On Graph-Based Cryptography and Symbolic Computations

We have been investigating the cryptographical properties of in nite families of simple graphs of large girth with the special colouring of vertices during the last 10 years. Such families can be used for the development of cryptographical algorithms (on symmetric or public key modes) and turbocodes in error correction theory. Only few families of simple graphs of large unbounded girth and arbitrarily large degree are known. The paper is devoted to the more general theory of directed graphs of large girth and their cryptographical applications. It contains new explicit algebraic constructions of in finite families of such graphs. We show that they can be used for the implementation of secure and very fast symmetric encryption algorithms. The symbolic computations technique allow us to create a public key mode for the encryption scheme based on algebraic graphs

On the key expansion of D(n, K)-based cryptographical algorithm

The family of algebraic graphs D(n, K) defined over finite commutative ring K have been used in different cryptographical algorithms (private and public keys, key exchange protocols). The encryption maps correspond to special walks on this graph. We expand the class of encryption maps via the use of edge transitive automorphism group G(n, K) of D(n, K). The graph D(n, K) and related directed graphs are disconnected. So private keys corresponding to walks preserve each connected component. The group G(n, K) of transformations generated by an expanded set of encryption maps acts transitively on the plainspace. Thus we have a great difference with block ciphers, any plaintexts can be transformed to an arbitrarily chosen ciphertex by an encryption map. The plainspace for the D(n, K) graph based encryption is a free module P over the ring K. The group G(n, K) is a subgroup of Cremona group of all polynomial automorphisms. The maximal degree for a polynomial from G(n, K) is 3. We discuss the Diffie-Hellman algorithm based on the discrete logarithm problem for the group τ-1Gτ, where τ is invertible affine transformation of free module P i.e. polynomial automorphism of degree 1. We consider some relations for the discrete logarithm problem for G(n, K) and public key algorithm based on the D(n, K) graphs

3D Modeling of the Two-Stage Combustion of Ekibastuz Coal in the Furnace Chamber of a PK-39 Boiler at the Ermakovo District Power Station

The processes of combustion of high-ash coal in the combustion chambers of steam boilers are numerically investigated using 3D mathematical modeling methods. The investigations are carried out for the example of combusting Ekibastuz coal in the furnace chamber of a PK-39 boiler at the Ermakovo district power station. The calculated fields of the velocities, temperature, and concentrations of CO, CO2, O2, CH4, and NOX along the furnace space are given and compared with experimental data

The International Algebraic Conference dedicated to the 100th anniversary of L.A. Kaluzhnin

The International Algebraic Conference dedicated to the 100th anniversary of an outstanding mathematician and teacher, the founder of Algebra and Mathematical Logic Department of Taras Shevchenko National University of Kyiv Professor L.A. Kaluzhnin was held on 7–12 July 2014 in Kyiv

Peraturan Bersama Menteri Agama dan Menteri dalam Negeri Nomor 08 dan 09 Tahun 2006 Tentang Pendirian Rumah Ibadat (Kajian dalam Perspektif Hak Asasi Manusia )

Pundamental 1945 Constitution as the rule has been set explicitly for religious freedom in the run by followers, who belong to one human rights has, but in reality the persecution of religious life and often inevitable. Between religious persecution can come from various directions such as harassing each other, mutual intimidate(violence) and that most often occurs between religious persecution that is prihal establishment synagogue. Therefore, in terms of the establishment of the synagogue there must be government intervention to regulate it, if in this case given the freedom and without any clear rules, the sectarian conflict will not be able to avoid. One step from the government to avoid conflict in the establishment of the synagogue is to be issued the Joint Decree of the Minister of Religious Affairs and the Minister of Home Affairs Number 08 and Number 09 Year 2006 About the Construction of Houses of Worship that aims to create harmony and peace between religious and have certainty Strong law

Results of long-term biological monitoring of pacific salmons in the hatcheries of Kamchatsky Krai

The following biological problems of the pacific salmons cultivation in Kamchatka are considered on the base of long-term monitoring data (2001-2013): 1) dynamics of cultivated salmons abundance in the water bodies of salmon hatcheries; 2) salmon otolith marking; 3) biological state of salmon juveniles and adults; 4) epizooty in hatcheries; 5) assessment of hatcheries effectiveness and prospects of salmon cultivation in Kamchatka. Four pacific salmon species are cultivated in Kamchatka: chum salmon (~ 60-70 %), sockeye salmon (~ 25-30 %), chinook salmon (~ 2-3 %), and coho salmon (~ 2-3 %). Their total annual release from Kamchatka hatcheries is estimated as approximately 36 million juveniles on average for the period 2001-2013. Mean contribution of chinook, sockeye and coho salmons cultivated in Kamchatka to the total release of these species from all Far-Eastern hatcheries is 100 %, 95 % and 35 %, respectively, but the contribution of chum salmon does not exceed 3-5 % of its total release. Total annual return of the salmons to Kamchatka hatcheries is about 38,000 on average, so the coefficients of return are usually < 1 % that means rather poor effectiveness of the hatcheries. The highest coefficient of return (2.1 %) is reached in Malkinsky hatchery that uses local geo-thermal water for rearing of salmon juveniles. To enhance the returns, illegal fishing (poaching) should be limited as much as possible and technologies of rearing have to be enhanced. Besides, the process of otoliths marking for cultivated juveniles in hatcheries has to be strictly controlled by technical standards for better evaluation of their contribution to commercial stocks. Promising ways of salmon fishery industry development in Kamchatka are ranching, supporting of wild salmon reproduction, and regulation of traditional fishery. All these measures should minimize effects of hatchery cultivation on structure of the stocks of pacific salmons. Health surveillance for hatchery-reared juveniles has to prevent and/or reduce their mortality in case of infectious, parasitical, alimentary and others diseases

Тенденції застосування рішень Європейського суду з прав людини в Україні

Войціховський, А. В. Тенденції застосування рішень Європейського суду з прав людини в Україні / А. В. Войціховський, О. С. Устименко // Urgent problems of law on the modern stage of statehood development: Conference proceedings, 20-21 October, 2017. - Lublin: Izdevnieciba «Baltija Publishing», 2017. - P. 240-243.У тезах доповіді проаналізовано Конвенцію про захист прав людини та основоположних свобод, Закон України "Про виконання рішень та застосування практики Європейського суду з прав людини".The Convection for the Protection of Human Rights and Fundamental Freedoms and the Ukrainian Law “On realization of decisions and application of European Court of Human Rights practice” are analyzed in the thesis.В тезисах доклада проанализировано Конвенцию о защите прав человека и основоположных свобод, закон Украины «Об исполнении решений и применении практики Европейского суда по правам человека»