Connected components in the space of composition operators on<Emphasis Type="Italic">H∞</Emphasis> functions of many variables

LetE be a complex Banach space with open unit ballB _e. The structure of the space of composition operators on the Banach algebra H∞, of bounded analytic functions onB _e with the uniform topology, is studied. We prove that the composition operators arising from mappings whose range lies strictly insideB _e form a path connected component. WhenE is a Hilbert space or aC _o(X)- space, the path connected components are shown to be the open balls of radius 2. The research of this author was supported by grant number SAB1999-0214 from the Ministerio de Educación, Cultura y Deporte during his stay at the Universidad de Valencia. The research of this author was partially supported DGES(Spain) pr. 96-0758. The research of this author was partially supported by Magnus Ehrnrooths stiftelse.     

Dissecting the Engrailed homeodomain-DNA interaction by phage-displayed shotgun scanning

Phage-displayed alanine shotgun scanning was used to dissect contributions by engrailed homedomain (En-HD) residues 17 through 46, which indirectly influence recognition of DNA. The relative contributions of such indirect contacts, quantified by shotgun scanning, highlight previously unexplored En-HD residues. Two motifs dominate En-HD function in this region. First, two surface-exposed aromatic residues (F20 and Y25) bracket the hydrophobic core. Second, two sets of turn-forming residues are highlighted, including carboxamide-requiring residues E22/N23 and a leucine/isoleucine splint. The En-HD hydrophobic core exhibits a surprising degree of malleability, as demonstrated by homolog shotgun scanning. Most selectants from in vitro shotgun scanning mirror the consensus human homeodomain sequence. Thus, natural evolution and in vitro selection use similar selection criteria: affinity, specificity, and stability. However, homolog shotgun scanning identified mutations capable of improving the affinity and specificity of En-HD.     

A useful mapping of triatomic potential energy surfaces

We present in this paper a mapping of triatomic three-dimensional Born-Oppenheimer potential energy surfaces V for which all arrangement channels are represented evenhandedly. This representation is very useful for visualizing the geometrical and dynamical properties of such surfaces.     

Triplet states in 1,3-butadiene

The electron impact excitation spectrum 0f 1,3-butadiene has been studied at 20, 35 and 55 eV impact energies and scattering angles of 10° to 80°. Two low lying states are observed with maxima at 3.2 and 4.9 eV, and are identified as the ³B_u state and ³A_g state respectively     

The structure and ordering of ε-MnO2

The presence of ε-MnO₂ as a major component of electrolytic manganese dioxide (EMD) has been demonstrated by a combined X-ray diffraction/transmission electron microscopy (TEM) study. ε-MnO₂ usually has a partially ordered defect NiAs structure containing 50% cation vacancies; these vacancies can be fully ordered by a low temperature (200 °C) heat treatment to form a pseudohexagonal but monoclinic superlattice.Numerous fine-scale anti-phase domain boundaries are present in ordered ε-MnO₂ and cause extensive peak broadening and a massive shift of a very intense, 0.37 nm superlattice peak. This suggests a radically different explanation of the ubiquitous, very broad ∼0.42 nm peak (∼21-22° 2θ, CuKα radiation) in EMDs, which heretofore has been attributed to Ramsdellite containing numerous planar defects. This work confirms the multi-phase model of equiaxed EMDs proposed by Heuer et al. [ITE Lett. 1(6) (2000) B50; Proc. Seventh Int. Symp. Adv. Phys. Fields 92 (2001)], rather than the defective single-phase model of Chabre and Pannetier [Prog. Solid State Chem. 23 (1995) 1] and Bowden et al. [ITE Lett. 4(1) (2003) B1].     

Violation of microscopic reversibility and the use of reverse quais-classical trajectories for calculating reaction cross sections

In order to calculate the transition probabilities (or cross sections) for reactive collisions, such as A + BC(ν, j)→ AB(ν′, j) + C, using the quasi-classical trajectory method, one quantizes the internal energy of the reagents and in addition adopts some algorithm for calculating the internal quantum numbers of the products. A serious consequence of this procedure is that the quasi-classical results do not obey microscopic reversibility. It is shown that for the collinear F + H₂(ν = 0) → FH(ν = 2, 3)+ H reaction (and its D₂ counterpart), the quasi-classical trajectory probabilities for the reverse reaction not only differ substantially from the forward ones but in general are in much better agreement with accurate quantum calculations. A similar situation was found for the collinear H + H₂(0) → H₂(1) + H reaction. We suggest that in doing quasi-classical calculations, the reverse of the process of interest should also be considered. Comparison of forward and reverse quasi-classical collinear calculations with accurate collinear quantum results could give an indication of whether forward or reverse calculations should be used for the three-dimensional case.     

Syntheses and Crystal Structures of the Thallium(I) Iodobismuthates(III) Tl7Bi3I16 and Tl3BiI6

Dark grey (dark red with transmitting light) crystals of heptathallium(I) hexadecaiodo‐tribismuthate(III), Tl₇Bi₃I₁₆, were obtained by slow cooling of a melt from 800 K to ambient temperature and, with higher crystal quality via solvothermal synthesis in aqueous HI by slowly cooling from 428 to 363 K. The compound is diamagnetic and melts congruently at 630(5) K. X‐ray diffraction on single‐crystals revealed that Tl₇Bi₃I₁₆ crystallizes in the orthorhombic space group Cmcm with lattice parameters a = 2473.4(5), b = 1441.9(2), c = 3616.9(7) pm. The crystal structure can be interpreted as a layered intergrowth of fragments from the CsNiCl₃ and K₅Dy₃I₁₂ structure types with isolated [BiI₆]^3? octahedra and [Bi₂I₁₀]^4? double octahedra. Rotation and distortion of the complex anions establish coordination numbers (c.n.) between 7 and 9 for the Tl⁺ cations. Dark red crystals of trithallium(I) hexaiodo‐bismuthate(III), Tl₃BiI₆, are only accessible via hydrothermal synthesis in aqueous HI and slowly cooling from 428 to 363 K. Thermal analysis reveals a peritectoid decomposition at 540(5) K into the neighboring phases Tl₇Bi₃I₁₆ and TlI. Tl₃BiI₆ crystallizes in the monoclinic space group P2₁/c with lattice parameters a = 1352.6(3), b = 899.6(2), c = 1353.8(3) pm, and β = 104.18(3)°. In the crystal structure isolated [BiI₆]^3? octahedra are arranged according to the motif of a face‐centered pseudo‐cubic packing. Due to the tilted orientation of the [BiI₆]^3? groups the Tl⁺ cations have c.n. of 8 and 9. Although the crystal structure of Tl₃BiI₆ looks like a distorted variant of the elpasolith type, there is no symmetry relation according to a group subgroup formalism.