On the representation of integers as sums of an odd number of squares

In a recent work, S. Cooper (J. Number Theory 103:135–162, [1988]) conjectured a formula for r _2k+1(p ²), the number of ways p ² can be expressed as a sum of 2k+1 squares. Inspired by this conjecture, we obtain an explicit formula for r _2k+1(n ²),n≥1. Dedicated to Srinivasa Ramanujan.     

Interaction of methoxy- and methylenedioxyamphetamines with carbon and polymeric adsorbents in polar liquids

Solid phase extraction (SPE) of methoxy- and methylenedioxyamphetamines from diluted aqueous solutions was investigated on carbon and polymeric adsorbents of different textures and chemical compositions. Those adsorbents were applied cartridges packed with three chemically modified carbons prepared from plum stones (initial A2PS, oxidized A2PS-O, and reduced A2PS-H) and commercially available adsorbents (polymeric LiChrolut EN, graphitized Hypercarb and Carboprep). Several factors influence the recovery rates of amphetamine derivatives such as the polarity of adsorbates (free energy of salvation), the specific surface area and surface composition of adsorbents, and the solvent characteristics. Different combinations of these factors affect the recovery rate (R1) for high- and low-surface area adsorbents. The minimal R1 values are observed for an amphetamine derivative at a maximal solvation effect and for a set of amphetamines adsorbed on graphitized carbons.      

The role of metrology communities under the WTO system: measurement science and conformity assessment procedures

Technical barrier to trade (TBT) has become one of the significant non-tariff measures with the advent of the WTO system in 1995. The key issue in TBT is that technical regulations, standards, and conformity assessment should not be used as barriers to trade. Regarding conformity assessment, the WTO/TBT Agreement recommends members to enter into negotiations for the mutual recognition of results of each other’s conformity assessment, as well as to permit participation of conformity assessment bodies located in other members. In this paper, it will be reviewed why the role of measurement science is important in terms of international effort to eliminate technical barriers to trade particularly in the area of conformity assessment.     

Surface redox induced bipolar switching of transition metal oxide films examined by scanning probe microscopy

The bipolar resistive switching mechanisms of a p-type NiO film and n-type TiO₂ film were examined using local probe-based measurements. Scanning probe-based current–voltage (I–V) sweeps and surface potential/current maps obtained after the application of dc bias suggested that resistive switching is caused mainly by the surface redox reactions involving oxygen ions at the tip/oxide interface. This explanation can be applied generally to both p-type and n-type conducting resistive switching films. The contribution of oxygen migration to resistive switching was also observed indirectly, but only in the cases where the tip was in (quasi-) Ohmic contact with the oxide.     

Influence of Basic Red 1 dye adsorption on thermal stability of Na-clinoptilolite and Na-bentonite

Influence of physically adsorbed basic red 1 (BR1) dye on the physicochemical properties of natural zeolite (clinoptilolite) and clay (bentonite) was compared using adsorption, FTIR, and TG/DTA methods. A larger adsorption of the dye was observed for bentonite (0.143 mmol/g) than for clinoptilolite (0.0614 mmol/g) per gram of an adsorbent. However, the adsorption values are the same per surface unit (1.8 μmol/m²). The result (per gram) is due to location of dye molecules in interlayer and interparticle space of bentonite with much larger specific surface area than that of clinoptilolite. The dye adsorption leads to a decrease in the specific surface area and the pore volume of both minerals. The adsorption changes also a character of active sites and thermal stability. A TG study shows that the dye adsorption on bentonite changes adsorbed water amounts, weight loss, and decomposition temperature. In the case of zeolite, the dye adsorption insignificantly influences the thermal stability. The dehydration energy distributions calculated from the Q-TG and Q-DTG data demonstrate a complex mechanism of water thermodesorption and the influence of adsorbed dye on this process.     

