On I-fuzzy topologies derived from a decreasing family of I-topologies

The aim of this paper is to study I-fuzzy topologies (fuzzy topologies in ostak's sense) derived from decreasing families of I-topologies (fuzzy topologies in Chang's sense), defined on a set X.     

Radiative lifetimes in Ce I and Ce II

New radiative lifetime measurements based on time-resolved laser-induced fluorescence techniques are reported for 18 even-parity levels belonging to the 4f5d^26p and 4f ²5d ² configurations of Ce I and 6 even-parity levels belonging to the 5d^26s, 4f5d6p, and 4f6s6p configurations of Ce II. Free neutral and singly ionized cerium atoms were produced by laser ablation. The Ce I and Ce II levels range in energy from 26 545 to 29 102 cm^-1, and 42 573 to 48 152 cm^-1, respectively. Received 25 September 2002 Published online 4 March 2003     

Spin polarization effect for Tc2 molecule

Density functional method (DFT) (B3p86) of Gaussian98 has been used to optimize the structure of the Tc_2 molecule. The result shows that the ground state for Tc_2 molecule is an 11-multiple state and its electronic configuration is {}^{11}Σ_g^-, which shows the spin polarization effect of Tc_2 molecule of a transition metal element for the first time. Meanwhile, we have not found any spin pollution because the wavefunction of the ground state does not mingle with wavefunctions of higher energy states. So, that the ground state for Tc_2 molecule is an 11-multiple state is indicative of the spin polarization effect of Tc_2 molecule of a transition metal element: that is, there exist 10 parallel spin electrons. The non-conjugated electron is greatest in number. These electrons occupy different spacious tracks, so that the energy of Tc_2 molecule is minimized. It can be concluded that the effect of parallel spin of the Tc_2 molecule is larger than the effect of the conjugated molecule, which is obviously related to the effect of electron d delocalization. In addition, the Murrell--Sorbie potential functions with the parameters for the ground state {}^{11}Σ_g^- and other states of Tc_2 molecule are derived. Dissociation energy D_e for the ground state of T_{c2} molecule is 2.266eV, equilibrium bond length R_e is 0.2841nm, vibration frequency ω_e is 178.52cm^{-1}. Its force constants f_2, f_3, and f_4 are 0.9200aJ·nm^{-2}, --3.5700aJ·nm^{-3}, 11.2748aJ·nm^{-4} respectively. The other spectroscopic data for the ground state of Tc_2 molecule ω_eχ_e, B_e, α_e are 0.5523cm^{-1}, 0.0426cm^{-1}, 1.6331×10^{-4}cm^{-1} respectively.     

Spectroscopic Studies of a Three-dimensional, Five-coordinated Copper(Ⅱ) Complex via Hydrogen Bonds: [Cu(PDA)(H_2O)_2](H_2PDA=Pyridine-2,6-dicarboxylic Acid)

IntroductionFive- coordinated complexes with d9- configuredcations have received much attention stereochemi-cally,spectrochemically and biologically,and havebeen comprehensively discussed[1] . Usually thereare two stable configurations for the copper( )complexes with five equal coordinating atoms:anapically elongated square pyramid( SP) and a com-pressed trigonal bipyramid( TBP) ,with an obviousenergetic preference for the latter coordination.When the ligands are rigid and provide angular d…     

Besov-Morrey spaces: Function space theory and applications to non-linear PDE

This paper is devoted to the analysis of function spaces modeled on Besov spaces and their applications to non-linear partial differential equations, with emphasis on the incompressible, isotropic Navier-Stokes system and semi-linear heat equations. Specifically, we consider the class, introduced by Hideo Kozono and Masao Yamazaki, of Besov spaces based on Morrey spaces, which we call Besov-Morrey or BM spaces. We obtain equivalent representations in terms of the Weierstrass semigroup and wavelets, and various embeddings in classical spaces. We then establish pseudo-differential and para-differential estimates. Our results cover non-regular and exotic symbols. Although the heat semigroup is not strongly continuous on Morrey spaces, we show that its action defines an equivalent norm. In particular, homogeneous BM spaces belong to a larger class constructed by Grzegorz Karch to analyze scaling in parabolic equations. We compare Karch's results with those of Kozono and Yamazaki and generalize them by obtaining short-time existence and uniqueness of solutions for arbitrary data with subcritical regularity. We exploit pseudo-differential calculus to extend the analysis to compact, smooth, boundaryless, Riemannian manifolds. BM spaces are defined by means of partitions of unity and coordinate patches, and intrinsically in terms of functions of the Laplace operator.

