Grammatical Verification for Mathematical Formula Recognition Based on Context-Free Tree Grammar

This paper proposes the use of a formal grammar for the verification of mathematical formulae for a practical mathematical OCR system. Like a C compiler detecting syntax errors in a source file, we want to have a verification mechanism to find errors in the output of mathematical OCR. A linear monadic context-free tree grammar (LM-CFTG) is employed as a formal framework to define “well-formed” mathematical formulae. A cubic time parsing algorithm for LM-CFTGs is presented. For the purpose of practical evaluation, a verification system for mathematical OCR is developed, and the effectiveness of the system is demonstrated by using the ground-truthed mathematical document database InftyCDB-1 and a misrecognition database newly constructed for this study.     

Numerical analysis of dipole sound source around high speed trains

As the maximum speed of high speed trains increases, the effect of aeroacoustic noise on the sound level on the ground becomes increasingly important. In this paper, the distribution of dipole sound sources at the bogie section of high speed trains is predicted numerically. The three-dimensional unsteady flow around a train is solved by the large eddy simulation technique. The time history of vortices shows that unstable shear layer separation at the leading edge of the bogie section sheds vortices periodically. These vortices travel downstream while growing to finally impinge upon the trailing edge of the section. The wavelength of sound produced by these vortices is large compared to the representative length of the bogie section, so that the source region can be regarded as acoustically compact. Thus a compact Green's function adapted to the shape can be used to determine the sound. By coupling the instantaneous flow properties with the compact Green's function, the distribution of dipole sources is obtained. The results reveal a strong dipole source at the trailing edge of the bogie section where the shape changes greatly and the variation of flow with time is also great. On the other hand, the bottom of the bogie section where the shape does not change, or the leading edge and boundary layer where the variation of flow with time is small, cannot generate a strong dipole source.     

High-speed recovery of germanium in a convection-aided mode using functional porous hollow-fiber membranes

A porous hollow-fiber membrane capable of recovery of germanium from a liquid stream was prepared by radiation-induced graft polymerization of an epoxy-group-containing vinyl monomer, glycidyl methacrylate, and subsequent functionalization with 2,2'-iminodiethanol, di-2-propanolamine, N-methylglucamine, and 3-amino-1,2-propanediol. The functional group density was as high as 1.4 mol per kg of the resultant hollow fiber. The polymer chains containing functional groups surrounding the pores enabled a high-speed recovery of germanium during permeation of a germanium oxide (GeO2) solution through the pores of the hollow fiber. Because of a negligible diffusional mass-transfer resistance, germanium concentration changes with the effluent volume, i.e., breakthrough curves, overlapped irrespective of the residence time of the solution, which ranged from 0.37 to 3.7 s across the hollow fiber. After repeated use of adsorption and elution, the adsorption capacity did not deteriorate.     

Light attenuation in a semitransparent foam sheet-Thickness measurement for industrial use

An optical method for measuring the thickness of heterogeneous materials has been studied. The method is based on the light attenuation theory. A complete system has been constructed in order to demonstrate the applicability of the present method for industrial use. The experimental set-up consists of semiconductor lasers, focusing lenses, photo-diodes serving as a power meter and a personal computer with an A/D converter for data acquisition. Averaging of numerous measurements is required in the present method because the heterogeneous cell structure of the foam material yields large fluctuations in transmitted light levels. The fluctuations can be reduced to below 1% of the transmitted light power by 80 times averaging. The error of the measurement is considered to be a few tens of micrometers in thickness. The present system is capable of sampling data at a rate of 400 Hz and has been successfully applied to a manufacturing process.     

Quantum Mechanics of the Composite System and Its Subsystems

We revisit the EPR problem and make clear what is a correct comprehension of its problem. When one applies the quantum mechanics correctly, it will be shown that there is no paradox. According to these lines of thought, a quantum teleportation scheme without resort to the von Neumann projection postulate is presented.     

Finite solvable groups whose $$\mathfrak{F}$$ -hypercenter contains all minimal subgroups

Archiv der Mathematik -     

syn-selective direct catalytic asymmetric Mannich-type reactions of hydroxyketones using Y{N(SiMe3)2}3/linked-BINOL complexes

[reaction, structure: see text] Chiral Y{N(SiMe3)2}3/linked-BINOL catalyst generated Y-enolate in situ from various hydroxyketones (R2 = aryl, heteroaryl). Beta-amino-alpha-hydroxy ketones (R1 = aryl, heteroaryl, alkenyl) were obtained syn-selectively (up to 96/4) in high ee (up to 98%) and good yield (up to 98% yield).