This paper presents lemmas and its corollaries on the combinatorial geometric series and summation of series of binomial coefficients. Also, the coefficient for each term in combinatorial geometric series refers to a binomial coefficient. These ideas can enable the scientific researchers to solve the real life problems.

This paper discusses an abelian group, also called a commutative group, under addition of the binomial coefficients of combinatorial geometric series. The combinatorial geometric series is derived from the multiple summations of geometric series The coefficient for each term in combinatorial geometric series refers to a binomial coefficient. This idea can enable the scientific researchers to solve the real life problems.

The effect of poly(ethylene glycol) (PEG) molar mass, pH, and temperature on interfacial tension was investigated for aqueous two-phase systems composed of PEG with molar masses of (1500, 4000, 6000, and 8000) g·mol–1 and potassium phosphate. The temperatures tested were (293 and 313) K at the pH values of 6, 7, and 9. Interfacial tension was determined by using a spinning drop tensiometer and the Vonnegut equation. An increase in both the PEG molar mass and the temperature resulted in an increase of interfacial tension values. The interfacial tension varied from (0.05 to 3.11) mN·m–1 for systems composed by PEG 4000 (mass fraction; w = 0.12) + potassium phosphate (w = 0.11) + water (w = 0.77) at pH 6.0 and 293 K and PEG 4000 (w = 0.19) + potassium phosphate (w = 0.16) + water (w = 0.65) at pH 7.0 and 313 K, respectively.

This paper discusses a commutative group, ring, and field under addition and multiplication of the binomial coefficients in combinatorial geometric series. The combinatorial geometric series is derived from the multiple summations of geometric series. The coefficient for each term in combinatorial geometric series refers to a binomial coefficient. This idea can enable the scientific researchers to solve the real life problems.

No abstract

A one-dimensional mathematical model for the description of solar drying of beds of sewage sludge is developed and implemented with the software Engineering-Equation-Solver. After the discussion of relevant literature, the assumptions and general conditions of the model are explained. Governing differential equations for heat and mass transport inside the sludge are derived, followed by a discussion about correlations used for the determination of surface transport phenomena and for the description of thermophysical properties. Numerical discretization is achieved locally through the Finite Difference Method and temporary through the Runge-Kutta-Method. Finally, a parametric analysis on the sludge drying process is carried out. The obtained results demonstrate the effect of ambient parameters such as solar radiation, airflow rate, gas temperature, geometric aspects etc. on the drying process. The developed model may be used for further prediction and estimation of drying characteristics under several conditions.

The objective of this work was to study the convective drying process used for cylindrical samples of two different pear varieties, one originating from Europe (Pyrus communis) and the other from Asia (Pyrus pyrifolia), submitted to two blanching treatments, as well as determine some coefficients referring to heat and mass transfer and thermodynamic parameters of the process, being: enthalpy (ΔH*), entropy (ΔS*) and Gibbs energy of activation (ΔG*). All samples were dried in a forced air oven at temperatures of (62, 76, 84 and 92)°C until reaching a constant mass. The heat and mass transfer coefficients referring to the constant and falling-rate drying periods were obtained by adjusting the experimental data to wet bulb temperature and liquid diffusion models, respectively. The heat and mass transfer coefficients varied linearly with temperature. Blanching altered the drying behavior of the two varieties in relation to the non-blanched samples, mainly at the elevated drying temperatures of 84°C and 92°C. ΔH* and ΔS* decreased while ΔG* increased with the elevation of drying temperature; therefore, it was possible to verify that variation in the diffusion process in pears during drying is dependent on energetic contributions of the environment.

Considering that many Nigerian roads are untarred, the effect of frequent plying of these untarred roads on passengers and the expected performance of suspension system of vehicles are important for health and safety reasons. This is significant because the transmission of vibration associated with suspension systems are dependent on the frequency spectrum of the road input, and the nature of the suspension system and the vehicle seating arrangement that is producing the vibration. Thus, this study focuses on the discomfort experienced by passengers based on parametric study of vehicle with semi-active suspension system under transient road conditions.  The modeling of the of semi-active vehicle suspension system properties are contrived on the mass- spring damper system for 4 degree-of–freedom half- car model integrated with 3 degrees of freedom human-seat arrangement. Using vehicle parameters, the severity of ride discomfort experienced by the passenger as the vehicle traversed transient road conditions (i.e., traversing obstruction) was evaluated in terms of the vibration dose value (VDV). Results of simulation based on the parametric studies are presented and the vibration dose values evaluated to show the dependence of vehicle ride comfort on the characteristics of the various elements of the vehicle suspension such as stiffness and damping characteristics. The result showed that the variation of sprung mass and suspension stiffness of the vehicle had more significant effects on passenger discomfort than the variation of the unsprung mass. The parametric study also revealed that suspension stiffness affects the suspension working space as the vehicle traversed transient road condition.