?-adic properties of smallest parts functions

We prove explicit congruences modulo powers of arbitrary primes for three smallest parts functions: one for partitions, one for overpartitions, and one for partitions without repeated odd parts. The proofs depend on ?-adic properties of certain modular forms and mock modular forms of weight 3/2 with respect to the Hecke operators T(?2m).     

Chemical Reaction Monitoring using Zero-Field Nuclear Magnetic Resonance Enables Study of Heterogeneous Samples in Metal Containers

We demonstrate that heterogeneous/biphasic chemical reactions can be monitored with high spectroscopic resolution using zero-field nuclear magnetic resonance spectroscopy. This is possible because magnetic susceptibility broadening is negligible at ultralow magnetic fields. We show the two-step hydrogenation of dimethyl acetylenedicarboxylate with para-enriched hydrogen gas in conventional glass NMR tubes, as well as in a titanium tube. The low frequency zero-field NMR signals ensure that there is no significant signal attenuation arising from shielding by the electrically conductive sample container. This method paves the way for in situ monitoring of reactions in complex heterogeneous multiphase systems and in reactors made of conductive materials while maintaining resolution and chemical specificity.     

Dinamica relativa di una particella con spin: un teorema di unicità

We prove anunicity theorem for spinning particles in the Papapetrou-Tulczyjew scheme; the theorem modifies the conclusive remarks of a preceding paper [1], i.e. the erroneous incompatibility of such scheme. The unicity is given using an intrinsic frame of reference (parallel to the generalized impulsion) and theresolvent equation of the differential problem, in terms of velocity (vectorial parameter).

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Sunto Si dimostra unteorema di unicità per lo schema di Papapetrou-Tulczyjew relativo ad una particella con spin in Relatività generale; il teorema vale a rettificare un precedente lavoro [1] che avanzava erroneamente, per tale schema, l’ipotesi di incompletezza. Il risultato si consegue operando (intrinsecamente) nelriferimento collineare all’impulso generalizzato, attraverso l’equazione risolvente per la velocità.

     

83Kr nuclear magnetic moment in terms of that of 3He

High resolution NMR spectroscopy was applied to precisely determine the ⁸³Kr nuclear magnetic dipole moment on the basis of new results available for nuclear magnetic shielding in krypton and helium‐3 atoms. Small amounts of ³He as the solutes and ⁸³Kr as the buffer gas were observed in ³He and ⁸³Kr NMR spectra at the constant external field, B₀ = 11.7578 T. In each case, the resonance frequencies (ν^He and ν^Kr) were linearly dependent on the density of gaseous solvent. The extrapolation of experimental points to the zero density of gaseous krypton allowed for the evaluation of both resonance frequencies free from intermolecular interactions. By combining these measurements with the recommended ⁸³Kr chemical shielding value, the nuclear magnetic moment could be determined with much better precision than ever before, μ(⁸³Kr) = ?0.9707297(32)μ_N, with the improvement due to the greater accuracy of the spectral data. Copyright © 2014 John Wiley & Sons, Ltd.     

Design of a Hyperpolarized Molecular Probe for Detection of Aminopeptidase N Activity

Aminopeptidase N (APN) is an important enzyme that is involved in tumor angiogenesis. Detection of APN activity can thus lead to early diagnosis and elucidation of tumor development. Although some molecular probes for APN have been developed, the detection of APN activity in opaque biological samples remains a challenge. To this end, we designed a hyperpolarized NMR probe [1‐¹³C]Ala‐NH₂ which satisfies the prerequisites for APN detection, namely, sufficient retention of the hyperpolarized state, a high reactivity to APN, and an APN‐induced chemical shift change. The [1‐¹³C]Ala‐NH₂ probe allowed sensitive detection of APN activity using ¹³C NMR spectroscopy.     

