A note on the growth of topological Sidon sets

We give an estimate for the number of elements in the intersection of topological Sidon sets inR ⁿ with compact convex subsets and deduce a necessary and sufficient conditions for an orbit of a linear transformation ofR ⁿ to be a topological Sidon set.     

Study of Ganga River – Groundwater Interaction Using Environmental Oxygen-18

The influent and effluent characteristics of river Ganga in the Hardwar-Narora sector in Uttar Pradesh, India was studied using environmental oxygen-18. δ¹⁸O of river water and also of groundwater close to the river course was monitored at 8 stations along the 220 km stretch for a period of ten months. δ¹⁸O of the river during the monsoon months (June to September) was about – 10 at all the stations. However, during the dry months from October to April, the δ¹⁸O of the river was enriched progressively from Hardwar to Narora. The enrichment indicated groundwater contribution to the river during the non-monsoon months. The contribution was comuted using the principle of isotope balance.     

Molar extinction coefficients of some carbohydrates in aqueous solutions

Molar extinction coefficients of some carbohydrates viz. l-arabinose (C₅H₁₀O₅), d-glucose (C₆H₁₂O₆), d-mannose (C₆H₁₂O₆), d-galactose (C₆H₁₂O₆), d(-) fructose (C₆H₁₂O₆) and maltose (C₁₂H₂₄O₁₂) in aqueous solutions have been determined at 81, 356, 511, 662, 1173 and 1332 keV by gamma ray transmission method in a narrow beam good geometry set-up. These coefficients have been found to depend upon the photon energy following a 4-parameter polynomial. These extinction coefficients for different sugars having the same molecular formula have same values varying within experimental uncertainty. Within concentration ranges studied, Beer-Lambert law is obeyed very well.     

Harmonious orbits of linear transformations

We describe necessary and sufficient conditions for orbits of linear transformations onR ⁿ ,n1, and sets arising as sums of elements from orbits, to be harmonious subsets. This is done via a generalization of the notion of Pisot-Vijayaraghavan and Salem numbers.     

Homoconjugation in the adamantane cage: DFT/IGLO studies of the 1, 3-dehydro-5-adamantyl cation, its isoelectronic boron analogue 1, 3-dehydro-5-boraadamantane, and related systems(1)(,)

The structure of 1,3-dehydro-5-adamantyl cation and its isoelectronic boron analogue 1,3-dehydro-5-boraadamantane as well as some related adamantane systems, hitherto unknown as persistent long-lived species, were investigated by using the density functional theory (DFT) method. (13)C and (11)B NMR chemical shifts of the compounds were also calculated using the IGLO method. Stabilization of the systems due to homoconjugation is discussed.     

Theoretical study of relative width of photonic band gap for the 3-D dielectric structure

Calculations for the relative width (Δω/ω₀) as a function of refractive index and relative radius of the photonic band gap for the fcc closed packed 3-D dielectric microstructure are reported and comparison of experimental observations and theoretical predictions are given. This work is useful for the understanding of photonic crystals and occurrence of the photonic band gap.     

离子液体作为溶剂/催化剂用于卤代烃对胺的选择性烷基化反应

在三乙胺存在下,在离子液体([bmim]I和[bmim]PF6)中进行了各种卤代烃对胺类化合物中氨基的选择性烷基化反应.反应在相对温和的条件下进行,转化率和选择性优异.离子液体可以回收并重复使用.     

High quality beam shaping by square soft-edge diaphragm combined with liquid crystal spatial light modulator

<正>The square soft-edge diaphragm with round angle is designed by Matlab,and is sent to a liquid crystal spatial light modulator by the computer.In order to obtain precompensation for the following laser system, local diaphragm transmission can be adjusted by feedback signals of surface-channel charge-coupled device (SCCD).This method can reduce the diffraction effect and realize no modulation,high stability,high homogeneity,and large scale laser beam.Several parameters of soft-edge diaphragms which affect the laser beam quality are studied systematically,and the optimized values are obtained.The method can avoid the serious modulation of hard edges and provide soft-edge diaphragms of different shapes in a fast and convenient way for the large scale laser beam system.     

Some further remarks on good sets

We show that in n-fold cartesian product, n ≥ 4, a related component need not be a full component. We also prove that when n ≥ 4, uniform boundedness of lengths of geodesics is not a necessary condition for boundedness of solutions of (1) for bounded function f.     

On the variation of magnetic susceptibility of a molecular crystal with temperature: the 2,4,6-triphenylverdazyl system

Magnetic susceptibilities of spin-1/2 systems of orthorhombic and higher crystal symmetries have been numerically investigated while taking possible anisotropy in the coupling constants along different crystal axes into account. The work relies on the magnon-based theory of ferromagnetic (FM) and antiferromagnetic (AFM) crystal systems of types FFF, AFF, AAF, and AAA [J. Chem. Phys. 111, 9009 (1999)]. The AAF crystal, in particular, shows interesting changes in the temperature dependence of magnetic susceptibility when the ferromagnetic exchange coupling constant is varied. We especially show that the susceptibility anomalies of molecular crystals fit naturally within the framework of the extended magnon-theoretical formalism, and do not necessarily imply a FM --> AFM or a reverse phase transition. A real system, molecular crystal of 2,4,6-triphenylverdazyl (2,4,6-TPV), has been investigated here. It was previously interpreted as an AAF system from observed susceptibility data [Tomiyoshi et al., Phys. Rev. B 49, 16031 (1994)]. The trend of the temperature dependence of magnetic susceptibility studied in the present work also indicates that the crystal belongs to the AAF category with a less prominent FM exchange coupling constant. To reinforce our conclusions, we have adopted a two-pronged strategy. First, the geometry of the 2,4,6-TPV monomer has been optimized here by ab initio unrestricted Hartree-Fock (UHF) calculations using the STO-3G basis set. The optimized geometry is almost planar. A subsequent calculation has been carried out with the phenyl rings twisted out of the plane of the nitrogen atoms. The STO-3G optimized geometry, and the same geometry except for the twisted phenyl rings, have been used to perform ab initio coupled-cluster (UCCSD-T) calculations with the same basis, and UHF as well as density-functional (UB3LYP) calculations using the 6-31G basis set. The calculated data can easily rationalize the twists while the species remains in crystal. The magnetic category of the crystal has been unambiguously confirmed as AFA from ab initio UHF and UB3LYP calculations of the total energy in different spin states of dimers and trimers along the crystal axes. The computed energy values, however, fail to yield accurate estimates of the exchange coupling constants Ja, Jb, and Jc, because the latter are on the order of 1kBK corresponding to energy differences on the order of 10(-6) hartree between different spin states. In the second approach, the observed features of the susceptibility minimum and maximum have been used to determine the best values of the exchange coupling constants from the theoretical formulas for an anisotropic AFA crystal. The AFM (Ja and Jc) and FM (Jb) exchange coupling constants and the Neel temperature (TN) found from this analysis correspond to Ja + Jc = -1.05 kBK, Jb = 1.35 kBK, and TN = 1.75 K. The calculated J values significantly differ from those estimated from a linear Heisenberg chain model, but generate a susceptibility versus temperature graph that mimics the experimental plot.