Probing for electrical inclusions with complex spherical waves

Let a physical body Ω in ?² or ?³ be given. Assume that the electric conductivity distribution inside Ω consists of conductive inclusions in a known smooth background. Further, assume that a subset Γ ? ?Ω is available for boundary measurements. It is proved using hyperbolic geometry that certain information about the location of the inclusions can be exactly recovered from static electric measurements on Γ. More precisely: given a ball B with center outside the convex hull of Ω and satisfying (B? ∩ ?Ω) ? Γ, boundary measurements on Γ with explicitly given Dirichlet data are enough to determine whether B intersects the inclusion. An approximate detection algorithm is introduced based on the theory. Numerical experiments in dimension two with simulated noisy data suggest that the algorithm finds the inclusion‐free domain near Γ and is robust against measurement noise. © 2007 Wiley Periodicals, Inc.     

Primary dependence of 7-aryl-2,5-di-t-butyl-1,3,5-cycloheptatriene valence tautomerism on the π-acceptor strength of the 7-aryl substituent

¹³C NMR studies showed that the population of the norcaradiene form of the title systems containing p-CH₃O, H, and p-CF₃ on the 7-aryl group increases in this order. The result is consistent with the prediction from the π-acceptor strength of the aryl group estimated by INDO calculations.     

Properties of holomorphic Wiener functions —skeleton,contraction, and local Taylor expansion

Summary We show that each holomorphic Wiener function has a skeleton which is intrinsic from several viewpoints. In particular, we study the topological aspects of the skeletons by using the local Taylor expansion for holomorphic Wiener functions.Supported in part by the Grant-in-Aid for Science Research 03740120 Min. Education     

Alternating copolymerization of carbon dioxide and epoxide by manganese porphyrin: The first example of polycarbonate synthesis from 1-atm carbon dioxide

The first successful example of the formation of polycarbonate from 1-atm carbon dioxide and epoxide was demonstrated by the alternating copolymerization of carbon dioxide and epoxide with manganese porphyrin as a catalyst. The copolymerization of carbon dioxide and cyclohexene oxide with (porphinato)manganese acetate proceeded under the 1-atm pressure of carbon dioxide to give a copolymer with an alternating sequence. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3549–3555, 2003     

A fully linear-time approximation algorithm for grammar-based compression

A linear-time approximation algorithm for the grammar-based compression is presented. This is an optimization problem to minimize the size of a context-free grammar deriving a given string. For each string of length n, the algorithm guarantees approximation ratio without suffix tree construction.     

Development of measuring magnetic Compton profiles by grazing incidence geometry

A novel technique of measuring a magnetic Compton profile using the grazing angle geometry against a sample surface (Grazing Incidence Magnetic Compton Profile) has been successively developed. Measurements of a magnetic moment and a magnetic Compton profile are possible for a Fe 200 nm film on a thick glass substrate. The estimated thinnest limit for measurements is 100 nm for a Fe film.     

Note on induced subgraphs of the unit distance graphE n

The unit distance graphE ⁿ is the graph whose vertices are the points in Euclideann-space, and two vertices are adjacent if and only if the distance between them is 1. We prove that for anyn there is a finite bipartite graph which cannot be embedded inE ⁿ as an induced subgraph and that every finite graph with maximum degreed can be embedded inE ^N ,N=(d ³ –d)/2, as an induced subgraph.     

Nuclearity of a nonnegative definite integral kernel on a separable metric space

The aim of this paper is to characterize the nuclearity of an integral operator, defined by a continuous non-negative definite square integrable kernel on a separable metric space, in terms of the integrability of the trace of the kernel function. Nuclearity here plays a role forU-statistics.     

Basic study of the gelation of dimethacrylate‐type crosslinking agents

An investigation was made of the gelation of dimethacrylate‐type crosslinking agents in view of an application for separation media. The study mainly centered on a crosslinking agent, glycerol dimethacrylate (GDMA), which is relatively hydrophilic because of a hydroxyl group in the middle of its structure. The gelation of GDMA was compared with that of other hydrophobic crosslinking agents such as ethylene glycol dimethacrylate and 1,6‐hexanediol dimethacrylate. The diluents used in the study were toluene, toluene with methanol, and cyclohexanol. The gelation was observed in real time with a charge coupled device camera and dynamic light scattering (DLS). Also, the separated dry gels were extensively characterized with scanning electron microscopy, BET (N₂ absorption and desorption isotherm), and Fourier transform infrared. DLS analysis showed a stronger molecular interaction of GDMA gelation in toluene, whereas this interaction was much weaker in an alcoholic solvent such as toluene with methanol or cyclohexanol. This indicated that GDMA gelation might proceed through hydrogen bonding as well as a crosslinking reaction of vinyl groups. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 949–958, 2006