Search results for "group theory"

Finite index subgroups of mapping class groups

2011

Let g ≥ 3 and n ≥ 0, and let Mg,n be the mapping class group of a surface of genus g with n boundary components. We prove that Mg,n contains a unique subgroup of index 2g−1(2g − 1) up to conjugation, a unique subgroup of index 2g−1(2g + 1) up to conjugation, and the other proper subgroups ofMg,n are of index greater than 2g−1(2g+1). In particular, the minimum index for a proper subgroup of Mg,n is 2g−1(2g − 1). AMS Subject Classification. Primary: 57M99. Secondary: 20G40, 20E28. 0 Introduction and statement of results The interaction between mapping class groups and finite groups has long been a topic of interest. The famous Hurwitz bound of 1893 showed that the mapping class group of a clo…

Optimality results in orbit transfer

2007

Abstract The objective of this Note is to present optimality results in orbital transfer. Averaging of the energy minimization problem is considered, and properties of the associated Riemannian metric are discussed. To cite this article: B. Bonnard, J.-B. Caillau, C. R. Acad. Sci. Paris, Ser. I 345 (2007).

Non subanalyticity of sub-Riemannian Martinet spheres

2001

Abstract Consider the sub-Riemannian Martinet structure (M,Δ,g) where M= R 3 , Δ= Ker ( d z− y 2 2 d x) and g is the general gradated metric of order 0 : g=(1+αy) 2 d x 2 +(1+βx+γy) 2 d y 2 . We prove that if α≠0 then the sub-Riemannian spheres S(0,r) with small radii are not subanalytic.

Computation of conjugate times in smooth optimal control: the COTCOT algorithm

2006

Conjugate point type second order optimality conditions for extremals associated to smooth Hamiltonians are evaluated by means of a new algorithm. Two kinds of standard control problems fit in this setting: the so-called regular ones, and the minimum time singular single-input affine systems. Conjugate point theory is recalled in these two cases, and two applications are presented: the minimum time control of the Kepler and Euler equations.

Symmetry-adapted tensorial formalism to model rovibrational and rovibronic spectra of molecules pertaining to various point groups

2004

International audience; We present a short review on the tensorial formalism developed by the Dijon group to solve molecular spectroscopy problems. This approach, originally devoted to the rovibrational spectroscopy of highly symmetrical species (spherical tops) has been recently extended in several directions: quasi-spherical tops, some symmetric and asymmetric tops, and rovibronic spectroscopy of spherical tops in a degenerate electronic state. Despite its apparent complexity (heavy notations, quite complex mathematical tools), these group theoretical tensorial methods have a great advantage of flexibility: a systematic expansion of effective terms for any rovib- rational/rovibronic probl…

Tensorial development of the rovibronic Hamiltonian and transition moment operators for octahedral molecules

2001

Abstract We present a development of the Hamiltonian, dipole moment and polarizability operators of octahedral XY 6 molecules in a degenerate electronic state. These rovibronic operators are written with the aid of a tensorial formalism derived from the one already used in Dijon in the case of molecules in a non-degenerate electronic state. Electronic operators are defined from the group theory properties. Transition moment operators are introduced in order to consider rovibronic transitions. Spectrum simulations are made thanks to a new version of the HTDS sofware [J. Quant. Spectrosc. Radiat. Transfer 66 (2000) 16] used for the calculation of rovibrational spectra.

The mKdV equation and multi-parameters rational solutions

2021

Abstract N -order solutions to the modified Korteweg–de Vries (mKdV) equation are given in terms of a quotient of two wronskians of order N depending on 2 N real parameters. When one of these parameters goes to 0, we succeed to get for each positive integer N , rational solutions as a quotient of polynomials in x and t depending on 2 N real parameters. We construct explicit expressions of these rational solutions for orders N = 1 until N = 6 .

On the tensor degree of finite groups

2013

We study the number of elements $x$ and $y$ of a finite group $G$ such that $x \otimes y= 1_{_{G \otimes G}}$ in the nonabelian tensor square $G \otimes G$ of $G$. This number, divided by $|G|^2$, is called the tensor degree of $G$ and has connection with the exterior degree, introduced few years ago in [P. Niroomand and R. Rezaei, On the exterior degree of finite groups, Comm. Algebra 39 (2011), 335--343]. The analysis of upper and lower bounds of the tensor degree allows us to find interesting structural restrictions for the whole group.

Normal, Abby Normal, Prefix Normal

2014

A prefix normal word is a binary word with the property that no substring has more 1s than the prefix of the same length. This class of words is important in the context of binary jumbled pattern matching. In this paper we present results about the number \(\textit{pnw}(n)\) of prefix normal words of length n, showing that \(\textit{pnw}(n) =\Omega\left(2^{n - c\sqrt{n\ln n}}\right)\) for some c and \(\textit{pnw}(n) = O \left(\frac{2^n (\ln n)^2}{n}\right)\). We introduce efficient algorithms for testing the prefix normal property and a “mechanical algorithm” for computing prefix normal forms. We also include games which can be played with prefix normal words. In these games Alice wishes t…

1992

The molecular packing and spatial correlations of polymers [CH 2 CR(COOR')] n (R= H, Me; R'= (CH 2 ) 11 + NMe 2 (CH 2 ) 3 SO 3 - ; (CH 2 ) 2 + N(Me)[(CH 2 ) 3 SO 3 - ][C 10 H 21 ]) are studied by means of X-ray analysis and conformational calculations. The analysis of the correlation functions and density distribution profiles suggest a double-layered molecular packing which is discussed for the three polymers investigated, with respect to their different chemical structures. Whereas the zwitterionic polymethacrylates studied exhibit liquid-like short-range order, the polyacrylate analog exhibits an ordered double-layered superstructure