A syzygetic approach to the smoothability of zero-dimensional schemes

We consider the question of which zero-dimensional schemes deform to a collection of distinct points; equivalently, we ask which Artinian k-algebras deform to a product of fields. We introduce a syzygetic invariant which sheds light on this question for zero-dimensional schemes of regularity two. This invariant imposes obstructions for smoothability in general, and it completely answers the question of smoothability for certain zero-dimensional schemes of low degree. The tools of this paper also lead to other results about Hilbert schemes of points, including a characterization of nonsmoothable zero-dimensional schemes of minimal degree in every embedding dimension d?4.     

Effect of flow on solutions of rodlike molecules

A flow field imposed on a solution of rodlike particles tends to align the rods owing to friction between the fluid and the rods. The potential energy of rods in a steady-state, homogeneous, and irrotational flow is superposed on the equilibrium Gibbs free energy of the quiescent solution to obtain the total free energy. The exact lattice treatment of Flory and Ronca is used in formulating the problem. Effects of flow on the orientational distribution function of rods and phase separation are analyzed with particular reference to elongational and pure shear flows. Calculations carried out for various compositions and flow characteristics reveal the presence of a region where the order parameter is sensitive to changes in prevailing flow conditions. Experimental determination of orientation by measuring flow birefringence is discussed.     

Synchrotron radiation induced photoionization and photodissociation of carbon monoxide in the 14–35 eV region

Carbon monoxide has been excited with monochromatic synchrotron radiation in the 14–35 eV range using the Swedish synchrotron facility MAX in Lund. The decay products were studied in various detection channels such as formed CO⁺ and C⁺ ions using mass spectroscopy and visible or VUV fluorescence using photon detection. A rich line structure is observed which is attributed to CO Rydberg series converging to theX,A,B,D,C andE states in CO⁺. While a great number of these lines are already known, some of them are classified here for the first time. The combination of information from the fluorescence spectra and the mass spectra contribute important information concerning the autoionization and predissociation of these various Rydberg series.     

Molecular structure,spectroscopic, and density functional theory studies of o-Dianisidine

o-Dianisidine has been characterized by the FT-IR, UV-Vis, and X-ray single-crystal determination. The compound crystallizes in the orthorhombic space group Pbca with a = 7.2593 (4) Å, b = 21.3485 (10) Å, c = 16.5835 (11) Å and Z = 8. Density functional theory has been used in the computation of the molecular geometry and harmonic vibrational wavenumbers. The calculated molecular geometry parameters have been compared with X-ray data. UV-Vis spectra of the compound have been predicted using the time-dependent density functional theory and good agreement between the calculated and experiment is determined. Besides, molecular electrostatic potential, frontier orbital analysis, and nonlinear optical properties were performed by using density functional theory calculations.     

Optical,magneto-optical and mössbauer spectroscopy on Co3+ substituted cobalt ferrite Co2+Fe2−xCo3+xO4(0 ⩽ x ⩽ 2)

The magneto-optical spectra of Co_1+xFe_2?xO₄ show with increasing Co³⁺ content an increasing intensity of the 4A₂ ? 4T₁(F) and 4A₂ ? 4T₁(P) transition of Co²⁺ at 0.8 and 2.0 eV. A decrease in the Co²⁺-Fe³⁺ charge transfer transitions on octahedral sites is found. In the optical spectra a strong increase in optical absorption is found with dominant transitions at 0.8, 1.6 and 2.6 eV due to Co³⁺ crystal field transitions on octahedral sites and a Co²⁺-Co³⁺ charge transfer. Conversion Electron Mössbauer Spectroscopy has been used to determine the cation distribution in the surface layer of the samples. The results indicate a shift of Co²⁺ from octahedral to tetrahedral sites when Co³⁺ is substituted in CoFe₂O₄. This results in enhanced optical absorption, enhanced magneto-optical effects and a lower Curie temperature.     

Continuous-wave quasi-phase-matched generation of 60 mW at 465 nm by single-pass frequency doubling of a laser diode in backswitch-poled lithium niobate

We report continuous-wave single-pass second-harmonic generation (SHG) in 4-mum -period 0.5-mm-thick backswitch-poled lithium niobate. Pump sources at 920-930 nm include both Ti:sapphire and diode-oscillator-amplifier lasers. SHG of a Ti:sapphire laser at 6.1%/W efficiency, producing 61 mW of power at 460 nm, is demonstrated in 50-mm-long periodically poled lithium niobate samples with a nonlinear coefficient d(eff) approximately 9pm/V, and 60 mW at 465 nm and 2.8%/W efficiency is obtained by SHG of a laser-diode source.     

An anthracene based fluorescent probe for the selective and sensitive detection of Chromium (III) ions in an aqueous medium and its practical application

An anthracene based fluorescent probe, integrated with thiophene moiety, exhibited selective and sensitive detection of chromium (III) ions over other metal ions. Its synthesis was achieved by simple mixing of two commercially available compounds, 2-aminoanthracene, and 2-thiophenecarboxaldehyde, in onestep without the needed complex purification process. The probe molecule ( ANT-Th ) offered exceptional features such as “turn-on” fluorescence response, low detection limit (0.4 μM), and fast response time (<1 min) via C=N bond hydrolysis. Also, a simple test paper system was developed for the rapid detection of chromium (III) ions with the naked eye.