Mixed finite-element methods for Hamilton-Jacobi-Bellman-type equations

The numerical solution of Dirichlet's problem for a second-orderelliptic operator in divergence form with arbitrary nonlinearitiesin the first- and zero-order terms is considered. The mixedfinite-element method is used. Existence and uniqueness of theapproximation are proved and optimal error estimates in L² aredemonstrated for the relevant functions. Error estimates arealso derived in L^q, 2q+     

Metal-oxygen-metal arrays in lamellar hybrid materials: cobalt and manganese 4-cyclohexene-1,2-dicarboxylates

We have obtained three layered hybrid materials from the hydrothermal reaction of 4-cyclohexene-1,2-dicarboxylic acid with Co and Mn salts: Co(C(8)H(8)O(4))[1], Mn(H(2)O)(C(8)H(8)O(4))[2], and Mn(4)(H(2)O)(C(8)H(8)O(4))(4).0.3(H(2)O)[3]. The structures for all materials were solved by single-crystal XRD ([1]P1, a=4.805(2) A, b=6.650(3) A, c=12.960(6) A, alpha=98.285(7) degrees, beta=98.986(7) degrees, gamma=95.689(7) degrees, V= 401.6(3) A(3), R(1)= 0.0438; [2] P2(1)/c, a=11.151(2) A, b=11.330(2) A, c=7.6560(15) A, beta=108.813(3) degrees , V=915.6(3) A(3), R(1)=0.0412; [3] P1, a= 11.412(3) A, b=12.136(4) A, c=13.809(4) A, alpha=104.703(6) degrees, beta=103.207(6) degrees, gamma=92.468(5) degrees, V=1790.6(9) A(3), R(1)=0.1056). While all three structures are two-dimensional overall, the metal-oxygen-metal dimensionality within the layers varies from isolated metal atoms in the case of [1] to 1D ribbons of vertex sharing MnO(6) octahedra [2] and 2D arrays of edge- and vertex-sharing polyhedra in [3].     

SUPERPOROUS HYDROGELS: FAST RESPONSIVE HYDROGEL SYSTEMS

ABSTRACT

Superporous hydrogels, hydrogels with pore sizes in the range of 100 μm and larger, were synthesized using N-isopropyl-acrylamide (NIPAM) and acrylamide (AM). The superporous hydrogels were synthesized by crosslinking polymerization of monomers in the presence of gas bubbles. The pores of superporous hydrogels were connected to each other to form open capillary channels, which provided fast response to the changes in the environmental temperature. Upon increase in temperature from 10°C to 65°C, the superporous hydrogel made from a monomer solution of NIPAM:AM = 9:1 shrank from the fully swollen state (volume of 36 cm³) to the fully collapsed state (volume of 6.5 cm³) in 72±14 sec. When the temperature was changed back to 10°C, the superporous hydrogel swelled to 36 cm³ in 78±15 sec. This deswelling-swelling cycle was repeated many times without changes in the thermo-reversible property of the superporous hydrogel. The response time of the superporous hydrogels was thousand times faster than that of conventional hydrogels. The fast response of the superporous hydrogels is due to the rapid uptake or exclusion of water molecules through the extensive capillary channels. Because superporous hydrogels still maintain the open capillary structure even after drying, the dried superporous hydrogels can also swell to the equilibrium swelling state within minutes. These fast responsive hydrogels can find many pharmaceutical and medical applications.     

Wedge Operations and Doubling Operations of Real Toric Manifolds

This paper deals with two things.First,the cohomology of canonical extensions of real topological toric manifolds is computed when coefficient ring G is a commutative ring in which 2 is unit in G.Second,the author focuses on a specific canonical extensions called doublings and presents their various properties.They include existence of infinitely many real topological toric manifolds admitting complex structures,and a way to construct infinitely many real toric manifolds which have an odd torsion in their cohomology groups.Moreover,some questions about real topological toric manifolds related to Halperin's toral rank conjecture are presented.     

Green approaches via nanocatalysis with nanoporous materials: Functionalization of mesoporous materials for single site catalysis

Among the various green keys, catalysis, especially using heterogeneous catalysts, has been powerfully applied to achieve greener chemical processes. Here are presented nanoporous materials which have mesoporosity with the functional groups on the inner pore walls. The materials were synthesized via a rather greener process, such as microwave synthesis, and over these nanocatalysts some of the green chemical reactions were carried out with high activities and selectivities. Cobalt species has been successfully functionalized and stabilized as a Co(III) complex onto SBA-15 support and proven to be an active catalyst in alkylaromatic oxidation with molecular oxygen, styrene epoxidation with tert-butyl hydroperoxide (TBHP), and allylic oxidation of cycloolefins with H₂O₂. Short-channeled amino-functionalized SBA-15 catalyst with hexagonal plate morphology was synthesized directly by using microwave synthesis from the co-condensation of aminopropyl triethoxysilane (APTES) and sodium metasilicate under a strong acidic condition. The catalyst showed high catalytic activity in liquid-phase Knoevenagel condensation reactions, due to easy diffusion and mass transfer of substrates into the short mesopore channel. The HO₃S–SBA-15 was prepared by grafting of mercaptopropyl trimethoxysilane onto the calcined mesoporous silica surface and subsequently oxidized with H₂O₂. The resulting catalyst was applied as a Bronsted solid-acid catalyst for the esterification of oleic acid with methanol.     

Stability of a von Karman equation with infinite memory

In this paper, we consider a von Karman equation with infinite memory. For von Karman equations with finite memory, there is a lot of literature concerning on existence of the solutions, decay of the energy, and existence of the attractors. However, there are few results on existence and energy decay rate of the solutions for von Karman equations with infinite memory. The main goal of the present paper is to generalize previous results by treating infinite history instead of finite history.     

Enhancement of catalytic activity in dehydrogenation ofn-dodecane over nano-structured Pt-Sn/SBA-16 catalysts by microwave drying

In the present investigation, experimental results from a study of cubic SBA-16-supported Pt-Sn bimetallic catalysts used to investigate dehydrogenation ofn-dodecane to 1-dodecene are presented. Pt (1 wt%)-Sn (1 wt%)/SBA-16 catalyst is synthesized using a simple co-impregnation (CI) method. Further, the impregnated catalysts are dried separately using microwave drying (MW-D) and conventional electrical drying (CE-D) techniques. The microwave-mediated drying of Pt (1%)-Sn (1%)/SBA-16 shows a better catalytic performance and time-on-stream activity for the target reaction.     

Lewis-type catalytic activity of direct incorporated Zr- and Sn-SBA-16 catalysts

Metal incorporation into nanoporous materials could give Lewis acid sites through the framework substitution of silica matrix, which are supposed to be in tetrahedral substitution of silica. In this work, Zr- and Sn-incorporated SBA-16 were directly synthesized by the microwave synthesis method. These microwave synthesized Zr- and Sn-incorporated mesoporous silica materials were applied in activation of ketones by Lewis acid sites to catalyze Meerwein-Ponndorf-Verly reduction of cyclohexanone and Baeyer-Villiger oxidation of adamantanone, respectively. Optimum incorporated Zr- and Sn-species gave almost 100% selectivity with high activity onto corresponding alcohol and lactone, respectively.