Frobenius distributions of elliptic curves in short intervals on average

The Ramanujan Journal - For an elliptic curve $$E/{\mathbb {Q}}$$ , let $$a_p$$ denote the trace of its Frobenius endomorphism over $${\mathbb {F}}_p$$ , where p is a prime of good reduction for E....     

Thermo-Hydraulic Behavior of Microchannel Heat Exchanger System

This article presents an experimental study of thermo-hydrodynamic phenomena in a microchannel heat exchanger system. The aim of this investigation is to develop correlations between flow/thermal characteristics in the manifolds and the heat transfer performance of the microchannel. A rectangular microchannel fabricated by a laser-machining technique with channel width and hydraulic diameter of 87 μm and 0.17 mm, respectively, and a trapezoidal-shaped manifold are used in this study. The heat sink is subjected to iso-flux heating condition with liquid convective cooling through the channels. The temporal and spatial evolutions of temperature as well as total pressure drop across the system are monitored using appropriate sensors. Data obtained from this study were used to establish relationships between parameters such as longitudinal wall conduction factor, residence and switching time, and thermal spreading resistance with Reynolds number. Result shows that there exist an optimum Reynolds number and conditions for the microchannel heat exchanger system to result in maximum heat transfer performance. The condition in which the inlet manifold temperature surpasses the exit fluid temperature results in lower junction temperature. It further shows that for a high Reynolds number, the longitudinal wall conduction parameter is greater than unity and that the fluid has sufficient dwelling time to absorb heat from the wall of the manifold, leading to high thermal performance.     

Natural radioactivity in cultivated land in the vicinity of a phosphate fertilizer plant in Nigeria

Natural radioactivity in soil and vegetable samples in cultivated land in the vicinity of an active phosphate fertilizer plant in Kaduna, Nigeria was carried out to assess the potential radiological impact of the plant on its immediate environment. The activity counting was carried out using sodium iodide gamma spectrometry. The annual committed effective dose for two vegetables in the farmlands due to uranium (²³⁸U) and thorium (²³²Th) was assessed. The mean activity concentration of radionuclides in the soil samples ranges from 20.5±7.3 to 31.6±4.1 Bq kg^?1 for ²²⁶Ra, 19.6±1.6 to 53.2±3.7 Bq kg^?1 for ²³²Th and 203.9±6.3 to 253.6±9.5 Bq kg^?1 for ⁴⁰K. The annual intake of ²³⁸U and ²³²Th from consumption of okra were 1.9 Bq kg^?1 and 5.22 Bq kg^?1 and for tomatoes 2.66 Bq kg^?1 and 5.1 Bq kg^?1 respectively. The committed effective doses from consumption of okra and tomatoes were 0.1 μSv y^?1 and 0.12 μSv y^?1 respectively.     

Assessment of indoor radon concentration in phosphate fertilizer warehouses in Nigeria

Indoor radon concentration level was measured in twelve selected phosphate fertilizer warehouses in Nigeria in order to establish potential hazards to persons using such warehouses as offices.The fertilizer warehouses were selected based on the brand of fertilizers stored, size, ventilation pattern and the number of workers in the warehouses during working hours. Electret Ion Chamber Technology (EIC) with the trade name E-PERM^TM was employed for the measurement of radon concentration in the warehouses. Average radon concentration in the warehouses range between 33.6 Bq m⁻³ and 117 Bq m⁻³with an arithmetic mean of 91.62±5.9 Bq m⁻³.     

A unified equation for matter transport: its derivation and application

The patterns formed by the limit to the range of (1) rill spacings on a given soil type, and (2) impact spacings of any two sets of waterdrops which differ minimally in pressure, obey the same boundary rules as any two consecutive natural numbers (CNN). The coefficients and exponents of the boundary rules can be multiplied so as to produce a unified equation for matter transport (UEMT). Subsequently, the UEMT can be used to determine the equivalents of environmental lapse rate, vertical wind velocities and temperatures above and below the earth for each of the seven independent co-ordinate systems of the earth. The rill field values agree closely with those measured from matching standard regions.