Ultrasonic system for accurate distance measurement in the air

This paper presents a system that accurately measures the distance travelled by ultrasound waves through the air. The simple design of the system and its obtained accuracy provide a tool for non-contact distance measurements required in the laser’s optical system that investigates the surface of the eyeball.     

Renormalization group approach to lattice gauge field theories

We study four-dimensional pure gauge field theories by the renormalization group approach. The analysis is restricted to small field approximation. In this region we construct a sequence of localized effective actions by cluster expansions in one step renormalization transformations. We construct also -functions and we define a coupling constant renormalization by a recursive system of renormalization group equations.     

The Monte-Carlo model of a light-emitting diode

The first complete Monte-Carlo model of a surface light-emitting diode is presented in this paper. In the model all important phenomena (including the two-dimensional diffusion of minority carriers before their recombination in the active region and the re-emission of radiation) are taken into account. The influence of various construction parameters on the external quantum efficiency of the homojunction GaAs diode is examined.     

Preparation and semiconducting properties of Th3As4

The resistivity, thermoelectric power and Hall constant in the temperature range of 78–830 K were determined for polycrystalline Th₃As₄ samples obtained by annealing thin thorium slabs in arsenic vapour. The samples examined were n-type semiconductors with a carrier concentration ranging from 1.0 × 10¹⁸cm^?3 to 2.8 × 10¹⁸ cm^?3 for which the effective mass was found to be equal to 0.55–0.76m₀. The Hall mobility, about 450cm²V^?1s^?1 at room temperature, obeys a $\text{T}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$ law at high temperatures. On the basis of the electrical measurements the forbidden gap of Th₃As₄ was found to be equal to 0.43 eV.     

A note on the Percus-Yevick and hypernetted chain theories of adsorption: The second and third virial coefficients for a hard-sphere gas in contact with a wall with a soft surface layer

The first three virial coefficients of a new type in the density expansion of the adsorption isotherm for hard spheres in contact with a wall with a soft surface layer are calculated. The results are compared with those for hard spheres in contact with a hard wall.     

GeneralizedG-theory

A generalization of theG-theory defined by A. Heilet al. is presented.     

Cauchy boundary andb-incompleteness of space-time

It is shown that if a space-time (M, g) is time-orientable and its Levi-Civita connection [in the bundle of orthonormal frames over (M, g)] is reducible to anO(3) structure, one can naturally select a nonvanishing timelike vector field and a Riemann metricg ⁺ onM. The Cauchy boundary of the Riemann space (M, g ⁺) consists of endpoints ofb-incomplete curves in (M, g); we call it theCauchy singular boundary. We use the space-time of a cosmic string with a conic singularity to test our method. The Cauchy singular boundary of this space-time is explicitly constructed. It turns out to consist of what should be expected.     

Blaschke-Süss type theorems for closed plane curves

A C¹-class of plane closed curves is considered, which contains all ovals and rosettes. This class is divided into some subclasses for which greatest lower bounds of numbers of antipodal and arc-antipodal sets are determined.     

An Asymptotic Ratio in the Complete Binary Tree

Let T _n be the complete binary tree of height n considered as the Hasse-diagram of a poset with its root 1 _n as the maximum element. For a rooted tree T, define two functions counting the embeddings of T into T _n as follows A(n;T)=|{S T _n  : 1 _n ∈S, S≅T}|, and B(n;T)=|{S T _n :1 _n ∉S, S≅T}|. In this paper we investigate the asymptotic behavior of the ratio A(n;T)/B(n;T), and we show that lim  _n→∞[A(n;T)/B(n;T)]=2^ℓ;−1−1, for any tree T with ℓ leaves. This revised version was published online in June 2006 with corrections to the Cover Date.