LOOKS of PROFESSOR V.H.DEMCHENKO (1831-1914) IN RELATION TO SHOWS OF WITNESSES AS PROOF IN RULE-MAKING IN TIME OF KYIV RUS

Historyof Law Kyiv Rus, without regard to the more than 200-years-old period of her research, continues to remain in the field of attention of scientists, and, also, politicians. One of important questions of History of Law these period is a question about rule-making and role in him shows of witnesses. This problem was studied thoroughly enough as early as ХІХ of century and one of active acting persons of discussion round this theme there was a historian of law, native of Ukraine, professor of the Kyiv university Vasyl Hryhorovych Demchenko. In the master's degree dissertation "Historical research is about the shows of witnesses as proof in matters of judicial, accoding the Russian law before Peter the Great" (in 1859), V.H. Demchenko considered becoming of such important institute of judicial law as institute of certificate in detail. A scientist marks the value of judicial proofs in general genesis of law, he underlines that before an arbitrariness was the only means of guard of rights, but development of society resulted in a volume, that next to this means already the guard of rights for cramps began to be used. He considered that the judicial aspects related to the shows of witnesses are system enough set forth in Russian True. A researcher paid attention to that Russian True talks about witnesses in most cases in connection with those the offences that must be by them validified, in accordance with every case, where this proof is required. Therefore resolutions about them matter general not rules that spread to all possible cases of their use, but touch only private, that have force only for those cases for that they are straight set. General rules some resolutions that is unconnected with determinations about separate offences matter only. A scientist underlined that the judicial role of witnesses accoding Russian True did not have been limited to only the value of them, as judicial proof. On occasion they got the certain participating in realization of process. It touched those judicial events application of that got to parties without every participation of some government bodies ( for example,zvid). In the research of V.H. Demchenko analysed a question about the capacity of witnesses for a certificate, specified also on space of application of proofs with participation of witnesses after Russian True, order of finishing telling with participation of witnesses, force of shows of witnesses. Thus, V.H. Demchenko no doubt, was one of the most skilled specialists on history law that investigated time of Kyiv Rus.

Lattice points in bodies of rotation with a dent

In the sense of the theory of lattice points in large bodies, a fairly general body of rotation [Formula: see text] in [Formula: see text] is considered whose convexity is being hampered by a “dent” (see Fig. 1). It turns out that, for [Formula: see text] a large real parameter, the true order of magnitude of the lattice discrepancy of [Formula: see text] essentially can be evaluated, contrary to the convex case.

A Bayesian Approach to Ranking and Rater Evaluation

We develop a Bayesian hierarchical model for the analysis of ordinal data from multirater ranking studies. The model for a rater’s score includes four latent factors: one is a latent item trait determining the true order of items and the other three are the rater’s performance characteristics, including bias, discrimination, and measurement error in the ratings. The proposed approach aims at three goals. First, three Bayesian estimators are introduced to estimate the ranks of items. They all show a substantial improvement over the widely used score sums by using the information on the variable skill of the raters. Second, rater performance can be compared based on rater bias, discrimination, and measurement error. Third, a simulation-based decision-theoretic approach is described to determine the number of raters to employ. A simulation study and an analysis based on a grant review data set are presented.

On the distribution of reducible polynomials

Let ℛn(t) denote the set of all reducible polynomials p(X) over ℤ with degree n ≥ 2 and height ≤ t. We determine the true order of magnitude of the cardinality |ℛn(t)| of the set ℛn(t) by showing that, as t → ∞, t 2 log t ≪ |ℛ2(t)| ≪ t 2 log t and t n ≪ |ℛn(t)| ≪ t n for every fixed n ≥ 3. Further, for 1 < n/2 < k < n fixed let ℛk,n(t) ⊂ ℛn(t) such that p(X) ∈ ℛk,n(t) if and only if p(X) has an irreducible factor in ℤ[X] of degree k. Then, as t → ∞, we always have t k+1 ≪ |ℛk,n(t)| ≪ t k+1 and hence |ℛn−1,n (t)| ≫ |ℛn(t)| so that ℛn−1,n (t) is the dominating subclass of ℛn(t) since we can show that |ℛn(t)∖ℛn−1,n (t)| ≪ t n−1(log t)2.On the contrary, if R ns(t) is the total number of all polynomials in ℛn(t) which split completely into linear factors over ℤ, then t 2(log t)n−1 ≪ R ns(t) ≪ t 2 (log t)n−1 (t → ∞) for every fixed n ≥ 2.

Linkage analysis in tetraploid species: a simulation study

A simulation study was performed to investigate methods for mapping single-dose (simplex) and double-dose (duplex) markers, and for identification of homologous chromosomes in an autotetraploid species, and to see how the map accuracy depends on the population size. An initial population of 1000 individuals was simulated, with 30 simplex and 10 duplex markers, and recombination fractions and lod scores were calculated between all pairs of markers. These were used to test the feasibility of mapping the simplex and duplex markers simultaneously. Smaller populations, from 500 to 75 individuals, were then simulated, and the estimates of the pairwise recombination fractions and the derived maps were compared with the true map. It was found that the accuracy of the estimates depended strongly on the type of markers involved, with simplex–simplex coupling pairs being most reliable and simplex–simplex repulsion pairs and duplex–duplex pairs in any configuration but coupling being least reliable. Maps can be assembled using recombination fractions and lod scores from pairs of simplex–simplex markers (coupling and repulsion), duplex–simplex (coupling and repulsion) and duplex–duplex (coupling). The agreement between the map order and the true order was good, although the map distance was generally underestimated at small sample sizes.