Search results for " Geometry"

On the arithmetic and geometry of binary Hamiltonian forms

2011

Given an indefinite binary quaternionic Hermitian form $f$ with coefficients in a maximal order of a definite quaternion algebra over $\mathbb Q$, we give a precise asymptotic equivalent to the number of nonequivalent representations, satisfying some congruence properties, of the rational integers with absolute value at most $s$ by $f$, as $s$ tends to $+\infty$. We compute the volumes of hyperbolic 5-manifolds constructed by quaternions using Eisenstein series. In the Appendix, V. Emery computes these volumes using Prasad's general formula. We use hyperbolic geometry in dimension 5 to describe the reduction theory of both definite and indefinite binary quaternionic Hermitian forms.

Dynamic Magnetic and Optical Insight into a High Performance Pentagonal Bipyramidal Dy(III) Single-Ion Magnet

2017

The pentagonal bipyramidal single-ion magnets (SIMs) are among the most attractive prototypes of high-performance single-molecule magnets (SMMs). Here, a fluorescence-active phosphine oxide ligand CyPh2PO (=cyclohexyl(diphenyl)phosphine oxide) was introduced into [Dy(CyPh2PO)2(H2O)5]Br3⋅2 (CyPh2PO)⋅EtOH⋅3 H2O, and combined dynamic magnetic measurement, optical characterization, ab initio calculation, and magneto-optical correlation of this high-performance pseudo-D5h DyIII SIM with large Ueff (508(2) K) and high magnetic hysteresis temperature (19 K) were performed. This work provides a deeper insight into the rational design of promising molecular magnets.

Abel transforms with low regularity with applications to X-ray tomography on spherically symmetric manifolds

2017

We study ray transforms on spherically symmetric manifolds with a piecewise $C^{1,1}$ metric. Assuming the Herglotz condition, the X-ray transform is injective on the space of $L^2$ functions on such manifolds. We also prove injectivity results for broken ray transforms (with and without periodicity) on such manifolds with a $C^{1,1}$ metric. To make these problems tractable in low regularity, we introduce and study a class of generalized Abel transforms and study their properties. This low regularity setting is relevant for geophysical applications.

An Arakelov inequality in characteristic p and upper bound of p-rank zero locus

2008

In this paper we show an Arakelov inequality for semi-stable families of algebraic curves of genus $g\geq 1$ over characteristic $p$ with nontrivial Kodaira-Spencer maps. We apply this inequality to obtain an upper bound of the number of algebraic curves of $p-$rank zero in a semi-stable family over characteristic $p$ with nontrivial Kodaira-Spencer map in terms of the genus of a general closed fiber, the genus of the base curve and the number of singular fibres. An extension of the above results to smooth families of Abelian varieties over $k$ with $W_2$-lifting assumption is also included.

Smooth structures on algebraic surfaces with cyclic fundamental group

1988

Automorphisms of hyperelliptic GAG-codes

2009

Abstract We determine the n –automorphism group of generalized algebraic-geometry codes associated with rational, elliptic and hyperelliptic function fields. Such group is, up to isomorphism, a subgroup of the automorphism group of the underlying function field.

Non-archimedean hyperbolicity and applications

2018

Inspired by the work of Cherry, we introduce and study a new notion of Brody hyperbolicity for rigid analytic varieties over a non-archimedean field $K$ of characteristic zero. We use this notion of hyperbolicity to show the following algebraic statement: if a projective variety admits a non-constant morphism from an abelian variety, then so does any specialization of it. As an application of this result, we show that the moduli space of abelian varieties is $K$-analytically Brody hyperbolic in equal characteristic zero. These two results are predicted by the Green-Griffiths-Lang conjecture on hyperbolic varieties and its natural analogues for non-archimedean hyperbolicity. Finally, we use …

Picard and the Italian Mathematicians: The History of Three Prix Bordin

2016

It is usually said that in the transition period between 19th and 20th centuries, French scholars (mainly Picard and Humbert) as well as Italian scholars (mainly Castelnuovo, Enriques and Severi) were interested in the study of algebraic surfaces, though using different methods.

Radiation from multi-GeV electrons and positrons in periodically bent silicon crystal

2014

A periodically bent Si crystal is shown to efficiently serve for producing highly monochromatic radiation in a gamma-ray energy spectral range. A short-period small-amplitude bending yields narrow undulator-type spectral peaks in radiation from multi-GeV electrons and positrons channeling through the crystal. Benchmark theoretical results on the undulator are obtained by simulations of the channeling with a full atomistic approach to the projectile-crystal interactions over the macroscopic propagation distances. The simulations are facilitated by employing the MBN Explorer package for molecular dynamics calculations on the meso-, bio- and nano-scales. The radiation from the ultra-relativist…

Inter-joint coordination of posture on a seesaw device

2016

Even though specific adjustments of the multi-joint control of posture have been observed when posture is challenged, multi-joint coordination on a seesaw device has never been accurately assessed. The current study was conducted in order to investigate the multi-joint coordination when subjects were standing on either a seesaw device or on a stable surface, with the eyes open or closed. Eighteen healthy active subjects were recruited. A principal component analysis and a Self-Organizing Maps analysis were performed on the joint angles in order to detect and characterize dominant coordination patterns. Intermuscular EMG coherence was analysed in order to assess the neurophysiological mechan…