Freshman rules in calculus

In this note we present a class of functions (f, g) that satisfy ‘freshman rules’ in calculus.     

State of the art on flow and heat transfer performance of compact fin-and-tube heat exchangers

Journal of Thermal Analysis and Calorimetry - The need for better thermal–hydraulic performance of heat exchangers remains the primary reason for further improving the design of heat...     

Characterization and modelling of density,thermal conductivity,and viscosity of TiN–W/EG nanofluids

Journal of Thermal Analysis and Calorimetry - Thermal conductivity, dynamic viscosity, and density of TiN nanofluids (NFs) with different base mediums have been characterized for the prospect of...     

Indirect voltammetric determination of caffeine content in coffee using 1,4-benzoquinone modified carbon paste electrode

In this paper a simple and highly sensitive electroanalytical method for the determination of caffeine content using 1,4-benzoquinone modified carbon paste electrode is presented. The method is based on suppression of 1,4-benzoquinone peak current on addition of caffeine. Square-wave and cyclic voltammetric techniques were utilised for the investigation. The 1,4-benzoquinone modified electrode exhibited a well-defined peak with reproducible peak current values for repetitive measurements; and showed a decrease in peak current value with an increase in caffeine content. The result revealed two linear range regions between 0 mmol L⁻¹ and 0.5 mmol L⁻¹ and 0.5 mmol L⁻¹ and 8.0 mmol L⁻¹, with detection limits of 0.3 μmol L⁻¹ and 5.1 μmol L⁻¹, respectively. The method was then successfully applied to the determination of caffeine content in coffee samples. The effects of pH, electrode composition, step potential, pulse amplitude and square-wave frequency on the voltammetric responses were also investigated.     

Computerized proof techniques for undergraduates

The use of computer algebra systems such as Maple and Mathematica is becoming increasingly important and widespread in mathematics learning, teaching and research. In this article, we present computerized proof techniques of Gosper, Wilf–Zeilberger and Zeilberger that can be used for enhancing the teaching and learning of topics in discrete mathematics. We demonstrate by examples how one can use these computerized proof techniques to raise students' interests in the discovery and proof of mathematical identities and enhance their problem-solving skills.     

An overdetermined problem in nonlinear elliptic equations of second order

We define some functionals involvingu(x) andx'u _i , whereu(x) is a classical solution of the equation (q ^p-2 u _i ) _i +k(u)q ^p =0,p > 1, and prove that such functionals satisfy a second order elliptic differential equation. By a suitable choice of such functionals we investigate an overdetermined problem.Partially supported by Regione Autonoma della Sardegna.