Firing-Induced Microstructural Properties of Quasi-Diamagnetic Carbonate-Based Porous Ceramics: a <Superscript>1</Superscript>H NMR Relaxation Correlation Study

This study deals with the application of two-dimensional proton nuclear magnetic resonance relaxometry (2D ¹H NMR-R) to the characterization of porous ceramics nearly free of magnetic compounds. Different microstructural properties were obtained by firing a diamagnetic mixture of kaolin, calcium, and magnesium carbonate over a wide range of maximum temperatures (600–1100 °C) and firing times at the maximum temperature (soaking times) (0–10 h). The 2D ¹H NMR-R method relies on the correlated measurement of ¹H longitudinal (T ₁) and transverse (T ₂) relaxation times of pore-filling water by which the properties of the interconnected pore space may be investigated. In the absence of significant magnetic susceptibility effect due to para- and ferro-magnetic compounds, the 2D ¹H NMR-R maps allow studying the conjoint effects on pore size distribution and inter-pore coupling due to the variations in both time and temperature of firing. The NMR experiments were performed with a low-field ¹H NMR sensor, which allows non-destructive and in situ analysis. For ceramic specimens fired at 600 and 700 °C, the fraction of smallest pores increases with firing time at the expenses of those with intermediate size. The pore shrinkage occurring at this stage, and likely associated with the transformation of kaolinite in metakaolinite, is affected in a similar way by soaking time and firing temperature, in line with the concept of equivalent firing temperature. At temperatures from 800 to 1100 °C, the structural modifications involving interconnectivity and average pore size are driven primarily by firing temperature and, secondarily, by soaking time. The 2D ¹H NMR-R results are confirmed by more traditional, but destructive, mineralogical, and structural analyses like X-ray powder diffraction, helium pycnometry, mercury intrusion porosimetry, and nitrogen adsorption/desorption method.     

Site-Specific Detection of Free Radicals in Membranes Using an Amphiphilic Spin Trap

The detection of free radicals and related species has attracted considerable attention in recent years due to their critical roles in physiological and pathological processes. Among the various methods for the detection of free radicals, electron spin resonance coupled with spin-trapping technique has been an effective approach for the characterization and quantification of free radicals due to its high specificity. In this study, we designed and synthesized a novel amphiphilic spin trap, 2-(diethoxyphosphoryl)-2-heptadecanyl-3,4-dihydro-2H-pyrrole-1-oxide (DEPHdPO), from 5-(diethoxyphosphoryl)-5-methyl-1-pyrroline-N-oxide with a long hydrocarbon chain at the C-5 position of the pyrroline ring, providing the amphiphilic character. The free-radical-trapping ability of DEPHdPO was evaluated by capturing hydroxyl radicals (^·OH), superoxide anions (\( {\text{O}}_{2}^{ \cdot - } \)), and carbon-centered free radicals in a model membrane prepared from sodium dodecyl sulfate (SDS). The results indicate that the hydrophobic hydrocarbon chain of DEPHdPO can be inserted into the inner core of SDS micelles, and the hydrophilic nitronyl functional moiety is located on the surface layer. Thus, various free radicals, including ^·OH radicals, \( {\text{O}}_{2}^{ \cdot - } \) anions, and carbon-centered radicals could be site-specifically detected near the membrane surface. Moreover, DEPHdPO could be successfully located on the surface of thylakoid membranes, and the nearby photo-initiated \( {\text{O}}_{2}^{ \cdot - } \) anions could be trapped site-specifically.     

<Superscript>27</Superscript>Al NMR Study of the Structure and Dynamics of Natrolite

The temperature dependences of nuclear magnetic resonance and magic angle spinning nuclear magnetic resonance spectra of ²⁷Al nuclei in natrolite (Na₂Al₂Si₃O₁₀· 2H₂O) have been studied. The influence of water molecules and sodium ions mobility on the shape of the ²⁷Al NMR spectrum and framework dynamics have been discussed The temperature dependences of the spin–lattice relaxation times T₁ of ²⁷Al nuclei in natrolite have also been studied. It has been shown that the spin–lattice relaxation of the ²⁷Al is governed by the electric quadrupole interaction with the crystal electric field gradients modulated by translational motion of H₂O molecules in the natrolite pores. The dipolar interactions with paramagnetic impurities become significant as a relaxation mechanism of the ²⁷Al nuclei only at low temperatures (<270 K).     

