Complexity Classes and Completeness in Algebraic Geometry

Foundations of Computational Mathematics - We study the computational complexity of sequences of projective varieties. We define analogues of the complexity classes P and NP for these and prove the...     

Spatial distribution and risk assessment of radioactivity and heavy metal levels of sediment,surface water and fish samples from Lake Van,Turkey

In this study, radioactivity levels of 228 lake water samples, 63 upper and depth sediment samples and 12 fish samples from Lake Van were investigated from 2005 to 2008 and the distribution patterns of the radionuclides were presented. Analysis included gross alpha–beta and total radium isotopes activities and uranium concentrations of the water, and gross alpha and gross beta activities and relevant ²³⁸U, ²³²Th and ⁴⁰K activity of the sediment and fish samples of the lake. Mean gross alpha, gross beta and radium isotopes activities of lake water were found 0.74 ± 0.46, 0.02 ± 0.01 and 0.06 ± 0.04 Bq/L, respectively. Mean gross alpha and beta activities in upper and depth sediments were found to be 41 ± 6 and 1,514 ± 74 Bq/kg; 77 ± 5 and 394 ± 24 Bq/kg at a 95 % confidence level, respectively. Mean activities of ²³⁸U, ²³²Th and ⁴⁰K activity concentrations in upper and depth sediments were determined to be 225 ± 22, 70 ± 7 and 486 ± 39 Bq/kg; 174 ± 4, 63 ± 3 and 263 ± 25 Bq/kg, respectively. The mean gross alpha and beta, ²³⁸U, ²³²Th and ⁴⁰K aktivities in fish samples were established as 47 ± 18, 470 ± 12, 0.57 ± 0.220, 0.022 ± 0.006, 319 ± 11 Bq/kg, respectively. The transfer factor from lake water to fish tissues, annual intake by humans consuming fish, and annual committed effective doses were estimated and evaluated.     

A rational approximate solution for generalized pantograph‐delay differential equations

In this paper, a new rational approximation based on a rational interpolation and collocation method is proposed for the solutions of generalized pantograph equations. A comprehensive error analysis is provided. The first part of the error analysis gives an upper bound for the absolute error. The second part is based on residual error procedure that estimates the absolute error. Some numerical examples are given to illustrate the method. The theoretical results support the numerical results. Copyright © 2015 John Wiley & Sons, Ltd.     

薁，苯并环丁二烯和戊搭烯的拓扑共振能

为了阐明芳香性及磁性原因，用Ａｉｈａｒａ提出的ＴＲＥ概念计算了　，苯并环丁二烯和戊搭烯等烃的共振能，环共振能和环电流．计算结果表明　因有正共振能具有芳香性并产生反磁性环电流，而苯并环丁二烯和戊塔烯因有负共振能具有反芳香性并产生顺磁性环电流．     

New olefinic centred binuclear clamshell type phthalocyanines: Design, synthesis, structural characterisation, the stability and the change in the electron cloud at olefine-based symmetrical diphthalonitrile fragment by the combined application of UV–Vis electronic structure and theoretical methods

The olefinic centred Schiff base (3) was obtained from the condensation of substituted dialdehyde (1) with 2-amino-4-methylphenol (2) in a 1:2 ratio. The diphthalonitrile derivative (5) was prepared by the reaction of 4-nitrophthalonitrile (4) and compound (3) in dry dimethylformamide/potassium carbonate. The key product (5) was obtained by nucleophilic substitution of an activated nitro group into an aromatic ring. The cyclotetramerization of compound (5) with phthalonitrile (6) in 1:6.15 ratio gave the expected metal-free phthalocyanine of clamshell type (7), and with metal salts of Zn(II), Ni(II), Co(II) and Cu(II) gave metallophthalocyanines of clamshell types (8-11), respectively in dimethylaminoethanol/1,8-diazabycyclo[5.4.0]undec-7-ene system. The products were purified by several techniques such as crystallization and preparative thin layer chromatography. The newly prepared compounds were characterised by a combination of elemental analyses, IR, ¹H/¹³C NMR, MS and UV-Vis spectroscopy.     

Surface chemistry studies of (CdSe)ZnS quantum dots at the air-water interface

Trioctylphosphine oxide- (TOPO-) capped (CdSe)ZnS quantum dots (QDs) were prepared through a stepwise synthesis. The surface chemistry behavior of the QDs at the air-water interface was carefully examined by various physical measurements. The surface pressure-area isotherm of the Langmuir film of the QDs gave an average diameter of 4.4 nm, which matched very well with the value determined by transmission electron microscopy (TEM) measurements if the thickness of the TOPO cap was counted. The stability of the Langmuir film of the QDs was tested by two different methods, compression/decompression cycling and kinetic measurements, both of which indicated that TOPO-capped (CdSe)ZnS QDs can form stable Langmuir films at the air-water interface. Epifluorescence microscopy revealed the two-dimensional aggregation of the QDs in Langmuir films during the early stage of the compression process. However, at high surface pressures, the Langmuir film of QDs was more homogeneous and was capable of being deposited on a hydrophobic quartz slide by the Langmuir-Blodgett (LB) film technique. Photoluminescence (PL) spectroscopy was utilized to characterize the LB films. The PL intensity of the LB film of QDs at the first emission maximum was found to increase linearly with increasing number of layers deposited onto the hydrophobic quartz slide, which implied a homogeneous deposition of the Langmuir film of QDs at surface pressures greater than 20 mN.m(-1).     

Transient thermal response of phase change material embedded with graphene nanoplatelets in an energy storage unit

This research was focused on the preparation of mixed metal oxide pigments doped with terbium ions with the general formula of Sn_0.752Co_0.08P_0.16Tb_0.008O₂. These pigments were synthesised by solid-state reactions at high calcination temperatures. The temperature range was chosen from 1350 to 1500 °C. The goal was to develop conditions for the synthesis of this type of pigments and to determine the influence of terbium ions on the colour properties of these compounds. All prepared pigments were applied into the organic matrix and into the ceramic glaze. Thermal behaviours of the reaction mixtures were investigated using differential thermal and thermogravimetric analysis. Synthesised Sn_0.752Co_0.08P_0.16Tb_0.008O₂ pigments were compared with concurrently prepared pigment Sn_0.760Co_0.08P_0.16O₂ depending on the calcination temperature with respect to the colour properties in CIE L*a*b* colour space, furthermore from the point of particle size distribution and phase composition. All compounds provided blue–violet hues that are stable in ceramic glazes.     

Temperature-dependent optical properties of GaSe layered single crystals

Optical properties of GaSe single crystals have been investigated using temperature-dependent transmission and room temperature reflection measurements in the wavelength range of 380–1100 nm. The analysis of the absorption data at room temperature showed the existence of indirect transitions in the crystal with energy band gap of 1.98 eV. Temperature dependence of the transmission measurements revealed the shift of the absorption edge toward lower energy as temperature is increased from 10 to 280 K. The rate of change of the indirect band gap was found as γ = ?6.6 × 10^?4 eV/K from the analysis of experimental data under the light of theoretical relation giving the band gap energy as a function of temperature. The absolute zero value of the band gap energy and Debye temperature were calculated from the same analysis. The Wemple–DiDomenico single-effective-oscillator model applied to refractive index dispersion data was used to determine the oscillator energy, dispersion energy, oscillator strength and zero-frequency refractive index values.     

A graphical method for determing the coefficient of viscosity of Newtonian liquids using an oscillating cylinder viscometer

Zusammenfassung Es wird ein zweites graphisches Verfahren dargestellt, welches gestattet, die Viskosität zäher Flüssigkeiten zu ermitteln.