Abstract:
As a part of a broad-scale study, this paper examines the current use and utilization potentials of renewable energies in the North Great Plain Region. Due to its structural properties, geographical situation, climate and morphology, the Region sees a most favorable situation in the field of geothermal energy, biomass and solar energy. The analyses having been performed so far support the assumption that agricultural combined energy production has significant potentials in rural development. With the combined exploitation of the renewable energy potential, agriculture in the North Great Plain Region may provide fir the energy demands of its own activities and the local surroundings. Agriculture as the local energy provider may create a new source of incomes in the sector seeing a shortage of financial resources, as well as an opportunity of breakthrough for rural communities.

Abstract:
Recently, the most spectacular result of urbanism has been the enormous growth of urban agglomerations with more than 10 million inhabitants. As of the 20th century megacities have been examined by researchers from a variety of approaches while governments have been concerned about their limitless growth. In the middle of the 20th century new terms were coined in an effort to express the limitless growth of urban agglomerations. In this study we examine the current status of two of these: Ecumenopolis and Megalopolis.

Abstract:
With the utilization of the available potentials and technologies, geothermal energy may contribute to the reduction of the quantities of the emitted contaminants and greenhouse gases, as well as the development of peripheral regions. Towards this end, such governmental measures are needed that set up a favourable regulatory environment, and put the financial funds for the support of implementation in place so that geothermal energy resources could complement the currently used, conventional energy carriers, and more efficient settlement development could be achieved. In this context, the University of Debrecen and the University of Oradea have conducted joint studies with the purpose of making a realistic assessment of geothermal energy resources in the region of S cueni–Létavértes and examining the options of long-term utilization. The research has been multidisciplinary, and thus embraced the field of geography, geodetics, well drilling, automation, mechanical engineering and tourism. The principal goal has been the utilization of geothermal energy with the largest possible efficiency in the area of S cueni and Létavértes.

Abstract:
According to the European Spatial Development Perspective (ESDP) basic element of the competitive economic development of the European Union is the balanced regional development through to achieve a polycentric spatial structure. At present, there is only one outstanding larger geographical zone of global economic integration: the core area of the EU, the pentagon defined by the metropolises of London, Paris, Milan, Munich and Hamburg. The monocentric spatial structure describes not only the territory of the EU, but also the territories of the member states and their regions. Analysis having designated by the European Spatial Planning Observatory Network (ESPON) points out that on the basis of the Functional Urban Areas Hungary is the most polycentric member state of the EU. Theoretically it is possible to analyse NUTS 2 regions but for lack of enough data ESPON could not fulfil that. The main purpose of this paper is to analyse the polycentricity of the Hungarian NUTS 2 regions on the basis of the rank-size distribution.

Abstract:
We develop Markov chain mixing time estimates for a class of Markov chains with restricted transitions. We assume transitions may occur along a cycle of $n$ nodes and on $n^\gamma$ additional edges, where $\gamma < 1$. We find that the mixing times of reversible Markov chains properly interpolate between the mixing times of the cycle with no added edges and of the cycle with $cn$ added edges (which is in turn a Small World Network model). In the case of non-reversible Markov-chains, a considerable gap remains between lower and upper bounds, but simulations give hope to experience a significant speedup compared to the reversible case.

Abstract:
Ledrappier and Young introduced a relation between entropy, Lyapunov exponents and dimension for invariant measures of diffeomorphisms on compact manifolds. In this paper, we show that a self-affine measure on the plane satisfies the Ledrappier-Young formula if the corresponding iterated function system (IFS) satisfies the strong separation condition and the linear parts satisfy the dominated splitting condition. We give sufficient conditions, inspired by Ledrappier and by Falconer and Kempton, that the dimensions of such a self-affine measure is equal to the Lyapunov dimension. We show some applications, namely, we give another proof for Hueter-Lalley's theorem and we consider self-affine measures and sets generated by lower triangular matrices.

Abstract:
In the last years considerable attention has been paid for the orthogonal and non-linear projections of self-similar sets. In this paper we consider orthogonal transformation-free self-similar sets in $\mathbb{R}^3$, i.e. the generating IFS has the form $\left\{ \lambda_i \underline{x} + \underline{t}_i \right\}_{i=1}^q$. We show that if the dimension of the set is strictly bigger than $1$ then the projection of the set under some non-linear functions onto the real line has dimension $1$. As an application, we show that the distance set of such self-similar sets has dimension $1$. Moreover, the third algebraic product of a self-similar set with itself on the real line has dimension $1$ if its dimension is at least $1/3$.

For up-to-date bolted joints, first of all in vehicles, high strength bolts of 10.9 or even 12.9 are used, which are pre-tightened up to 90% or even 100% of the yield strength. The primary aim of this high degree utilization is the weight reduction. For the analytic dimensioning of bolted joints, the VDI 2230 Richtlinien German standard provides support. However, the analytic model can mostly consider the true structural characteristics only in a limited way. The analytic modeling is especially uncertain in case of multiple bolted joints when the load distribution among the bolts depends reasonably upon the elastic deformation of the participating elements in the joints over the geometry of the bolted joint. The first part of this paper deals with the problems of numerical modeling and stress analysis, respectively specifying the analytic dimensioning procedure by applying elastic or rather elastic-plastic material law. The error magnitude in bolted joint calculation was examined in case of omitting the existing threaded connection—between the bolt and the nut—in order to simplify the model. The second part of the paper deals with the dimensioning of stands and cantilevers

Abstract:
We consider the interlacement Poisson point process on the space of doubly-infinite Z^d-valued trajectories modulo time-shift, tending to infinity at positive and negative infinite times. The set of vertices and edges visited by at least one of these trajectories is the random interlacement at level u of Sznitman arXiv:0704.2560 . We prove that for any u>0, almost surely, (1) any two vertices in the random interlacement at level u are connected via at most ceiling(d/2) trajectories of the point process, and (2) there are vertices in the random interlacement at level u which can only be connected via at least ceiling(d/2) trajectories of the point process. In particular, this implies the already known result of Sznitman arXiv:0704.2560 that the random interlacement at level u is connected.

Abstract:
We provide bounds on the mixing rate of a Markov chain whose mixing properties are improved by a combination of adding long distance edges and introducing non-reversibility. Our model is built on a cycle graph and involves selecting a sublinear number of nodes and adding all edges connecting them. We show that there is a square factor improvement of the mixing rate compared to the reversible version of the Markov chain. Our result suggests that the combination of the two techniques is a promising concept in a more general setting.