On regular graphs, V

AbstractLet Γ3 be an infinite regular tree of valence 3. There exist subgroups B of Aut (Γ3) which are 5-regular on Γ3, i.e., sharply transitive on the set of 5-arcs of Γ3. We prove that any two such subgroups are conjugate in Aut (Γ3). The pair (Γ3, B) is a universal 5-regular action in the sense that if (G, A) is a pair consisting of a cubical graph G and a 5-regular subgroup A of automorphisms of G then (G, A) can be “covered” by (Γ3, B) in a certain natural way

On regular graphs, VI

AbstractLet G be a connected regular graph of valence p + 1 where p is an odd prime. Let A be a subgroup of Aut(G) which is s-regular (s ≥ 0). We prove that s ≤ 3 and the cases s = 0, 1, 2, 3 do occur

A few new orders for D-optimal matrices

The first examples of D-optimal matrices of orders 222, 234, 258 and 278 are constructed.Comment: 9 pages, 3 table

Forecasting maize yield in the Republic of Serbia by using Box-Jenkins methodology

As food supply is one of the most important issues for national security, forecasting agricultural production represents a necessity for every country. Forecasting yields and production volume is a very complex task that requires both application of formal statistical methods and assessment of experts. Considering not only the significant role of maize in the immediate diet and processing industry in the Republic of Serbia, but also its absolute dominance in the structure of sown areas, the analysis of the time series and projections of future maize yield were carried out. Maize yield projections obtained through Box-Jenkins methodology, for 2017 and 2018, are 4.97 t/ha and 7.01 t/ha. Comparing the projected with realized yield in 2017 (for which there is available data), it was noticed that the model's forecast indicated a smaller reduction than actually realized. According to the results of the conducted study, it is clear that although the time series model cannot anticipate precise yield quantities, it can certainly be useful in terms of predicting future tendencies in maize yield oscillations

Interfacial crack behavior in the stationary temperature field conditions

The brittle coatings, made of different materials, when subjected to elevated temperatures and in the heat exchange conditions, are susceptible to delamination. Those coatings, as well as thin films, can be used for various therm insulating deposits, e.g. in turbines of thermal power plants. Due to environmental temperature change, in layers made of materials having different thermal expansion coefficients, appear thermal stresses. In this paper driving forces causing delamination of one layer from the other are analyzed i.e. the interfacial fracture in the two-layered, bi-material sample. This analysis was limited to considering the sample behavior when exposed to the stationaiy temperature field. The energy release rate G, which is the driving force for this interfacial fracture, is changing with temperature and that variation is increasing with increase of the temperature difference between the environment and the sample. Analysis of this relation, between the G variation and temperature difference, can be used to predict the maximal temperature difference, which the two-layered sample can be subjected to, without appearance of delamination between layers

Fundamental Problems of Modeling the Fracture Processes in Concrete II: Size Effect and Selection of the Solution Approach

AbstractTheory of concrete fracture, despite all the efforts of numerous researchers, still did not provide the clear answer to the problem of modeling the fracture processes of concrete. Three well known theories are at hand: fracture mechanics, plasticity theory and mechanics of continuous damages. The fundamental assumptions, those theories are based on, do not completely correspond to the nature of concrete. They all are confronted with numerous problems, out of which the four are fundamental: damages micromechanics, damages localization, size effects and the dilemma when to apply the phenomenological and when the micromechanical approach to considering this problem. In this paper are considered the last two of those problems: size effect (scaling laws) and decision making what would be the best way in solving problems of modeling the fracture processes in concrete and concrete structures

Interfacial crack behavior in the stationary temperature field conditions

The brittle coatings, made of different materials, when subjected to elevated temperatures and in the heat exchange conditions, are susceptible to delamination. Those coatings, as well as thin films, can be used for various therm insulating deposits, e.g. in turbines of thermal power plants. Due to environmental temperature change, in layers made of materials having different thermal expansion coefficients, appear thermal stresses. In this paper driving forces causing delamination of one layer from the other are analyzed i.e. the interfacial fracture in the two-layered, bi-material sample. This analysis was limited to considering the sample behavior when exposed to the stationaiy temperature field. The energy release rate G, which is the driving force for this interfacial fracture, is changing with temperature and that variation is increasing with increase of the temperature difference between the environment and the sample. Analysis of this relation, between the G variation and temperature difference, can be used to predict the maximal temperature difference, which the two-layered sample can be subjected to, without appearance of delamination between layers

Influence of temperature on behavior of the interfacial crack between the two layers

In this paper is considered a problem of the semi-infinite crack at the interface between the two elastic isotropic layers in conditions of the environmental temperature change. The energy release rate needed for the crack growth along the interface was determined, for the case when the two-layered sample is cooled from the temperature of the layers joining down to the room temperature. It was noticed that the energy release rate increases with the temperature difference increase. In the paper is also presented the distribution of stresses in layers as a function of the temperature and the layers' thickness variations. Analysis is limited to the case when the bimaterial sample is exposed to uniform temperature