Nondisruptive Dissolution of Hyperpolarized 129Xe into Viscous Aqueous and Organic Liquid Crystalline Environments

Studies of hyperpolarized xenon‐129 (hp‐¹²⁹Xe) in media such as liquid crystals and cell suspensions are in demand for applications ranging from biomedical imaging to materials engineering but have been hindered by the inability to bubble Xe through the desired media as a result of viscosity or perturbations caused by bubbles. Herein a device is reported that can be reliably used to dissolve hp‐¹²⁹Xe into viscous aqueous and organic samples without bubbling. This method is robust, requires small sample volumes (<60 μL), is compatible with existing NMR hardware, and is made from readily available materials. Experiments show that Xe can be introduced into viscous and aligned media without disrupting molecular order. We detected dissolved xenon in an aqueous liquid crystal that is disrupted by the shear forces of bubbling, and we observed liquid‐crystal phase transitions in (MBBA). This tool allows an entirely new class of samples to be investigated by hyperpolarized‐gas NMR spectroscopy.     

A Nanoparticle Catalyst for Heterogeneous Phase Para‐Hydrogen‐Induced Polarization in Water

Para‐hydrogen‐induced polarization (PHIP) is a technique capable of producing spin polarization at a magnitude far greater than state‐of‐the‐art magnets. A significant application of PHIP is to generate contrast agents for biomedical imaging. Clinically viable and effective contrast agents not only require high levels of polarization but heterogeneous catalysts that can be used in water to eliminate the toxicity impact. Herein, we demonstrate the use of Pt nanoparticles capped with glutathione to induce heterogeneous PHIP in water. The ligand‐inhibited surface diffusion on the nanoparticles resulted in a ¹H polarization of P=0.25 % for hydroxyethyl propionate, a known contrast agent for magnetic resonance angiography. Transferring the ¹H polarization to a ¹³C nucleus using a para‐hydrogen polarizer yielded a polarization of 0.013 %. The nuclear‐spin polarizations achieved in these experiments are the first reported to date involving heterogeneous reactions in water.     

Heterogeneous 1H and 13C Parahydrogen-Induced Polarization of Acetate and Pyruvate Esters

Magnetic resonance imaging of [1-¹³C]hyperpolarized carboxylates (most notably, [1-¹³C]pyruvate) allows one to visualize abnormal metabolism in tumors and other pathologies. Herein, we investigate the efficiency of ¹H and ¹³C hyperpolarization of acetate and pyruvate esters with ethyl, propyl and allyl alcoholic moieties using heterogeneous hydrogenation of corresponding vinyl, allyl and propargyl precursors in isotopically unlabeled and 1-¹³C-enriched forms with parahydrogen over Rh/TiO₂ catalysts in methanol-d₄ and in D₂O. The maximum obtained ¹H polarization was 0.6±0.2 % (for propyl acetate in CD₃OD), while the highest ¹³C polarization was 0.10±0.03 % (for ethyl acetate in CD₃OD). Hyperpolarization of acetate esters surpassed that of pyruvates, while esters with a triple carbon-carbon bond in unsaturated alcoholic moiety were less efficient as parahydrogen-induced polarization precursors than esters with a double bond. Among the compounds studied, the maximum ¹H and ¹³C NMR signal intensities were observed for propyl acetate. Ethyl acetate yielded slightly less intense NMR signals which were dramatically greater than those of other esters under study.     

15N SABRE Hyperpolarization of Metronidazole at Natural Isotope Abundance

Signal Amplification By Reversible Exchange (SABRE) is gaining increased attention as a tool to enhance weak Nuclear Magnetic Resonance (NMR) signals. In SABRE, spin order is transferred from parahydrogen (H₂ in its nuclear singlet spin state) to a substrate molecule in a transient Ir-based complex. In recent years, SABRE polarization of biologically active substrates has been demonstrated, notably of metronidazole – an antibiotic and antiprotozoal drug. In this work, we study ¹⁵N SABRE polarization of metronidazole at natural isotope abundance. We are able to demonstrate significant ¹⁵N polarization reaching 15 %, which corresponds to a signal enhancement of 46,000 at 9.4 T for the nitrogen atom with lone electron pair. Additionally, the other two N-atoms can be polarized, although less efficiently. We present a detailed study of the field dependence of polarization and explain the maxima in the field dependence using the concept of coherent polarization transfer at level anti-crossings in the SABRE complex. A study of spin relaxation phenomena presented here enables optimization of the magnetic field for efficient storage of non-thermal polarization.