On the maximum values of the additive representation functions

Let $A$ and $B$ be sets of nonnegative integers. For a positive integer $n$ let $R_{A}(n)$ denote the number of representations of $n$ as the sum of two terms from $A$. Let $\displaystyle s_{A}(x) = \max_{n \le x}R_{A}(n)$ and \displaystyle d_{A,B}(x) = \max_{\hbox{t: a_{t} \le x$or$b_{t} \le x}}|a_{t} - b_{t}|. In this paper we study the connection between $s_{A}(x)$, $s_{B}(x)$ and $d_{A,B}(x)$. We improve a result of Haddad and Helou about the Erd\H{o}s - Tur\'an conjecture

Radiodiagnostic method for studying the dynamics of Anguillicola crassus (Nematoda: Dracunculoidea) infection and pathological status of the swimbladder in Lake Balaton eels

Swimbladder changes resulting from Anguillicola crassus infection of the European eel Anguilla anguilla have been the subject of several studies reported in the literature. These investigations, however, studied exclusively the status of infection at a given point in time and did not deal with changes in swimbladder infection in eels suffering from anguillicolosis over a period of time. In this study, A. crassus-induced pathological changes were monitored in 78 eels naturally infected in Lake Balaton and subsequently kept in the laboratory, thus excluding the possibility of further infection. During the 3 mo study, the status of the swimbladder was checked by radiographic examination on 4 occasions. At the end of the study the eels were dissected and the gross pathological changes in the swimbladders were compared with the radiographic findings. As compared to their starting condition, by the end of the study the pathological status of the swimbladder had deteriorated in 55 % and remained the same in 37 % of the cases. Tendency to improvement (1 %) and variable findings (7 %) were recorded in a low percentage of cases only. With the help of the radiographs presented, the dynamics of A. crassus infection and of changes in the swimbladder of individual eel specimens can be monitored easily

Intraoligochaete development of Myxobolus intimus (Myxosporea: Myxobolidae), a gill myxosporean of the roach (Rutilus rutilus)

The infection with Myxobolus intimus Zaika, 1965 in the gills of the roach Rutilus rutilus (L.) from Lake Balaton was recorded in 28 out of the 39 fish examined. Developing and mature plasmodia were detected on the gills exclusively in the spring. The Myxobolus intimus infection was found only in 2- to 3-year-old fish. In histological sections, young plasmodia were found in capillaries of the secondary lamellae. More mature, round plasmodia 0.4-0.6 mm in diameter, deformed the respiratory lamellae. The intraoligochacte development of M. intimus was studied in experimentally infected oligochaetes. In two experiments, uninfected Tubifex tubifex Muller and Limnodrilus hoffmeisteri (Claparede) were exposed to mature myxospores of M. intimus. In both experiments, typical triactinospores developed in T. tubifex specimens but no infection was found in L. hoffmeisteri. In semithin sections, developmental stages, pansporocysts and actinospores, were found within the proliferated gut epithelium of T. tubifex. Triactinospores were first released from oligochaetes 37 and 58 days after initial exposure in the two experiments, respectively. Each triactinospore had three pyriform polar capsules and a cylindrical sporoplasm with 32 secondary cells. The spore body joined the 3 caudal projections with a moderately long style

On minimal additive complements of integers

Let $C,W\subseteq \mathbb{Z}$. If $C+W=\mathbb{Z}$, then the set $C$ is called an additive complement to $W$ in $\mathbb{Z}$. If no proper subset of $C$ is an additive complement to $W$, then $C$ is called a minimal additive complement. Let $X\subseteq \mathbb{N}$. If there exists a positive integer $T$ such that $x+T\in X$ for all sufficiently large integers $x\in X$, then we call $X$ eventually periodic. In this paper, we study the existence of a minimal complement to $W$ when $W$ is eventually periodic or not. This partially answers a problem of Nathanson.Comment: 13 page

Multiphase Eulerian simulations of a sedimentation process in a solid-fluid particle-laden flow

