Similarity of Matrices Over Local Rings of Length Two

Let R be a (commutative) local principal ideal ring of length two, for example, the ring R = Z/p(2)Z with p prime. In this paper, we develop a theory of normal forms for similarity classes in the matrix rings M-n (R) by interpreting them in terms of extensions of R t]-modules. Using this theory, we describe the similarity classes in M-n (R) for n <= 4, along with their centralizers. Among these, we characterize those classes which are similar to their transposes. Non-self-transpose classes are shown to exist for all n > 3. When R has finite residue field of order q, we enumerate the similarity classes and the cardinalities of their centralizers as polynomials in q. Surprisingly, the polynomials representing the number of similarity classes in M-n (R) turn out to have non-negative integer coefficients.

In-plane elastic responses of circular cell honeycombs and bundled circular tubes in a diamond array structure

Assemblages of circular tubes and circular honeycombs in close packed arrangement are presently both competing and complementing regular honeycomb structures (HCS). The intrinsic isotropy of bundled tubes/rings in hexagonal arrays restricts their use to applications with isotopic need. With the aim of extending the utility of tubes/rings assemblages to anisotropic needs, this paper explores the prospects of bundled tubes and circular honeycombs in a general diamond array structure (DAS) to cater these needs. To this end, effective transverse Young's moduli and Poisson's ratio for thick/thin DAS are obtained theoretically. Analysis frameworks including thin ring theory (TRT), curved beam theory (CBT) and elasticity formulations are tested and corroborated by FEA employing contact elements. Results indicate that TRT and CBT are reasonable for thin tubes and honeycombs. Nevertheless, TRT yields compact formulae to study the anisotropy ratio, moduli spectrum and sensitivity of the assemblage as a function of thicknesses and array structure. These formulae supplement designers as a guide to tailor the structures. On the other hand, elasticity formulation can estimate over a larger range including very thick tubes/rings. In addition, this formulation offers to estimate refined transverse strengths of assemblages. (C) 2015 Elsevier Ltd. All rights reserved.

Substituent Effects on the Stability and Antioxidant Activity of Spirodiazaselenuranes

Spirodiazaselenuranes are structurally interesting compounds and the stability of these compounds depends highly on the nature of the substituents attached to the nitrogen atoms. Aromatic substituents are known to play important roles in stabilizing the Se-N bonds in spiro compounds. In this study, several spirodiazaselenuranes are synthesized by introducing benzylic and aliphatic substituents to understand their effect on the stability of the Se-N bonds and the antioxidant activity. Replacement of phenyl substituent by benzyl/alkyl groups significantly reduces the stability of the spirodiazaselenuranes and slows down the oxidative cyclization process. The selenium centre in the spiro compounds undergoes further oxidation to produce the corresponding selenurane oxides, which are stable at room temperature. Comparison of the glutathione peroxidase (GPx) mimetic activity of the compounds showed that the diaryl selenides having heterocyclic rings are significantly more active due to the facile oxidation of the selenium centre. However, the activity is reduced significantly for compounds having aliphatic substituents. In addition to GPx activity, the compounds also inhibit peroxynitrite-mediated nitration and oxidation reaction of protein and small molecules, respectively. The experimental observations suggest that the antioxidant activity is increased considerably upon substitution of the aromatic group with the benzylic/aliphatic substituents on the nitrogen atoms.

Interpenetrated and Catenated Zinc Thiosulfates Frameworks with dia and qtz Nets: Synthesis, Structure, and Properties

Reactions between Zn(NO3)(2)center dot 6H(2)O, Na2S2O3, 4,4'-bipyridine (bpy), 1,2-bis(4-pyridyl)ethene (bpe), 1,2-bis (4-pyridyl) ethane (bpa), and 1,3-bis(4-pyridyl)propane (bpp) under solvothermal conditions resulted in four new zinc thiosulfate hybrid compounds. Compound I has four-membered zinc thiosulfate rings connected by the ligand, 1,3-bis(4-pyridyl)propane (bpp) forming a two-dimensional structure. Compounds II-IV have one-dimensional zinc thiosulfate chains connected by the ligands, bpy (II), bpe (III), and bpa (IV) giving rise to three-dimensional structures. All the four-structures exhibit 3-fold interpenetration. Proton conductivity studies indicate reasonable proton mobility at 34 degrees C and at 98% relative humidity. The compounds also exhibit Lewis acid character and good photocatalytic activity for the decomposition of cationic dyes.