The gauge theorem for a class of additive functionals of zero energy

Summary In earlier works, the gauge theorem was proved for additive functionals of Brownian motion of the form ₀ ^t q(B _s )ds, whereq is a function in the Kato class. Subsequently, the theorem was extended to additive functionals with Revuz measures in the Kato class. We prove that the gauge theorem holds for a large class of additive functionals of zero energy which are, in general, of unbounded variation. These additive functionals may not be semi-martingales, but correspond to a collection of distributions that belong to the Kato class in a suitable sense. Our gauge theorem generalizes the earlier versions of the gauge theorem.Research supported in part by NSA grant MDA-92-H-30324     

Rigidity of harmonic maps of maximum rank

Thehomotopical rank of a mapf:M →N is, by definition, min{dimg(M) ¦g homotopic tof}. We give upper bounds for this invariant whenM is compact Kähler andN is a compact discrete quotient of a classical symmetric space, e.g., the space of positive definite matrices. In many cases the upper bound is sharp and is attained by geodesic immersions of locally hermitian symmetric spaces. An example is constructed (Section 9) to show that there do, in addition, exist harmonic maps of quite a different character. A byproduct is construction of an algebraic surface with large and interesting fundamental group. Finally, a criterion for lifting harmonic maps to holomorphic ones is given, as is a factorization theorem for representations of the fundamental group of a compact Kähler manifold. The technique for the main result is a combination of harmonic map theory, algebra, and combinatorics; it follows the path pioneered by Siu in his ridigity theorem and later extended by Sampson.     

Molecular Rectangle Formed by Head-to-tail Self-Assembly of 1-(Dipyrrin-2-yl)-1-(dipyrrin-3-yl)methane

Summary. 1-(Dipyrrin-2-yl)-1-(dipyrrin-3-yl)methane, the N-confused analog of biladiene-ac, is prepared by condensation of 2,3-dipyrromethane with two molecules of 2-formylpyrrole in dichloromethane in the presence of hydrogen bromide. Self-assembly of the ligand with Zn(II) in dichloromethane and methanol offers a dinuclear dimeric complex with a ligand:metal ratio of 2:2. X-Ray crystal structure analysis reveals two ligands bound through a head-to-tail pattern to two zinc centers to form a severely distorted helical conformation, which has the shape of a rectangle.     

γ-sets and other singular sets of real numbers

A family of $\text{J}$ of open subsets of the real line is called an ω-cover of a set X iff every finite subset of X is contained in an element of $\text{J}$. A set of reals X is a γ-set iff for every ω-cover $\text{J}$ of X there exists $\text{〈D}{}_{\mathrm{n}}\text{: n < ω〉?}\text{J}{}^{\mathrm{\omega }}$ such that

In this paper we show that assuming Martin's axiom there is a γ-set X of cardinality the continuum.     

R?ntgenspektrometrische Bestimmung von Eisen-55 in Luftstaub- und Niederschlagsproben

Zusammenfassung Eisen-55 wurde in Neuherberg bei München seit März 1970 in monatlich gesammelten Luftstaubproben und seit Januar 1971 in Monatsniederschlagsproben bestimmt. Nach dem Veraschen der Proben wurde Eisen durch Extraktion' mit Di-iso-propyläther abgetrennt. Zur weiteren Entfernung störender Radionuklide des Fallouts wurde eine Ionenaustauschertrennung angeschlossen. Nach der elektrolytischen Abscheidung des Eisens auf Kupferplättchen wurden die Röntgenspektren mit einem Proportionalzähler sowie einem Si(Li)-Detektor aufgenommen.Die mittlere spezifische Luftaktivität betrug in Neuherberg 1,0 fCi/m³ im Jahr 1970 (ab März), 1,2 fCi/m³ im Jahr 1971 und 0,36 fCi/m³ im Jahr 1972. Die dem Boden durch den Niederschlag zugeführte Aktivität wurde zu 697 pCi/m² · Jahr für 1971 und 178 pCi/m² · Jahr für 1972 bestimmt.Vortrag anläßlich der Tagung Spurenanalyse, 2. bis 5. April 1973 in Erlangen.     

Some positive cotes numbers for the chebyshev weight function

We show that, for the Chebyshev weight function (1–x ²)^–1/2, the Cotes numbers for the quadrature rule with nodes at the zeros of the ultraspherical polynomialP _n ^/() are nonnegative if and only if –1/2<1.     

Structural effects in electron transfer reactions: comparative interfacial electrochemical kinetics for cis- versus trans-dioxorhenium(V)(bi)pyridine oxidation

The comparative interfacial oxidation kinetics of the approximate structural isomers trans-(O)₂Re^V(py)⁺₄ and cis-(O)₂Re^V(bpy)(py)⁺₂ (py, pyridine; bpy, 2,2′-bipyridine) have been assessed in aqueous solution via conventional cyclic voltammetry at a highly ordered pyrolytic graphite (HOPG) electrode. HOPG was employed because of its known propensity to diminish interfacial electron transfer (ET) rates (by ca. three to four orders of magnitude) and because of a probable lack of importance of kinetic work terms (diffuse double-layer corrections). Measured rates for the trans complex exceed those for the cis by about a factor of 3. Expressed as an effective activation Gibbs energy difference ΔG^*, this corresponds to a cis-trans difference of ca. 3 kJ mol⁻¹. The actual vibrational barriers to ET have determined from a combination of published X-ray structural results (trans complex) and new resonance Raman results (cis complex). The values are 0.6 kJ mol ⁻¹ for the trans oxidation and 4.4 kJ mol⁻¹ for the cis oxidation (i.e. close to the barrier difference inferred from rate measurements). Further analysis shows that most of the barrier difference is associated with displacement of a (predominantly) Re-N(bpy) stretching mode found only in the cis system. Differences in metal-oxo displacements (cis > trans) are also implicated.     

2-芳基吲哚的敏化光氧化偶合反应

本文研究了十七种2-芳基吲哚(1a-1q)在甲醇-乙酸介质中的亚甲基蓝(MB)敏化光氧化反应, 发现有十五种吲哚(1a-1o)以85%-95%的产率给出2,2'-二芳基-[2,3'-联-1H-吲哚]-3(2H)-酮(2a-2o), 而2-(4-硝基苯基]吲哚(1p)和2-联苯基吲哚(1q)则分别生成2-甲氧基-2-(4-硝基苯基)-1,2-二氢-3H-吲哚-3-酮(7p)和2-联苯基-4H-3,1-苯并恶嗪-4-酮(11q), 其中7p在分离过程中失去甲醇分子给出2-(4-硝基苯基)-3H-吲哚-3-酮(10p)。     

A new quantum group associated with a ‘nonstandard’ braid group representation

A new quantum group is derived from a nonstandard braid group representation by employing the Faddeev-Reshetikhin-Takhtajan constructive method. The classical limit is not a Lie superalgebra, despite relations like x ²–y ²=0. We classify all finite-dimensional irreducible representations of the new Hopf algebra and find only one- and two-dimensional ones.     

On coherent states for the simplest quantum groups

The coherent states for the simplest quantum groups (q-Heisenberg-Weyl, SU _q (2) and the discrete series of representations of SU _q (1, 1)) are introduced and their properties investigated. The corresponding analytic representations, path integrals, and q-deformation of Berezin's quantization on , a sphere, and the Lobatchevsky plane are discussed.