Universal Models For Real Submanifolds

In previous papers by the present author, a machinery for calculating automorphisms, constructing invariants, and classifying real submanifolds of a complex manifold was developed. The main step in this machinery is the construction of a “nice” model surface. The nice model surface can be treated as an analog of the osculating paraboloid in classical differential geometry. Model surfaces suggested earlier possess a complete list of the desired properties only if some upper estimate for the codimension of the submanifold is satisfied. If this estimate fails, then the surfaces lose the universality property (that is, the ability to touch any germ in an appropriate way), which restricts their applicability. In the present paper, we get rid of this restriction: for an arbitrary type (n,K) (where n is the dimension of the complex tangent plane, and K is the real codimension), we construct a nice model surface. In particular, we solve the problem of constructing a nondegenerate germ of a real analytic submanifold of a complex manifold of arbitrary given type (n,K) with the richest possible group of holomorphic automorphisms in the given class.     

Förster energy transfer from poly(arylene–ethynylene)s to an erbium–porphyrin complex

We study the infrared emission at 1.54 μm of an organolanthanide complex, Er(III)-tetraphenylporphyrin [Er(TPP)acac], both as a result of direct optical excitation and via energy transfer from host π-conjugate polymers of type poly(arylene–ethynylene) [PAE]. In the first case, the emission of the neat complex is characterized in inert transparent materials and a value of the quantum yield at 1.54 μm φ_IR=4×10⁻⁴ is measured. Then, fluorescence resonance transfer is investigated in blends of Er(TPP)acac with PAEs by monitoring the quenching of the polymer fluorescence along with the enhancement of both the visible emission of the ligand and the near-infrared band of Er³⁺. These different procedures allow a detailed analysis of the transfer efficiency within a specific implementation of the Förster model for polymeric donors. The experimental values of the critical radius R₀, ranging from 1.3 to 2.5 nm for the different blends, are in good agreement with theory for a wide interval of the physical and spectroscopic parameters. This suggests that other mechanisms for excitation transfer do not play a significant role in these materials.     

Experimental characterization of hexatic smectic phases through electro-optic studies and dielectric relaxation spectroscopy

The electro-optic and complex dielectric behaviour of an antiferroelectric liquid crystal 4-(1-methylheptyloxycarbonyl)phenyl 4'-(n-butanoyloxyprop-1-oxy)biphenyl-4-carboxylate, having chiral SmC_A* and hexatic smectic phases, have been investigated. Complex dielectric permittivities were measured as a function of frequency, d.c. bias field and temperature. Spontaneous polarization was measured by the current reversal technique; tilt angle was measured under a polarizing microscope using a low frequency electric field. The electro-optic properties and dielectric behaviour of the material are compared with results obtained by DSC and polarizing optical microscopy. Dielectric relaxation processes in SmC_A* and hexatic smectic phases were determined. The dielectric strength at the SmC_A* to hexatic smectic phase transition is discussed in terms of coupling between the long range bond orientational order and smectic C director. It seems from the results of spontaneous polarization and dielectric relaxation spectroscopy that the material might possess an additional phase between the SmC_A* and hexatic smectic I* phases.     

Estimate for the Best Approximation of Summable Functions of Several Variables with a Certain Symmetry of Fourier Coefficients

An upper bound for the best approximation of summable functions of several variables by trigonometric polynomials in the metric of L is determined in terms of Fourier coefficients. We consider functions representable by trigonometric series with certain symmetry of coefficients satisfying a multiple analog of the Sidon–Telyakovskii conditions.     

Study of the dissolution and growth of salt single crystals in inhomogeneous acoustic fields: I. A standing acoustic wave

The growth of the isolated (100) face of a KDP crystal at exposure of the phase boundary to the initial ultrasound field and a standing acoustic wave has been investigated. A significant growth response of this face, exposed to sound normally along the acoustic axis in the near zone of a piston-like half-wave vibrator with f = 20 kHz and tangentially in the pulsed two-frequency (f = 600 and 900 kHz) standing-wave mode, has been revealed. It is shown that the mechanisms of mass exchange enhancement in these acoustic modes are different. The results obtained show a fundamental possibility of controlling crystal growth and dissolution by varying the parameters of inhomogeneous acoustic field.     

Doping of KDP single crystals with cerium: Growth and optical properties

The features of doping of KDP crystals with cerium ions and organocerium complexes with alizarin complexon and arsenazo III have been investigated. It is established that “direct” doping by introducing cerium salts into the initial solution cannot be implemented. The effect of organometallic complexes of cerium on the crystal growth has been studied. Organocerium complexes predominantly enter the prismatic or pyramidal growth sectors. It is shown that the complex arsenazo III + Ce blocks the growth of the prismatic sector. Cerium-doped KDP crystals exhibit a photoluminescence band peaking at the wavelength λ_max= 350 nm.