Multivariate Liouville distributions

A random vector (X₁, …, X_n), with positive components, has a Liouville distribution if its joint probability density function is of the formf(x₁ + … + x_n)x₁^a₁.1 … x_n^a_n.1 with thea_i all positive. Examples of these are the Dirichlet and inverted Dirichlet distributions. In this paper, a comprehensive treatment of the Liouville distributions is provided. The results pertain to stochastic representations, transformation properties, complete neutrality, marginal and conditional distributions, regression functions, and total positivity and reverse rule properties. Further, these topics are utilized in various characterizations of the Dirichlet and inverted Dirichlet distributions. Matrix analogs of the Liouville distributions are also treated, and many of the results obtained in the vector setting are extended appropriately.     

Hybrid improper ferroelectricity: a mechanism for controllable polarization-magnetization coupling

First-principles calculations are presented for the layered perovskite Ca3Mn2O7. The results reveal a rich set of coupled structural, magnetic, and polar domains in which oxygen octahedron rotations induce ferroelectricity, magnetoelectricity, and weak ferromagnetism. The key point is that the rotation distortion is a combination of two nonpolar modes with different symmetries. We use the term "hybrid" improper ferroelectricity to describe this phenomenon and discuss how control over magnetism is achieved through these functional antiferrodistortive octahedron rotations.     

The ν4 fundamental of three isotopic species of CF4

The vibration-rotation spectra of the ν₄ fundamental of ¹²CF₄, ¹³CF₄, and ¹⁴CF₄ have been observed with 0.06 cm^?1 resolution. A least squares fit of the data has been used to evaluate the pertinent molecular constants. The band centers are 631.199, 629.285, and 627.348 cm^?1 for ¹²CF₄, ¹³CF₄, and ¹⁴CF₄, respectively. The Coriolis constant ζ₄ has been estimated for the three isotopes.     

Neutron powder diffraction of metal-organic frameworks for hydrogen storage

We review recent structural studies that we have undertaken aimed at elucidating the fundamental properties of metal-organic framework materials and their interactions with hydrogen. We have shown that exposing coordinatively unsaturated metal centers can greatly enhance the hydrogen binding energy and that they result in a significant increase of the surface packing density of adsorbed hydrogen molecules on materials’ surface. We will review some of the structural aspects of these materials, especially the adsorbed hydrogen molecule surface packing density in one type of metal-organic framework, MOF-74, which can be packed even denser than that in solid hydrogen.      

Cubane,Bicyclo[1.1.1]pentane and Bicyclo[2.2.2]octane: Impact and Thermal Sensitiveness of Carboxyl-, Hydroxymethyl- and Iodo-substituents

With the burgeoning interest in cage motifs for bioactive molecule discovery, and the recent disclosure of 1,4-cubane-dicarboxylic acid impact sensitivity, more research into the safety profiles of cage scaffolds is required. Therefore, the impact sensitivity and thermal decomposition behavior of judiciously selected starting materials and synthetic intermediates of cubane, bicyclo[1.1.1]pentane (BCP), and bicyclo[2.2.2]octane (BCO) were evaluated via hammer test and sealed cell differential scanning calorimetry, respectively. Iodo-substituted systems were found to be more impact sensitive, whereas hydroxymethyl substitution led to more rapid thermodecomposition. Cubane was more likely to be impact sensitive with these substituents, followed by BCP, whereas all BCOs were unresponsive. The majority of derivatives were placed substantially above Yoshida thresholds—a computational indicator of sensitivity.     

Specht Modules and Simple Modules for Centralizer Algebras of the Symmetric Group

Let Σ_n be the symmetric group on n letters. For l ≤ n identify Σ_l with a subgroup of Σ_n in the natural way. Let k be an algebraically closed field of characteristic p. This article begins to develop a theory for modules over the centralizer algebras kΣ_n^Σ_l that is analogous to James's theory of permutation modules, Specht modules, and simple modules over kΣ_n. We make a conjecture about how to construct all simple kΣ_n^Σ_l-modules, we develop tools to test the conjecture, and we prove that it is correct for all n when l < p.