On a core concept of Arhangel'ski?

Arhangel'ski? [A.V. Arhangel'ski?, Locally compact spaces of countable core and Alexandroff compactification, Topology Appl. 154 (2007) 625-634] has introduced a weakening of σ-compactness: having a countable core, for locally compact spaces, and asked when it is equivalent to σ-compactness. We settle several problems related to that paper.     

Dynamic mathematics and the blending of knowledge structures in the calculus

This paper considers the role of dynamic aspects of mathematics specifically focusing on the calculus, including computer software that responds to physical action to produce dynamic visual effects. The development builds from dynamic human embodiment, uses arithmetic calculations in computer software to calculate ‘good enough’ values of required quantities and algebraic manipulation to develop precise symbolic values. The approach is based on a developmental framework blending human embodiment, with the symbolism of arithmetic and algebra leading to the formalism of real numbers and limits. It builds from dynamic actions on embodied objects to see the effect of those actions as a new embodiment that needs to be calculated accurately and symbolised precisely. The framework relates the growth of meaning in history to the mental conceptions of today’s students, focusing on the relationship between potentially infinite processes and their consequent embodiment as mental concepts. It broadens the strategy of process-object encapsulation by blending embodiment and symbolism.     

Sensitive determination of diuron on zinc oxide nanoparticles modified carbon paste electrode in soil and water samples

An electrochemical sensor based on Zinc oxide nanoparticles (ZnONPs) modified carbon paste electrode was designed for the toxic diuron pesticide detection. The ZnONPs were synthesized through the hydrothermal route and their structural properties were investigated via scanning electron microscopy (SEM) and X-ray diffraction powder (XRD). The designed ZnONPs-modified carbon paste electrode (ZnONPs-CPE) was characterized using cyclic voltammetry and electrochemical impedance spectroscopy. The sensor showed significantly enhanced sensitivity on the diuron oxidation peak current, compared to the bare carbon paste electrode. Qualitative and quantitative analysis were performed using cyclic voltammetry (CV) and square wave voltammetry (SWV). Experimental parameters such as pH, amount of ZnONPs and frequency were evaluated and the optimized conditions were obtained with 0.1 M phosphate buffer solution at pH=8, a frequency of 50 Hz and a quantity of 5 mg of ZnONPs. Under these conditions, linear responses ranging from 1.3 to 7.7 μM and 8.6 to 30 μM of diuron were obtained, with correlation coefficients of R²=0.994 and 0.996 respectively. Detection and quantification limits of 0.22 μM and 0.84 μM (S/N=3) were respectively achieved based on the 3σ method. The interference of some ions on the oxidation peak of diuron on ZnONPs-CPE was also evaluated and no interference was observed, therefore demonstrating the selectivity of the sensor. The proposed sensor, designed with ecofriendly materials, is sensitive, selective and was effectively used for diuron determination in soils and water samples with recoveries ranging from 98 % to 101.5 %.