Abstract:
This note provides an elementary proof of the folklore fact that draws from a Dirichlet distribution (with parameters less than 1) are typically sparse (most coordinates are small).

Abstract:
Bruise Resistance Coefficient (BRC) and Bruise Sensitivity (BS) of stored apples and raw cherries were studied by the quasi-static compression of simple fruits between two plates. The results obtained show that both parameters depend on the extent of compression. For the lowest deformations they were zero. Starting from some characteristic values of the absorbed energy and/or the work of loading the BRC and the BS increased with increasing absorbed energy and the work of loading, respectively. This behaviour was observed mainly for 8 % deformation of apples. For higher deformations (up to the 30 % in the case of cherries) the BRC and/or BS rather decreased with an increasing extent of compression. The initial characteric values of the absorbed energy and the work of loading from which both the BRC and BS increased with the increasing extent of deformation seems to be connected with a characteristic value of the relative absorbed energy for which common value of 0.52 for both apples and the cherries was observed.

Abstract:
The article devoted to the results of cherries breeding by Institute of irrigated horticulture during 2004-2011 in southern steppe of Ukraine. The selection was done by productivity, fruits quality, and resistance to unfavorable conditions of winter period and to fungous diseases. Short description of perspective cherries sorts is presented.

Abstract:
Let G be an n-vertex graph that contains linearly many cherries (i.e., paths on 3 vertices), and let c be a coloring of the edges of the complete graph K_n such that at each vertex every color appears only constantly many times. In 1979, Shearer conjectured that such a coloring c must contain a properly colored copy of G. We establish this conjecture in a strong form, showing that it holds even for graphs G with O(n^(4/3)) cherries and moreover this bound on the number of cherries is best possible up to a constant factor. We also prove that one can find a rainbow copy of such G in every edge-coloring of K_n in which all colors appear bounded number of times. Our proofs combine a framework of Lu and Szekely for using lopsided Lovasz local lemma in the space of random bijections together with some additional ideas.

Abstract:
Effect of drying conditions on Allahidyen (Salihli) sweet cherries (Prunus avium L.) cultivated in Turkey was studied with the following treatments: dipping in 2 per cent Na2S2O5 for 7 minute, or in 0.5 per cent K2CO3 for one minute at 90°C before drying. The pretreatment were compared with untreated samples. The initial moisture contents of all the samples were 5.4528 gram H2O/gram dry matter (g.H2O/g.DM) while final moisture contents were 0.5254, 0.7796 and 0.6102 g.H2O/g. DM for control, Na2S2O5 and K2CO3 treated samples, respectively. The total soluble solids of dried samples were 66.9 for control, 63.3 and 60.3 per cent for Na2S2O5 and K2CO3 treatments. A decline pattern in ascorbic acid concentration was noted. The anthocyanin extracts from salified samples showed increase in optical density as compare to control and the K2CO3 treated ones. The results indicated that there were no significant differences between the chemical and physical properties of the untreated (control) dried sweet cherries and those treated with Na2S2O5 or K2CO3. Such conclusion enhanced the possibility of drying sweet cherries without any chemical treatments, a trend which will have a direct effect on human health by preventing the harmful effect of chemical additives and supporting the pattern of reaching "food safety".

Abstract:
We consider the urn setting with two different objects, ``good'' and ``bad'', and analyze the number of draws without replacement until a good object is picked. Although the expected number of draws for this setting is a standard textbook exercise, we compute the variance, and show that this distribution converges to the geometric distribution.

Abstract:
We consider exact enumerations and probabilistic properties of ranked trees when generated under the random coalescent process. Using a new approach, based on generating functions, we derive several statistics such as the exact probability of finding k cherries in a ranked tree of fixed size n. We then extend our method to consider also the number of pitchforks. We find a recursive formula to calculate the joint and conditional probabilities of cherries and pitch- forks when the size of the tree is fixed.

