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.     

Inégalités de Gagliardo-Nirenberg pour les semi-groupes d'opérateurs et applications

One shows the equivalence between an abstract form of a Gagliardo-Nirenberg inequality and an estimate of the decay of the L ¹–L norm of a semigroup of operators. This equivalence, contrary to the one with the classical Sobolev inequalities, allows the treatment of situations where the decay is exponential. Related results and applications are given.

Cet article a pu être terminé pendant un séjour de l'auteur à l'université d'Edimbourg.     

Reactivity of pyrrole pigments. Part 9 MINDO/3 calculations on dipyrrolic partial models of bile pigments

The applicability of the MINDO/3 method is evaluated for calculations on dipyrrolic partial structures of bile pigments. It is shown that this method cannot be used for an accurate conformational analysis. However, when applying the frontier orbital model for reactivity parameters, a good picture of the HOMO and the LUMO distribution can be obtained in this type of molecules.

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Reaktivität von Pyrrolpigmenten, 9. Mitt. MINDO/3-Rechnungen von dipyrrolischen Partialmodellen von Gallenpigmenten

Zusammenfassung Es werden die Einsatzmöglichkeiten von MINDO/3 für den Fall dipyrrolischer Partialstrukturen der Gallenpigmente aufgezeigt. Die Methode ist für eine genaue Konformationsanalyse nicht geeignet. Unter Verwendung der Reaktionsparameter des Frontier-Orbital-Modells läßt sich jedoch ein gutes Bild der HOMO- und LUMO-Verteilung für diesen Verbindungstyp gewinnen.

     

Root determination by use of Padé approximants

In this paper we describe a new technique for generating iteration formulas — of arbitrary order — for determining a zero (assumed simple) of a functionf, assumed analytic in a region containing the zero. The 1/p Padé Approximant (p22w832w32067v3/xxlarge8807.gif" alt="gE" align="MIDDLE" BORDER="0">0) to the functiong(t)22w832w32067v3/xxlarge8801.gif" alt="equiv" align="MIDDLE" BORDER="0">f(z) is formed wherez=w+t, using the Taylor series forf at the pointw, an approxination to the zero off. The value oft for which the 1/p Padé Approximant vanishes provides the basis of iteration formulas of orderp+2.Some known iteration formulas, e.g., Newton-Raphson's, Halley's and Kiss's of order of convergence two, three and four, are directly obtained by settingp=0,1 and 2, respectively.     

Moduli spaces of arrangements of 10 projective lines with quadruple points

We classify moduli spaces of arrangements of 10 lines with quadruple points. We show that moduli spaces of arrangements of 10 lines with quadruple points may consist of more than 2 disconnected components, namely 3 or 4 distinct points. We also present defining equations to those arrangements whose moduli spaces are still reducible after taking quotients of complex conjugations.     

Radon–Nikodým indexes and measures of weak noncompactness

The aim of this paper is to present a quantitative version of the Radon–Nikodým property and some other results related to it. This approach gives an extra insight to the classical results. We introduce two indexes: an index of representability of measures and an index of dentability. We review classic results in order to obtain relationships between these and other indexes.     

PRME AND k-PRIME IDEALS IN Ω-GROUPS

Abstract

In this paper we define two concepts of prime ideals for Ω-groups. The first generalizes the definitions of prime ideal in rings, nearrings, Γ-rings, associative algebras and Lie algebras. The second generalizes a concept defined for groups by ??ukin ([21]). We show that both lead to radicals in the sense of Hoehnke ([10]). Furthermore in the case of rings, Γ-rings, abelian zero-symmetric nearrings and cubic rings these two definitions coincide, thus obtaining a new characterization for the prime ideal. Zero-symmetric Ω-groups are defined analogously to the nearring case and a new characterization in term of ideals is given.     

Rational wavelets on the real line

In this note a representation of the discrete Green's function of a compact discretization of a two point boundary value problem of order n 2 is given which among other things allows a direct proff of the convergence (and divergence) properties.     

Automorphisms of Hilbert schemes of points on a generic projective K3 surface

We study automorphisms of the Hilbert scheme of n points on a generic projective K3 surface S, for any . We show that is either trivial or generated by a non‐symplectic involution and we determine numerical and divisorial conditions which allow us to distinguish between the two cases. As an application of these results we prove that, for any , there exist infinitely many admissible degrees for the polarization of the K3 surface S such that 22732715-aa51-426e-828e-e6b98070bb4d/mana201800557-math-0004.png"> admits a non‐natural involution. This provides a generalization of the results of [7] for .     

Carlsson's rank conjecture and a conjecture on square-zero upper triangular matrices

Let k be an algebraically closed field and A the polynomial algebra in r variables with coefficients in k. In case the characteristic of k is 2, Carlsson [9] conjectured that for any DG-A-module M of dimension N as a free A-module, if the homology of M is nontrivial and finite dimensional as a k-vector space, then $2^r\le N$. Here we state a stronger conjecture about varieties of square-zero upper triangular $N\times N$ matrices with entries in A. Using stratifications of these varieties via Borel orbits, we show that the stronger conjecture holds when $N<8$ or $r<3$ without any restriction on the characteristic of k. As a consequence, we obtain a new proof for many of the known cases of Carlsson's conjecture and give new results when $N>4$ and $r=2$.