A numerical investigation of the solution of a class of fourth-order eigenvalue problems

This paper is concerned with the accurate numerical approximation of the spectral properties of the biharmonic operator on various domains in two dimensions. A number of analytic results concerning the eigenfunctions of this operator are summarized and their implications for numerical approximation are discussed. In particular, the asymptotic behaviour of the first eigenfunction is studied since it is known that this has an unbounded number of oscillations when approaching certain types of corners on domain boundaries. Recent computational results of Bjorstad & Tjostheim, using a highly accurate spectral Legendre-Galerkin method, have demonstrated that a number of these sign changes may be accurately computed on a square domain provided sufficient care is taken with the numerical method. We demonstrate that similar accuracy is also achieved using an unstructured finite-element solver which may be applied to problems on domains with arbitrary geometries. A number of results obtained from this mixed finite-element approach are then presented for a variety of domains. These include a family of circular sector regions, for which the oscillatory behaviour is studied as a function of the internal angle, and another family of (symmetric and non-convex) domains, for which the parity of the least eigenfunction is investigated. The paper not only verifies existing asymptotic theory, but also allows us to make a new conjecture concerning the eigenfunctions of the biharmonic operator

Evidence of Vortex Jamming in Abrikosov Vortex Flux Flow Regime

We report on dynamics of non-local Abrikosov vortex flow in mesoscopic superconducting Nb channels. Magnetic field dependence of the non-local voltage induced by the flux flow shows that vortices form ordered vortex chains. Voltage asymmetry (rectification) with respect to the direction of vortex flow is evidence that vortex jamming strongly moderates vortex dynamics in mesoscopic geometries. The findings can be applied to superconducting devices exploiting vortex dynamics and vortex manipulation, including superconducting wires with engineered pinning centers.Comment: 5 pages, 3 figure

Growing skull fracture

Background. Growing skull fracture or craniocerebral erosion is a rare complication of linear skull fracture in childhood. It is characterized by progressive diastatic enlargement of the fracture line, which leads to a cranial defect, dural cleft, and cerebral herniation. It is presented as a soft pulsabile scalp swelling above the fracture, with a clear cranial defect. Case report. In this paper we presented a patient, an 8-month-old boy with the growing skull fracture revealed four weeks after the injury. After the surgical treatment, the boy was in a good general condition without the presence of neurologic impairment. Conclusion. Early recognition of craniocerebral erosion is very important. Timely detection prevents further progression of the disease and the evolution of neurological impairment. Surgery is the method of choice for treating a growing skull fracture

ГOPOДCKAЯ OБЩИHA B CPEДHEBEKOBOЙ ДAЛMAЦИИ И ДРЕВHEГPEЧECKИЙ IIOЛИC

The author starts with the statement that the ancient city commune has recently much been studied and that we are faced with a real explosion of interest for the earlier historical periods of the Dalmatian cities. A number of sources from those periods is accessible to scholars, and the history of the mediaeval Dalmatian cities presents a picture of real life, able to be compared with the phenomena of the European history. A series of examples from the communal life in the cities of Zadar, Split, Trogir and Kotor, covering the period between 1260 and 1400 are quoted by the author. That was a period of a stirring development of all forms of life, a period of development of the city commune and administration. We learn the »Conslilium generale maius« of Dubrovnik for the first time in 1235, of Split in 1241, and of Zadar about 1260. Municipal offices for keeping of documents, offices of public notaries, archives and other elements of city administaration have been established in the 13th century. The communal laws and statutes came into being at Split, Zadar, Trogir and Šibenik. The article then covers the period of the autonomous cities, extending from 1100 to 1260, preceded by an earlier form of communes, which the author tries to prove. The beginning of that stage probably was in the second half of the 9th century. Then follow sporadic data relating to the emergence of trades, market-places, fish-markets, etc., which period is called pre-communal by the author. These are no elected functions yet, and the city has nog yet its definite shape with regard to planning, architecture, etc. The author emphasizes the existence of tribunes in the mediaeval Dalmatian cities. The relation to land and the distribution of land among the citizens is specially presented. Examples are quoted in connection with land on the Peninsula of Pelješac, in Kotor, Trogir and Zadar. There is also some information about the colonization of Venetian citizens in Zadar. The distribution of communal land in Split is also dealt with. This, according to the author, became a tradition in the city, and also a peculiar rustic way of life and consciousness. The question why land takes such a significant place in the life of citizens is also answered by the author. The penetration of peasants into the cities from the Roman era on is widely described. According to M. Suić, who had made investigations in the environs of Dalmatian cities in order to find out whether there are traces of the Roman system of field walls, known as »agri centuriati«, established ten of thousands kilometres of such traces in the fields around Zadar, Split, Pula. That ancient agrarian practice survived many centuries. The author then surveys the municipal services known from the ancient city statutes. The commune was constituted only by the members of the Major Council, i. e. the mobility, while the remaining citizens composed a body called »universitas«. The services were rendered without remouneration. The magistracy was divided into two categories: a higher one (the nobility) and a lower one (common people). Closing his article, the author emphasizes that all the exposed characteristics of Dalmatian cities should be sought in analogy with the ancient polis

