Inner derivations on ultraprime normed real algebras

We show that the set of all inner derivations of an ultraprime real Banach algebra is closed within all bounded derivations. More concretely, we show that for such an algebra A there exists a positive number γ (depending only on the “constant of ultraprimeness” of A) satisfying γ ∥ a+Z(A) ∥≦∥ D _a ∥ for all a in A, where Z(A) denotes the centre of A and D _a denotes the inner derivation on A induced by a. This result is an extension of the corresponding complex version obtained by the authors in [Proc. Amer. Math. Soc., to appear]. The proof relies on the following theorem: ultraproducts of a family of central ultraprime real Banach algebras with a unit and with constant of ultraprimeness greater than or equal to a fixed positive constant K are central ultraprime Banach algebras with a unit. This fact is obained via a general result for real Banach algebras that reads as follows: If A is a central real Banach algebra with a unit 1, then for every a in A satisfying ∥ 1+a ² ∥<1 we have [1+√1?||1+1a ²||]²≦2(|?l+M _a ||+||D _a ||) where M _a denotes the two-sided multiplication operator by a on A.     

Analysis and Optimization of Stability Robustness Bounds for Discretized Systems

In this paper, robustness bounds for the perturbations of continuous-time systems to ensure the stability of their discretized counterparts are developed. Both zero-order hold and P-step matrix integrators are considered. The effect of the sampling time on the robustness bounds is studied via examples. To determine how well a simulated system will retain the robustness properties of the continuous-time system being simulated, a new criterion for the selection of the simulation method and time step is introduced. Both implicit and explicit robustness measures for sampled-data systems are obtained.     

The algebra of hyperboloids of revolution

If we change the sign of p ? m columns (or rows) of an m × m positive definite symmetric matrix A, the resultant matrix B has p negative eigenvalues. We give systems of inequalities for the eigenvalues of B and of the matrix obtained from B by deleting one row and column. To obtain these, we first develop characterizations of the eigenvalues of B which are analogous to the minimum-maximum properties of the eigenvalues of a symmetric A, i.e. the Courant-Fischer theorem. These results arose from studying probability distributions on the hyperboloid of revolution

$\text{x}{}^2{}_1\text{+ ? + x}{}^2{}_{\mathrm{m?p}}\text{? x}{}^2{}_{\mathrm{m\; ?\; p\; +\; 1}}\text{? ? ? x}{}^2{}_{\mathrm{m}}\text{= 1}$

. By contrast, the familiar results are associated with the sphere x²₁ + ? + x²_m = 1.     

X-ray crystal structure and1H-NMR chiral shift reagent study of a crown trimer

3,4,5-Trimethoxybenzyl alcohol was cyclooligomerized with a bentonite clay used as a catalyst. Results of the crystal structure analysis of the racemic (±) nonamethoxy[1,1,1]orthocyclophane trimer, C₃₀H₃₆O₉, are described. The structure was determined by X-ray diffraction at 293 K and shown to belong to the triclinic space group P . The compound possesses a distorted crown conformation with unusual C–H...O intermolecular interactions, and with a crystal packing not observed before in other related derivatives. The racemic mixture was also discriminated in its two enantiomeric isomers, using proton NMR and Eu(III) as a chiral shift reagent.     

Density functional theory study of water activation and COads + OHads reaction on pure platinum and bimetallic platinum/ruthenium nanoclusters

A density functional theory study of the elementary steps that lead to the removal of CO(ads(Pt)) over alloyed and sequentially deposited Pt/Ru bimetallic nanoclusters is presented. The reaction energies and activation barriers for the H2O(ads(Ru)) dissociation and CO(ads(Pt)) + OH(ads(Ru)) reaction are estimated in solid-gas interface and in a microsolvated environment to determine which surface morphology is more tolerant to COads poisoning. On the basis of the energetics, the sequentially deposited Pt/Ru nanocluster is predicted to be a much more promising anode catalyst than the alloy cluster surface in fuel cell applications.     

Interfacial properties of poly(maleic acid-alt-1-alkene) disodium salts at water/hydrocarbon interfaces

The interfacial properties of poly(maleic acid-alt-1-alkene) disodium salts at hydrocarbon/water interfaces are determined. In all the studied systems, the interfacial tension decreases markedly with the polyelectrolyte concentration as the side-chain length increases. The results of the standard free energy of adsorption, DeltaG(ads)(0), are a linear function of the number of carbon atoms in the polyelectrolyte side chain. The contribution to DeltaG(ads)(0) per mol of methylene group varies from -0.64 to -0.52 kJ/mol for the n-octane/water to n-dodecane/water interfaces. DeltaG(ads)(0) data also reveal that the adsorption process is mainly determined by adsorption efficiency. Comparatively, the adsorption effectiveness seems to play a less important role. The theoretical interaction energies calculated for the insertion of one hydrocarbon molecule into the space formed by two neighboring polyelectrolyte side chains are in good agreement with the experimental results. The latter results are consistent with van der Waals-type interactions between the hydrocarbon molecules and the polyelectrolyte side chains.     

Surface properties of poly(N-monoalkylmaleamic acid-alt-styrene) sodium salts: effect of the molecular weight and the side chain length

The surface properties of poly(N-monoalkylmaleamic acid-alt-styrene) sodium salts are studied as a function of the molecular weight and the size of the linear alkyl lateral chain of the polyelectrolyte. The experimental results are well described by the Gibbs-Szyszkowski treatment. Both the surface tension behavior and the standard free energy of adsorption depend on the polyelectrolyte side chain and on the average molecular weight, M(w). An M(w)-dependent contribution to the free energy of adsorption ranging from -1.21 to -1.05 kJ for mole of methylene groups is found. The area covered by monomer units increases with M(w) and the sizes of side chains are similar to those reported in small-molecule systems. The nature of the functional group amide in the side chain has practically no effect on the surface properties as compared with the ester group in this kind of polyelectrolytes.     

Autoradiography of mineral ions in green leaves and flowers,absorbed with and without synthetic fulvic acids

The disproportionation of pentavalent plutonium is traditionally represented by two inconsistent equations. The inconsistency puts the widely-accepted, fourth-power hydrogen-ion dependence of the reaction into question. The balanced reaction equation suggests that both the stoichiometry and the acid-dependence of Pu(V) disproportionation depend on the pH of the plutonium solution.Los Alamos National Laboratory is operated for the U.S. Department of Energy by the University of California under Contract No. W-7405-ENG-36.