Orientations of chain groups

We prove generalizations to chain groups, of Minty's Arc Colouring Lemma and its extension, the well-known Farkas Lemma. In these the orientation of the edges is replaced by an arbitrary chain.A function on a chain groupN isrepresentable if there exists a chainR such that (X)=R·X for allXN. Anorientation is a chain with values ±1. We prove that for a regular chain group a linear function that is representable by an orientation for each chainXN locally, is representable by an orientation globally.     

Generalized self-dual Yang-Mills flows,explicit solutions and reductions

An evolution equation is added to the generalized self-dual Yang-Mills equations. The evolution equation contains terms of negative powers of the spectral parameter as well as terms of positive powers. The Darboux matrix method is used to obtain explicit solutions, especially single and multiple solitons. All integrable soliton equations in the framework of AKNS system (inR ⁿ⁺¹ orR ¹⁺¹) can be derived from the generalized Yang-Mills flows by reduction.Supported by Chinese research project Nonlinear Science and K.C. Wong Education Foundation, Hong Kong.     

Efficient nonparametric estimation of distribution density in the basis of algebraic polynomials

A nonparametric estimatef ^* of an unknown distribution densityf W is called locally minimax iff it is minimax for all not too small neighborhoodsW _g ,g W, simultaneously, whereW is some dense subset ofW. Radaviius and Rudzkis proved the existence of such an estimate under some general conditions. However, the construction of the estimate is rather complicated. In this paper, a new estimate is proposed. This estimate is locally minimax under some additional assumptions which usually hold for orthobases of algebraic polynomial and is almost as simple as the linear projective estimate. Thus, it takes a form convenient for the construction of an adaptive estimator, which does not usea-priori information about the smoothness of the density. The adaptive estimation problem is briefly discussed and an unknown density fitting by Jacobi polynomials is investigated more explicitly.     

The Dold-Lashof-Fuchs construction revisited

Sia dato uno spazio topologicoE con azione di un monoide topologicoH e siaE→B una funzione continue che, su ogni apertoU di una partizione dell'unità diB, sia, a meno di omotopia, la proiezioneU×H→U (ovvero una fibrazione numerabile). Un classico risultato di A. Dold e R. Lashof (1959) permette di costruire, a partire daE→B, una funzione continuaE _∞→B_∞, conE _∞ debolmente contraibile e munito di azione diH: laH-fibrazione universale associata daH. Tale funzione, in generale, non è purtroppo numerabile e quindi non si presta alla classificazione delleH-fibrazioni numerabili. Successivamente (1971), M. Fuchs ha trovato un modo di modificare la costruzione di Dold-Lashof per recuperare la numerabilità. La costruzione di Dold-Lashof-Fuchs è, da allora, uno dei principali strumenti nella teoria degli spazi classificanti di monoidi topologici, anche se vi è un uso di topologie alquanto complesse e quindi poco maneggevoli. In questo lavoro ci proponiamo di mostrare come, lavorando nella categoria conveniente deik-spazi, sia possibile descrivere la costruzione di Dold-Lashof-Fuchs in modo estremamente semplificato ed adattarla anche alla classificazione delleF-fibrazioni numerabili.

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Conferenza tenuta da R. Piccinini il 15 maggio 1995     

A note on theΠ 2 0 -induction rule

It is well-known (due to C. Parsons) that the extension of primitive recursive arithmeticPRA by first-order predicate logic and the rule of ₂ ⁰ -induction ₂ ⁰ -IR is ₂ ⁰ -conservative overPRA. We show that this is no longer true in the presence of function quantifiers and quantifier-free choice for numbersAC ^0,0-qf. More precisely we show that :=PRA ² + ₂ ⁰ -IR+AC ^0,0-qf proves the totality of the Ackermann function, wherePRA ² is the extension ofPRA by number and function quantifiers and ₂ ⁰ -IR may contain function parameters.This is true even forPRA ² + ₁ ⁰ -IR+ ₂ ⁰ -IR ^–+AC ^0,0-qf, where ₂ ⁰ -IR ^– is the restriction of ₂ ⁰ -IR without function parameters.I am grateful to an anonymous referee whose suggestions led to an improved discussion of our results     

BV periodic solutions of an evolution problem associated with continuous moving convex sets

This paper is concerned with BV periodic solutions for multivalued perturbations of an evolution equation governed by the sweeping process (or Moreau's process). The perturbed equation has the form –DuN _C (t)(u(t))+F(t,u(t)), whereC is a closed convex valued continuousT-periodic multifunction from [0,T] to ^d ,N ^C (t)(u(t)) is the normal cone ofC(t) atu(t),F: [0,T]× ^{d d} is a compact convex valued multifunction and Du is the differential measure of the periodic BV solutionu. Several existence results for this differential inclusion are stated under various assumptions on the perturbationF.     

A regularity result for critical points of conformally invariant functionals

Let be an open set inR ² andI be a conformally invariant functional defined onH ¹(,R ^d ). Letu be a critical point ofI. We show that, ifu is apriori assumed to be bounded, thenu is smooth in , up to (ifu _| is smooth). This is a partial (positive) answer to a conjecture of S. Hildebrandt [13]. As an application, we establish a regularity result for weak solutions to the equation of surfaces of prescribed mean curvature in a three-dimensional compact riemannian manifold.     

Free-field realization of theWKP(N) algebra

TheW _KP ^(N) algebra has been identified with the second Hamiltonian structure in theNth Hamiltonian pair of the KP hierarchy. In this Letter, by constructing the Miura map that decomposes the second Hamiltonian structure in theNth pair of the KP hierarchy, we show thatW _KP ^(N) can also be decomposed toN independent copies ofW _KP ⁽¹⁾ algebras, therefore its free-field realization can be worked out by constructing free fields for each copy ofW _KP ⁽¹⁾ . In this way, the free fields may consist ofN + 2n number of bosons, among them, 2n are in pairs, wheren is an arbitrary integer between 1 andN. We also express the currents ofW _KP ^(N) in terms of the currents ofN —n copies of U(1) andn copies of SL(2,R) _k algebras with levelk = 1. By reductions, we give similar results forW ^(N) andW ₃ ⁽²⁾ algebra.     

The influence of cyclodextrin complexation on proton transfer in piperidinomethyl-2-naphthol

Summary Piperidinomethyl-2-naphthol forms inclusion complexes with -cyclodextrin with an equilibrium constant of 265M ^–1 in aqueous solution. The proton transfer equilibrium between the neutral and the zwitterionic form is strongly influenced by the association.

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Der Einfluß der Komplexierung mit -Cyclodextrin auf das Protontransfer-Gleichgewicht in Piperidino-2-naphthol (Kurze Mitt.)

Zusammenfassung Piperidinomethyl-2-naphthol bildet Einschlußkomplexe mit -Cyclodextrin mit einer Gleichgewichtskonstante von 265M ^–1. Das Protontransfer-Gleichgewicht zwischen neutraler Form und zwitterionischer Struktur wird durch diese Assoziation stark beeinflußt.

     

Base-catalyzed cyclization of β-(2-arylaminoethoxy)styrenes

-(2-Arylaminoethoxy)styrenes undergo cyclization in the presence of KOH to giveN-aryl-2-benzyloxazolidines inca. 90 % yield. The structures of the products were confirmed by IR and NMR spectroscopy.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 340–341, February, 1994.