4,7‐Diiodo‐2,1,3‐benzothiadiazole and 7,7′‐diiodo‐4,4′‐bi(2,1,3‐benzothiadiazole)

In the crystal structures of the title compounds, C₆H₂I₂N₂S, (I), and C₁₂H₄I₂N₄S₂, (II), respectively, a large number of short inter‐heteroatom contacts, such as S?N, I?I and N?I, are observed. In (II), which is non‐centrosymmetric, two halves of the mol­ecule are related by a crystallographic twofold axis.     

Effect of HF addition on the microwave-assisted acid-digestion for the determination of metals in coal by inductively coupled plasma-atomic emission spectrometry

The microwave-assisted acid-digestion for the determination of metals in coal by ICP-AES was investigated, especially focusing on the necessity of adding HF. By testing five certified reference materials, BCR-180, BCR-040, NIST-1632b, NIST-1632c, and SARM-20, it was found that the two-stage digestion without HF (HNO₃ + H₂O₂ was used) was very effective for the pretreatment of ICP-AES measurement. Both major metals (Al, Ca, Fe, and Mg) and minor or trace metals (Co, Cr, Cu, Mn, Ni, Pb, and Zn) in coal gave good recoveries for their certified or reference values. The possibility of ‘HF-memory effect’ was cancelled by the use of a set of vessels which had been never contacted with HF. Twenty-four Japanese standard coals (SS coals) were analyzed by the present method, and the concentrations of major metals measured by the present method provided very high accordance with those from the authentic JIS (Japanese Industrial Standard) method.     

The crystal structures of α- and β-CdUO4

The structural parameters of α- and β-CdUO₄ crystals are determined by X-ray powder diffraction technique. α-CdUO₄ is rhombohedral and cell parameters are a = 6.233(3) Å and α = 36.12(5)°. β-CdUO₄ crystallizes in a C-centered orthorhombic cell with a = 7.023(4), b = 6.849(3), c = 3.514 (2) Å. The space groups are $\text{R}\text{3}\text{m}$ for α-CdUO₄ and Cmmm for β-CdUO₄. α-CdUO₄: 1U in (000), 1Cd in ($\text{1}\text{2}\text{1}\text{2}\text{1}\text{2}$), 2O(1) in ±(uuu), 2O(2) in ±(vvv); u = 0.113, v = 0.350, Z = 1. β-CdUO₄: 2U in ($\text{000;}\text{1}\text{2}\text{1}\text{2}\text{0}$), 2Cd in ($\text{1}\text{2}\text{0}\text{1}\text{2}\text{; 0}\text{1}\text{2}\text{,}\text{1}\text{2}$), 4O(1) in ($\text{0, ±y, 0;}\text{1}\text{2}\text{,}\text{1}\text{2}\text{±y, 0}$), 4O(2) in ($\text{±x, 0,}\text{1}\text{2}\text{;}\text{1}\text{2}\text{±x,}\text{1}\text{2}\text{,}\text{1}\text{2}$); x = 0.159, y = 0.278, Z = 2. β-CdUO₄ contains collinear uranyl UO²⁺₂ groups with a UO(1) distance of 1.91 Å, located either along or parallel to the c axis whereas the UO(1) bond length in α-CdUO₄ is 1.98 Å which is longer than the usual uranyl bond length.     

An infeasible interior-point arc-search algorithm for nonlinear constrained optimization

Numerical Algorithms - In this paper, we propose an infeasible arc-search interior-point algorithm for solving nonlinear programming problems. Most algorithms based on interior-point methods are...     

Chemical algebra. II: Discriminating pairing products

The algebra of stereogenic pairing equlibria is presented in a very general context. Starting from the notions of fuzzy subgroup and conjugacy link, chemical pairing constants between molecular speciesu andv having a skeletal symmetry groupG are formulated as pairing products on aG-Hilbert space. Discriminating pairing productsK are defined by the conditions: K 1 and K = 1 the representative vectors of the paired species areG-equivalent. WhenG has only two elements, the pairing product is always discriminating. For several skeletal symmetries, if the vectors are enantiomorphic (v = u, ² =e, G), thenK is greater than 1 and reaches 1 only ifu is achiral: chirality indexes and general permutational indexes are then defined fromK(u u). The general model is illustrated by some examples.     

Chemical algebra. IV: “Length” of transformation pathways between skeletal analogs

Even if the eq. of completely G-invariant distance extensions derived from a pairing product is not resolved, a distance is defined by means of a metric obtained by differential resolution. Under specified conditions, the linear element solution do² is homogeneous to square coordinate differentials. Integration of da along a curve of E affords a length relative to doe. Boundaries of the curve represent skeletal analogs u and v, whereas inner points represent intermediates in the transformation u v, where the ligand parameters are supposed to vary continuously: a stereogenic pairing equilibrium between infinitesimally close skeletal analogs is assumed. If the curve runs orthogonal to a unit representation space of G, the length is infinite and the curve might be regarded as a fractal transformation pathway. The thermodynamic gap D_p is always shorter than the kinetic distance of the metric do².