λ-Automorphisms of a Riemannian Foliation II

In Pak (Ann. Global Anal. Geom.13 (1995), 281–288), the notion of -automorphisms of a harmonic Riemannian foliation was extended to a general Riemannian foliation. By applying the characterization obtained in Pak of a -automorphism to be transversal Killing, we here consider the problem that a transversal conformal or projective field is transversal Killing. A special condition, namely _{B B} = 0, is discussed.     

Hyperbolic Geometry with Clifford Algebra

The Clifford algebra in D. Hestenes formulation is used to study hyperbolic geometry and some interesting theorems are obtained. The computational power of this formulation is fully revealed by the ease of extending old results and discovering new ones. An important new result is the formulas on the area and perimeter of a convex polygon, based on extending Gauss equalities.     

A Numerical Comparison of Some Modified Controlled Random Search Algorithms

In this paper we propose a new version of the Controlled Random Search(CRS) algorithm of Price. The new algorithmhas been tested on thirteen global optimization test problems. Numericalexperiments indicate that the resulting algorithm performs considerablybetter than the earlier versions of the CRS algorithms. The algorithm,therefore, could offer a reasonable alternative to many currently availablestochastic algorithms, especially for problems requiring direct searchtype methods. Also a classification of the CRS algorithms is made based onglobal technique – local technique and the relative performance ofclasses is numerically explored.     

Double Circulant Codes over \mathbb{Z}_4 and Even Unimodular Lattices

With the help of some new results about weight enumerators of self-dual codes over we investigate a class of double circulant codes over , one of which leads to an extremal even unimodular 40–dimensional lattice. It is conjectured that there should be Nine more constructions of the Leech lattice     

Diborane as a reducing agent IX: Reduction of aTris(trifluoroacetyl)enaminospiroindoline

Summary Reduction of the title compound (2) with diborane furnishes 1-trifluoroethyl-3-(2-(trifluoroethylamino)ethyl)-3-vinylindoline (4), 1-hydroxy-trifluoroethyl-3-(2-(trifluoroethylamino)ethyl)indole (5), and 1-methyl-2-trifluoroethyl-1,2,3,4-tetrahydro--carboline (6). However, treatment of2 with lithium aluminum hydride, H₂/Pd on charcoal, and sodium borohydride affords hydroxyspiroindolenine8, hydroxy-bis(trifluoroacetyl)enaminospiroindoline9, andN-ethyltryptamine7, respectively. The results are discussed and the mechanisms of the reactions leading to4–8 are presented.

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Diboran als Reduktionsmittel, 9. Mitt.: Reduktion einesTris(trifluoroacetyl)enaminospiroindolins

Zusammenfassung Reduktion der Titelverbindung (2) mit Diboran ergibt 1-Trifluoroethyl-3-(2-(trifluoroethylamino)ethyl)-3-vinylindolin (4), 1-Hydroxy-trifluoroethyl-3-(2-(trifluoroethylamino)ethyl)indol (5) und 1-Methyl-2-trifluoroethyl-1,2,3,4-tetrahydro--carbolin (6). Behandlung von2 mit Lithiumaluminiumhydrid, H₂/Pd auf Aktivkohle und Natriumborhydrid führt jedoch zu Hydroxyspiroindolenin8, Hydroxy-bis(trifluoroacetyl)enaminospiroindolin9 und N-Ethyltryptamin (7). Die Ergebnisse werden diskutiert und die Mechanismen der zu den Produkten4–8 führenden Reaktionen werden vorgestellt.

     

Determinants,Grassmanniannians and Elliptic Boundary Problems for the Dirac Operator

We study the relations between different determinants of the Dirac operator over a manifold with boundary considered as sections of a holomorphic line bundle over the Grassmannian of boundary conditions of Atiyah–Patodi–Singer type.     

Hydrogen bonding cooperativity of water to nucleotide recognition: structure of octadecahydrated inosine 5′-monophosphate, 2(C10H12N4O8P)·18H2O at atomic resolution

The crystal structure of an octadecahydrated complex between two inosine 5-monophosphate (IMP) has been determined at atomic resolution, which reveals the hydrogen bonding and the coordination cooperativity of water molecules to nucleotide recognition. The crystal belongs to monoclinic space group P2₁ with cell dimensions a = 8.65(1), b = 21.90(1), c = 12.37(1)Å, and = 110.38(9)°. The ribose hydroxyls, purine N7, keto(O6) bonded water molecules W1, W2, W5, W6, W8 and the phosphate bridge forming water oxygens of W4, W7, W11 appear to play an invariant role in their hydrogen bonding interactions with the IMPs. The synergistic role of the water molecules W5, W6, W8 in the purine staking domain N27W5=2.583,O16W8=2.759,O2627W6=2.723 Åhave been clearly observed for the first time. The complexation of the water molecules through variable hydrogen bonding coordination indicate their functional involvement through extensive cooperative donor-acceptor network mechanism. The occurrence of hydrogen-bonded water spines, water bridges and their interplay in the structural association of IMPs could indicate the possible viability of those aquatic centers in the biological situation.     

Maximal resolvability of totally bounded and ℵ0-bounded groups

The maximal resolvability of totally bounded groups (and, under the assumption that the generalized continuum hypothesis holds, of ₀-bounded groups) is proved.Translated fromMatematicheskie Zametki, Vol. 63, No. 4, pp. 593–598, April, 1998.This research was supported by the Russian Foundation for Basic Research under grant No. 94-01-01374.     

A Characterization of Monotone and Regular Divergences

In this paper we characterize the local structure of monotone and regular divergences, which include f-divergences as a particular case, by giving their Taylor expansion up to fourth order. We extend a previous result obtained by encov, using the invariant properties of Amari's -connections.