     

The rank of Hankel operators on harmonic Bergman spaces

We show that on the harmonic Bergman spaces, the Hankel operators with nonconstant harmonic symbol cannot be of finite rank.

     

Multilinear interpolation between adjoint operators

Multilinear interpolation is a powerful tool used in obtaining strong-type boundedness for a variety of operators assuming only a finite set of restricted weak-type estimates. A typical situation occurs when one knows that a multilinear operator satisfies a weak L^q estimate for a single index q (which may be less than one) and that all the adjoints of the multilinear operator are of similar nature, and thus they also satisfy the same weak L^q estimate. Under this assumption, in this note we give a general multilinear interpolation theorem which allows one to obtain strong-type boundedness for the operator (and all of its adjoints) for a large set of exponents. The key point in the applications we discuss is that the interpolation theorem can handle the case q?1. When q>1, weak L^q has a predual, and such strong-type boundedness can be easily obtained by duality and multilinear interpolation (cf. Interpolation Spaces, An Introduction, Springer, New York, 1976; Math. Ann. 319 (2001) 151; in: Function Spaces and Applications (Lund, 1986), Lecture Notes in Mathematics, Vol. 1302, Springer, Berlin, New York, 1988; J. Amer. Math. Soc. 15 (2002) 469; Proc. Amer. Math. Soc. 21 (1969) 441).     

A novel synthesis of 5-perfluorophenyl 4,5-dihydro-1H-pyrazoles in THF or water

5-Perfluorophenyl 4,5-dihydro-1H-pyrazoles were synthesized from 1,3-dipolar cycloaddition reaction of perfluorobenyl 2,4,6-triisopropylbenzenesulfonylhydrazone and α,β-unsaturated carbonyl compounds or acrylonitrile in THF or water. It was worthy to note that better results were obtained when water was employed as the solvent, which was considered as an effective, economic and environmentally friendly method to synthesize these pyrazole derivatives.     

Estimation of growth rate in unidirectionally solidified multicrystalline silicon by the growth-induced striation method

Multicrystalline silicon was grown by unidirectional solidification method using the accelerated crucible rotation technique. The application of the accelerated crucible rotation technique in unidirectional solidification method induced growth striations across the axial direction of the grown crystal. This striation pattern was observed from carbon concentration distribution, obtained by using Fourier transform infrared spectroscopy. The generated striation pattern was found to be weak and discontinuous. Some striations were absent, probably due to back melting, caused during each crucible rotation. From the growth striations and applied time period in crucible rotation, the growth rate was estimated by using Fourier transformation analysis.     

Eu- and Yb-induced reconstructions on a vicinal Si(1 0 0) surface

Early stages of rare-earth metal (Yb and Eu) growth on a vicinal, single-domain Si(1 0 0)2 × 1 surface have been studied in the coverage range of 0.1-0.3 monolayer (ML) by low energy electron diffraction, scanning tunneling microscopy, and synchrotron radiation photoemission spectroscopy. We show that Yb induces the 2 × 3 periodicity in the whole range of coverage studied. The 2 × 3 reconstruction coexists with the local 3 × 2/4 × 2 structure at about 0.2 ML of Yb. In contrast, Eu forms the 3 × 2 periodicity at 0.1-0.2 ML, whereas this structure is converted into the 2 × 3 phase at about 0.3 ML. The atomic arrangement and electronic properties of these reconstructions and the adsorbate-mediated modification of surface morphology are investigated.