**Abstract**

General expressions for the moments of probability <rn^{k}> and <m^{k}> in the random walk problem are obtained. These are expressed as power series in the mean number of steps in one direction <n>.

**Abstract**

General expressions for the moments of probability <rn^{k}> and <m^{k}> in the random walk problem are obtained. These are expressed as power series in the mean number of steps in one direction <n>.

**Abstract**

The behavior of gases is usually described by the ideal gas law *pV = NkT.* While such a description often gives a sufficiently good account of how gases behave, higher-order approximations are sometimes needed. For example, phase transitions cannot be explained by the ideal gas law. Such phenomena, however, are described by the higher-order approximation Van-der-Waals equation of state. In this paper, we investigate the effect of a weak 1/r potential on gases composed of monatomic molecules that do not interact with each other. 1/r potentials are particularly interesting because the two most dominant interactions in the macroscopic level, gravitational and electrical, are described by such a potential. We evaluate the classical partition function of the system, from which we obtain the equation of state. Read More

**Abstract**

**T**he question arose whether *Dunaliella acidophila *is not strictly autotrophic but rather is auxotrophic. A still unknown partner microorganism could be supplying it with growth factors (e.g. vitamins). Using ^{14}C-labelled vitamins as tracers, it was tested whether this alga can take-up vitamins when introduced in the medium. Data gathered suggest the presence of uptake mechanisms for biotin, folic acid and pantothenic acid. The calculated K_{M} values are in the micromolar concentrations. The permeability coefficient (P_{s}) of the *D. acidophila *plasmalemma for the vitamins tested ranged from 1.5 – 5.7 x 10^{–}^{11} ms^{-1}. Read More

**Abstract**

In this paper, we consider the class of harmonic functions of bounded mean oscillation (BMOH) in the upper half space R_{+}^{m+l} (m ≥ 1). We will give a characterization for BMOH (R_{+}^{m+l}) and show how this class is related to a special class of Ba spaces which was introduced by Ding and Luo in general form.

**Abstract**

The usual concept of representation is illustrated by examples from Group Theory, Semigroup Theory and Lattice Theory. The generalized concept of representation introduced by Pavel Pudlak in 1985 is then presented and the use of the new approach is shown by proving a representation theorem for finite distributive lattices.