Abstract. We obtain growth comparison results of logarithmic differences, difference quotients and logarithmic derivatives for finite order meromorphic functions. Our results are both generalizations and extensions of previous results. We construct examples showing that the results obtained are best possible in certain sense. Our findings show that there are marked differences between the growt...

SUMMARY – An ActiveX component to calculate temperature and vapour fraction in a geothermal reservoir using the quartz solubility geothermometry was written in Visual Basic. The approach is based on the conservation of mass and energy (enthalpy). Four representative types of regression equations for quartz solubility: (i) a quadratic regression equation of 1/T and pressure P, (ii) a linear equa...

One-dimensional projections of (at least) almost all orbits of many multidimensional dynamical systems are shown to follow Benford’s law, i.e. their (base b) mantissa distribution is asymptotically logarithmic, typically for all bases b. As a generalization and unification of known results it is proved that under a (generic) non-resonance condition on A ∈ Cd×d, for every z ∈ Cd real and imagina...

Many problems of computational electromagnetics [1,2], stationary heat transfer [3,4] and elasticity theory [5] can be naturally reduced to integral equations of the first kind (IEFK) with a weak singularity. So we shall name the equations with a logarithmic peculiarity in one-dimensional case and equation with a peculiarity of an aspect 1 0 rMM in two-dimensional case, where rMM 0 is distance ...

In this article we are interested in quantitative homogenization results for linear elliptic equations the nonstationary situation of a straight interface between two heterogeneous media. This extends previous work [M. Josien, Comm. Partial Differential Equations, 14 (2019), pp. 907--939] to substantially more general setting, which surrounding media may be periodic or random stationary and erg...

In this paper, we present a computational method for solving boundary integral equations with logarithmic singular kernels which occur as reformulations of a boundary value problem for Laplace’s equation. The method is based on the use of the Galerkin method with CAS wavelets constructed on the unit interval as basis. This approach utilizes the nonuniform Gauss-Legendre quadrature rule for appr...

The main purpose of this paper is to investigate the strong convergence and exponential stability in mean square of the exponential Euler method to semi-linear stochastic delay differential equations (SLSDDEs). It is proved that the exponential Euler approximation solution converges to the analytic solution with the strong order [Formula: see text] to SLSDDEs. On the one hand, the classical sta...

A logarithmic term is applied to account for the charge transfer overvoltage with most empirical polarization curve fitting equations for polymer electrolyte membrane fuel cells. The logarithmic term applied with state-of-the-art fitting equations is proportional to the logarithm of the cell output current density. This provides good fitting characteristics with large current densities, but res...