we derive error estimates in the appropriate norms, for the streamlinediffusion (sd) finite element methods for steady state, energy dependent,fermi equation in three space dimensions. these estimates yield optimal convergencerates due to the maximal available regularity of the exact solution.high order sd method together with implicit integration are used. the formulationis strongly consistent...

We provide an explicit [Formula: see text] error term for the Riemann–von Mangoldt formula by making results of Wolke [On Mangoldt, II, J. London Math. Soc. 2(3) (1983) 406–416] and Ramaré [Modified truncated Perron formulae, Ann. Blaise Pascal 23(1) (2016) 109–128] explicit. also include applications to primes between consecutive powers, in prime number theorem inequality Ramanujan.

By combining and improving recent techniques results, we provide explicit estimates for the error terms |π(x)−li(x)|, |θ(x)−x| |ψ(x)−x| appearing in prime number theorem. For example, show all x≥2 that |ψ(x)−x|≤9.39x(log⁡x)1.515exp⁡(−0.8274log⁡x). Our rely heavily on zero-free regions zero-density Riemann zeta-function, improve existing bounds prime-counting functions large values of x.

Groundwater aquifers are an important source of water supply for agriculture, industry and drinking. The present study investigates the changes in the quality of groundwater using geostatistical methods in the Ravar plain during a 10-year period. In this study, after selecting the appropriate spatial interpolation method to draw water quality parameters such as TDS, SAR and EC, zoning maps of R...