On the mechanism of intermode vibration-to-vibration energy transfer in CH3F excited by a tea CO2 laser

The v₃ mode of CH₃F was excited by irradiation with a TEA CO₂ laser pulse, and the time-resolved emission spectra of the v₃ overtone and the 3 μ;m region were observed. The results indicate that the population of the v₄ level behaves kinetically in the same manner as that of 2v₃ or 3v₃. This suggests an efficient energy transfer between these levels.     

Conformally invariant powers of the Dirac operator in Clifford analysis

The paper deals with conformally invariant higher‐order operators acting on spinor‐valued functions, such that their symbols are given by powers of the Dirac operator. A general classification result proves that these are unique, up to a constant multiple. A general construction for such an invariant operators on manifolds with a given conformal spin structure was described in (Conformally Invariant Powers of the Ambient Dirac Operator. ArXiv math.DG/0112033, preprint), generalizing the case of powers of the Laplace operator from (J. London Math. Soc. 1992; 46 :557–565). Although there is no hope to obtain explicit formulae for higher powers of the Laplace or Dirac operator on a general manifold, it is possible to write down an explicit formula on Einstein manifolds in case of the Laplace operator (see Laplacian Operators and Curvature on Conformally Einstein Manifolds. ArXiv: math/0506037, 2006). Here we shall treat the spinor case on the sphere. We shall compute the explicit form of such operators on the sphere, and we shall show that they coincide with operators studied in (J. Four. Anal. Appl. 2002; 8 (6):535–563). The methods used are coming from representation theory combined with traditional Clifford analysis techniques. Copyright © 2010 John Wiley & Sons, Ltd.     

Ricci-corrected derivatives and invariant differential operators

We introduce the notion of Ricci-corrected differentiation in parabolic geometry, which is a modification of covariant differentiation with better transformation properties. This enables us to simplify the explicit formulae for standard invariant operators given in [A. ?ap, J. Slovák, V. Sou?ek, Invariant operators on manifolds with almost hermitian symmetric structures, III. Standard operators, Differential Geom. Appl. 12 (2000) 51-84], and at the same time extend these formulae from the context of AHS structures (which include conformal and projective structures) to the more general class of all parabolic structures (including CR structures).     

The Generalized Dolbeault Complex in Two Clifford Variables

The Penrose transform is used to construct a complex starting with the Dirac operator in two Clifford variables. The corresponding relative BGG complex and its direct image is computed for cohomology with values in line bundles induced by representations in singular infinitesimal character. The limit of the induced spectral sequence is computed in cases connected with the Dirac operator in two Clifford variables. The work presented here is a part of the research project MSM 0021620839 and was supported also by the grants GAUK 447/2004 and GA ČR 201/05/2117.     

Graphs of finite mass which cannot be approximated in area by smooth graphs

In this note we shall show that there are obstructions of homotopic and not just of homological nature to the approximability in area of graphs of finite mass by graphs of smooth maps. We shall present a class of closed graphs with finite mass which cannot be approximated weakly and in area by smooth graphs. This work has been partially supported by the Ministero dell'Universitá e della Ricerca Scientifica, by C.N.R. contract n. 91.01343.CT01, and by the European Research Project GADGET     

Remarks on the lower semicontinuity of quasiconvex integrals

We prove lower semicontinuity of quasiconvex integrals with integrands controlled by the minors.This work has been partially supported by the Ministero dell'Università e della Ricerca Scientifica and by the European Research Project GADGET II     

Characterization of acoustic streaming and heating using synchronized infrared thermography and particle image velocimetry

Real-time measurements of acoustic streaming velocities and surface temperature fields using synchronized particle image velocimetry and infrared thermography are reported. Measurements were conducted using a 20 kHz Langevin type acoustic horn mounted vertically in a model sonochemical reactor of either degassed water or a glycerin-water mixture. These dissipative phenomena are found to be sensitive to small variations in the medium viscosity, and a correlation between the heat flux and vorticity was determined for unsteady convective heat transfer.     

Area and the area formula

Conferenza tenuta da Mariano Giaquinta il 28 settembre 1992     

Synthesis and characterization of cyclotetraphosphato complexes of Rh(I), Ir(I), Ru(II), and Pd(II)

The cyclotetraphosphate ion (P(4)O(12)(4)(-)) as a PPN (PPN = (PPh(3))(2)N(+)) salt reacts with [MCl(cod)](2) (M = Rh, Ir; cod = 1,5-cyclooctadiene) to give the dinuclear complexes (PPN)(2)[[M(cod)](2)(P(4)O(12))], in which the two metal moieties are situated trans to each other with respect to the P(4)O(4) ring in the solid state. In solution, however, these complexes exist as mixtures of trans and cis isomers. On the other hand, the P(4)O(12)(4)(-) ion reacts with 4 equiv of [Rh(cod)(MeCN)(x)](+) cation to give the tetranuclear complex [[Rh(cod)](4)(P(4)O(12))], where the four Rh(cod) fragments are bound to the P(4)O(12) platform alternately on both sides of the P(4)O(4) ring. Dinuclear P(4)O(12) complexes of ruthenium and palladium are also synthesized.     

On Primitives and Conjugate Harmonic Pairs in Hermitian Clifford Analysis

The notion of a conjugate harmonic pair in the context of Hermitian Clifford analysis is introduced as a pair of specific harmonic functions summing up to a Hermitian monogenic function in an open region $\Omega $ of $\mathbb C ^n$ . Hermitian monogenic functions are special monogenic functions, which are at the core of so-called Clifford analyis, a straightforward generalization to higher dimension of the holomorphic functions in the complex plane. Under certain geometric conditions on $\Omega $ the conjugate harmonic to a given specific harmonic is explicitly constructed and the potential or primitive of a Hermitian monogenic function is determined.