On the Parameterization of Rational Ringed Surfaces and Rational Canal Surfaces

Ringed surfaces and canal surfaces are surfaces that contain a one-parameter family of circles. Ringed surfaces can be described by a radius function, a directrix curve and vector field along the directrix curve, which specifies the normals of the planes that contain the circles. In particular, the class of ringed surfaces includes canal surfaces, which can be obtained as the envelopes of a one-parameter family of spheres. Consequently, canal surfaces can be described by a spine curve and a radius function. We present parameterization algorithms for rational ringed surfaces and rational canal surfaces. It is shown that these algorithms may generate any rational parameterization of a ringed (or canal) surface with the property that one family of parameter lines consists of circles. These algorithms are used to obtain rational parameterizations for Darboux cyclides and to construct blends between pairs of canal surfaces and pairs of ringed surfaces.     

Identification of Intermediates in Zeolite‐Catalyzed Reactions by In Situ UV/Vis Microspectroscopy and a Complementary Set of Molecular Simulations

The optical absorption properties of (poly)aromatic hydrocarbons occluded in a nanoporous environment were investigated by theoretical and experimental methods. The carbonaceous species are an essential part of a working catalyst for the methanol‐to‐olefins (MTO) process. In situ UV/Vis microscopy measurements on methanol conversion over the acidic solid catalysts H‐SAPO‐34 and H‐SSZ‐13 revealed the growth of various broad absorption bands around 400, 480, and 580 nm. The cationic nature of the involved species was determined by interaction of ammonia with the methanol‐treated samples. To determine which organic species contribute to the various bands, a systematic series of aromatics was analyzed by means of time‐dependent density functional theory (TDDFT) calculations. Static gas‐phase simulations revealed the influence of structurally different hydrocarbons on the absorption spectra, whereas the influence of the zeolitic framework was examined by using supramolecular models within a quantum mechanics/molecular mechanics framework. To fully understand the origin of the main absorption peaks, a molecular dynamics (MD) study on the organic species trapped in the inorganic host was essential. During such simulation the flexibility is fully taken into account and the effect on the UV/Vis spectra is determined by performing TDDFT calculations on various snapshots of the MD run. This procedure allows an energy absorption scale to be provided and the various absorption bands determined from in situ UV/Vis spectra to be assigned to structurally different species.     

Statistical testing of optimality conditions in multiresponse simulation-based optimization

This article studies simulation-based optimization with multiple outputs. It assumes that the simulation model has one random objective function and must satisfy given constraints on the other random outputs. It presents a statistical procedure for testing whether a specific input combination (proposed by some optimization heuristic) satisfies the Karush–Kuhn–Tucker (KKT) first-order optimality conditions. The article focuses on “expensive” simulations, which have small sample sizes. The article applies the classic t test to check whether the specific input combination is feasible, and whether any constraints are binding; next, it applies bootstrapping (resampling) to test the estimated gradients in the KKT conditions. The new methodology is applied to three examples, which gives encouraging empirical results.     

Substituent effects on the disproportionation—combination rate constant ratios for gas‐phase halocarbon radicals,Part 5: Reactions of CF3 + CF3CH2CHCH3 and CF3CH2CHCH3 + CF3CH2CHCH3

Rate constant ratios, k_d/k_c for the disproportionation/combination reaction have been measured as 0.07 ± 0.02 when an H is removed from the CH₂ position of the CF₃CH₂CHCH₃ radical and as 0.24 ± 0.03 when the H is removed from the CH₃ position in the reaction with the CF₃ radical. For the self‐reaction between two CF₃CH₂CHCH₃ radicals, k_d/k_c has been measured as 0.27 ± 0.03 when the H is removed from the CH₂ position and as 0.47 ± 0.04 when the H is removed from the CH₃ position. The branching fraction, corrected for the number of hydrogens at each site, is 0.70 favoring the methyl position when the acceptor radical is CF₃ and 0.54 when CF₃CH₂CHCH₃ is the acceptor radical. Branching fraction results show that the CF₃ substituent on the CF₃CH₂CHCH₃ radical hinders disproportionation when CF₃ is the acceptor radical. When the accepting radical is CF₃CH₂CHCH₃ the CF₃ substituent may slightly impede the disproportionation reaction, but the branching ratio is nearly statistical. The effect of substituents on the donor radical, CF₃CH₂CHX, will be discussed for the series X = H, CF₃, Cl, and CH₃ when the acceptor radical is CF₃. © 2001 John Wiley & Sons, Inc. Int J Chem Kinet 33: 549–557, 2001     

Limited packings in graphs

We define a k-limited packing in a graph, which generalizes a 2-packing in a graph, and give several bounds on the size of a k-limited packing. One such bound involves the domination number of the graph, and here we show all trees attaining the bound can be built via a simple sequence of operations. We consider graphs where every maximal 2-limited packing is a maximum 2-limited packing, and characterize their structure in a number of cases.     

Iridium and Rhodium as Permanent Chemical Modifiers for the Determination of Ag, As, Bi, Cd, and Sb by Electrothermal Atomic Absorption Spectrometry

Performance of graphite platforms coated with Ir, Rh, and a mixture of both, as permanent modifiers for Ag, As, Bi, Cd, and Sb, was evaluated. The coating process is very simple: a solution containing Ir, Rh, or a mixture of both is pipetted on the platform inserted in a graphite tube, and this is submitted to a temperature program. High pyrolysis temperatures are allowed, especially for As and Bi, 1400°C, in the Ir + Rh-coated platform. The sensitivity remains about the same for all analytes with different coatings, except for As in the Ir-coated platform, for which a remarkable gain was obtained in comparison to the other coatings. The lifetimes of the treated tubes were in the range 50 to more than 1000 cycles, being especially long for Sb and Ag in the Rh-coated platform, more than 600 and 1000 cycles, respectively. The Rh coating could not be used for Bi and Cd. Analysis of a certified reference water and of acid oyster tissue digests showed the absence of interference and good precision. Advantages of the permanent coatings are the possibility of low blanks byin situcleaning of the modifier and shorter analysis time.     

Twist points of the von Koch snowflake

It is known that the set of twist points in the boundary of the von Koch snowflake domain has full harmonic measure. We provide a new, simple proof, based on the doubling property of the harmonic measure, and on the existence of an equivalent measure, invariant and ergodic with respect to the shift.