Géométries Lorentziennes de dimension 3 : classification et complétude

We classify three-dimensional Lorentz homogeneous spaces G/I having a compact manifold locally modeled on them. We prove a completeness result: any compact locally homogeneous Lorentz threefold M is isometric to a quotient of a Lorentz homogeneous space G/I by a discrete subgroup Γ of G acting properly and freely on G/I. Moreover, if I is noncompact, G/I is isometric to a Lie group L endowed with a left invariant Lorentz metric, where L is isomorphic to one of the following Lie groups:

Hyperspectral Imaging in the Medical Field: Present and Future

Abstract

Hyperspectral imaging is an optical method that provides a large amount of information about the investigated object. Its medical applications are reviewed in this article, including tumor delimitation and identification, assessing tissue perfusion and its pathological conditions (including some complications like diabetic foot ulceration), making accurate surgical decisions, evaluating the health of dental structures, etc. Many of the articles show very promising results that required brief comments by the authors. It is clear that choosing the appropriate hyperspectral imaging system for each medical field, together with the most reliable hyperspectral image processing methods, are the main goals of future studies, before hyperspectral imaging becomes a widely applicable evaluation method in medicine. The authors try to answer some questions on this topic and set up some directions for future research.     

Integrable Scalar Cosmologies I. Foundations and links with String Theory

We build a number of integrable one-scalar spatially flat cosmologies, which play a natural role in inflationary scenarios, examine their behavior in several cases and draw from them some general lessons on this type of systems, whose potentials involve combinations of exponential functions, and on similar non-integrable ones. These include the impossibility for the scalar to emerge from the initial singularity descending along asymptotically exponential potentials with logarithmic slopes exceeding a critical value (“climbing phenomenon”) and the inevitable collapse in a Big Crunch whenever the scalar tries to settle at negative extrema of the potential. We also elaborate on the links between these types of potentials and “brane supersymmetry breaking”, a mechanism that ties together string scale and scale of supersymmetry breaking in a class of orientifold models.     

Approximation of periodic solutions for a dissipative hyperbolic equation

This paper studies the numerical approximation of periodic solutions for an exponentially stable linear hyperbolic equation in the presence of a periodic external force $f$ . These approximations are obtained by combining a fixed point algorithm with the Galerkin method. It is known that the energy of the usual discrete models does not decay uniformly with respect to the mesh size. Our aim is to analyze this phenomenon’s consequences on the convergence of the approximation method and its error estimates. We prove that, under appropriate regularity assumptions on $f$ , the approximation method is always convergent. However, our error estimates show that the convergence’s properties are improved if a numerically vanishing viscosity is added to the system. The same is true if the nonhomogeneous term $f$ is monochromatic. To illustrate our theoretical results we present several numerical simulations with finite element approximations of the wave equation in one or two dimensional domains and with different forcing terms.     

CR immersions and Lorentzian geometry

We study the geometry of the second fundamental form of pseudohermitian immersions among nondegenerate CR manifolds. In particular we study existence and uniqueness of pseudohermitian immersions $\phi : M \rightarrow S^{2n+3}$ of a strictly pseudoconvex CR manifold $M$ into an odd dimensional sphere, as determined by the pseudohermitian Gauss and Weingarten equations.     

The Transition Towards Immortality: Non-linear Autocatalytic Growth of Citations to Scientific Papers

We discuss microscopic mechanisms of complex network growth, with the special emphasis of how these mechanisms can be evaluated from the measurements on real networks. As an example we consider the network of citations to scientific papers. Contrary to common belief that its growth is determined by the linear preferential attachment, our microscopic measurements show that it is driven by the nonlinear autocatalytic growth. This invalidates the scale-free hypothesis for the citation network. The nonlinearity is responsible for a dramatic dynamical phase transition: while the citation lifetime of majority of papers is 6–10 years, the highly-cited papers have practically infinite lifetime.     

Search for a mixed quark-hadron phase of QCD matter at the JINR nuclotron

Physics aspects of a JINR project to reach the planned 5 A GeV energy for the Au and U beams and to increase the bombarding energy up to 10 AGeV are discussed. The project aims to search for a possible formation of a strongly interacting mixed quark-hadron phase. The relevant problems are exemplified. The need for scanning heavy-ion interactions in bombarding energy, collision centrality, and isospin asymmetry is emphasized. The text was submitted by the authors in English.     

A Possibilistic Approach of the Max-Product Bernstein Kind Operators

By analogy with the probabilistic approach of the classical Bernstein polynomials, in this paper firstly we give the proof for the uniform convergence of the nonlinear max-product Bernstein operator by using the theory of possibility. This new approach, which interprets the max-product Bernstein operator as a possibilistic expectation of a particular fuzzy variable having a possibilistic Bernoulli distribution, does not only offer a good justification for the max-product Bernstein operator, but also allows to extend the method to other discrete max-product Bernstein type operators.     

Catalytic and Atom‐Economic C −C Bond Formation: Alkyl Tantalum Ureates for Hydroaminoalkylation

Atom‐economic and regioselective C ?C bond formation has been achieved by rapid C?H alkylation of unprotected secondary arylamines with unactivated alkenes. The combination of Ta(CH₂SiMe₃)₃Cl₂, and a ureate N,O‐chelating‐ligand salt gives catalytic systems prepared in situ that can realize high yields of β‐alkylated aniline derivatives from either terminal or internal alkene substrates. These new catalyst systems realize C?H alkylation in as little as one hour and for the first time a 1:1 stoichiometry of alkene and amine substrates results in high yielding syntheses of isolated amine products by simple filtration and concentration.     

Solvation of phenylglycine- and leucine-derived chiral stationary phases: molecular dynamics simulation study

A theoretical study of the solvation of ( R)- N-(3,5-dinitrobenzoyl)phenylglycine- and ( R)- N-(3,5-dinitrobenzoyl)leucine-derived chiral stationary phases (CSPs) is presented. Semiflexible models of the chiral selectors are prepared from B3LYP/6-311G** calculations, and these are used in the molecular dynamics simulations of the corresponding interface. The chiral interface is examined for four solvents: 100% hexane, 90:10 hexane:2-propanol, 80:20 hexane:2-propanol, and 100% 2-propanol. Despite the similarities between phenylglycine and leucine, the interfaces are distinct both in terms of the selector orientations at the surface and in the number of hydrogen bonds formed with 2-propanol. We also find that an increase in alcohol concentration alters the preferred orientations of the selectors.