Global continuum of positive solutions for discrete <Emphasis Type="Italic">p</Emphasis>-Laplacian eigenvalue problems

We discuss the discrete p-Laplacian eigenvalue problem,

$$\left\{ \begin{gathered} \Delta (\phi _p (\Delta u(k - 1))) + \lambda a(k)g(u(k)) = 0,k \in \{ 1,2,...,T\} , \hfill \\ u(0) = u(T + 1) = 0, \hfill \\ \end{gathered} \right.$$

where T > 1 is a given positive integer and φ _p (x):= |x| ^p?2 x, p > 1. First, the existence of an unbounded continuum C of positive solutions emanating from (λ, u) = (0, 0) is shown under suitable conditions on the nonlinearity. Then, under an additional condition, it is shown that the positive solution is unique for any λ > 0 and all solutions are ordered. Thus the continuum C is a monotone continuous curve globally defined for all λ > 0.

     

A well-balanced and asymptotic-preserving scheme for the one-dimensional linear Dirac equation

The numerical approximation of one-dimensional relativistic Dirac wave equations is considered within the recent framework consisting in deriving local scattering matrices at each interface of the uniform Cartesian computational grid. For a Courant number equal to unity, it is rigorously shown that such a discretization preserves exactly the \(L^2\) norm despite being explicit in time. This construction is well-suited for particles for which the reference velocity is of the order of \(c\), the speed of light. Moreover, when \(c\) diverges, that is to say, for slow particles (the characteristic scale of the motion is non-relativistic), Dirac equations are naturally written so as to let a “diffusive limit” emerge numerically, like for discrete 2-velocity kinetic models. It is shown that an asymptotic-preserving scheme can be deduced from the aforementioned well-balanced one, with the following properties: it yields unconditionally a classical Schrödinger equation for free particles, but it handles the more intricate case with an external potential only conditionally (the grid should be such that \(c \Delta x\rightarrow 0\)). Such a stringent restriction on the computational grid can be circumvented easily in order to derive a seemingly original Schrödinger scheme still containing tiny relativistic features. Numerical tests (on both linear and nonlinear equations) are displayed.     

Block partitions of sequences

Given a sequence A = (a ₁, …, a _n ) of real numbers, a block B of A is either a set B = {a _i , a _i+1, …, a _j } where i ≤ j or the empty set. The size b of a block B is the sum of its elements. We show that when each a _i ∈ [0, 1] and k is a positive integer, there is a partition of A into k blocks B ₁, …, B _k with |b _i ?b _j | ≤ 1 for every i, j. We extend this result in several directions.     

A Rolle Type Theorem for Cyclicity of Zeros of Families of Analytic Functions

Let \({\{ {f_{\lambda ;j}}\} _{\lambda \in V;1 \leqslant j \leqslant k}}\) be families of holomorphic functions in the open unit disk \({\text{D}} \subset {\Bbb C}\) ? ? depending holomorphically on a parameter λ ∈ V ? ? ⁿ . We establish a Rolle type theorem for the generalized multiplicity (called cyclicity) of zeros of the family of univariate holomorphic functions \({\left\{ {\sum\nolimits_{j = 1}^k {{f_{\lambda ;j}}} } \right\}_{\lambda \in V}}\) at 0 ∈ D. As a corollary, we estimate the cyclicity of the family of generalized exponential polynomials, that is, the family of entire functions of the form \(\sum\nolimits_{k = 1}^m {{P_k}(z){e^{{Q_k}(z)}}} \), z ∈ ?, where P _k and Q _k are holomorphic polynomials of degrees p and q, respectively, parameterized by vectors of coefficients of P _k and Q _k .     

Gelfand-Kirillov dimension of algebras with locally nilpotent derivations

Let R be a finitely generated algebra over a field of characteristic 0 with a locally nilpotent derivation δ ≠ 0. We show that if {ie313-1}, where the invariants {ie313-2} are prime and satisfy a polynomial identity, then {ie313-3}. Furthermore, when R is a domain, the same conclusion holds without the assumption that R is finitely generated. This enables us to obtain a result on skew polynomial rings. These results extend work of Bell and Smoktunowicz on domains with GK dimension in the interval [2, 3).     

Approximability of HNN-extensions with central associated subgroups by a root class of groups

HNN-extensions of a group with central associated subgroups are considered. Several conditions are obtained for the approximability of such HNN-extensions by a class of groups which have the root property and is closed with respect to factorization.