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.     

The effect of various calcination treatments on the photocatalytic activity of a rod-type TiO<Subscript>2</Subscript> electrode for oxidation of ethanethiol

It was found that the photoelectrochemical performance and photocatalytic activity of rod-type TiO₂ electrodes were affected by various post-calcination treatments, for example, calcination in NH₃ or under vacuum. Post-calcination treatment in NH₃ at 773 K was particularly effective in increasing the photoelectrochemical performance and photocatalytic activity of rod-type TiO₂ electrodes. A unique photoelectrochemical circuit was constructed by connecting a rod-type TiO₂ electrode to a Pt electrode through a silicon solar cell in which the negative bias was applied on the rod-type TiO₂ electrode. It was found that the photoelectrochemical circuit can effectively oxidize ethanethiol in water into CO₂.     

Probabilistic evaluation of interconnectable capacity for wind power generation

We propose a novel framework for probabilistic evaluation of interconnectable capacity for wind power generation. This is based on mathematical modeling of load frequency control systems, which captures their nonlinear (saturation and rate limiting) dynamical characteristics, and stochastic uncertainty of wind power output deviation. The method called stochastic linearization is used to analyze resulting power quality. The effectiveness of the proposed method is examined by numerical simulation.     

Determination of kynurenic acid levels in rat brain microdialysis samples and changes in kynurenic acid levels induced by N‐acetylaspartic acid

The levels of kynurenic acid, an endogenous antagonist of α₇ nicotinic acetylcholine and N‐methyl‐D ‐aspartate receptors, were measured in microdialysis samples obtained from the prefrontal cortices of rats using column‐switching high‐performance liquid chromatography with fluorescence detection. When the perfusate was constantly infused at a rate of 1.0 μ/min, the in vitro recovery of kynurenic acid through the dialysis membrane was approximately 20.4%, and the precision was within 1.31%. Endogenous kynurenic acid in the microdialysis sample was clearly detected using column‐switching high‐performance liquid chromatography. As an application study, N‐acetyl‐L ‐aspartic acid, an endogenous metabolite and precursor of N‐acetyl‐L ‐aspartyl‐L ‐glutamic acid, which is an agonist of metabotropic glutamate receptors, was infused for 120 min through the microdialysis probe. The kynurenic acid level significantly increased during the infusion of N‐acetyl‐L ‐aspartic acid, suggesting that kynurenic acid might have some association with N‐acetyl‐L ‐aspartic acid in vivo. Copyright © 2009 John Wiley & Sons, Ltd.     

Fast computation of incomplete elliptic integral of first kind by half argument transformation

We developed a new method to calculate the incomplete elliptic integral of the first kind, F(j|m){F(\varphi|m)} , by using the half argument formulas of Jacobian elliptic functions. The method reduces the magnitude of j{\varphi} by repeated usage of the formulas while fixing m. The method is sufficiently precise in the sense that the maximum relative error is 3–5 machine epsilons at most. Thanks to the simplicity of the half argument formulas, the new procedure is significantly faster than the existing procedures. For example, it runs 20–60% faster than Bulirsch’ function, el1, and 1.9–2.2 times faster than the method using Carlson’s function, R _F .     

Toroidal surgeries on hyperbolic knots

For a hyperbolic knot in , a toroidal surgery is Dehn surgery which yields a -manifold containing an incompressible torus. It is known that a toroidal surgery on is an integer or a half-integer. In this paper, we prove that all integers occur among the toroidal slopes of hyperbolic knots with bridge index at most three and tunnel number one.

     

Determination of fluoxetine enantiomers in rat plasma by pre-column fluorescence derivatization and column-switching high-performance liquid chromatography

A column-switching HPLC method employing both octadecylsilica (ODS) and chiral columns with fluorescence detection was developed for the determination of enantiomer of fluoxetine (FLX), an antidepressant drug, in rat plasma. Racemic FLX was derivatized with a fluorescent reagent, 4-(N-chloroformylmethyl-N-methyl)amino-7-nitro-2,1,3-benzoxadiazole (NBD-COCl) or 4-(N-chloroformylmethyl-N-methyl)amino-7-N,N-dimethylaminosulfonyl-2,1,3-benzoxadiazole (DBD-COCl) and the enantiomeric separation of the resultant derivatives was examined on an amylose-based chiral column (CHIRALPAK AD-RH) in the reversed-phase mode. The derivative with NBD-COCl (NBD-FLX) showed a sufficient separation factor (a) and resolution (Rs) compared with that with DBD-COCl. Thus, FLX was derivatized with NBD-COCl and the resultant NBD-FLX was first quantified on the ODS column and then introduced to the CHIRALPAK AD-RH column via a six-port switching valve to examine the enantiomeric ratio. The intra- and inter-day accuracy (97.6-112.7%) and precision (1.47-10.60%) were satisfactory in the range 10-1000 nM FLX and the limit of quantification was approximately 10 nM. The absolute recoveries of FLX with hexane from rat plasma were in the range 87.5-92.2% (n = 3). The method was applied to determine FLX enantiomers in the plasma of rats administered FLX orally, and it was shown that the R-isomer was eliminated faster than the S-isomer.     

Supramolecular graphyne: a C(sp)-H...N hydrogen-bonded unique network structure of 2,4,6-triethynyl-1,3,5-triazine

The crystallization of 2,4,6-triethynyl-1,3,5-triazine (2) leads to a pi-stacked layered structure of a C(sp)-H...N hydrogen-bonded unique hexagonal network structure, which may be regarded as a supramolecular analogue of a hitherto unknown graphyne network: in-plane intermolecular interactions are short and linear H...N contacts (2.31 and 2.34 A) and the interlayer separation is 3.23 A.