Some functional equations originating from number theory

We will introduce new functional equations (3) and (4) which are strongly related to well-known formulae (1) and (2) of number theory, and investigate the solutions of the equations. Moreover, we will also study some stability problems of those equations.     

Baseline studies of radon/thoron concentration levels in and around the Lambapur and Peddagattu areas in Nalgonda district, Andhra Pradesh, India

Studies conducted by Atomic Minerals Directorate of Exploration and Research (AMD) of Hyderabad, India had established the presence of higher concentrations of uranium in Lambapur and Peddagattu areas of Nalgonda district, AP, India and it was estimated that it could be a viable source for commercial extraction. The envisaged extraction process involves dispersion of radioactive particulate matter into atmosphere. Environmental radioactive studies in and around proposed mining areas at this point of time will be extremely useful for establishing base line data before a large scale uranium extraction process comes into existence. To this end, Solid State Nuclear Track Detectors were installed to evaluate indoor radon and thoron concentration levels in the dwellings of the area. The geometric means of radon and thoron concentration levels were found to be (7.1±0.2)×10¹ and (6.7±0.3)×10¹ Bq/m³, respectively. Simultaneously, natural background radiation measurements were also made and these levels are found to vary from 770 to 3995 μGy/y in the spatial distribution.     

High-energy gamma-rays accompanying the spontaneous fission of 252Cf

The γ-ray spectrum of ²⁵²Cf(sf) was measured in the Darmstadt-Heidelberg Crystal Ball spectrometer, with a double ionization chamber mounted inside to detect the fission fragments. The measurement was aimed at a better understanding of an unusual component found in the high-energy region between 3 and 8 MeV, with fragment mass splits near symmetry. This component was proved to be predominantly emitted by the heavier fragment, to reach its highest intensity at a fragment mass split of 132:120, and to have an almost isotropic angular distribution. Calculations with the statistical code CASCADE could reproduce the main features.     

Evaluation of compatibility in polymer blend systems by simultaneous DSC-FTIR measurement

The concept of crystallization dynamics method evaluating the miscibility of binary blend system including crystalline component was proposed. Three characteristic rates, nucleation, crystal growth rates (N*, G*) and growth rate of conformation (G _c*) were used to evaluate the miscibility of PVDF/at-PMMA and PVDF/iso-PMMA by the simultaneous DSC-FTIR. N*, G* and G _c* depended remarkably on both temperature and blend fraction (ϕ_PMMA) for PVDF/at-PMMA system, which indicated the miscible system. PVDF/iso-PMMA showed small ϕ_PMMA dependency of N*, G* and G _c*, was estimated the immiscible system. The ΔT/T _m⁰ values, corresponding to Gibbs energy required to attend the constant G* and G _c*, evaluated from G* and G _c* showed the good linear relationships with different slope. The experimental results suggested that the concentration fluctuation existed in PVDF/iso-PMMA system.     

Characteristics of Ti0.97Co0.03O2:Sb0.01 dilute magnetic semiconducting thin films deposited at 500 °C by pulsed laser deposition

Epitaxial Ti_0.97Co_0.03O₂:Sb_0.01(TCO:Sb) films were deposited on R-Al₂O₃ (1 1 0 2) substrates at 500 °C in various deposition pressures by pulsed laser deposition. The solubility of cobalt within the films increases with decreasing deposition pressure at a deposition temperature of 500 °C. The TCO:Sb films deposited at 5×10⁻⁶ Torr exhibit a p-type anomalous Hall effect having a hole concentration of 6.1×10²²/cm³ at 300 K. On the other hand, films deposited at 4×10⁻⁴ Torr exhibits an n-type anomalous Hall effect having an electron concentration of about 1.1×10²¹/cm³. p- or n-type DMS characteristics depends on the change of the structure of TCO:Sb films and the solubility of Co is possible by controlling the deposition pressure.     

Badge-type diffusive sampler using 3-methyl-2-benzothiazolinone hydrazone for measuring formaldehyde in indoor air.

The evaluation of a badge-type diffusive sampler for measuring formaldehyde using 3-methyl-2-benzothiazolinone hydrazone (MBTH) was investigated. On average, the formaldehyde concentration in blanks was reduced by approximately 31% by cleaning procedures. The cleaning techniques did not significantly differ in effectiveness. The maximum sampling rate was 22.4 +/- 3.5 mL min(-1) at MBTH concentrations of 0.05%. The formaldehyde concentration in blanks did not appreciably increase over a period of about 1 month at room temperature, and was 0.36 +/- 0.03 microg, with a relative standard deviation of 8%. The diffusive sampler had good precision and accuracy for measuring formaldehyde in indoor environments. For a 24-h exposure time, the limits of detection and quantification calculated with the field blanks were 9.7 and 13.8 ppb, respectively. The minimum exposure times were calculated based on the measured and calculated limits of quantification, the sampling rate, and the atmospheric formaldehyde concentration. The capacity of the diffusive sampler with 0.5% MBTH was 3 ppm h(-1), approximately 1.5-times the capacity when the MBTH concentrations were 0.05%.     

Penetration of a magnetic field into a thin unclosed ellipsoidal sheath in the presence of a thick-walled conducting spherical sheath

The solution of the problem of magnetic field penetration into a conducting unclosed ellipsoidal sheath in the presence of a conducting thick-walled spherical sheath is reduced to the solution of the integral Fredholm equation of the second kind. The effect of the apex angle of the unclosed ellipsoidal sheath, geometric parameters of the screens, and electrophysical properties of the spherical sheath material on the field attenuation coefficient inside the ellipsoidal sheath is studied numerically.