When do Toeplitz and Hankel operators commute?

We completely classify all Toeplitz and Hankel operators which commute; namely, we prove that that a non-trivial Hankel operator and a non-trivial Toeplitz operator commute if and only if the Hankel operator has symbolz, where is the symbol of the Toeplitz operator, and is an affine function of the characteristic function of certain anti-symmetric sets of the unit circle.     

Permittivity,dielectric loss and dc conductivity of NaNO3 crystals grown by epitaxy

The temperature dependence of the d.c. conductivity, the dielectric loss and the permittivity of NaNO₃ single crystals prepared by epitaxial accretion of the (111) plane of NaNO₃ on the (001) plane of mica were investigated. The measurements were performed in a temperature range from 20–300C. Below the melting point a region of intrinsic conductivity (U _I=3·08 eV), caused by Na⁺ ions which are in interstitial sites, was observed. At lower temperature a region II (U _II= 0·87 eV), where the conductivity is due to the presence of divalent impurities, probably Ca^{+ +} followed (structurally sensitive region). Up to 250C polarization is observed, most probably due to ion and electron shifting only. Above that temperature the influence of the relaxed orientation of the NO ₃ ^– groups becomes evident. At 275C the NO ₃ ^s- groups behave in a completely disordered way as indicated by a sudden increase of the permittivity plotted against temperature.We should like to express our gratitude to RNDr. A. Kessler, DrSc, for his very valuable advice.     

Solar UVB and plant damage irradiances for different Argentinean regions

We calculated the integrated UVB and plant damage irradiances for Argentina, a country in the Southern Hemisphere spread over a large latitudinal range. The irradiances were calculated for clear sky days using the Madronich code for the average conditions of the months corresponding to the summer and winter solstices and the fall and spring equinoxes. Ozone, aerosol and ground albedo typical for each region and for each period of the year have been considered. A comparison was made of the behavior of these irradiances at the different locations. A more pronounced time dependence of the plant damage irradiance was obtained because of the fact that the corresponding spectrum is largely concentrated at a small wavelength of the UVB interval. We established a correlation between both irradiances, which can be approximated by a quadratic function. Because the plant damage irradiance is a quantity that is not directly measured by instruments, we showed the utility of the correlation by determining this biological effectiveness from the integrated UVB irradiance measured at the Astronomical Observatory of Rosario, Argentina, on clear sky days of the year 2001, as a characteristic example of the midlatitude near-sea level location of a highly productive agricultural region, which can be extended to other regions of the world. The plant damage results are relative ones (as is the case for the erythemal irradiance). So, they can be used to determine the maximum/minimum and asymmetry ratios, to study the influence of atmospheric variables and to make comparisons with other geographical locations.     

On the capriciousness of the FCCF Karplus curve

Numerous well-behaved Karplus curves correlating dihedral angle (phi) and NMR coupling constants (3JXY) exist for X-C-Z-Y fragments with X or Y = H, C, F, and P. Absent is the enigmatic F-C-C-F moiety. By calculating the four Ramsey contributions to 3JFF for F-CH2-CH2-F, a pleasing phi/3JFF curve with both positive and negative regions arises. Unlike the H-C-C-H curve, F-C-C-F is PSO vs FC dominated. The latter and the F lone electron pairs cause both the negative J values and the substituent-induced J-leveling effect.     

1,4,8,11-tetrakis(2-pyridylmethyl)-1,4,8,11-tetraazacyclotetradecane

The crystal structure of the ligand 1,4,8,11-tetrakis(2-pyridylmethyl)-1,4,8,11-tetraazacyclotetradecane (tpmc) has been determined. The compound crystallizes in triclinic space group P with a = 6.1927(3), b = 11.3771(3), c = 11.8229(3) Å = 84.368(2), = 98.77(1), = 78.533(2)° V = 810.84(5) ų; and Z = 1.     

Variational convergence for vector-valued functions and its applications to convex multiobjective optimization

The aim of this work is to study a notion of variational convergence for vector-valued functions. We show that it is suitable for obtaining existence and stability results in convex multiobjective optimization. We obtain various of properties of the variational convergence. We characterize it via the set convergence of epigraphs, coepigraphs, level sets, and some infima. We also characterize it by means of two metrics. We compare it with other notions of convergence for vector-valued functions from the literature and we show that it is more general than most of them. For obtaining the existence and stability results we employ an asymptotic method that has shown to be very useful in optimization theory. In this method we couple the variational convergence with notions of asymptotic analysis (asymptotic cones and functions).     

Optimal control of wave-packets: a semiclassical approach

We studied the optimal quantum control of a molecular rotor in tilted laser fields using the time-sliced Herman–Kluk propagator for the evaluation of the optimal pulse and the light–dipole interaction as the control mechanism. The proposed methodology was used to study the effects of an optimal pulse on the evolution of a wave-packet in a double-well potential and in the effective potential of a molecular rotor in a collinear tilted fields setup. The amplitude and frequency of the control pulse were obtained in such a way that the transition probability between two rotational wave-packets was maximised.