Shadowing with multidimensional time in Banach spaces

We study linear dynamical systems with multidimensional time in Banach spaces. Using Taylor functional calculus we prove that under additional assumptions hyperbolic systems have shadowing property.     

Global and local optimization using radial basis function response surface models

The focus of this paper is the optimization of complex multi-parameter systems. We consider systems in which the objective function is not known explicitly, and can only be evaluated through computationally intensive numerical simulation or through costly physical experiments. The objective function may also contain many local extrema which may be of interest. Given objective function values at a scattered set of parameter values, we develop a response surface model that can dramatically reduce the required computation time for parameter optimization runs. The response surface model is developed using radial basis functions, producing a model whose objective function values match those of the original system at all sampled data points. Interpolation to any other point is easily accomplished and generates a model which represents the system over the entire parameter space. This paper presents the details of the use of radial basis functions to transform scattered data points, obtained from a complex continuum mechanics simulation of explosive materials, into a response surface model of a function over the given parameter space. Response surface methodology and radial basis functions are discussed in general and are applied to a global optimization problem for an explosive oil well penetrator.     

Second Dissociation Constants of 4-[N-morpholino]butanesulfonic Acid and N-[2-hydroxyethyl]piperazine-N′-4-butanesulfonic Acid from 5 to 55°C

The values of the second dissociation constant, pK ₂, for the dissociation of the NH⁺ charge center of the zwitterionic buffer compounds 4-(N-morpholino)butanesulfonic acid (MOBS), and N-(2-hydroxyethyl)piperazine-N-4-butanesulfonic acid (HEPBS) have been determined from 5 to 55°C, including, 37°C at intervals of 5°C. The electromotive-force (emf) measurements have been made utilizing hydrogen electrodes and silver–silver chloride electrodes. The value of pK ₂ for MOBS was found to be 7.702 ± 0.0005, and 8.284 ± 0.0004 for HEPBS, at 25°C, respectively. The related thermodynamic quantities, G ^o, H ^o, S ^o, and C _p ^o for the dissociation processes of MOBS and HEPBS have been derived from the temperature coefficients of pK ₂. Both the MOBS and HEPBS buffer materials are useful as primary pH standards for the control of pH 7.3 to 8.6 in the region close to that of physiological fluids.     

On equilibrium distributions and detailed balance relations in non-isothermal systems

The significance of the detailed balance principle and equilibrium solutions of the master equation is discussed from a thermodynamic point of view for isolated and isothermal systems. Starting from a master equation for all the time dependent degrees of freedom it is shown that the uniqueness of the equilibrium distribution as a stationary solution is ensured if the detailed rate constants are balanced with the aid of the distribution which maximizes the entropy subject to the thermodynamic constraints. This procedure should precede physical assumptions which simplify the original master equation, e.g. the assumption that rapidly relaxing modes can be described by canonical distribution functions.     

Beiträge zur Ringofenmethodik. XV

Microchimica Acta - Ein Trennungsschema für Cs(I), Ag(I), Ba(II), Zn(II), Cd (II), Mn(II), Pb(II), Cu(II), Ni(II), Co(II), Bi(III), Al(III) und Fe(III) unter Verwendung von Dithiooxamid als...     

Efficient Demethylation of Methyl Esters with Anhydrous Trifluoroacetic Acid

Trifluoroacetic acid (TFA) is an effective reagent for the demethylation of methyl esters under anhydrous conditions, affording the parent acids and methyl trifluoroacetate.     

p-sd Shell gap reduction in neutron-rich systems and cross-shell excitations in 20 O

Excited states in 20O were populated in the reaction 10Be(14C,alpha) at Florida State University (FSU). Charged particles were detected with a particle telescope consisting of 4 annularly segmented Si surface barrier detectors and gamma radiation was detected with the FSU gamma detector array. Five new states were observed below 6 MeV from the alpha-gamma and alpha-gamma-gamma coincidence data. Shell model calculations suggest that most of the newly observed states are core-excited 1p-1h excitations across the N=Z=8 shell gap. Comparisons between experimental data and calculations for the neutron-rich O and F isotopes imply a steady reduction of the p-sd shell gap as neutrons are added.