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 .     

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.     

Possible one-dimensional 3He quantum fluid formed in nanopores

Heat capacity measurements have been made down to 5 mK for 3He fluid films adsorbed in one-dimensional (1D) nanometer-scale pores, 28 A in diameter, preplated with 4He of 1.47 atomic layers. At low 3He density, the heat capacity shows a density-dependent, Schottky-like peak near 150 mK asymptoting to the value corresponding to a 2D Boltzmann gas at high temperatures. The peak behavior is attributed to the crossover from a 2D gas to a 1D state at low temperatures. The degenerate state of the 1D 3He fluid is indicated by a predominantly linear temperature dependence below about 30 mK.     

Quasi-stadium laser diodes with an unstable resonator condition

We have observed lasing in a complicated eigenmode of a quasi-stadium laser diode with an unstable resonator consisting of two curved end mirrors obeying an unstable resonator condition and two straight sidewall mirrors. The laser was fabricated by application of a reactive-ion-etching technique to a molecular beam epitaxy-grown graded-index separate-confinement heterostructure single-quantum-well GaAs/AlGaAs structure. The far-field pattern shows that the lasing mode corresponds to the complicated lowest-loss mode obtained numerically by an extended Fox-Li method.     

On Sobolev and Capacitary Inequalities for Contractive Besov Spaces over d-sets

We derive Sobolev inequalities for Besov spaces B ^p,p (F), 0<<1, 1p< on d-sets F in R ⁿ , dn, from a metric property of the Bessel capacity on R ⁿ . We first extend Kaimanovitch's result on the equivalence of Sobolev and capacitary inequalites for contractive p-norms in a general setting allowing unbounded Lévy kernels. A simple part of the Jonsson–Wallin trace theorem for Besov spaces and some basic properties of Bessel and Besov capacities on R ⁿ are then utilized in getting the desired inequalities. When p=2, the Besov space being considered is a non-local regular Dirichlet space and gives rise to a jump type symmetric Markov process M over the d-set. The upper bound of the transition function of M and metric properties of M -polar sets are then exhibited.     

Helium-4 Bose fluids formed in one-dimensional 18 A diameter pores

Bose fluids restricted in one dimension (1D) are realized by adsorbing 4He atoms on the 1D pore walls with a diameter of about 18 A. The Bose fluid appears above an adsorbed amount after the pore walls are coated with the inert 4He atoms. Heat capacity of the fluid was observed to have a temperature-linear term at low temperatures. This corresponds to the phonon heat capacity of the Bose fluid in the 1D pores. We estimate the phonon velocity and the interaction of the 1D Bose fluid.