Abstract:
In present study the quantification of total phenolics content (TPC), total antioxidant activity (TAA) and their relation in sweet and tart cherries were studied. Aqueous and pure polar solvents were used to compare the yield of present phenolic compounds in prepared extracts. The solubility of phenolics was the most effective in sweet cherry extracts with using of 50 % methanol and in tart cherry extracts with using of 50 % acetone. The yield of TPC of both tested cherry fruit extracts was higher with pure methanol in comparison to pure acetone. Substantial TPC assessed with Folin-Ciocealteu assay in tart cherry extracts were in range from 70.6±8.46 mg to 241.4±7.26 mg GAE/100 g FW. Extracts from lyophilised tart cherries (methanolic and water-acetone mixtures) contain in average 2-times higher amount of polyphenols than ethanol extracts. The DPPH antiradical efficiency values of the both tested fruit extracts were higher in extracts of tart cherries (from 5.4 to 9.9 % of inhibition of DPPH radical) when compared to those of sweet cherries (from 2.4 to 3.5 % of inhibition of DPPH radical). Total antioxidant activity (TAA) of sweet cherry extracts (using 70 % ethanol and with 70 % methanol) and of tart cherry extracts (with 50 % methanol) depended on phenolics content.

Abstract:
This work continues \cite{bib1} where the construction of Hamiltonian $H$ for the system of three quantum particles is considered. Namely the system consists of two fermions with mass $1$ and another particle with mass $m>0$. In the present paper, like in \cite{bib1}, we study the part $T_{l=1}$ of auxilliary operator $T = \oplus_{l=0}^{\infty} T_l$ involving the construction of the resolvent for the operator $H$. In this work together with the previous one two constants $0m_0$ the operator $T_{l=1}$ is selfadjoint but for $m \leqslant m_0$ it has the deficiency indexes $(1,1)$; 2) for $m_1 n_0\}$ with the asymptotics \[ \lambda_n = \lambda_0 e^{\delta n} + O(1),\quad n\to\infty, \] where $\lambda_0 <0$, $\delta >0$, $n_0>0$ and there is'nt other spectrum on the interval $\lambda < \lambda_{n_0}$.

Abstract:
The Psychosis Screening Questionnaire and the Harvard Trauma Questionnaire (assessing trauma exposure and PTSD) were administered in an epidemiological survey of 1245 adults (response rate 80.6%) in a rural and an urban setting in Timor Leste. We defined PSQ screen-positive cases as those people reporting at least one psychotic-like symptom (paranoia, hallucinations, strange experiences, thought interference, hypomania).The prevalence of PSQ screen-positive cases was 12 percent and these persons were more disabled. PSQ cases were more likely to reside in the urban area, experienced higher levels of trauma exposure and a greater prevalence of PTSD. PTSD only partially mediated the relationship between trauma exposure and psychotic-like symptoms.Psychotic-like symptoms may be prevalent in countries exposed to mass conflict. The cultural and contextual meaning of psychotic-like symptoms requires further inquiry in low-income, post-conflict settings such as Timor Leste.Knowledge has accrued about the prevalence of psychotic-like symptoms such as hallucinations, paranoia and strange experiences in the general community [1-3]. The relatively high rates of psychotic-like experiences at a community-wide level suggests a distinction between these phenomena and clinical psychotic disorders, which have much lower prevalence rates. A clinical diagnosis of a psychotic disorder requires the simultaneous occurrence and persistence of symptoms, whereas persons experiencing isolated psychotic-like symptoms appear to be more common and are less likely to attract clinical attention [1,4].Past studies suggest that psychotic-like symptoms are associated with being female, low levels of social support, alcohol [5] and cannabis use [6], and a family history of mental illness [5,6]. Psychotic-like symptoms appear to be more prevalent in some ethnic groups [7], but available data are restricted to minorities living in developed countries.Trauma exposure appears to be associated with psychot