Polytypism in the lithium-aluminum layered double hydroxides: the [LiAl2(OH)6]+ layer as a structural synthon

The [LiAl(2)(OH)(6)](+) layer obtained from gibbsite-Al(OH)(3) belongs to the layer group symmetry P-312/m. This layer satisfies the defining characteristics of a synthon in that it predicts all the polymorphic modifications of the layered double hydroxides of Li and Al. The various possible ways of stacking these layers can be derived by the systematic elimination of the principal symmetry elements comprising the layer group. This approach yields the complete universe of possible structures. When the 3 axis of the layer is conserved in the stacking, the resultant crystal adopts the structure of the 1H, 2H, or 3R polytypes (H, hexagonal; R, rhombohedral). When the 3 axis is destroyed and the 2/m axis is retained, the crystal adopts monoclinic symmetry and crystallizes in the structures of the 1M(1) or 1M(2) (M, monoclinic) polytypes; the two polytypes differ only in their translational component. Experimentally, gibbsite-based precursors yield the 2H polytype, and bayerite-based precursors yield the 1M polytype. Faulted structures incorporating differently oriented 1M(1) motifs or a mixture of 1M(1) and 1M(2) motifs are also obtained. These stacking faults result in cation disorder along the c axis and produce signature effects on the line shapes of select reflections in the powder X-ray diffraction patterns. This symmetry-guided approach is general and can be extended to other classes of layered solids.     

Pyrido[2,3-d]pyrimidines and pyrido[2,3-d; 5-d′]dipyrimidines as potential chemotherapeutic agents. VIII

Reactions of 5-dimethylaminomethylene-6-imino-1,3-dimethyluracil hydrochloride (1) with active methylene compounds 2 and 4 yielded bi- and tricyclic heterocyclic compounds 3 and 5 . All the prepared compounds were screened for chemotherapeutical activities but none were active.     

Determination of lead by the precipitation of lead molybdate from a homogeneous solution by the diffusion method

A satisfactory quantitative method for the determination of lead as lead molybdate by precipitation from a homogeneous solution has been developed. The method employs the diffusion of ammonia into a solution containing lead and sodium molybdate in nitric acid medium. The precipitation of lead in the range of 28·0–280·0 mg is complete within 8–9 hours. Anions like sulphate, arsenate, phosphate, tungstate and chromate in moderate concentrations and cations such as Zn (II), Cu (II), Ni (II), Co (II), Mn (II), Cd (II), Hg (II), Ag (I), Ti (IV), As (V), Mg (II) and Al (III) do not contaminate the precipitate. The precipitate gets constant weight at 120°. This eliminated the ignition of the precipitate,i.e., the contamination of molybdic oxide by the precipitate was reduced.     

Weight diagrams for lie group representations: A computer implementation of Freudenthal's algorithm in ALGOL and FORTRAN

Implementations in FORTRAN and ALGOL of the Dynkin and Freudenthal algorithms for computing weight systems and for determining the multiplicities of the weights for irreducible representations of simple Lie algebras are described. Reasonable computing times are found for algebras of rank less than or equal to 8 and for representations of dimension less than 1000.     

Self-consistent quasi-particle model

Here we review the recently developed self-consistent quasi-particle model of QGP and apply it to fit the lattice QCD data on (2+1) flavor QGP.     

Fixed point theorems for generalized weakly S-contractive mappings in partial metric spaces

In this paper, we establish some unique xed point theorems for generalized weakly S-contractive with nondecreasing and weakly increasing mappings in complete partial metric space. Also, we give some examples for strengthens of our main results.     

Conic mixed-integer rounding cuts

A conic integer program is an integer programming problem with conic constraints. Many problems in finance, engineering, statistical learning, and probabilistic optimization are modeled using conic constraints. Here we study mixed-integer sets defined by second-order conic constraints. We introduce general-purpose cuts for conic mixed-integer programming based on polyhedral conic substructures of second-order conic sets. These cuts can be readily incorporated in branch-and-bound algorithms that solve either second-order conic programming or linear programming relaxations of conic integer programs at the nodes of the branch-and-bound tree. Central to our approach is a reformulation of the second-order conic constraints with polyhedral second-order conic constraints in a higher dimensional space. In this representation the cuts we develop are linear, even though they are nonlinear in the original space of variables. This feature leads to a computationally efficient implementation of nonlinear cuts for conic mixed-integer programming. The reformulation also allows the use of polyhedral methods for conic integer programming. We report computational results on solving unstructured second-order conic mixed-integer problems as well as mean–variance capital budgeting problems and least-squares estimation problems with binary inputs. Our computational experiments show that conic mixed-integer rounding cuts are very effective in reducing the integrality gap of continuous relaxations of conic mixed-integer programs and, hence, improving their solvability. This research has been supported, in part, by Grant # DMI0700203 from the National Science Foundation.     

Single Step Synthesis of MoSe2−MoO3 Heterostructure for Highly Sensitive Amperometric Detection of Nitrite in Water Samples of Industrial Areas

The present work reports a simple and single‐step hydrothermal synthesis of MoSe₂?MoO₃ composite for highly sensitive and selective electrochemical oxidation of nitrite. FESEM of the MoSe₂?MoO₃ hybrid revealed the formation of composite as laminated structure of different sizes piled up together as finger‐like MoSe₂ bars whilst other physico‐chemical characterizations (XRD, FTIR, UV‐Vis, XPS) confirmed that co‐existence of MoO₃ as a major by‐product of hydrothermal synthesis. The as‐fabricated MoSe₂?MoO₃ composite based nitrite sensor showed remarkable selectivity and reproducibility with <3s of response time, excellent sensitivity and detection limit of 10.84 A M^?1 cm^?2 (R²=0.996) and 0.1 μM, respectively, in the range of 2.5–80 μM. The obtained sensitivity can be credited to the high surface area obtained from 1T phase MoSe₂ and α phase MoO₃ as the sensing material. The developed sensor was effectively evaluated for electrochemical recognition of nitrite in the water samples (potable and tap water) gathered from an industrial area. This new and efficient MoSe₂?MoO₃ based electrode material offers a new frontier for the progress of a novel composites by simple and single‐step approach which can be used for progress of non‐enzymatic and inexpensive electrochemical sensors for a wide range of analytical applications.     

Detecting lateral interfaces with focus‐engineered coherent anti‐Stokes Raman scattering microscopy

Focus‐engineered coherent anti‐Stokes Raman scattering (FE‐CARS) microscopy is used to highlight the lateral interfaces between chemically distinct media. Interface highlighting is achieved by using a HG10 mode for the Stokes laser beam and a HG00 mode for the pump laser beam in the forward detection scheme. The spectral and the orientation dependence of FE‐CARS are found to be in agreement with theoretical predictions. A brief discussion on the relevance of this technique for imaging third‐order nonlinear susceptibility interfaces in thin samples of biological or chemical importance is presented. Copyright © 2008 John Wiley & Sons, Ltd.