On The Spaces of Linear Operators Acting Between Asymmetric Cone Normed Spaces

An asymmetric norm is a positive sublinear functional p on a real vector space X satisfying \(x=\theta _X\) whenever \(p(x)=p(-x)=0\). Since the space of all lower semi-continuous linear functionals of an asymmetric normed space is not a linear space, the theory is different in the asymmetric case. The main purpose of this study is to define bounded and continuous linear operators acting between asymmetric cone normed spaces. After examining the differences with symmetric case, we give some results related to Baire’s characterization of completeness in asymmetric cone normed spaces.     

Low temperature H2O and NO2 coadsorption on theta-Al2O3/NiAl(100) ultrathin films

The coadsorption of H(2)O and NO(2) molecules on a well-ordered, ultrathin theta-Al(2)O(3)/NiAl(100) film surface was studied using temperature programmed desorption (TPD), infrared reflection absorption spectroscopy (IRAS), and X-ray photoelectron spectroscopy (XPS). For H(2)O and NO(2) monolayers adsorbed separately on the theta-Al(2)O(3)/NiAl(100) surface, adsorption energies were estimated to be 44.8 and 36.6 kJ/mol, respectively. Coadsorption systems prepared by sequential deposition of NO(2) and H(2)O revealed the existence of coverage and temperature-dependent adsorption regimes where H(2)O molecules and the surface NO(x) species (NO(2)/N(2)O(4)/NO(2)(-),NO(3)(-)) form segregated and/or mixed domains. Influence of the changes in the crystallinity of solid water (amorphous vs crystalline) on the coadsorption properties of the NO(2)/H(2)O/theta-Al(2)O(3)/NiAl(100) system is also discussed.     

The bi-objective Pollution-Routing Problem

The bi-objective Pollution-Routing Problem is an extension of the Pollution-Routing Problem (PRP) which consists of routing a number of vehicles to serve a set of customers, and determining their speed on each route segment. The two objective functions pertaining to minimization of fuel consumption and driving time are conflicting and are thus considered separately. This paper presents an adaptive large neighborhood search algorithm (ALNS), combined with a speed optimization procedure, to solve the bi-objective PRP. Using the ALNS as the search engine, four a posteriori methods, namely the weighting method, the weighting method with normalization, the epsilon-constraint method and a new hybrid method (HM), are tested using a scalarization of the two objective functions. The HM combines adaptive weighting with the epsilon-constraint method. To evaluate the effectiveness of the algorithm, new sets of instances based on real geographic data are generated, and a library of bi-criteria PRP instances is compiled. Results of extensive computational experiments with the four methods are presented and compared with one another by means of the hypervolume and epsilon indicators. The results show that HM is highly effective in finding good-quality non-dominated solutions on PRP instances with 100 nodes.     

Quadratic sums of Gaussian q-binomial coefficients and Fibonomial coefficients

The Ramanujan Journal - In this paper we evaluate quadratic sums of Gaussian q-binomial coefficients with two additional parameters. We obtain a general summation theorem using a combination of...     

A Study of Adsorption of Water Vapour on Wool under Static and Dynamic Conditions

Adsorption of water vapour on wool provides not only textile comfort, but also convenience in transportation due to increase in its bulk density. The adsorption and desorption isotherms of water vapour for wool were determined by both volumetric technique using a Coulter Omnisorp 100CX instrument and gravimetric method employing a Cahn 2000 electronic microbalance. Adsorption isotherm fitting to B.E.T. model and hysteresis on desorption was observed. The average effective diffusion coefficient of water in wool was found to be 8.4 × 10^-14 m²s^-1 at 25°C from gravimetric data. The effects of packing height and air velocity on the breakthrough curves were also investigated in the wool packed columns. For pseudo first order model, k values changing between 0.33 × 10^-6 – 69 × 10^-6 s^-1 was obtained for 2.2–6.4 cm s^-1 air velocity and 0.05–0.20 m packing height ranges.     

Photoconductive novel mesomorphic oxotitanium phthalocyanines

The synthesis and photoconductivity properties of the alkylthia and triethyleneoxysulfonyl substituted oxotitanium(IV) phthalocyanines (1a and 2a) are reported for the first time. The new compounds have been characterized by elemental analysis, IR, ¹H and ¹³C NMR spectroscopy, electronic spectroscopy and mass spectroscopy. The mesogenic properties of these new materials were studied by differential scanning calorimetry and optical microscopy. The electrical dark conductivities (σ_d) and photoconductivities (σ_ph) of deposited films of 1a and 2a were investigated in various media with different concentrations of oxygen. Molecular oxygen increases photoconductivities (σ_ph) significantly. The photoconductivity mechanism and formation of Pc⁺ which is positive charge carrier under the light irradiation of the phthalocyanine molecules are demonstrated using the theoretical calculations. The geometries of the oxotitanium(IV) phthalocyanines (TiOPc) are optimized with PM3 semi-empirical method, and their visible absorption maxima are calculated with ZINDO/S method. The results agree well with the observed values. It was found that for the calculation of visible absorption of neutral and positively charged substituted TiOPc molecules using ZINDO/S method could rapidly yield excellent results. Dipole moment, HOMO, LUMO energies and atomic charges are also calculated for clarification of the oxygen effect on the photoconductivity using PM3 and ZINDO/S methods.