Activation and structural and adsorption features of activated carbons with highly developed micro-, meso- and macroporosity

Three sets of activated carbons (ACs) were prepared with the same precursor but activated differently (by CO₂ or water vapour) with various burn-off levels. The ACs demonstrate increased deviation of the pore shape from the slitshaped model with increasing burn-off and contributions of pores of different sizes depending on the activation type. Significant re-arrangement of adsorption complexes, especially of the Van der Waals type characteristic for nonpolar or weakly polar adsorbates (H₂, CH₄, CH₂Cl₂, CHCl₃), occurs in both micropores and mesopores of ACs with decreasing temperature. The behaviour of their mixtures with water and DMSO can strongly differ from that of individual adsorbates.     

Chaos-enhanced accelerated particle swarm optimization

There are more than two dozen variants of particle swarm optimization (PSO) algorithms in the literature. Recently, a new variant, called accelerated PSO (APSO), shows some extra advantages in convergence for global search. In the present study, we will introduce chaos into the APSO in order to further enhance its global search ability. Firstly, detailed studies are carried out on benchmark problems with twelve different chaotic maps to find out the most efficient one. Then the chaotic APSO (CAPSO) will be compared with some other chaotic PSO algorithms presented in the literature. The performance of the CAPSO algorithm is also validated using three engineering problems. The results show that the CAPSO with an appropriate chaotic map can clearly outperform standard APSO, with very good performance in comparison with other algorithms and in application to a complex problem.     

Viscoelastic behavior,order-disorder transition,and phase equilibria in mixtures of a block copolymer and an endblock-associating resin

The viscoelastic behavior, order-disorder transition, and phase equilibria in mixtures of a block copolymer and an endblock-associating resin were investigated. The block copolymer was a polystyrene-block-polyisoprene-block-polystyrene (KRATON® D-1107, Shell Development Co.) copolymer. The endblock-associating resins investigated were two different grades of a commercially available random copolymer of poly(α-methyl styrene) and polystyrene, one with a weight-average molecular weight \[\bar M_{\rm w}\] of 710 (KRISTALEX® 3085, Hercules Inc.) and the other with \[\bar M_{\rm w}\] = 4100 (KRISTALEX® 5140, Hercules Inc.). Mixtures of various proportions of the block copolymer and the endblock-associating resin were prepared in toluene solvent. With the mixtures, measurements of dynamic viscoelastic properties were made, namely, dynamic storage modulus G″ and dynamic loss modulus G″ as a function of temperature from temperature scans of the samples using a Rheometrics Mechanical Spectrometer. The following observations were made. (1) The plateau modulus of the block copolymer increased with increasing amount of KRISTALEX 3085 or KRISTALEX 5140, indicating that the low-molecular-weight resin was associated with the polystyrene microdomains of the block copolymer. (2) When KRISTALEX 3085 (up to 30 wt %) was added to the block copolymer, the glass transition temperature (T_g) of the polyisoprene midblock of the SIS block copolymer was shifted toward higher temperatures, indicating that part of the KRISTALEX 3085 added had associated with the rubbery midblock of the block copolymer. Also investigated was the order-disorder transition behavior of the mixtures, using a rheological technique (log G′ versus log G″ plots) recently introduced by Han and Kim. It has been found that the order-disorder transition temperature T_r of mixtures of the SIS block copolymer and KRISTALEX 3085 decreased steadily with increasing amount of KRISTALEX 3085, whereas the addition of KRISTALEX 5140 increased the T_r of the block copolymer. It was found by light scattering and hot-stage microscopy that macrophase separation occurred in the KRATON 1107/KRISTALEX 5140 mixtures while microdomains of polystyrene were present in the block copolymer.     

夹心半群S(X,Y,θ)上的α-同余

本文讨论了夹心半群T(X,Y,θ)上的α-同余与集合Y上Tθ-等价关系之间的联系,证明了对于每个Tθ-等价关系E,夹心半群同余格C(T(X,Y,θ))的完全子格γ-1(E)中的最大元是一个α-同余,并判明Symons同余l,d都是α-同余.对于某些拓扑空间X,Y,确定了夹心半群S(X,Y,θ)上的最小(最大)真α-同余.