Search results for "group"

6-Methyluracil: a redetermination of polymorph (II)

2019

6-Methyluracil, C5H6N2O2, exists in two crystalline phases: form (I), monoclinic, space group P21/c [Reck et al. (1988). Acta Cryst. A44, 417–421] and form (II), monoclinic, space group C2/c [Leonidov et al. (1993). Russ. J. Phys. Chem. 67, 2220–2223]. The structure of polymorph (II) has been redetermined providing a significant increase in the precision of the derived geometric parameters. In the crystal, molecules form ribbons approximately running parallel to the c-axis direction through N—H...O hydrogen bonds. The radical differences observed between the crystal packing of the two polymorphs may be responsible in form (II) for an increase in the contribution of the polar canonical forms…

A novel approach to nonlinear variable-order fractional viscoelasticity.

2020

This paper addresses nonlinear viscoelastic behaviour of fractional systems with variable time-dependent fractional order. In this case, the main challenge is that the Boltzmann linear superposition principle, i.e. the theoretical basis on which linear viscoelastic fractional operators are formulated, does not apply in standard form because the fractional order is not constant with time. Moving from this consideration, the paper proposes a novel approach where the system response is derived by a consistent application of the Boltzmann principle to an equivalent system, built at every time instant based on the fractional order at that instant and the response at all the previous ones. The ap…

Abelian Integrals: From the Tangential 16th Hilbert Problem to the Spherical Pendulum

2016

In this chapter we deal with abelian integrals. They play a key role in the infinitesimal version of the 16th Hilbert problem. Recall that 16th Hilbert problem and its ramifications is one of the principal research subject of Christiane Rousseau and of the first author. We recall briefly the definition and explain the role of abelian integrals in 16th Hilbert problem. We also give a simple well-known proof of a property of abelian integrals. The reason for presenting it here is that it serves as a model for more complicated and more original treatment of abelian integrals in the study of Hamiltonian monodromy of fully integrable systems, which is the main subject of this chapter. We treat i…

Regularity of a Degenerated Convolution Semi-Group Without to Use the Poisson Process

2011

We translate in semi-group theory our regularity result for a degenerated convolution semi-group got by the Malliavin Calculus of Bismut type for Poisson processes.

Polaroid-Type Operators

2018

In this chapter we introduce the classes of polaroid-type operators, i.e., those operators T ∈ L(X) for which the isolated points of the spectrum σ(T) are poles of the resolvent, or the isolated points of the approximate point spectrum σap(T) are left poles of the resolvent. We also consider the class of all hereditarily polaroid operators, i.e., those operators T ∈ L(X) for which all the restrictions to closed invariant subspaces are polaroid. The class of polaroid operators, as well as the class of hereditarily polaroid operators, is very large. We shall see that every generalized scalar operator is hereditarily polaroid, and this implies that many classes of operators acting on Hilbert s…

Applications in Mathematical Physics

2009

It turns out that pip-space methods have many applications in physics, although they are seldom mentioned as such. To draw on a literary analogy, like Moliere’s Monsieur Jourdain speaking in prose without knowing so, many authors have been using pip-space language without realizing it. In particular, chains or lattices of Hilbert spaces are quite common in many fields of mathematical physics. Some of these applications will be discussed at length in this chapter. To mention a few examples: quantum mechanics, in particular singular interactions (Section 7.1.3), scattering theory (Section 7.2), quantum field theory (Section 7.3), representations of Lie groups (Section 7.4), etc.

Multiparametric Rational Solutions of Order N to the KPI Equation and the Explicit Case of Order 3

2021

We present multiparametric rational solutions to the Kadomtsev-Petviashvili equation (KPI). These solutions of order N depend on 2N − 2 real parameters. Explicit expressions of the solutions at order 3 are given. They can be expressed as a quotient of a polynomial of degree 2N(N +1)−2 in x, y and t by a polynomial of degree 2N(N +1) in x, y and t, depending on 2N − 2 real parameters. We study the patterns of their modulus in the (x,y) plane for different values of time t and parameters.

Central units, class sums and characters of the symmetric group

2010

CCDC 846271: Experimental Crystal Structure Determination

2012

Related Article: G.Callebaut, S.Mangelinckx, L.Kiss, R.Sillanpaa, F.Fulop, N.De Kimpe|2012|Org.Biomol.Chem.|10|2326|doi:10.1039/c2ob06637h

Les groupes nominaux sans déterminant

2021

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