Abstract:
In order to find a superdominant gene for yield, a collection of 350 samples with genes mutations and different expression in different phases of growth and development: fruit size, leaf shape, plant architecture, number of fruits, etc., has been studied (through multi-year research). Current seed production at the Institute for Vegetable Crops in Smederevska Palanka includes 26 hybrids and two in acceptation process, of different purposes and characteristics. The most common mutation genes in tomato selection at the Institute are: sp (self-pruning) inbuilt in determinant hybrids (Balkan F1, Marko F1, Rebus F1) and varieties (Narvik SPF, SP-109, Adonis), u (uniform ripening) - Lido F1, Atina F1, Danubius F1, rin (ripening inhibitor)- Nada F1, ampion F1, Sef F1, Sidra F1, Rebus F1, j (jointless) - Narvik, Adonis, SP-109, c (potato leaf) - Mi-13, Enigma F1, Rebus F1, Ph -2 (Phytophtora infestans resistance) - Luna F1, Zlatni jubilej F1, Sef F1. Quality of tomato fruits is defined by two groups of genes which determinate the organoleptic traits and nutrition composition. Organoleptic quality includes taste and smell, colour and texture of fruits established in variety differences, nutritive regime of plants, maturity phase and yield. Little is known about gene regulation, responsible for variation of these traits.

Abstract:
Archaeological interpretation often links both the European Mesolithic and the complexity with reduced mobility and permanent or semi-permanent settlements. The Iron Gates Gorge (IGG) Mesolithic, on the banks of the Danube, with substantial formal disposal areas for the dead and canonized architecture, especially as manifested at the site of Lepenski Vir, fully conforms to this notion. Different aspects of bioarchaeological analysis – when evaluated concurrently – offer a counter-intuitive picture: at the time of its most complex development, the site of Lepenski Vir represented a focal point for a larger, more mobile hunter-gatherer group that identified with the site, its burials and its smaller resident population. The article explores the evidence provided by human skeletal remains and possible reasons behind these contradictory results.

Abstract:
The article raises two questions: why do sociologists in Western Europe hold expectations of theoretical innovations in sociology in (post-)transitional Eastern European countries, and why is it that sociologists from Eastern Europe do not meet these expectations. The assumption is that these expectations are primarily a response to the theoretical crisis of modern sociology itself, rather than the effect of its knowledge of changes in transitional countries or its willingness to really listen to sociologists from those countries and accept them as equal partners. The attempt to answer the second question involves an analysis of the multilayered reality of sociology in post-socialism, including the loss of the socialist and civil-society utopias which have been replaced by pragmatic endeavors to re-establish a market society and its institutions. Despite the differences between the social situations in the East and West, today’s “Eastern” and “Western” social scientists are confronted by similar global problems and challenges. While the present crisis of the capitalist economy and neo-liberalism certainly has its structural causes, what needs to be questioned here are the very assumptions underlying the world order and the key mechanisms of its functioning.

Abstract:
This paper provides a brief overview of the evolution of views on interest from ancient times to the present day. Historical changes, including legal acts prohibiting and restricting interest as well as theological and economic views and disputes about the justification of its existence, are followed. It turned out that life has sought and found ways to bypass bans, and that placing man at the center of the universe after the Renaissance decidedly marked a shift towards the legalization of interest. It was continuously tolerated in Orthodox countries, with less confrontations than in the West.

Abstract:
The paper has two parts: in the first one, economic aspect of regionalization is considered, in the second a financial one. Regionalization, like every type of decentralization, represents a serious reform of a state and brings upon several expected as well as unexpected although significant effects on political, social, and economic life. Its goal is an improvement of political, social, and economic functions of a state, not their deterioration. Unfortunately, experience of other countries does not support overwhelming optimism. Most frequently, regionalization is done due to political considerations; economic considerations are of secondary importance or even neglected. Such a dominance of political reasoning neglects fundamental principles and arguments of the economic science, standards of rational approach to decentralization, and even economic efficiency and equality between citizens. Because of that, the emphasis in this paper is on economic and financial aspects of regionalization in Serbia. In the first part the author explores economic aspects of regionalization; four state functions (regulation, stabilization, redistribution, and allocation) in decentralized setting; relations between regionalization, deregulation, and privatization; vertical distribution of functions (exclusive functions by the state, exclusive functions by regions, shared functions). After that he explores advantages of the selected model of creating regions and distribution of authorities in Serbia, particularly economic authorities of regions (1. land planning, urban land use, housing; 2. development and maintenance of infrastructure of regional importance and coordination of public utilities in municipalities; 3. agriculture; 4. tourism; 5. forestry 6. hunting and fishing; 7. vocational training and employment; 8. ecology; 9. public works). Separate section is devoted to social protection (financial transfers and institutions). In the second part of the paper (Financing the Regions) the author first examines certain issues in principle (fiscal revenues, vertical and horizontal balance, debts and moral hazard) and then considers topics of financing regions in Serbia, such as revenues subsidies, and debts.

