Two point one sided rendezvous

In a rendezvous search two or more teams called seekers try to minimize the time needed to find each other. In this paper, we consider two seekers in the plane. This is a one sided problem since Seeker 1 begins at a predetermined point O  . Seeker 2 begins at one of a finite set of points _xi$x_i$ with probability _pi$p_i$. We first discuss the general situation and then consider the specific case when Seeker 2 can begin from one of two points.     

Unitarity of Generalized Fourier–Gauss Transforms

Abstract

A generalized Fourier–Gauss transform is an operator acting in a Boson Fock space and is formulated as a continuous linear operator acting on the space of test white noise functions. It does not admit, in general, a unitary extension with respect to the norm of the Boson Fock space induced from the Gaussian measure with variance 1 but is extended to a unitary isomorphism if the Gaussian measure is replaced with the ones with different covariance operators. As an application, unitarity of a generalized dilation is discussed.     

A Permselective CeOx Coating To Improve the Stability of Oxygen Evolution Electrocatalysts

Highly active NiFeO_x electrocatalysts for the oxygen evolution reaction (OER) suffer gradual deactivation with time owing to the loss of Fe species from the active sites into solution during catalysis. The anodic deposition of a CeO_x layer prevents the loss of such Fe species from the OER catalysts, achieving a highly stable performance. The CeO_x layer does not affect the OER activity of the catalyst underneath but exhibits unique permselectivity, allowing the permeation of OH^? and O₂ through while preventing the diffusion of redox ions through the layer to function as a selective O₂‐evolving electrode. The use of such a permselective protective layer provides a new strategy for improving the durability of electrocatalysts.     

Second-generation total synthesis of haterumalide NA using B-alkyl Suzuki-Miyaura coupling

Second-generation total synthesis of haterumalide NA, a potent cytotoxic marine macrolide, was achieved by using B-alkyl Suzuki-Miyaura coupling and Nozaki-Hiyama-Kishi coupling as key steps (1.2% in 33 steps). Compared to our first-generation approach, the second-generation synthesis is much improved in the yield of key intermediate.     

Determination of cadmium in grains by isotope dilution ICP–MS and coprecipitation using sample constituents as carrier precipitants

A coprecipitation method using sample constituents as carrier precipitants was developed that can remove molybdenum, which interferes with the determination of cadmium in grain samples via isotope dilution inductively coupled plasma mass spectrometry (ID-ICPMS). Samples were digested with HNO₃, HF, and HClO₄, and then purified 6 M sodium hydroxide solution was added to generate colloidal hydrolysis compounds, mainly magnesium hydroxide. Cadmium can be effectively separated from molybdenum because the cadmium forms hydroxides and adsorbs onto and/or is occluded in the colloid, while the molybdenum does not form hydroxides or adsorb onto the hydrolysis colloid. The colloid was separated by centrifugation and then dissolved with 0.2 M HNO₃ solution to recover the cadmium. The recovery of Cd achieved using the coprecipitation was >97%, and the removal efficiency of Mo was approximately 99.9%. An extremely low procedural blank (below the detection limit of ICPMS) was achieved by purifying the 6 M sodium hydroxide solution via Mg coprecipitation using Mg(NO₃)₂ solution. The proposed method was applied to two certified reference materials (NIST SRM 1567a wheat flour and SRM 1568a rice flour) and CCQM-P64 soybean powder. Good analytical results with small uncertainties were obtained for all samples. This method is simple and reliable for the determination of Cd in grain samples by ID-ICPMS. Figure Overview of a coprecipitation method using sample constituents     

Unidirectional crystallization of charged colloidal silica due to the diffusion of a base

Dilute aqueous dispersions of charged colloidal silica (particle volume fraction = approximately 0.03-0.04, particle diameter = 110 nm) exhibit unidirectional crystal growth due to the diffusion of a weak base, pyridine (Py). Similar diffusion-crystallization is enabled by a salt of a weak acid and a strong base, sodium hydrogen carbonate (NaHCO3). The resulting crystals consist of columnar (or cubic) crystal grains with a maximum height of a few centimeters and a maximum width of 1 cm. The crystal growth process is attributed to a combination of (i) the diffusion of Py or NaHCO3 accompanied by a charging reaction of the silica particles and (ii) the charge-induced crystallization of the silica colloids. Theoretical growth curves based on the reaction-diffusion model for the case of Py were in good agreement with the observed curves. We also report the immobilization of the resulting large crystals by using a polymer hydrogel matrix.     

Chirality induction in cyclopolymerization. VI. Enantioselective cationic cyclopolymerization of divinyl ethers with chiral 10-camphorsulfonic acid/zinc chloride initiating system

Cyclopolymerization of benzaldehyde divinyl acetal ( 1 ) and 1,2-divinyloxybenzene ( 4 ) was carried out using (+)- or (−)-camphorsulfonic acid [(+)- or (−)- 2 ]/ZnCl₂ initiating system. Polymer 3 obtained from monomer 1 consisted essentially of cyclic repeating units, whereas polymer 5 from 4 possessed a small amount of residual vinyloxy groups. Both polymers 3 and 5 using (+)- 2 /ZnCl₂ showed optical activity with a negative sign of optical rotation. The molar optical rotation values of polymer 3 using ZnCl₂ · OEt₂ were larger than those using ZnCl₂. The CD spectra of the polymer with [Φ] = −30.1° ((−)- 3 ) and (4S,6S)-4,6-dimethyl-2-phenyl-1,3-dioxane showed a negative Cotton effect at 210 nm, whereas the polymer with [Φ] = +24.1° ((+)- 3 ) and (4R,6R)-4,6-dimethyl-2-phenyl-1,3-dioxane had mirror image CD curves with a positive Cotton effect at 210 nm. The absolute configurations of the major chiral cyclic units in (−)- and (+)- 3 were the SS- and RR-forms, respectively. © 1997 John Wiley & Sons, Inc.