Granite and marble are widely used in building construction, so possible radioactive nuclides inside them may contribute to the exposure dose to human health. The purpose of this study was to investigate the natural radioactivity concentration and assess the radiological risk limits and health care. The samples of marble and granite were pulverized into small, fine, smooth pieces and counted with the GAMMA-X (GMX) spectrometer to measure the radioactivity concentrations of 238 U, 232 Th, and 40 K. The radiological dose, internal and external hazards, and radium equivalent activity were calculated with a standard formula. The results showed that the radioactive concentrations of 238 U, 232 Th, and 40 K in granite were higher than those in marble. The external hazard for granite samples was below unity, while its internal hazard exceeded unity. The radium equivalent activity did not exceed the critical legal level of 370 Bq/kg as a safe level. For marble, the external and internal hazards and radium equivalent activities showed good agreement with the safe construction level. Its external and internal hazards were less than unity, whereas the radium equivalent activities were less than the critical legal level.
Displaying projectile in a resisting medium for two dimension have two forms; An Ordinary differential equation and a fractional differential equation describe its behavior. The two equations include a nonlinear term, which represents the effect of the air resistance on the motion of the projectile. The development of the Ordinary differential equations for all nonlinear cases is obtained using a developed technique that combines the linear operator Laplace transform and the Adomian decomposition method (ADM) to solve the nonlinear part. To discuss the behavior of the projectile motion we plot the obtained results for several values and study the effect of the order of the nonlinear term on the achievable maximum height. On the other hand, the effects of the proportional factor and the projected mass on the motion have been shown by substituting different values and in the equations of motion. In addition to the Laplace Decomposition Method (LDM), we use the Caputo definition of the fractional derivative to investigate the fractional form of the projectile motion equation. The results show that all the results obtained in the ordinary case may be obtained from the fractional case when α=1.
Mathematics Subject Classification 70K25; 34K37; 44Axx
Particular thermal properties of internal energy, entropy, specific heat capacity and pressure are indicated using static fluctuation approximation (SFA) for specified temperatures and densities where the interaction between particles is still valid. This ab initio study starts initially from the most reliable krypton interatomic potential and develops with complementary SFA assumptions that depend mainly on substituting the local field mean value instead of its operator, thus developing a numerical solution of a nonlinear close set equation by iteration technique. The results are matched with the ideal gas and show a considerable sense.
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