Menezesite, the first natural heteropolyniobate, from Cajati, Sao Paulo, Brazil: Description and crystal structure

Menezesite, ideally Ba2MgZr4(BaNb12O42)center dot 12H(2)O, occurs as a vug mineral in the contact zone between dolomite carbonatite and ""jacupirangite"" (=a pyroxenite) at the Jacupiranga mine, in Cajati county, Sao Paulo state, Brazil, associated with dolomite, calcite, magnetite, clinohumite, phlogopite, ancylite-(Ce), strontianite, pyrite, and tochilinite. This is also the type locality for quintinite-2H. The mineral forms rhombododecahedra up to I mm, isolated or in aggregates. Menezesite is transparent and displays a vitreous luster; it is reddish brown with a white streak. It is non-fluorescent. Mohs hardness is about 4. Calculated density derived from the empirical formula is 4.181 g/cm(3). It is isotropic, 1.93(1) (white light); n(calc) = 2.034. Menezesite exhibits weak anomalous birefringence. The empirical formula is (Ba1.47K0.53Ca0.3,Ce0.17Nd0.10Na0.06La0.02)(Sigma 2.66)(Mg0.94Mn0.23Fe0.23Al0.03)(Sigma 1.43)(Zr2.75Ti0.96Th0.29)(Sigma 4.00)[(Ba0.72Th0.26U0.02)(Sigma 1.00)(Nb9.23Ti2.29Ta0.36Si0.12)Sigma O-12.00(42)]center dot 12H(2)O. The mineral is cubic, space group 10 (204), a = 13.017(1) angstrom, V = 2206(1) angstrom(3), Z = 2. Menezesite is isostructural with the synthetic compound Mg-7[MgW12O42](OH)(4)center dot 8H(2)O. The mineral was named in honor of Luiz Alberto Dias Menezes Filho (born 1950), mining engineer, mineral collector and merchant. Both the description and the name were approved by the CNMMN-IMA (Nomenclature Proposal 2005-023). Menezesite is the first natural heteropolyniobate. Heteropolyanions have been employed in a range of applications that include virus-binding inorganic drugs (including the AIDs virus), homogeneous and heterogeneous catalysts, electro-optic and electrochromic materials, metal and protein binding, and as building blocks for nanostructuring of materials.

Approximations of modal logics: K and beyond

Inspired by the recent work on approximations of classical logic, we present a method that approximates several modal logics in a modular way. Our starting point is the limitation of the n-degree of introspection that is allowed, thus generating modal n-logics. The semantics for n-logics is presented, in which formulas are evaluated with respect to paths, and not possible worlds. A tableau-based proof system is presented, n-SST, and soundness and completeness is shown for the approximation of modal logics K, T, D, S4 and S5. (c) 2008 Published by Elsevier B.V.

On AGM for Non-Classical Logics

The AGM theory of belief revision provides a formal framework to represent the dynamics of epistemic states. In this framework, the beliefs of the agent are usually represented as logical formulas while the change operations are constrained by rationality postulates. In the original proposal, the logic underlying the reasoning was supposed to be supraclassical, among other properties. In this paper, we present some of the existing work in adapting the AGM theory for non-classical logics and discuss their interconnections and what is still missing for each approach.

Description of costandard modules for Schur superalgebra S(2 vertical bar 1) in positive characteristic

We describe the characters of simple modules and composition factors of costandard modules for S(2 vertical bar 1) in positive characteristics and verify a conjecture of La Scala-Zubkov regarding polynomial superinvariants for GL(2 vertical bar 1).

Formation and decomposition of N-alkyinaphthalimides: experimental evidences and ab initio description of the reaction pathways

The kinetics of hydrolysis of 1,8-N-butyl-naphthalimide (1,8-NBN) to 1,8-N-butyl-naphthalamide (1,8-NBAmide) and of 2,3-N-butyl-naphthalimide (2,3-NBN) to 2,3-N-butyl-naphthalamide (2,3-NBAmide), as well as the formation of the respective anhydrides from the amides were investigated in a wide acidity range. 1,8-NBN equilibrates with 1,8-NBAmide in mild alkali. Under the same conditions 2,3-NBN quantitatively yields 2,3-NBAmide. Over a wide range of acidities the reactions of the 1,8- and 2,3-N-butyl-naphthalamides (or imides) yield similar products but with widely different rates and at distinct pH`s. Anhydride formation in acid was demonstrated for 1,8-NBAmide. The reactions mechanisms were rationalized in the manifold pathways of ab initio calculations. The differences in rates and pH ranges in the reactions of the 1,8- and 2,3-N-butyl-naphthalamides were attributed to differences in the stability of the tetrahedral intermediates in alkali as well as the relative stabilities of the five and six-membered ring intermediates. The rate of carboxylic acid assisted 1,8-N-Butyl-naphthalamide hydrolysis is one of the largest described for amide hydrolysis models. Copyright (C) 2010 John Wiley & Sons, Ltd.