. Approximately 84% of the DNA was released upon core dissolution and membrane disruption, with 12% membrane bound. The yield of encapsulation was 96%. Leakage of DNA from intact microspheres/capsules was not observed. DNA microcapsules and microspheres were recovered intact from rat feces following gavage and gastrointestinal transit. Higher recoveries (60%) and reduced shrinkage during transit were obtained with the alginate microspheres. DNA was recovered and purified from the microcapsules and microspheres by chromatography and differential precipitation with ethanol. This is the first report of microcapsules or microspheres containing biologically active material (DNA) being passed through the gastrointestinal tract, with the potential for substantial recovery.     

Nonlinear-optical and micro-Raman diagnostics of thin films and nanostructures of ABO3 ferroelectrics

Ferroelectric composite two-dimensional ferroelectric/aluminum oxide nanostructures were studied. A porous aluminum oxide matrix was used as a template into which a ferroelectric precursor was introduced, followed by annealing. The prepared nanostructures were studied using optical second harmonic generation and micro-Raman scattering.     

On the quantization of solid body rotation

A general method for solving the problem of quantization of a top is proposed that allows for finding the Hamiltonian eigenfunctions in the form of polynomials of various degree n in the Cartesian coordinates with the use of the Lamé functions. All three coordinates x, y, and z are equivalently involved in computations, as well as their relations with ellipsoidal coordinates, which makes the computations symmetric.     

On parabolic equations with a small parameter

A singularly perturbed parabolic equation with a nonlinear right-hand side of a special form is examined. A numerical analytical study of such equations is performed.     

100-TW femtosecond laser based on parametric amplification

In experiments on the parametrical amplification of femtosecond pulses in wide-aperture DKDP crystals, a power of more than 100 TW has been reached, which is much higher than the record level achieved in such lasers. The energy efficiency obtained for the parametric amplifier is equal to 27%. The energy of a 72-fs pulse is equal to 10 J.