A note on inverses in arithmetic with fuzzy numbers

Algorithms for systematical search of inverse in arithmetic operations with fuzzy numbers are discussed. The fuzzy number derived is considered either in a discrete representation of its support or described by the parameters of the corresponding membership function formula. Both algorithms are easy to be programmed for desk calculators.     

Five-step phase-shifting algorithms with unknown values of phase shift

The presented work offers new algorithms for phase evaluation in interferometric measurements. Several phase-shifting algorithms with an arbitrary but constant phase-shift between captured intensity frames are proposed. These phase calculation algorithms need to measure five frames of the intensity of the interference field. The algorithms are similarly derived as so called Carré algorithm. The phase evaluation process then does not depend on the linear phase shift errors. Furthermore, the detailed analysis of the algorithms with respect to most important factors, which affect interferometric measurements, is carried out. It is also studied the dependency of the evaluation algorithms on the phase shift values, and the proposed phase calculation algorithms are compared with respect to the resulting phase errors. The influence of most important factors in the measurement and evaluation process was simulated as systematic and random errors using a proposed mathematical model.     

Determination of uranium by thermal and epithermal neutron activation in natural waters and in human urine

Uranium is determined via its ²³⁹U nuclide (74.0 keV, t_{$\text{1}\text{2}$} = 23.5 min) in natural waters down to 0.03 ng U ml^-1 after preconcentration with activated carbon and oxine; 30-min irradiation and counting times are used. No preconcentration is required for samples containing more than 4 ng U ml^-1 with 10-min irradiation and counting times. Uranium in urine can be determined under a boron shield at the 5 ng ml^-1 level after 30-min irradiation and counting.     

Thermodynamic Properties and Melting Behavior of Bi–Sn–Zn Alloys

Summary. The partial and integral enthalpies of mixing of liquid Bi–Sn–Zn alloys were determined at 500°C by a drop calorimetric technique using a Calvet-type microcalorimeter. The ternary interaction parameters in the Bi–Sn–Zn system were fitted using the Redlich-Kister-Muggianu model for substitutional solutions, and isoenthalpy curves of the integral molar enthalpy of mixing at 500°C were constructed. Furthermore, a DSC technique was used to determine the liquidus temperatures in three sections (3, 5, and 7 at.% Zn) as well as the invariant reaction temperature of the ternary eutectic L ⇄ (Bi) + (Sn) + (Zn). The ternary eutectic reaction was found at 135°C.     

Theoretical studies of photodissociation and rydbergization in the first triplet state (3s3A″2) of ammonia

Ab initio investigations at the RHF and CI levels have been carried out on a section of the potential energy surface of the Rydberg 3s³A″₂ state of NH₃ leading to dissociation into NH₂(²B₁) and H(²S). It was found that the barrier towards dissociation is due to a Rydberg-valence transformation. The barrier height calculated with the CI wavefunction is significantly smaller than at the RHF level The results may explain the difficulties associated with experimental observation of the 3s³A″₂ state.     

Renormalized inner projection—a case study: The octic oscillator

The upper and lower bounds of a harmonic oscillator with an octic perturbation are studied with the use of renormalized inner projection. It is shown that this relatively simple technique works even in the infinite coupling constant limit. Symbolic computation is very convenient and useful in these types of problems, where only a finite number of operations are required.     

Synthesis and x-ray crystal structure of [(THF)Zn(O(2)(OH)SiR)](4) (R = (2,6-i-Pr(2)C(6)H(3))N(SiMe(3))): enroute to larger aggregates

Reaction of aminosilanetriol RSi(OH)(3) (1) (R = (2,6-i-Pr(2)C(6)H(3))N(SiMe(3))) with diethyl zinc at room temperature in 1:1 stoichiometric ratio affords [(THF)Zn(O(2)(OH)SiR)](4) (2) (R = (2,6-i-Pr(2)C(6)H(3))N(SiMe(3))) in good yield. The single-crystal X-ray diffraction studies reveal that 2 is monoclinic, P2(1), with a = 17.117(3) A, b = 16.692(5) A, c = 17.399(4) A, alpha = gamma = 90 degrees, beta = 91.45(7) degrees, and Z = 2. The molecular structure of 2 contains two puckered eight-membered Zn(2)Si(2)O(4) rings, which are connected by the Zn-O bonds and form two planar four-membered Zn(2)O(2) rings. Compound 2 contains an unreacted hydroxyl group on each silicon atom, and hence, we carried out the reactions of 2 with dimethylzinc and methyllithium to form [Zn(4)(THF)(4)(MeZn)(4)(O(3)SiR)(4)] (3) (R = (2,6-i-Pr(2)C(6)H(3))N(SiMe(3))) and [(L)ZnLi(O(3)SiR)](4) (4) (L = 1,4-(Me(2)N)(2)C(6)H(4), R = (2,6-i-Pr(2)C(6)H(3))N(SiMe(3))), respectively. This suggested that 2 could be an intermediate product formed during the synthesis of 3 and 4.     

The dispersion relation of the charge and current compensated relativistic electron beam-plasma system

Analysing the general dispersion relation numerically, the unstable regions of the relativistic electron-beam plasma system were determined. The external parameters were varied to ensure more effective instability excitations. The full charge and current compensation presumptions lead to new synchronism predictions. The return current's slow space charge wave and return current's slow cyclotron wave are synchronous with the plasma ion wave.     

A New Alkylation-Elimination Method for Synthesis of Antiviral Fluoromethylenecyclopropane Analogues of Nucleosides

A new method for the synthesis of fluoromethylenecyclopropane nucleosides by alkylation-elimination procedure is described. Fluorination of methylenecyclopropane carboxylate 6 gave fluoroester 7. Treatment of 7 with phenylselenenyl bromide afforded the desired ethyl (E)-2-bromomethyl-1-fluoro-2-phenylselenenylcyclopropane-1-carboxylate 11 in 85% yield. DIBALH reduction of 11 gave 13, which after acetylation to 14 was reacted with 2-amino-6-chloropurine to give the 9-alkylated product 15 in 87% yield. Se-oxidation of 15 with hydrogen peroxide afforded 16, which underwent smooth elimination in a mixture of THF-DMF at 60 °C giving rise to a Z,E mixture of protected nucleosides 17. Deacetylation gave Z-1a and E-1a which were separated on a silica gel column. Both Z-1a and E-1a were converted into the respective guanine analogues Z-1b and E-1b.