Generating and counting valid patterns in routes between two points

Given two points on a plane, any rectilinear route between them can be specified by directions and lengths of constituent line segments. A word (pattern) over the alphabetN, E, S, andW is defined to represent a sequence of directions. The length of each line segment is ignored. In this paper we characterize and count all valid words, that is, those words representing non-selfcrossing routes.Notation V _n The set of all valid words of lengthn. - P ⁿ The set of all words of lengthn.     

Calculation of elastic electron-helium scattering at intermediate energies

The two-potential eikonal approximation is applied to the calculation of the differential cross section for elastic scattering of electrons by ground state helium atoms at energies 50 and 100 rV. The results agree very well with experiments.     

Doppler-limited dye laser excitation spectroscopy of DCF

The dye laser excitation spectrum of the vibronic transition of DCF was observed between 17 200 and 17 400 cm⁻¹ with the Doppler-limited resolution. DCF was produced by the reaction of microwave-discharged CF₄ with CD₃F. The observed spectra, which were found to be nearly free of perturbations, were assigned to 858 transitions of the K′_a − K″_a = 4−5, 3−4, 2−3, 1−2, 0−1, 1−0, 2−1, 3−2, 3−3, 2−2, 1−1, 0−0, 2−0, and 0−2 subbands, and were analyzed to determine the rotational constants and centrifugal distortion constants for both the and à states. The rotational constants of DCF thus determined were combined with those of HCF to calculate the structural parameters for this molecule: r(C---H) = 1.138 Å, r(C---F) = 1.305 Å, and HCF = 104.1° for the ground state, and r(C---H) = 1.063 Å, r(C---F) = 1.308 Å, and HCF = 123.8° for the excited à state.     

Binding and catalytic behavior of modified γ-cyclodextrins

Modified -cyclodextrins appended by an aromatic moiety show unique binding behavior, including a guest molecule together with the appended moiety in their -cyclodextrin cavities. Excimer formation, photoresponsive binding, association with -cyclodextrin and enhanced catalytic activity have been explained on this basis.     

Reinvestigation of thiabenzenes A new result of the reaction of 9-phenylthioxanthylium salt and phenyllithium

“9,10-Diphenyl-10-thiaanthracene” was found to be a mixture of monomeric species such as 9-phenyl-, 9,9-diphenyl-, 3,9-diphenyl-, 3,9,9-triphenyl- and 4,9,9-triphenylthioxanthenes, and several kinds of dimers and so on. Some of them were formed by radical phenylation. The mechanism was proposed.     

Oxidation of substrates having labile hydrogens by superoxide in the presence of phosgene dimer

Superoxide (O₂^?) oxidized substrates having labile hydrogens to ketones in the presence of phosgene dimer. Oxidations with similar treatment of alkynes were examined. The reaction mechanism was also discussed.     

An Orientable Secondary Emission Detector for Plasma Experiments

An orientable secondary emission detector is described. Its response to the fast neutral atom flux emitted by a plasma allows to measure the density profile, the phase space distribtuion function and the average energy of the plasma ions.