Abstract:
This paper studies the loss of the semimartingale property of the process $g(Y)$ at the time a one-dimensional diffusion $Y$ hits a level, where $g$ is a difference of two convex functions. We show that the process $g(Y)$ can fail to be a semimartingale in two ways only, which leads to a natural definition of non-semimartingales of the \textit{first} and \textit{second kind}. We give a deterministic if and only if condition (in terms of $g$ and the coefficients of $Y$) for $g(Y)$ to fall into one of the two classes of processes, which yields a characterisation for the loss of the semimartingale property. A number of applications of the results in the theory of stochastic processes and real analysis are given: e.g. we construct an adapted diffusion $Y$ on $[0,\infty)$ and a \emph{predictable} finite stopping time $\zeta$, such that $Y$ is a semimartingale on the stochastic interval $[0,\zeta)$, continuous at $\zeta$ and constant after $\zeta$, but is \emph{not} a semimartingale on $[0,\infty)$.

Abstract:
In this note we generalise the Phillips theorem on the subordination of Feller processes by Levy subordinators to the class of additive subordinators (i.e. subordinators with independent but possibly nonstationary increments). In the case where the original Feller process is Levy we also express the time-dependent characteristics of the subordinated process in terms of the characteristics of the Levy process and the additive subordinator.

Abstract:
This paper studies an approximation method for the log-likelihood function of a nonlinear diffusion process using the bridge of the diffusion. The main result (Theorem \refthm:approx) shows that this approximation converges uniformly to the unknown likelihood function and can therefore be used efficiently with any algorithm for sampling from the law of the bridge. We also introduce an expected maximum likelihood (EML) algorithm for inferring the parameters of discretely observed diffusion processes. The approach is applicable to a subclass of nonlinear SDEs with constant volatility and drift that is linear in the model parameters. In this setting, globally optimal parameters are obtained in a single step by solving a linear system. Simulation studies to test the EML algorithm show that it performs well when compared with algorithms based on the exact maximum likelihood as well as closed-form likelihood expansions.

Abstract:
Let $\tau(x)$ be the epoch of first entry into the interval $(x,\infty)$, $x>0$, of the reflected process $Y$ of a L\'evy process $X$, and define the overshoot $Z(x) = Y(\tau(x))-x$ and undershoot $z(x) = x - Y(\tau(x)-)$ of $Y$ at the first-passage time over the level $x$. In this paper we establish, separately under the Cram\'{e}r and positive drift assumptions, the existence of the weak limit of $(z(x), Z(x))$ as $x$ tends to infinity and provide explicit formulae for their joint CDFs in terms of the L\'{e}vy measure of $X$ and the renewal measure of the dual of $X$. We apply our results to analyse the behaviour of the classical M/G/1 queueing system at the buffer-overflow, both in a stable and unstable case.

Abstract:
Let $\xi_1,\xi_2,\ldots$ be an iid sequence with negative mean. The $(m,n)$-segment is the subsequence $\xi_{m+1},\ldots,\xi_n$ and its \textit{score} is given by $\max\{\sum_{m+1}^n\xi_i,0\}$. Let $R_n$ be the largest score of any segment ending at time $n$, $R^*_n$ the largest score of any segment in the sequence $\xi_{1},\ldots,\xi_n$, and $O_x$ the overshoot of the score over a level $x$ at the first epoch the score of such a size arises. We show that, under the Cram\'er assumption on $\xi_1$, asymptotic independence of the statistics $R_n$, $R_n^* -y$ and $O_{x+y}$ holds as $\min\{n,y,x\}\to\infty$. Furthermore, we establish a novel Spitzer-type identity characterising the limit law $O_\infty$ in terms of the laws of $(1,n)$-scores. As corollary we obtain: (1) a novel factorization of the exponential distribution as a convolution of $O_\infty$ and the stationary distribution of $R$; (2) if $y=\gamma^{-1}\log n$ (where $\gamma$ is the Cram\'er coefficient), our results, together with the classical theorem of Iglehart \cite{Iglehart}, yield the existence and explicit form of the joint weak limit of $(R_n, R_n^* -y,O_{x+y})$.