1-Substituted morpholino ethenes—III: Carbocyclic and aliphatic heterocyclic compounds from 5-membered ring derivatives

[4+2] Cycloaddition reaction of 1-(cyclopenten-1-y1)-1-morpholino ethene with β-nitrostyrene leads to tetrahydroindan and tetrahydroindanone derivatives. A [4+2] adduct of interest is also obtained in the reaction of the same substrate with mesyl chloride. Reactivity of the same electrophiles with the morpholino enamine of cyclopentyl-methyl ketone is also examined. Some stereochemical aspects of the above mentioned reactions are discussed.     

Sur la stabilité du fibré de PicardOn the stability of the Picard bundle

We study the stability of the Picard bundle on the moduli space of stable vector bundles of fixed rank and determinant, over an irreducible, smooth, algebraic curve of genus g?2. To cite this article: V. Savin, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 885–888.     

ExperimentalJ/ψ hadronic production from 150 to 280 GeV/c

A detailed study ofJ/ψ hadronic production has been performed in a high statistics experiment (more than 1.5 10⁶ J/ψ observed in their dimuon decay mode). Data have been taken with incident π^±,K ^±,p ^±, on hydrogen and platinum targets, at 150, 200 and 280 GeV/c. We find from the observed nuclear dependance of the cross sections, that about 18% of theJ/ψ are produced diffractively. Using known structure functions of the quarks in the nucleon and in the pion, we derive estimations for the gluon structure functions.     

On Smooth Mesoscopic Linear Statistics of the Eigenvalues of Random Permutation Matrices

Journal of Theoretical Probability - We study the limiting behavior of smooth linear statistics of the spectrum of random permutation matrices in the mesoscopic regime, when the permutation follows...     

Multi-instanton check of the relation between the prepotential F and the modulus u in N = 2 SUSY Yang-Mills theory

By examining multi-instantons in N = 2 supersymmetric SU(2) gauge theory, we derive, on very general grounds, and to all orders in the instanton number, a relationship between the prepotential

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(Φ), and the coordinate on the quantum moduli space u = TrΦ². This relation was previously obtained by Matone in the context of the explicit Seiberg-Witten low-energy solution of the model. Our findings can be viewed as a multi-instanton check of the proposed exact results in supersymmetric gauge theory.     

En Route to Stimuli‐Responsive Boron‐, Nitrogen‐, and Sulfur‐Doped Polycyclic Aromatic Hydrocarbons

Replacing both meso carbon atoms of the polycyclic aromatic hydrocarbon (PAH) bisanthene by boron atoms creates an efficient blue fluorophore with a strong electron‐accepting character. The corresponding meso‐B,S‐doped bisanthene exhibits a solvent‐dependent green‐to‐orange photoluminescence and undergoes a reversible reduction at E =?2.06 V (vs. FcH/FcH⁺). After oxidation of the sulfur atom, the resulting sulfoxide emits in the blue range of the spectrum, shows only negligible solvatochromism, and a reversible redox transition at E =?1.74 V. Several related B, N‐ and B, S‐containing PAHs have been prepared following the same modular synthetic procedure and are also described herein. In order to systematically compare their optoelectronic properties, all products have been investigated by cyclic voltammetry as well as UV/Vis absorption/emission spectroscopy.     

Subconvexity for sup-norms of cusp forms on $$\mathrm{PGL}(n)$$

Let F be an \(L^2\)-normalized Hecke Maaß cusp form for \(\Gamma _0(N) \subseteq {\mathrm{SL}}_{n}({\mathbb {Z}})\) with Laplace eigenvalue \(\lambda _F\). If \(\Omega \) is a compact subset of \(\Gamma _0(N)\backslash {\mathrm{PGL}}_n/\mathrm{PO}_{n}\), we show the bound \(\Vert F|_{\Omega }\Vert _{\infty } \ll _{ \Omega } N^{\varepsilon } \lambda _F^{n(n-1)/8 - \delta }\) for some constant \(\delta = \delta _n> 0\) depending only on n.     

Duality Between Spin Networks and the 2D Ising Model

The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a fermionic and a bosonic Gaussian integral formulation for each of these functions and we show that they are the inverse of each other (up to some explicit constants) by exhibiting a supersymmetry relating the two formulations. We investigate three aspects and applications of this duality. First, we propose higher order supersymmetric theories that couple the geometry of the spin networks to the Ising model and for which supersymmetric localization still holds. Secondly, after interpreting the generating function of spin network evaluations as the projection of a coherent state of loop quantum gravity onto the flat connection state, we find the probability distribution induced by that coherent state on the edge spins and study its stationary phase approximation. It is found that the stationary points correspond to the critical values of the couplings of the 2D Ising model, at least for isoradial graphs. Third, we analyze the mapping of the correlations of the Ising model to spin network observables, and describe the phase transition on those observables on the hexagonal lattice. This opens the door to many new possibilities, especially for the study of the coarse-graining and continuum limit of spin networks in the context of quantum gravity.