Cascade Mi (i = 1–5) subshell X‐ray emission at incident photon energies across the Lj (j = 1–3) subshell absorption edges of 66Dy

The total M shell and the M_k (k = ξ, αβ, γ, m) X‐ray production cross sections for ₆₆Dy have been measured at incident photon energies across its L_j (j = 1–3) subshell absorption edge energies, ranging 7.8–9.2 keV. This study aims to investigate the evolution of the probability for cascade decay of L_j subshell vacancies as the tunable incident energy ionizes progressively different ₆₆Dy L_j subshells. The experimental X‐ray production cross sections have been compared with theoretical ones calculated using the nonrelativistic Hartree–Fock–Slater (HFS) model‐based photoionization cross sections; three sets of the X‐ray emission rates, fluorescence and Coster–Kronig yield based on the nonrelativistic Hartree–Slater (NRHS) model, Dirac–Hartree–Slater (DHS) model and Dirac–Fock (DF) model; the L_j (j = 1–3) subshell to the M_i (i = 1–5) subshell vacancy transfer probabilities evaluated in the present work. Presently measured total M shell and the M_αβ X‐ray production cross sections are found to be significantly lower than the theoretical ones evaluated using physical parameters based on the relativistic Dirac–Fock/Dirac–Hartree–Slater model calculations, whereas a much better agreement is observed with respect to the NRHS model‐based calculations; however, the measured X‐ray production cross sections are still systematically lower than the NRHS values.     

Neutron diffraction study of quasi-one-dimensional spin-chain compounds Ca<Subscript>3</Subscript>Co<Subscript>2–<Emphasis Type="Italic">x</Emphasis></Subscript>Fe<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>O<Subscript>6</Subscript>

We report the results of the DC magnetization, neutron powder diffraction and neutron depolarization studies on the spin-chain compounds Ca₃Co_2–x Fe _x O₆ (x = 0, 0.1, 0.2 and 0.4). Rietveld refinement of neutron powder diffraction patterns at room temperature confirms the single-phase formation for all the compounds in rhombohedral structure with space group Rc. Rietveld refinement also confirms that Fe was doped at the trigonal prism site, 6a (0, 0, 1/4) of Co. The high temperature magnetic susceptibility obeys the Curie-Weiss law; the value of the paramagnetic Curie temperature (θ _p) decreases as the concentration of iron increases and it becomes negative for x = 0.4. No extra Bragg peak as well as no observable enhancement in the intensity of the fundamental (nuclear) Bragg peaks has been observed in the neutron diffraction patterns down to 30 K. No depolarization of neutron beam has been observed down to 3 K confirming the absence of ferro- or ferrimagnetic-like correlation.      

Mild and Efficient Tf2O-Mediated Synthesis of 3-Amino-1-benzofurans

Russian Journal of Organic Chemistry - A mild and efficient procedure has been developed for the synthesis of 3-amino-1-benzofurans by intramolecular cyclization of the corresponding...     

Isometries of absolute order unit spaces

Positivity - We prove that a unital, bijective linear map between absolute order unit spaces is an isometry if and only if it is absolute value preserving. We deduce that, on (unital) JB-algebras,...     

Bianchi type II,VIII, and IX cosmological models in Lyra's geometry

The Bianchi type II, VIII, and IX models are investigated in Lyra's geometry (in normal gauge) when the gauge function is time dependent. The physical behavior of these models in vacuum and in the presence of the Zeldovich fluid is discussed.     

Barycentric coordinates for convex sets

In this paper we provide an extension of barycentric coordinates from simplices to arbitrary convex sets. Barycentric coordinates over convex 2D polygons have found numerous applications in various fields as they allow smooth interpolation of data located on vertices. However, no explicit formulation valid for arbitrary convex polytopes has been proposed to extend this interpolation in higher dimensions. Moreover, there has been no attempt to extend these functions into the continuous domain, where barycentric coordinates are related to Green’s functions and construct functions that satisfy a boundary value problem. First, we review the properties and construction of barycentric coordinates in the discrete domain for convex polytopes. Next, we show how these concepts extend into the continuous domain to yield barycentric coordinates for continuous functions. We then provide a proof that our functions satisfy all the desirable properties of barycentric coordinates in arbitrary dimensions. Finally, we provide an example of constructing such barycentric functions over regions bounded by parametric curves and show how they can be used to perform freeform deformations.      

A Summation Formula for Estimating the Surface Areas of Ellipsoids

In this paper a summation formula for finding the surface area of general ellipsoids is derived.     

多孔压电线性理论中的唯一性定理、互易定理和特征值问题

假定弹性场和电场为正定,在多孔压电线性理论中建立起唯一性定理和互易定理．在准静态电场近似下,证明多孔压电材料线性理论中的一般性定理．利用弹性场的正定性,唯一性定理得到证明．在与多孔压电体自由振动相联系的特征值问题的研究中,给出了简明的公式．文中还研究了有关算子的某些特性．以简明公式为基础,利用变分法和算子法,研究了由于小扰动产生的频移问题．还给出了特殊情况下的扰动分析．     

Pressure broadened line widths of BrCN in the microwave region

The line widths of cyanogen bromide (BrCN) have been measured at room temperature (305 K) by using a double modulation microwave spectrograph. The self-broadening of two quadrupole hyperfine lines of the transition J = 3 → 4 has been measured. The foreign gas broadening by OCS, CO₂, N₂, CH₃CN, CH₃I, HCHO and CH₃CHO molecules has been measured only for the intense line at 32·957 GHz. These measured line widths have been compared with the calculated line widths using Anderson [6] as well as Murphy and Boggs [8] theories of pressure broadening.