Practical aspects of shimming a high resolution magic angle spinning probe

High resolution magic angle spinning (HRMAS) has become an extremely versatile tool to study heterogeneous systems. HRMAS relies on magic angle spinning of the sample to average out to zero magnetic susceptibility differences in the sample and to obtain resonance linewidths approaching those of liquid state NMR. Shimming such samples therefore becomes an important issue. By analyzing the different sources of magnetic field perturbations present in a sample under MAS conditions, we propose a simple protocol to obtain optimum shim settings in HRMAS. In the case of aqueous samples, we show that the lock level cannot be used as a reliable indicator of the quality of the shims at high spinning speeds. This effect is explained by the presence of temperature gradients imparted by the sample rotation.     

Ambient noise cross correlation in free space: theoretical approach

It has been experimentally demonstrated that the Green's function between two points could be recovered using the cross-correlation function of the ambient noise measured at these two points. This paper investigates the theory behind this result in the simple case of a homogeneous medium with attenuation.     

On quadratic fields with large 3-rank

Davenport and Heilbronn defined a bijection between classes of binary cubic forms and classes of cubic fields, which has been used to tabulate the latter. We give a simpler proof of their theorem then analyze and improve the table-building algorithm. It computes the multiplicities of the general cubic discriminants (real or imaginary) up to in time and space , or more generally in time and space for a freely chosen positive . A variant computes the -ranks of all quadratic fields of discriminant up to with the same time complexity, but using only units of storage. As an application we obtain the first real quadratic fields with , and prove that is the smallest imaginary quadratic field with -rank equal to .

     

A generalization of a theorem on biseparating maps

In J. Math. Anal. Appl. 12 (1995) 258–265, Araujo et al. proved that for any linear biseparating map  from C(X) onto C(Y), where X and Y are completely regular, there exist ω in C(Y) and an homeomorphism h from the realcompactification vX of X onto vY, such that

The compact version of this result was proved before by Jarosz in Bull. Canad. Math. Soc. 33 (1990) 139–144. In Contemp. Math., Vol. 253, 2000, pp. 125–144, Henriksen and Smith asked to what extent the result above can be generalized to a larger class of algebras. In the present paper, we give an answer to that question as follows. Let A and B be uniformly closed Φ-algebras. We first prove that every order bounded linear biseparating map from A onto B is automatically a weighted isomorphism, that is, there exist ω in B and a lattice and algebra isomorphism ψ between A and B such that

(a)=ωψ(a) for all aA.

We then assume that every universally σ-complete projection band in A is essentially one-dimensional. Under this extra condition and according to a result from Mem. Amer. Math. Soc. 143 (2000) 679 by Abramovich and Kitover, any linear biseparating map from A onto B is automatically order bounded and, by the above, a weighted isomorphism. It turns out that, indeed, the latter result is a generalization of the aforementioned theorem by Araujo et al. since we also prove that every universally σ-complete projection band in the uniformly closed Φ-algebra C(X) is essentially one-dimensional.     

Comparison of graphs associated to a commutative Artinian ring

Let R be a commutative ring with \(1\ne 0\) and the additive group \(R^+\). Several graphs on R have been introduced by many authors, among zero-divisor graph \(\Gamma _1(R)\), co-maximal graph \(\Gamma _2(R)\), annihilator graph AG(R), total graph \( T(\Gamma (R))\), cozero-divisors graph \(\Gamma _\mathrm{c}(R)\), equivalence classes graph \(\Gamma _\mathrm{E}(R)\) and the Cayley graph \(\mathrm{Cay}(R^+ ,Z^*(R))\). Shekarriz et al. (J. Commun. Algebra, 40 (2012) 2798–2807) gave some conditions under which total graph is isomorphic to \(\mathrm{Cay}(R^+ ,Z^*(R))\). Badawi (J. Commun. Algebra, 42 (2014) 108–121) showed that when R is a reduced ring, the annihilator graph is identical to the zero-divisor graph if and only if R has exactly two minimal prime ideals. The purpose of this paper is comparison of graphs associated to a commutative Artinian ring. Among the results, we prove that for a commutative finite ring R with \(|\mathrm{Max}(R)|=n \ge 3\), \( \Gamma _1(R) \simeq \Gamma _2(R)\) if and only if \(R\simeq \mathbb {Z}^n_2\); if and only if \(\Gamma _1(R) \simeq \Gamma _\mathrm{E}(R)\). Also the annihilator graph is identical to the cozero-divisor graph if and only if R is a Frobenius ring.     

The biologically important surfactin lipopeptide induces nanoripples in supported lipid bilayers

Under specific conditions, lipid membranes form ripple phases with intriguing nanoscale undulations. Here, we show using in situ atomic force microscopy (AFM) that the biologically important surfactin lipopeptide induces nanoripples of 30 nm periodicity in dipalmitoyl phosphatidylcholine (DPPC) bilayers at 25 degrees (i.e. well below the pretransition temperature of DPPC). Whereas most undulations formed the classical straight orientation with characteristic angle changes of 120 degrees , some of them also displayed unusual circular orientations. Strikingly, ripple structures were formed at 15% surfactin but were rarely or never observed at 5 and 30% surfactin, emphasizing the important role played by the surfactin concentration. Theoretical simulations corroborated the AFM data by revealing the formation of stable surfactin/lipid assemblies with positive curvature.     

On the role of vacancies in pore formation in the course of anodizing of silicon carbide

Experimental data on the preparation of stoichiometric nanoporous silicon carbide are analyzed. Theoretical calculations are performed under the assumption that nanopores are formed through the vacancy diffusion mechanism. The results obtained confirm the hypothesis that the formation of pores with a steadystate radius of several tens of nanometers in silicon carbide can be associated with the diffusion and clustering of vacancies. The experimental data indicating that the proposed mechanism of formation of nanoporous silicon carbide correlates with the existing model of formation of porous silicon carbide with a fiber structure are discussed. This correlation can be revealed by assuming that nanopores are formed at the first stage with subsequent transformation of the nanoporous structure into a fiber structure due to the dissolution of the material in an electrolyte.     

Ab Initio and DFT Studies on CO2 Interacting with Znq+–Imidazole (q=0, 1, 2) Complexes: Prediction of Charge Transfer through σ‐ or π‐Type Models

Using first‐principles methodologies, the equilibrium structures and the relative stability of CO₂@[Zn^q+Im] (where q=0, 1, 2; Im=imidazole) complexes are studied to understand the nature of the interactions between the CO₂ and Zn^q+–imidazole entities. These complexes are considered as prototype models mimicking the interactions of CO₂ with these subunits of zeolitic imidazolate frameworks or Zn enzymes. These computations are performed using both ab initio calculations and density functional theory. Dispersion effects accounting for long‐range interactions are considered. Solvent (water) effects were also considered using a polarizable continuum model approach. Natural bond orbital, charge, frontier orbital and vibrational analyses clearly reveal the occurrence of charge transfer through covalent and noncovalent interactions. Moreover, it is found that CO₂ can adsorb through more favorable π‐type stacking as well as σ‐type hydrogen‐bonding interactions. The inter‐monomer interaction potentials show a significant anisotropy that might induce CO₂ orientation and site‐selectivity effects in porous materials and in active sites of Zn enzymes. Hence, this study provides valuable information about how CO₂ adsorption takes place at the microscopic level within zeolitic imidazolate frameworks and biomolecules. These findings might help in understanding the role of such complexes in chemistry, biology and material science for further development of new materials and industrial applications.