In this paper, modelling details have been investigated for a multiphase settling process in a two-dimensional particle-laden flow. Unsteady simulations have been performed by using an Eulerian-Eulerian multiphase approach. A preliminary mesh sensitivity study showed that the numerical results might become oscillatory when the grid spacing is comparable with the solid particle diameter, which indicates that excessive mesh refinement is undesirable. In these multiphase flows, the interaction between the fluid and solid phases is modelled relying on purely heuristic arguments, which is a major source of uncertainties. Therefore fluid-solid exchange and drag coefficient models have been compared and assessed in terms of their accuracy. Since the ANSYS-FLUENT commercial software package provides only a few of these approaches, the majority of the models have been implemented through User-Defined Functions (UDFs) in C programming language. The results showed that the choice of an exchange model has considerable impact on the solution and the best agreement has been achieved by employing the formulation proposed by Schiller and Naumann [8]. However, only minor differences have been experienced between the distinct drag models for this specific problem due to their similar behaviour over the investigated settling Reynolds number range

The Social Aspects and Public Acceptance of Biomass Giving the Example of a Hungarian Region

Biomass energy sources are the most promising, and most heavily subsidized renewable energy sources. The future of biomass energy in the global energy system depends on on many major factors, among others on the attitude of society to the biomass energy and the renewable energy resources. The purpose of the paper is to analyze the opportunities of utilization of biomass energy sources giving example of a Hungarian study area furthermore to study the public acceptance of renewable energy sources in a certain region. The study aims to explore the general knowledge, innovative attitude, acceptance and willingness of application as well as the estimation of the benefits of the use of RES within the inhabitants. Data collection has carried out by primary (questionnaire survey) and secondary ways in order to gain deep information from the target group (local people). The conclusion we can drawn from the analysis is that society take the biomass energy into consideration and its importance and responsibility is increasing. As far as the consciousness is concerned, the knowledge and the environmental friendly approach of inhabitants are also sufficient

Accelerating Universe as Window for Extra Dimensions

Homogeneous cosmological solutions are obtained in five dimensional space time assuming equations of state $p = k\rho$ and $p_{5}= \gamma\rho$ where p is the isotropic 3 - pressure and $p_{5}$, that for the fifth dimension. Using different values for the constants k and $\gamma$ many known solutions are rediscovered. Further the current acceleration of the universe has led us to investigate higher dimensional gravity theory, which is able to explain acceleration from a theoretical view point without the need of introducing dark energy by hand. We argue that the terms containing higher dimensional metric coefficients produce an extra negative pressure that apparently drives an acceleration of the 3D space, tempting us to suggest that the accelerating universe seems to act as a window to the existence of extra spatial dimensions. Interestingly the 5D matter field remains regular while the \emph{effective} negative pressure is responsible for the inflation. Relaxing the assumptions of two equations of state we also present a class of solutions which provide early deceleration followed by a late acceleration in a unified manner. Interesting to point out that in this case our cosmology apparently mimics the well known quintessence scenario fuelled by a generalised Chaplygin-type of fluid where a smooth transition from a dust dominated model to a de Sitter like one takes place.Comment: 20 pages,3 figure

Comparison of soil erosion dynamics under extensive and intensive cultivation based on basic soil parameters

The conservation of soil and its elemental feature, t he soil fertility has not just national and agricultural business interest, since the fertile soil is an elemental part of the material turnover in the environment. The soil erosion can reach huge spatial e xtensions and starts with the most valuable part: the upper, fertile layer. So, its research is crucial for our future survival. Our studied area can be found in Gerézdpuszta at the Koppány -valley of Hungary, which is a sensitive erosion area. We sampled the upper 30 cm of soil layer in every 10 meters that resulted 32-32 point samples on the arable and on the grassland, respectively. One sample was taken under the forest as r eference. We analyzed the basic soil parameters: CaCO 3 , pH, AL-P 2 O 5 , AL-K 2 O, Kuron’s higroscopicity, SOM and the particle size di stribution was determined. Besides, we examined the connection between the given results from laboratory soil analyses and the Munsell-type and Google Earth satellite image colors. O ur results show the erosion dynamic on our sample slope, and the main differences in basic soil paramet ers between different intensities. The main indicator of soil erosion dynamic were the CaCO 3 , the SOM, AL-P 2 O 5 and the particle size distribution, where the SOM and CaCO 3 were correlate with the Munsell and Google Earth col or also