Deduction as Reduction, from a Categorical Point of View

Deduction systems and graph transformation systems are compared within a common categorical framework. This comparison results in a proposal for a new deduction method in diagrammatic logics, allowing the deletion of intermediate lemmas.     

Categorical (binary) difference terms and protomodularity

In this paper we obtain an intrinsic syntactical characterization of protomodularity, via so-called categorical difference terms, similar to the one known in the case of varieties involving binary terms d satisfying d(x, x) = d(y, y). We also show that purely categorical modifications of the condition in the characterization give characterizations of Mal’tsev and additive categories, thus revealing a new conceptual link between these three classes of categories, and hence, also between the corresponding classes of varieties.     

Modeling of rod-structures in nonlinear elasticity

This Note deals with the modeling of a structure made of straight elastic rods whose thickness tends to 0. We show that, upon an adequate scaling, the infimum of the total elastic energy tends to the minimum of a functional which depends on fields defined on the centerlines of the rods.     

Synthesis and characterization of substituted garnet and perovskite-based lithium-ion conducting solid electrolytes

Titanium, tantalum-substituted Li₇La₃Zr_2-xA_xO₁₂ (LLZO, A?=?Ta, Ti) garnets, and chromium-substituted La_(2/3)-xLi_3xTi_1-yCr_yO₃ (LLTO) perovskites were prepared by a conventional solid-state reaction and the Pechini processes. The desired crystal phases were obtained by varying the calcination temperature and time, as well as the substitution concentration. All samples indicated decomposition of the precursors when heated above 750 °C and formation of the desired phase after heat treatment at higher temperatures. Neutron diffraction data shows the formation of a predominant cubic phase in the case of Ta-LLZO, and monoclinic phase with minor impurity phases for Cr-LLTO. Ionic conductivity for Ti-LLZO (Li₇La₃Zr_1.4Ti_0.6O₁₂), Ta-LLZO (Li_6.03La₃Zr_1.533Ta_0.46O₁₂), and Cr-LLTO (La_(2/3)-xLi_3xTi_0.9Cr_0.1O₃) at room temperature were found to be 5.21?×?10^?6, 1.01?×?10^?6, and 1.2?×?10^?4 S cm^?1, respectively. The activation energies of the compounds were determined from the Arrhenius plot and were 0.44 eV (Ti_0.6-LLZO), 0.54 eV (Ta_0.5-LLZO), and 0.20 eV (Cr_0.1-LLTO).     

Maxima and minima of the displacement components for the Lamb modes

This paper revisits the vanishing of the transverse component of the particle displacement vector in free surfaces of an isotropic homogeneous plate, for both symmetric and antisymmetric Lamb waves. Drawing on well-known analytical expressions from Viktorov's book [(1967) Rayleigh and Lamb Waves: Physical Theory Applications, Chap. II, pp. 67-121], two distinct frequency-thickness product expressions, in cases where this vanishing occurs, are derived: one for the symmetric modes and another for the antisymmetric modes. At these frequency-thickness products, phase and group velocities have appreciable values which are discussed herein. It appears that these velocities depend on the transverse bulk wave velocity only. This is the specific condition of the Lame? modes. Moreover, theoretical and experimental investigations of displacements in the surface of a plate in air have been carried out. The theoretical part shows that the normal and transverse displacements have, respectively, a local maximum and a local minimum in the vicinity of these frequency-thickness products. The experimental part corroborates the presence of the local maximum of the S(0) Lamb mode for various materials.     

Site-selective lanthanide doping in a nonanuclear yttrium(III) cluster revealed by crystal structures and luminescence spectra

A series of lanthanide-doped nonanuclear yttrium(III) clusters with general formulas (Y(9-x)Ln(x))(acac)(16)(μ(3)-OH)(8)(μ(4)-O)(μ(4)-OH) (Ln = Pr, Eu, Tb, Dy, and Yb) were synthesized. Characterization by single-crystal X-ray diffraction allowed for analysis of relative populations of yttrium (Z = 39) and dopant trivalent lanthanide (Z = 59-70) at every crystallographic metal position. Nonuniform distribution of ions along the three different sites seems to be correlated to the site volume and the ratio of ionic radii. In support, luminescence spectra of europium(III)-doped nonanuclear clusters were measured over a wide range of dopant concentrations. Emission intensities of peaks characteristic of specific sites correlate well with the site population determined through X-ray diffraction.     

Synthesis of branched oxime-linked peptide mimetics of the MUC1 containing a universal T-helper epitope

Our goal was to develop mimics of MUC1, highly immunogenic to induce an efficient immune response against the tumor-associated form of MUC1, and sufficiently different from the natural antigen to bypass the tolerance barrier in humans. With the aim of obtaining a well-defined peptide construct as a means of evoking the precise immune responses required in immunotherapy, we synthesized artificial mimics of the MUC1 protein composed of two MUC1 repeat units of inverse orientation and a universal T-helper epitope. To synthesize these heteromeric peptide constructs, we followed a convergent approach using chemoselective ligation based on oxime chemistry. A stem peptide was first synthesized bearing two orthogonally masked aldehydes. After successive deprotection, two oxime bonds can be specifically generated. The proposed strategy proved to be concise and robust, and allowed the synthesis of the tri-branched protein in a very satisfactory yield. The different constructs were tested for their ability to generate antibodies able to recognize the MUC1 protein.     

An improved approximation for the Rayleigh wave equation

We derive a simple expression, which gives an approximate value of the Rayleigh wave velocity in an isotropic solid. This approximation is five times better than that given by Viktorov. The velocity equation can be easily inverted in order to obtain an accurate determination of the elastic constants. This procedure can be worthwhile for elastic microanalysis of bulk materials by scanning acoustic microscopy.