Search

During the years 1994-1997, the emulsion target of the CHORUS detector was exposed to the wide-band neutrino beam of the CERN SPS collecting about 10 6 neutrino interactions. A measurement of ?¯µ-induced charm production is performed by using the presence of a 5% ?¯µ component in the ?µ beam. The measurement takes advantage of the capability to observe the decay topology in the emulsion. The analysis is based on a sample of charged-current interactions with at least one identified muon. About 100000 were located in the emulsion target and fully reconstructed. By requiring a positive muon charge as determined by the CHORUS muon spectrometer, 32?¯µ-induced charm events were observed with an estimated background of 3.2 events. At an average antineutrino energy in the neutrino beam of 18 GeV, the charm production rate induced by antineutrinos is measured to be ?(?¯µN›µ+c¯X)/?(?¯µN›µ+X) =(5.0-0.9+1.4(stat)±0.7(syst))%. The ratio between neutral and charged charm production rates in this process is (2.6-1.0+1.7(stat)±0.8(syst)). The charm production rate as a function of the antineutrino energy is found to be in good agreement with previous results derived from di-lepton data. © 2004 Elsevier B.V. All rights reserved. Bundesministerium für Bildung und Forschung Promotion and Mutual Aid Corporation for Private Schools of Japan Grant Foundation: KRF-2003-005-C00014 Israel Science Foundation: 328/94 CERN Brussels Instituut voor Milieubeheer Instituto Nazionale di Fisica Nucleare Foundation for Fundamental Research on Matter Korean Foundation for Cancer Research We gratefully acknowledge the help and support of the neutrino-beam staff and of the numerous technical collaborators who contributed to the detector construction, operation, emulsion pouring, development, and scanning. The experiment was made possible by grants from the Institut Interuniversitaire des Sciences Nucléaires and the Interuniversitair Instituut voor Kernwetenschappen (Belgium); the Israel Science Foundation (Grant 328/94) and the Technion Vice President Fund for the Promotion of Research (Israel); CERN (Geneva, Switzerland); the German Bundesministerium für Bildung und Forschung (Germany); the Institute of Theoretical and Experimental Physics (Moscow, Russia); the Istituto Nazionale di Fisica Nucleare (Italy); the Promotion and Mutual Aid Corporation for Private Schools of Japan and Japan Society for the Promotion of Science (Japan); Korea Research Foundation Grant (KRF-2003-005-C00014) (Republic of Korea); the Foundation for Fundamental Research on Matter FOM and the National Scientific Research Organization NWO (The Netherlands); and the Scientific, and Technical Research Council of Turkey (Turkey). We gratefully acknowledge their support.

In this survey the classical results of Abel, Liouville, Galois, Picard, Vessiot, Kolchin, and others on the solvability and unsolvability of equations in explicit form are discussed. The one-dimensional topological version of Galois theory is presented in detail (this version describes topological obstructions to the representability of functions by quadratures).

We define a class of L-convex-concave subsets of $\Bbb{R}P^n$, where L is a projective subspace of dimension l in $\Bbb{R}P^n$. These are sets whose sections by any (l+1)-dimensional space L' containing L are convex and concavely depend on L'. We introduce an L-duality for these sets, and prove that the L-dual to an L-convex-concave set is an $L^*$-convex-concave subset of $(\Bbb RP^n)^*$. We discuss a version of Arnold hypothesis for these sets and prove that it is true (or wrong) for an L-convex-concave set and its L-dual simultaneously., Comment: 23pp

ContentsIntroduction §1. Newton polygons, the Pascal relation, and the Vieta relation §2. Newton polygons and Weil numbers §3. Parametrization of one-dimensional orbits on a torus surface §4. Curves on a torus surface §5. Polygons without interior integer-valued points §6. Polygon ΔD with an interior integer-valued point §7. Polygon ΔD without interior integer-valued points §8. Meromorphic vector functions on compact curves §9. Refinement of Weil's theorem §10. Abel's theorem and the Vieta relation §11. Singularities of the characteristic curve and Newton polygons Bibliography

We prove a version of the Aleksandrov-Fenchel inequality for mixed volumes of coconvex bodies. This version is motivated by an inequality from commutative algebra relating intersection multiplicities of ideals., Comment: 5 pages

In this paper we deal with branched coverings over the complement to finitely many exceptional points on the Riemann sphere having the property that the local monodromy around each of the branching points is of finite order. To such a covering we assign its \textit{signature}, i.e. the set of its exceptional and branching points together with the orders of local monodromy operators around the branching points. What can be said about the monodromy group of a branched covering if its signature is known? It seems at first that the answer is nothing or next to nothing. Indeed, generically it is so. However there is a (small) list of signatures of \textit{elliptic} and \textit{parabolic} types, for which the monodromy group can be described completely, or at least determined up to an abelian factor. This appendix is devoted to investigation of these signatures. For all these signatures (with one exception) the corresponding monodromy groups turn out to be solvable. Linear differential equations of Fuchs type related to these signatures are solvable in quadratures (in the case of elliptic signatures --- in algebraic functions). A well-known example of this type is provided by Euler differential equations, which can be reduced to linear differential equations with constant coefficients. The algebraic functions related to all (but one) of these signatures are expressible in radicals. A simple example of this kind is provided by the possibility to express the inverse of a Chebyshev polynomial in radicals. Another example of this kind is provided by functions related to division theorems for the argument of elliptic functions. Such functions play a central role in the work [1] of Ritt., To be submitted for publication in proceedings of 6th European Congress of Mathematics

The well-known Bernstein–Kushnirenko theorem from the theory of Newton polyhedra relates algebraic geometry and the theory of mixed volumes. Recently, the authors have found a far-reaching generalization of this theorem to generic systems of algebraic equations on any algebraic variety. In the present note we review these results and their applications to algebraic geometry and convex geometry.

The basic notions and constructions of the theory of integration over the Euler characteristic are introduced and explained. A few examples from the theory of convex polytopes show usefulness of this non-classical integration. The analog of the Radon transform with respect to the Euler characteristic is constructed and illustrated by a topological example

We associate convex bodies to a wide class of graded G-algebras where G is a connected reductive group. These convex bodies give information about the Hilbert function as well as multiplicities of irreducible representations appearing in the graded algebra. We extend the notion of Duistermaat-Heckman measure to graded G-algebras and prove a Fujita type approximation theorem and a Brunn-Minkowski inequality for this measure. This in particular applies to arbitrary G-line bundles giving an equivariant version of the theory of volumes of line bundles. We generalize the Brion-Kazarnowski formula for the degree of a spherical variety to arbitrary G-varieties. Our approach follows some of the previous works of A. Okounkov. We use the asymptotic theory of semigroups of integral points and Newton-Okounkov bodies developed in our ealier work arXiv:0904.3350, Comment: 23 pages. Revised in several places and made considerably shorter. Final version, to appear in Moscow Mathematical Journal volume in honor of V. I. Arnold

A subgroup H of a reductive group G is horospherical if it contains a maximal unipotent subgroup. We describe the Grothendieck semigroup of invariant subspaces of regular functions on G/H as a semigroup of convex polytopes. From this we obtain a formula for the number of solutions of a generic system of equations on G/H in terms of mixed volume of polytopes. This generalizes Bernstein-Kushnirenko theorem from toric geometry., Comment: 17 pages