On the second eigenfunctions of the Laplacian in R2

A conjecture about the nodal line of a second eigenfunction states that the nodal line of a second eigenfunction divides the domain by intersecting with the boundary of transversely, where is a bounded convex domain ofR ². We prove this conjecture provided has a symmetry. Also, we prove the multiplicity of the second eigenvalue is two at most provided is a bounded convex domain ofR ².Supported in part by NSF DMS 84-09447Home Institution: Department of Mathematics, University of California, San Diego, La Jolla, CA 92093, USA     

Synthesis, band structure, and optical properties of Ba2ZnV2O8

A novel compound Ba₂ZnV₂O₈ has been synthesized in high temperature solution reaction and its crystal structure has been characterized by means of single crystal X-ray diffraction analysis. It crystallizes in monoclinic system and belongs to space group P2₁/c with a=7.9050(16), b=16.149(3), , β=90.49(3). It builds up from 1-D branchy chains of [ZnV₂O₈⁴⁻]_∞, and the Ba²⁺ cations are located in the space among these chains. The IR spectrum, ultraviolet-visible diffuse reflection integral spectrum and fluorescent spectra of this compound have been investigated. The calculated results of energy band structure by the density functional theory method show that the solid-state compound of Ba₂ZnV₂O₈ is an insulator with direct band gap of 3.48 eV. The calculated total and partial density of states indicate that the top valence bands are contributions from the mixings of O-2p, V-3d, and Zn-3d states and low conduction bands mostly originate from unoccupied antibonding states between the V-3d and O-2p states. The V-O bonds are mostly covalence characters and Zn-O bonds are mostly ionic interactions, and the ionic interaction strength is stronger between the Ba-O than between the Zn-O. The refractive index of n_x, n_y, and n_z is estimated to be 1.7453, 1.7469, and 1.7126, respectively, at wavelength of 1060 nm for Ba₂ZnV₂O₈ crystal.     

Further explorations on bridged 1,2,4-trioxanes

Three new bicyclo[3.2.1]-type 1,2,4-trioxanes have been designed and synthesized. One of them demonstrates better tolerance of the intramolecular hemiketals to steric crowding in hydroperoxidation. The other represents a prototype for possible manipulation of the transient radicals generated in cleavage reactions. A new substitution pattern in the bridged system is explored through synthesis of the third molecule. The configurations of all stereogenic centers in the bridged system can be effectively controlled by the chirality of the allyl alcohol as illustrated by the enantioselective synthesis of the fourth molecule. Finally, similar bicyclo[3.3.1]-type 1,2,4-trioxanes are shown very difficult to be synthesized because of the involvement of a conformer with two substituents at axial positions at the same time.     

FFC-1离子交换纤维对酸碱有害气体吸附性能的研究

系统考察了不同直径及反离子形式的FFC-1聚羧酸离子交换纤维对酸碱有害气体的穿透吸附,各种温、湿度条件下的吸水率,以及作为有害气体吸附滤除材料的重复使用与再生性能。研究表明:FFC-1纤维直径的减小有利于提高对有害气体的动态吸附容量。在体系温度、相对湿度分别为15℃、50%时,以3D腈纶为起始原料的钠型FFC-1离子交换纤维的吸水率≥350mg/g.纤维;对SO2的穿透吸附容量可达200mg/g.纤维。FFC-1离子交换纤维具有良好的重复使用与再生能力,经20次再生循环使用后,纤维交换容量未见明显变化。     

Organic phase conversion of bulk (wurtzite) ZnO to nanophase (wurtzite and zinc blende) ZnO

We describe the all-organic phase conversion of bulk commercial ZnO in the wurtzite modification to sub-30 nm ZnO that we find to be partially in the zinc blende [, a=4.568(3) Å] modification. The conversion involves refluxing ZnO in 2,4-pentanedione (acetylacetone) at 413 K to form the zinc 2,4-pentanedionate, which is decomposed by heating at 573 K in an appropriate high-temperature solvent such as dibenzylether to form nanophase ZnO. This nanophase, partially zinc blende ZnO can also be obtained in a single step by heating commercial zinc 2,4-pentanedionate in refluxing dibenzylether. Thermodiffractometry suggests that the conversion of zinc blende ZnO to wurtzite ZnO commences near 650 K.     

Unusually sharp dependence of water exchange rate versus lanthanide ionic radii for a series of tetraamide complexes

The tetraamide ligand, DOTA-tetra(glycine ethyl ester), forms complexes with the lanthanide(III) cations that exist in solution predominantly as the square antiprism structure with single, slowly exchanging inner-sphere water molecule. Variable-temperature 1H and 17O NMR studies revealed that the bound water lifetimes in these complexes were sharply dependent upon the ionic radius of Ln3+ cation. A novel lanthanide-induced shift technique was used to unmask the bound water 17O resonance of SmL3+ and YL3+ complexes from the bulk water resonance. The bound water lifetime (tauM298) was approximately 800 mus in the EuL3+ complex but became much shorter (several microseconds) for Ln3+ cations with larger and smaller ionic radii. This demonstrates that water exchange is exquisitely fine-tuned in this macrocyclic tetraamide system and that a variety of Ln3+ complexes meet with the exchange requirement, Deltaomega*tauM >/= 1, necessary for an efficient MT agent.