In dimension two, we investigate a free energy and the ground state of Schrödinger–Poisson system coupled with logarithmic nonlinearity in terms underlying functional inequalities which take into account scaling invariances problem. Such can be considered as nonlinear Schrödinger equation cubic but nonlocal Poisson nonlinearity, local nonlinearity. Both cases repulsive attractive forces are con...

In this paper we prove that the maximal operator of the subsequence of logarithmic means of Walsh-Fourier series is weak type (1,1). Moreover, the logarithmic means tmn (f) of the function f ∈ L converge a.e. to f as n →∞. In the literature, it is known the notion of the Riesz’s logarithmic means of a Fourier series. The n-th mean of the Fourier series of the integrable function f is defined by...

The number L(a, b) = a−b ln a−ln b for a 6= b and L(a, a) = a, is said to be the logarithmic mean of the positive numbers a, b. We shall say that a sequence (an) ∞ n=1 with positive terms is a logarithmic sequence if an = L(an−1, an+1). In the present paper some basic estimations of the terms of logarithmic sequences are investigated.

The Multi-Dimensional Logarithmic Number System (MDLNS), with similar properties to the Logarithmic Number System (LNS), provides more degrees of freedom than the LNS by virtue of having two orthogonal bases and the ability to use multiple digits. Unlike the LNS, there is no direct functional relationship between binary/floating point representation and the MDLNS representation. Traditionally l...