Non-compact symmetric spaces and the Toda molecule equations

It has been shown by Olshanetsky and Perelomov that the Toda molecule equations associated with any Lie groupG describe special geodesic motions on the Riemannian non-compact symmetric space which is the quotient of the normal real form ofG, G ^N, by its maximal compact subgroup. This is explained in more detail and it is shown that the fundamental Poisson bracket relation involving the Lax operatorA and leading to the Yang-Baxter equation and integrability properties is a direct consequence of the fact that the Iwasawa decomposition forG ^N endows the symmetric space with a hidden group theoretic structure.Supported by CNP _q (Brasil)     

Structural properties of ultra-small thorium and uranium dioxide nanoparticles embedded in a covalent organic framework

We report the structural properties of ultra-small ThO₂ and UO₂ nanoparticles (NPs), which were synthesized without strong binding surface ligands by employing a covalent organic framework (COF-5) as an inert template. The resultant NPs were used to observe how structural properties are affected by decreasing grain size within bulk actinide oxides, which has implications for understanding the behavior of nuclear fuel materials. Through a comprehensive characterization strategy, we gain insight regarding how structure at the NP surface differs from the interior. Characterization using electron microscopy and small-angle X-ray scattering indicates that growth of the ThO₂ and UO₂ NPs was confined by the pores of the COF template, resulting in sub-3 nm particles. X-ray absorption fine structure spectroscopy results indicate that the NPs are best described as ThO₂ and UO₂ materials with unpassivated surfaces. The surface layers of these particles compensate for high surface energy by exhibiting a broader distribution of Th–O and U–O bond distances despite retaining average bond lengths that are characteristic of bulk ThO₂ and UO₂. The combined synthesis and physical characterization efforts provide a detailed picture of actinide oxide structure at the nanoscale, which remains highly underexplored compared to transition metal counterparts.

ThO₂ and UO₂ nanoparticles synthesized using a COF-5 template exhibit unpassivated surfaces and provide insight into nanoscale properties of actinides.     

Elementary school teachers’ growth in inquiry-based teaching of mathematics

This article reports on a self-directed, school-based, practice-based professional development (PD) experience aimed at helping elementary school teachers to develop knowledge and expertise in inquiry-based teaching of mathematics. It discusses the characteristics of the self-directed orientation of this PD that supported the teachers’ learning, the nature of the inquiry-based knowledge they constructed, and the impact on their teaching. It highlights the centrality of agency, practical knowledge, and situated learning in this PD approach. The findings suggest that this approach can help mathematics teachers who want to be the architect of their own learning to transform their classrooms in meaningful and desirable ways.     

Response to tilted magnetic fields in Bi(2)Sr(2)CaCu(2)O(8) with columnar defects: evidence for transverse Meissner effect

The transverse Meissner effect (TME) in the highly layered superconductor Bi(2)Sr(2)CaCu(2)O(8+y) with columnar defects is investigated by transport measurements. We present evidence for the persistence of the Bose glass phase for H(perpendicular)H(+)(perpendicular c), moving kink chains consistent with a commensurate-incommensurate transition scenario are observed. These results show the existence of the TME for H(perpendicular)相似文献   

Primordial supersymmetric inflation

We discuss the motivations for reconsidering cosmological inflation in supersymmetric theories as contrasted with conventional GUTs. Radiative corrections to the effective potential can be made arbitrarily small in supersymmetric GUTs, removing some of the obstacles to inflation. We analyze general renormalizable potentials at the tree level and show that the required fine-tuning of parameters becomes less acute if inflation takes place before the grand unified phase transition, a hypothesis we term primordial inflation. We show how the grand unified monopole problem can be solved in supersymmetric GUTs embodying primordial inflation.     

Roughness analysis of the cracked surfaces of a face centered cubic alloy

Intergranular and transgranular fracture surfaces obtained in a face centered cubic alloy are studied using 3D maps reconstructed by scanning electron microscopy stereo imaging. The roughness exponents measured in the intergranular and transgranular surfaces, respectively, zeta = 0.83 +/- 0.05 and zeta = 0.75 +/- 0.05, are in agreement with the universal roughness value of 3D fractures. However, the slightly smaller value related to the transgranular surface could be a consequence of crystallographic transgranular zones disseminated on the surface whose roughness exponent zeta = 0.65 +/- 0.07 is close to the one usually measured on 2D fractures.     

Vertex operators for non-simply-laced algebras

A vertex operator construction is given for the level one representations of the affine Kac-Moody algebras associated with non-simply-laced finite-dimensional Lie algebras, using free boson and interacting fermion fields. The fermion fields are constructed explicitly and a detailed discussion is given of the theory of the cocycles necessary for this and other vertex operator constructions. The construction is related in detail to the folding of Dynkin diagrams and a generalisation of it yields Freudenthal's magic square.On leave from the Weizmann Institute, Israel     

Fermions and octonions

We analyse further the algebraic structure of dependent fermions, namely ones interrelated by the vertex operator construction. They are associated with special sorts of lattice systems which are introduced and discussed. The explicit evaluation of the relevant cocycles leads to the result that the operator product expansion of the fermions is related in a precise way to one or another of the division algebras given by complex numbers, quaternions or octonions. The latter case is seen to be realised in the light cone formalism of superstring theory.