Separately polynomial functions

It is known that if $f\colon {\mathbb R}^2 \to {\mathbb R}$ is a polynomial in each variable, then $f$ is a polynomial. We present generalizations of this fact, when ${\mathbb R}^2$ is replaced by $G\times H$, where $G$ and $H$ are topological Abelian groups. We show, e.g., that the conclusion holds (with generalized polynomials in place of polynomials) if $G$ is a connected Baire space and $H$ has a dense subgroup of finite rank or, for continuous functions, if $G$ and $H$ are connected Baire spaces. The condition of continuity can be omitted if $G$ and $H$ are locally compact or complete metric spaces. We present several examples showing that the results are not far from being optimal.Comment: 14 page

Surface activation of High Impact Polystyrene substrate using dynamic atmospheric pressure plasma

Over the last decade, the number of researches has increased in the field of bonding technologies. Researchers attempt to improve surface adhesion properties by surface treatments. Adhesive bonding is one of these bonding techniques, where it is important to see what surfaces will be bonded. One such surface property is wetting, which can be improved by several types of surface treatment. In recent years, atmospheric pressure plasmas have appeared, with which research is ongoing on surface treatments. In our research, we will deal with the effects of plasma surface treatment at atmospheric pressure and its measurement. In addition, we summarize the theoretical background of adhesion, surface tension and surface treatment with atmospheric pressure plasma. Our goal is to improve adhesion properties and thus the adhesion quality

Transformer Model Identification by Ārtap: A Benchmark Problem

The paper presents how Ārtap can be used for determining the equivalent circuit parameters of a one phase transformer as a benchmark problem. The following unknown parameters of the equivalent circuit are identified: primary resistance and primary leakage reactance, secondary resistance and secondary leakage reactance, finally magnetizing resistance, and magnetizing reactance. The known quantities from measurement are the primary voltage, primary current, power factor, secondary voltage, and the load resistance. Algorithms implemented in Ārtap are used for determining the transformer parameters and the results are compared with the analytical solution

Formation of Oxide Layers with Femtosecond Laser on Steel Surfaces for Color Marking

With the appearance of ultrashort pulse lasers, the researchers have begun working on various laser marking technology. Atmospheric heating and ablation of a surface induce laser coloration of metal surfaces. However, their application is still problematic today in the industry. With the appearance of femtosecond pulse lasers, a new concept became available for color marking. This concept is based on the formation of laser-induced periodic surface structures (LIPSS) on metal surfaces. The purpose of this article is to summarize the literature of laser color marking with ultrashort pulse lasers

The discrete Pompeiu problem on the plane

We say that a finite subset E of the Euclidean plane has the discrete Pompeiu property with respect to isometries (similarities), if, whenever is such that the sum of the values of f on any congruent (similar) copy of E is zero, then f is identically zero. We show that every parallelogram and every quadrangle with rational coordinates has the discrete Pompeiu property with respect to isometries. We also present a family of quadrangles depending on a continuous parameter having the same property. We investigate the weighted version of the discrete Pompeiu property as well, and show that every finite linear set with commensurable distances has the weighted discrete Pompeiu property with respect to isometries, and every finite set has the weighted discrete Pompeiu property with respect to similarities

FITTING TRAFFIC TRACES WITH DISCRETE CANONICAL PHASE TYPE DISTRIBUTIONS AND MARKOV ARRIVAL PROCESSES

Recent developments of matrix analytic methods make phase type distributions (PHs) and Markov Arrival Processes (MAPs) promising stochastic model candidates for capturing traffic trace behaviour and for efficient usage in queueing analysis. After introducing basics of these sets of stochastic models, the paper discusses the following subjects in detail: (i) PHs and MAPs have different representations. For efficient use of these models, sparse (defined by a minimal number of parameters) and unique representations of discrete time PHs and MAPs are needed, which are commonly referred to as canonical representations. The paper presents new results on the canonical representation of discrete PHs and MAPs. (ii) The canonical representation allows a direct mapping between experimental moments and the stochastic models, referred to as moment matching. Explicit procedures are provided for this mapping. (iii) Moment matching is not always the best way to model the behavior of traffic traces. Model fitting based on appropriately chosen distance measures might result in better performing stochastic models. We also demonstrate the efficiency of fitting procedures with experimental result