NMR elucidation of novel SQ109 derivatives

The NMR elucidation of five novel SQ109 analogues including SQ109 is reported herein. These derivatives were synthesized as potential anti-tuberculosis candidates. One-dimensional NMR (¹H and ¹³C) techniques show a series of overlapping signals from the methine and methylene groups of these compounds, thereby making it extremely difficult to assign all NMR signals. Two-dimensional (2D) NMR techniques were instrumental in overcoming these challenges. This paper appears to be a rare report on the complete structure elucidation of mono-substituted adamantane moieties.     

Synthesis and NMR assignment of pentacycloundecane precursors of potential pharmaceutical agents

The synthesis and complete NMR elucidation of eight novel pentacycloundecane (PCU) derivatives are reported. These compounds are precursors in the synthesis of PCU‐based anti‐tuberculosis (TB) agents and potential human immunodeficiency virus (HIV) protease inhibitors. Two‐dimensional (2D) NMR techniques were used to assign the NMR spectra for these compounds. Substitution of the cage molecule at (C‐8/11) further complicates the assignment, since some of the substituted alkyl chain groups overlap with the cage proton signals. The side chain heteroatoms also introduce a rare through‐space deshielding effect to some of the carbon atoms of the cage skeleton. Ring strain in the rigid cage skeleton appears to induce drastic electronic changes in some parts of the cage framework. This observation is more dramatic for the C‐4 methylene group of the cage diols and the cage ethers. Copyright © 2010 John Wiley & Sons, Ltd.     

Half-regular and regular points in compact polygons

We investigate the derived structures of compact polygons at half-regular and at regular points. This enables us to give a geometric characterization of the real or complex split Cayley hexagon.     

Schrödinger equation with delta potential in superspace

A superspace version of the Schrödinger equation with a delta potential is studied using Fourier analysis. An explicit expression for the energy of the single bound state is found as a function of the super-dimension M in case M is smaller than or equal to 1. In the case when there is one commuting and 2n anti-commuting variables also the wave function is given explicitly.     

On the nonexistence of certain Hughes generalized quadrangles

In this paper, we prove that the Hermitian quadrangle is the unique generalized quadrangle Γ of order (q ², q ³) containing some subquadrangle of order (q ², q) isomorphic to such that every central elation of the subquadrangle is induced by a collineation of Γ. Dedicated to Dan Hughes on the occasion of his 80th birthday.     

Ultraviolet Absorption Induces Hydrogen‐Atom Transfer in G⋅C Watson–Crick DNA Base Pairs in Solution

Ultrafast deactivation pathways bestow photostability on nucleobases and hence preserve the structural integrity of DNA following absorption of ultraviolet (UV) radiation. One controversial recovery mechanism proposed to account for this photostability involves electron‐driven proton transfer (EDPT) in Watson–Crick base pairs. The first direct observation is reported of the EDPT process after UV excitation of individual guanine–cytosine (G?C) Watson–Crick base pairs by ultrafast time‐resolved UV/visible and mid‐infrared spectroscopy. The formation of an intermediate biradical species (G[?H]?C[+H]) with a lifetime of 2.9 ps was tracked. The majority of these biradicals return to the original G?C Watson–Crick pairs, but up to 10 % of the initially excited molecules instead form a stable photoproduct G*?C* that has undergone double hydrogen‐atom transfer. The observation of these sequential EDPT mechanisms across intermolecular hydrogen bonds confirms an important and long debated pathway for the deactivation of photoexcited base pairs, with possible implications for the UV photochemistry of DNA.     

A new construction of the Clifford-Fourier kernel

In this paper, we develop a new method based on the Laplace transform to study the Clifford-Fourier transform. First, the kernel of the Clifford-Fourier transform in the Laplace domain is obtained. When the dimension is even, the inverse Laplace transform may be computed and we obtain the explicit expression for the kernel as a finite sum of Bessel functions. We equally obtain the plane wave decomposition and find new integral representations for the kernel in all dimensions. Finally we define and compute the formal generating function for the even dimensional kernels.     

Convergence of the Two‐Dimensional Dynamic Ising‐Kac Model to

The Ising‐Kac model is a variant of the ferromagnetic Ising model in which each spin variable interacts with all spins in a neighborhood of radius γ ^{? 1} for around its base point. We study the Glauber dynamics for this model on a discrete two‐dimensional torus for a system size and for an inverse temperature close to the critical value of the mean field model. We show that the suitably rescaled coarse‐grained spin field converges in distribution to the solution of a nonlinear stochastic partial differential equation. This equation is the dynamic version of the quantum field theory, which is formally given by a reaction‐diffusion equation driven by an additive space‐time white noise. It is well‐known that in two spatial dimensions such equations are distribution valued and a Wick renormalization has to be performed in order to define the nonlinear term. Formally, this renormalization corresponds to adding an infinite mass term to the equation. We show that this need for renormalization for the limiting equation is reflected in the discrete system by a shift of the critical temperature away from its mean field value.© 2016 by the authors. Communications on Pure and Applied Mathematics is published by Wiley Periodicals, Inc., on behalf of the Courant Institute of Mathematics.