The Steady-State ALTADENA RASER Generates Continuous NMR Signals**

A RASER (Radio Amplification by Stimulated Emission of Radiation) facilitates the study of nonlinear phenomena, as well as the determination of NMR parameters with high precision. To achieve maximum sensitivity in the desired operating mode, it is crucial to control the RASER over long periods of time. So far, this was only possible at ultra-low magnetic fields. Here, we introduce a way to control the operating regime of a RASER at a magnetic field of 1.45 T. We employ a continuous-flow RASER, pumped by PHIP (ParaHydrogen Induced Polarization). The hydrogenation of vinyl acetate (VA) with parahydrogen provides the required negative polarization on the methyl group of the product ethyl acetate (EA). The protons within the methyl group, separated by a 7 Hz J-coupling, are RASER active. This system demonstrates five RASER phenomena: inequivalent and equivalent amplitudes in the “normal NMR mode”, period doublings, frequency combs, and chaos. The experiments match with simulations based on a theoretical model of two nonlinear-coupled RASER modes. We predict the RASER regime at set conditions and visualize the prediction in a bifurcation diagram.     

Computational (DFT) and Experimental (NMR) Study of the Chelation of an Iridium Hyperpolarization Transfer Catalyst by Amino Acids

Non-hydrogenative Para-Hydrogen Induced Hyperpolarization (nhPHIP) is a Nuclear Magnetic Resonance (NMR) hyperpolarization technique which has experimentally been used to analyze complex biological samples containing amino acids using the Ir-IMes hyperpolarization transfer catalyst. A computational study based on Density Function Theory (DFT) was performed on all relevant stereoisomers of [Ir(H)₂(IMes)(AA)(Py)] (with AA=glycine, alanine, valine; Py=pyridine), for which R/S chirality and orientation of the amino acid chelation (C/A) were considered. A total of 30 structures were calculated comprising of 6 stereoisomers for achiral glycine, and 12 stereoisomers for each of the chiral amino acids. The abundances derived from the DFT energies confirmed the trends observed in thermal (non-hyperpolarized) NMR experiments. Additionally, theoretical calculations of electronic (Wiberg bond indices, Natural Bond Orders, Frontier Orbital Analysis), bond dissociation energies, transition states, and activation energies related to interconversion between binding modes, and steric factors (Solid angle) were performed to provide detailed explanations for NMR experimental observations.     

Flat cyclotomic polynomials of order three

We say that a cyclotomic polynomial Φn has order three if n is the product of three distinct primes, p<q<r. Let A(n) be the largest absolute value of a coefficient of Φn. For each pair of primes p<q, we give an infinite family of r such that A(pqr)=1. We also prove that A(pqr)=A(pqs) whenever s>q is a prime congruent to .     

On a problem of K. Mahler: Diophantine approximation and Cantor sets

Let K denote the middle third Cantor set and . Given a real, positive function ψ let denote the set of real numbers x in the unit interval for which there exist infinitely many such that |x − p/q| < ψ(q). The analogue of the Hausdorff measure version of the Duffin–Schaeffer conjecture is established for . One of the consequences of this is that there exist very well approximable numbers, other than Liouville numbers, in K—an assertion attributed to K. Mahler. Explicit examples of irrational numbers satisfying Mahler’s assertion are also given. Dedicated to Maurice Dodson on his retirement—finally!     

On embeddability and stresses of graphs

Gluck has proven that triangulated 2-spheres are generically 3-rigid. Equivalently, planar graphs are generically 3-stress free. We show that already the K ₅-minor freeness guarantees the stress freeness. More generally, we prove that every K _r+2-minor free graph is generically r-stress free for 1≤r≤4. (This assertion is false for r≥6.) Some further extensions are discussed. Supported by an I.S.F. grant.     

On inverse problems in electromagnetic field in classical mechanics at fixed energy

In this article, we consider inverse scattering and inverse boundary value problems at sufficiently large and fixed energy for the multidimensional relativistic and nonrelativistic Newton equations in a static external electromagnetic field (V, B), V∈C², B∈C¹ in classical mechanics. Developing the approach going back to Gerver-Nadinashvili 1983's work on an inverse problem of mechanics, we obtain, in particular, theorems of uniqueness.     

On the quantum potential

We survey various origins and expressions for the quantum potential, expanding and extending the treatment given in a previous paper [R. Carroll, quant-ph 0401082].     

Matrices related to the Bell polynomials

In this paper, we study the matrices related to the partial exponential Bell polynomials and those related to the Bell polynomials with respect to Ω. As a result, the factorizations of these matrices are obtained, which give unified approaches to the factorizations of many lower triangular matrices. Moreover, some combinatorial identities are also derived from the corresponding matrix representations.     

Inverse cyclotomic polynomials

Let Ψn(x) be the monic polynomial having precisely all non-primitive nth roots of unity as its simple zeros. One has Ψn(x)=(xn−1)/Φn(x), with Φn(x) the nth cyclotomic polynomial. The coefficients of Ψn(x) are integers that like the coefficients of Φn(x) tend to be surprisingly small in absolute value, e.g. for n<561 all coefficients of Ψn(x) are ?1 in absolute value. We establish various properties of the coefficients of Ψn(x), especially focusing on the easiest non-trivial case where n is composed of 3 distinct odd primes.