Variability of Phomopsis populations in sunflower (Helianthus annuus L.)

Various reports state that the sunflower disease, primarily caused by Diaporthe/Phomopsis helianthi Munt.-Cvet. et al., has a wide geographic distribution in Europe, USA, Argentina and Australia. Various Phomopsis isolates obtained during this investigation of the sunflower disease differed in conidial type (α, β, α and β). Phomopsis helianthi was the only isolate producing exclusively β-conidia and perithecia on debris (Diaporthe helianthi). The other Phomopsis isolates were saprobes on sunflower plants.nul

Mountain border area of eastern Serbia in the function of the spring zones of surface water

Border mountain area of eastern Serbia has a distinct potential and importance in the function of surface water sources, which are characterized by range of geographical and environmental characteristics and similarities determined by mountainous character of the territory. For the purposes of this paper, border area of Serbia towards Bulgaria is provisionally determined by iso-border of 25 km. On the defined area of eastern Serbia there are 11 individual territories allocated in the function of being surface water source. Key objects for the realization of the goals of rational and functional exploitation of surface water sources are accumulations. They are the link between the system of surface water sources and water supply system

Sustainаble development of protected rural area of Serbia

Одрживи развој заштићених руралних простора Србије, односно административних територија насеља која припадају њиховом геопросторном обухвату, подразумева интеграцију низа фундаменталних и апликативних проблема и циљева...Sustainable development of the protected rural area of Serbia, or belonging settlements and administrative territories, implies the integration of a range of fundamental and applied problems and objectives, characteristic as per scientific complexity and social importance, so the growing topicality as well. Problem-solving and spatial framework of the research is motivated by the perception of this issue as a scientifically and empirically demanding, integrated, non-schematic, challenging and socially useful. Also, with the conviction that the theoretical and methodological assumptions of modern science on the environment – its fundamental (environment, geoecology, anthropogeography and others), and applicational (nature protection, sustainable development, urban planning, practice of social development, GIS and others) disciplines, it is possible to solve this multi-disciplinary oriented subject. Writing of the thesis is followed by the continuity of transformation and expansion of the epistemological/ontological and theoretical/applicational properties as the environmental science and its core disciplines, so as the normative planning practice of the protection of space. The applied approach of the perception of system „protected landscape areas – rural areas – sustainable development“ has been extended to the position of anthropocentrism (the paradigm of human excellence) as a determinant value of geospace. The anthropocentric approach, in addition to the importance of original nature, also implies the value of traditional and environmentally friendly economic, settlement, demographic and other potentials. That is why, instead of protection in the spirit of ecology and conservation, the preferred forms and mechanisms of sustainable, that is channeled and controlled, development have been proposed with holding the consistency principle – focus on specific values of individual protected territories. This view of the sustainability, by nature, is close to geographers, environmental geographers, social ecologists, tourism experts, spatial planners, demographers, economists and others. Starting from the hypothesis that environmental restrictions aimed at rural areas do not harm the opportunities for their development and do not threaten existential security of the population, an ecological-geographic approach of environmental management in rural areas whose territories partially or completely belong to the protected areas in the Republic of Serbia, was proposed in dissertation. The researches have shown that current models of the protected rural areas management are characterized by exaggerated formal, or normative-planning, and at the same time de facto dysfunctional environmental protection. Long-term effects of this situation have often degraded rare and valuable elements of nature as motives of protection and enlarged developmental disproportions in the territory of Serbia. The empirical researches of diverse and representative model systems clearly show that , in the past, the numerous inherited and generated new negative effects of the importance for the environmental and socio-economic status of the protected rural areas of Serbia have survived. IV The cumulative effects of the above mentioned processes (at the local level) are well advanced environmental degradation and economic and settlement-demographic devastation of these areas, which at the regional and national level encourage the deepening and complexity of development issues. In contrast, the proposed model of sustainable development of the protected rural areas of Serbia contributes to enlargement of rational and environmentally justified valorization of the national territory and the total development potentials. By a such practice, their sustainable development, would, by the mechanisms of the desired direction and control (by type and intensity), reduce current developmental delay and poverty level, and increase the ability of local communities towards a rational and purposeful use of resources with the ultimate objective of their preservation. So far adopted planning documents in Serbia do not explicitly deal with sustainable development of the rural areas in spatial coverage of the protected areas. In this sense, the necessity of making this type of documents would represent the starting point for the proper management of these territories in the direction of finding a solution that would allow the survival of the settlements, and which revitalization would contribute to major development opportunities of the protected area. The market economy as decentralized and privatizing model of development and other effects of the transition of society, were reflected in unrealistic valuation of environmental services and protection of space. Therefore, it was necessary to investigate the mechanisms and move the initiative in the direction of redefition of the mutual relation and total ecological and social role of the protected rural areas of Serbia. Such starting points in further considerations imply that these areas should not be observed and treated only as parts (elements) of particularly valuable and important territories in the function of protection, which is often accentuated approach, but as potentially significant development projects. The presented starting points, analyses, results and proposed models suggest that the thesis had two spatial and problem solutions – in order to give the solution for the empirical issues of the local scope and theoretical issues of regional and global scope. The results can serve as a basis for future research papers, with the aim of a more complex analysis and verification of directions and opportunities for sustainable development of the protected rural areas of Serbia. This paper presents an attempt to answer another request – basic axiological assumption that its results are practically useful as well. The above mentioned gains importance in the way that these issues are taken into consideration in, for them, time of crisis, in which the crisis is not only manifested by accumulated problems, but also acute shortage of ideas and resources for their research and solving

