On algebraic relations for Ramanujan’s functions

Let P,Q, and R denote the Ramanujan Eisenstein series. We compute algebraic relations in terms of P(q ⁱ ) (i=1,2,3,4), Q(q ⁱ ) (i=1,2,3), and R(q ⁱ ) (i=1,2,3). For complex algebraic numbers q with 0<|q|<1 we prove the algebraic independence over ? of any three-element subset of {P(q),P(q ²),P(q ³),P(q ⁴)} and of any two-element subset of {Q(q),Q(q ²),Q(q ³)} and {R(q),R(q ²),R(q ³)}, respectively. For all the results we use some expressions of $P(q^{i_{1}}), Q(q^{i_{2}}) $ , and $R(q^{i_{3}}) $ in terms of theta constants. Computer-assisted computations of functional determinants and resultants are essential parts of our proofs.     

Transcendence of reciprocal sums of binary recurrences

Let {R _n } _n≥0 be a binary linear recurrence defined by R _n+2 = A R _n+1 + B R _n (n ≥ 0), where A, B, R ₀, R ₁ are integers and Δ = A ² + 4B > 0. We give necessary and sufficient conditions for the transcendence of the numbers

Possibility of the existence of divalent actinium in aqueous solution

Radiopolarographic reduction of Ac(III) was investigated in aqueous solutions. It was found that a very large shift of the half-wave potential was induced by the addition of 1, 4, 7, 10, 13, 16-hexaoxacyclooctadecane (18-CROWN-6) to the aqueous solution. The shift was explained by complex formation of Ac(II) with 18-CROWN-6. The ionic radius and the electronic configuration of Ac²⁺ were determined to be 1.25 Å and [Rn] 6d¹.     

Surface cleaning of metals by pulsed-laser irradiation in air

The surface-cleaning effect of metals was investigated using KrF-excimer-laser irradiation of metal surfaces in air. The laser-induced cleaning of copper, stainless steel and aluminum surfaces was studied. It is found that laser cleaning is an effective cleaning process for metals even if the metal surfaces are heavily contaminated. It is also found that short wavelength and pulse duration are necessary for laser surface-cleaning. The energy density of the laser pulse is an important parameter in the cleaning process. Low energy density results in a cleaner surface but a larger pulse number is required, whereas high energy density can achieve higher cleaning efficiency but the temperature rise can cause surface oxidation and secondary contamination. In contrast to the KrF-excimer-laser, the pulsed CO₂ laser is not effective in surface-cleaning. The mechanisms of laser cleaning may include laser photodecomposition, laser ablation and surface vibration due to the impact of the laser pulse. Laser cleaning provides a new dry process to clean different substrate surfaces and can replace the conventional wet cleaning processes such as ultrasonic cleaning with CFC and other organic solvents.     

Agents for the treatment of overactive detrusor. III. Synthesis and structure-activity relationships of N-(4-amino-2-butynyl)acetamide derivatives.

A series of N-(4-amino-2-butynyl)acetamides were synthesized and examined for their inhibitory activity on detrusor contraction and mydriatic activity as an index of anticholinergic side effect. Among those compounds synthesized, (+)-2-cyclohexyl-N-(4-dimethylamino-2-butynyl)-2-hydroxy-2-phenylacet amide hydrochloride ((+)-13b.HCl), 2-cyclohexyl-2-hydroxy-N-(4-methylamino-2-butynyl)-2-phenylacetamide+ ++ hydrochloride (13c.HCl), N-(4-dimethylamino-2-butynyl)-2,2-diphenyl-2-hydroxyacetamide hydrochloride (14a.HCl), and 2,2-diphenyl-N-(4-ethylamino-2-butynyl)-2-hydroxyacetamide hydrochloride (14b.HCl) showed equipotent inhibitory activity on detrusor contraction to oxybutynin (1) and less mydriatic activity. Further evaluation of these compounds as an agent for the treatment of overactive detrusor has been examined.     

Asymmetric synthesis and determination of the absolute configuration of FK584, an agent for the treatment of overactive detrusor

FK584[(-)-N-tert-butyl-4,4-diphenyl-2-cyclopentenylamine hydrochloride, (-)-4-HCl], a potential candidate for the treatment of overactive detrusor, was synthesized in a 4-step approach starting with Sharpless oxidation of cyclopentenol 6 (kinetic resolution). This epoxidation is a rare case in that the empirical rule does not work. Regio- and stereoselective introduction of tert-butylamine to the obtained epoxycyclopentanol 5 and subsequent conversion of the resulting diol to an olefin completed the synthesis. The absolute configuration of FK584 was determined to be S by X-ray crystallographic analysis of the salt of S-(+)-mandelic acid.     

Evolved gas analysis-mass spectrometry using skimmer interface and ion attachment mass spectrometry

Summary A new EGA-MS instrument consisted of a combination of skimmer interface with no change of evolved gaseous species and IAMS (Ion Attachment Mass Spectrometry) with no fragmentation during the ionization has been developed successfully. As its application of evolved gaseous species from PVA as firing process of alumina ceramics binder, the method has indicated detection of gaseous species which have not been detected with Py-GC-MS.     

Measurement of neutron emission from a SiO2−D2 system

As a new fact, the neutron emission from the d-d nuclear fusion reaction in a SiO₂–D₂ system has been confirmed as well as that in the Ti–D₂ system. By using a liquid scintillation detector, the neutron emissions from 8 sample materials consisted of SiO₂, in which a small amount of deuterium was adsorbed chemically on the surface layer, were measured in the range of temperature between liquid nitrogen temperature and 400 °C. As a result, it was demonstrated that the neutron-emission reactions take place predominantly on the surface layer of sample material.     

Preparation of lanthanide sulfide films by chemical vapor deposition using β-diketone chelates

Preparation of thin films of lanthanide (Ln) sulfides has been studied by the chemical vapor deposition (CVD) method, using metal -diketonato chelates with 2,2,6,6-tetramethyl-3,5-heptanedione and reactant H₂S gas as starting materials. Two kinds of sulfides, Ln₂O₂S oxysulfides and EuS monosulfide, were obtained as thin films at temperatures as low as 390–570 °C. The CVD method was confirmed to be suited for the above purpose.     

Isotopic analysis of243Cm and244Cm by internal conversion electron spectrometry

The electrodeposition of uranium and trace quantities of²³⁹Pu,²³⁴Th,¹⁴⁴Ce on a stainless steel disk has been investigated from 0.5–2.0M NaOH and the two-phase system: extract of actinides in TBP-aqueous solution of NaOH. The electrodeposition yield of the above elements reaches 98–100% in 40 min of electrolysis with current density 0.4–0.5 A/cm². The presence of 0.5M Na₂CO₃, 2.0M NaNO₃, 2.0M NaNO₂, 0.2M NaF in alkaline solutions does not decrease the electrodeposition yield. The electrodeposited films meet all the requirements of -spectrometry. The uranium oxidation states (V) and (IV) have been determined in the electrodeposited films.