Mountain border area of eastern Serbia in the function of the spring zones of surface water

Border mountain area of eastern Serbia has a distinct potential and importance in the function of surface water sources, which are characterized by range of geographical and environmental characteristics and similarities determined by mountainous character of the territory. For the purposes of this paper, border area of Serbia towards Bulgaria is provisionally determined by iso-border of 25 km. On the defined area of eastern Serbia there are 11 individual territories allocated in the function of being surface water source. Key objects for the realization of the goals of rational and functional exploitation of surface water sources are accumulations. They are the link between the system of surface water sources and water supply system

Kinetics and mechanism of synthetic CoS oxidation process

The results of investigation of kinetics and mechanism for synthetic a-CoS oxidation process are presented in this paper. Based on experimental data obtained using DTA and XRD analysis and constructed PSD diagrams for Co-S-O system, mechanism of synthetic a-CoS oxidation process is suggested. Characteristic kinetic parameters were obtained for experimental isothermal investigations of desulfurization degree using Sharp method

THE IMPACT OF LESSON STUDY ON Pre-service Kindergarten Teachers’ Mathematics Teaching Anxi

These articles are a result of the bilateral cooperation project ”Assumptions and possibilities of developing innovative models of teaching for accomplishing transparency of university education and for raising competitiveness in national and international knowledge markets”, carried out and financied by the University of Kragujevac, Faculty of Education, Jagodina (Republic of Serbia) and the University of Primorska, Faculty of Education, Koper (Republic of Slovenia), in the period 2017–2019.In today’s society teachers are expected to have adequate knowledge and skills to teach effectively even before graduation. Such expectations can cause anxiety in teachers, especially in inexperienced ones. Lesson Study is recognized as an effective tool for providing high-quality learning experiences for future teachers which enables them to learn from engaging in and observing teaching in contrast to traditional pedagogy courses. This study aimed to investigate the effects of Lesson Study on mathematics teaching anxiety of pre-service kindergarten teachers. The quasi-experimental design with two parallel groups was used. The sample consisted of 49 students divided into control (27) and experimental group (22). The students in the experimental group followed an adjusted Lesson Study design, while the control group followed the traditional way of teaching practice. The results showed that there was no significant difference in mathematics teaching anxiety scores between groups. However, there was a significant difference in the findings referring to ability to control the class favoring the experimental group. The findings of the current researchers’ study cannot be generalized due to certain limitations (small sample size, quasi-experimental design). The results can be used as support to encourage further investigations of the effects of Lesson Study in teacher education programmes.Publishe