Searching of gapped repeats and subrepetitions in a word

A gapped repeat is a factor of the form $uvu$ where $u$ and $v$ are nonempty words. The period of the gapped repeat is defined as $|u|+|v|$. The gapped repeat is maximal if it cannot be extended to the left or to the right by at least one letter with preserving its period. The gapped repeat is called $\alpha$-gapped if its period is not greater than $\alpha |v|$. A $\delta$-subrepetition is a factor which exponent is less than 2 but is not less than $1+\delta$ (the exponent of the factor is the quotient of the length and the minimal period of the factor). The $\delta$-subrepetition is maximal if it cannot be extended to the left or to the right by at least one letter with preserving its minimal period. We reveal a close relation between maximal gapped repeats and maximal subrepetitions. Moreover, we show that in a word of length $n$ the number of maximal $\alpha$-gapped repeats is bounded by $O(\alpha^2n)$ and the number of maximal $\delta$-subrepetitions is bounded by $O(n/\delta^2)$. Using the obtained upper bounds, we propose algorithms for finding all maximal $\alpha$-gapped repeats and all maximal $\delta$-subrepetitions in a word of length $n$. The algorithm for finding all maximal $\alpha$-gapped repeats has $O(\alpha^2n)$ time complexity for the case of constant alphabet size and $O(n\log n + \alpha^2n)$ time complexity for the general case. For finding all maximal $\delta$-subrepetitions we propose two algorithms. The first algorithm has $O(\frac{n\log\log n}{\delta^2})$ time complexity for the case of constant alphabet size and $O(n\log n +\frac{n\log\log n}{\delta^2})$ time complexity for the general case. The second algorithm has $O(n\log n+\frac{n}{\delta^2}\log \frac{1}{\delta})$ expected time complexity

Liva 1 – The First Medieval Sámi Site with Rectangular Hearths in Murmansk Oblast (Russia)

In 2017–2018, the Kola Archaeological Expedition of the Institute of the History of Material Culture (IHMC) RAS carried out excavations at the medieval site of Liva 1 (a hearth-row site)in the Kovdor District of Murmansk Oblast. Sites of this type are fairly well studied in the western part of Sapmi – the area inhabited by the Sámi – but until now they have not beenknown in Russia. The site was found by local residents in 2010. Some of the structures there were destroyed or damaged when searching for artefacts with a metal detector. A total ofnine archaeological structures have been discovered (7 rectangular stone hearths, 1 mound, 1 large pit). Four hearths were excavated. They are of rectangular shape, varying in size from 2.0 x 1.15 to 2.5 x 1.7 metres. The fireplaces are lined with large stone blocks in one course, and the central part is filled with small stones in 2–3 layers. Animal bones, occasionallyforming concentrations, were found near the hearths. Throughout the area of the settlement, numerous iron objects (tools or their fragments) and bronzes were collected includingornaments made in manufacturing centres of Old Rus’, Scandinavia and the Baltic countries. The settlement is dated with radiocarbon analysis and the typology of the ornaments to the11th – 14th centuries

Analyzing Social Policy from a Network Perspective

Governance models influence the approach that public service organizations take when implementing programs, policies, and practices. The networked model of governance supports the involvement of multiple actors who span organizational boundaries and roles to implement solutions to address complex social problems. This paper presents the utility of network analysis for the study of policy implementation from a network perspective. The paper describes networks within the context of social work policy implementation, basic network components, common structural variables, and sources of data for the study of policy implementation. A study of a statewide policy implementation is partially presented as an illustration of the use of network analysis in social policy research. The illustration uses primary and secondary data with network analysis techniques to identify and describe the patterns of interactions that comprise the structure of the implementation network. The illustration will present examples of the study findings to demonstrate the utility of network analysis in identifying central network actors and describing the density of the network according to different network variables. The paper concludes with a summary of the utility of network analysis in the study of policy implementation with recommendations for future research

Early Metal Age Dwellings in Eastern Lapland: Investigations of the Kola Archaeological Expedition (IHMC) in 2004–2014

After 10 years of field investigation by the Kola Archaeological Expedition (Institute for the History of Material Culture, Russian Academy of Sciences; IHMC RAS) it is now evident that a single archaeological culture (phase) prevailed on the Arctic coast from Tromsø (Norway) to Yokanga (Russia) during the Younger Stone Age and Early Metal Period. A close similarity between the assemblages of this culture is recognised in stone and bone artefacts, as well in dwelling constructions. This paper presents the results of the fieldwork in 2004–2014 and discusses the dwellings excavated at the Zavalishina 5 site

On the maximal sum of exponents of runs in a string

A run is an inclusion maximal occurrence in a string (as a subinterval) of a repetition $v$ with a period $p$ such that $2p \le |v|$. The exponent of a run is defined as $|v|/p$ and is $\ge 2$. We show new bounds on the maximal sum of exponents of runs in a string of length $n$. Our upper bound of $4.1n$ is better than the best previously known proven bound of $5.6n$ by Crochemore & Ilie (2008). The lower bound of $2.035n$, obtained using a family of binary words, contradicts the conjecture of Kolpakov & Kucherov (1999) that the maximal sum of exponents of runs in a string of length $n$ is smaller than $2n$Comment: 7 pages, 1 figur

Scratch-Healing Behavior of Ice by Local Sublimation and Condensation

[Image: see text] We show that the surface of ice is scratch healing: micrometer-deep scratches in the ice surface spontaneously disappear by thermal relaxation on the time scale of roughly an hour. Following the dynamics and comparing it to different mass transfer mechanisms, we find that sublimation from and condensation onto the ice surface is the dominant scratch-healing mechanism. The scratch-healing kinetics shows a strong temperature dependence, following an Arrhenius behavior with an activation energy of ΔE = 58.6 ± 4.6 kJ/mol, agreeing with the proposed sublimation mechanism and at odds with surface diffusion or fluid flow or evaporation–condensation from a quasi-liquid layer

Properties of coatings on the basis of carbon, tungsten, boron, and titanium obtained by the pulsed vacuum-arc method

Results of an investigation of the properties of coatings on the basis of carbon, tungsten, boron, and titanium obtained by the pulsed vacuum-arc method are presented. It has been found that the adhesion characteristics of coatings based on boron and titanium may be improved using a composite carbon-based coating, doped with tungsten, boron, and titanium, which, moreover, has a microhardness greater than those of a coating based on titanium and boro

Анализ состояния вопроса утилизации низкопотенциальных энергетических ресурсов на объектах малой энергетики

Studying the issues of recovery of low-potential energy at smallscale energy facilities allowed to show the promising character of the organic Rankine cycle (ORC) technology as a technology for recovery or conversion of low-potential energy.The most promising developments in the field of the use and recovery of waste heat are described regarding application of ORC, which is widely used in geothermal sources, hot water boilers, gas turbine plants. Due to the constantly growing diversity of working fluids, ORC can be used within a wide temperature range from 100°C to over 350°C. Also, developments are underway in the design of ORC generators to increase reliability of its individual system units, such as turbines and expanders. Based on the above factors, it can be concluded that with a deeper study of the problems of adopting ORC technologies, they can become a very promising direction in development of heat power engineering.It has been determined that the main factor hindering the widespread adoption of the ORC technology is associated with high cost of heat exchange equipment due to increased heat exchange surfaces. It is shown that design of mini power plants and energy centres based on the use of low-potential energy requires improvement of mathematical modelling methods to reliably determine operating modes and characteristics of each of the units. Methods for modelling evaporation and condensation systems, including turbines and expanders using organic low-boiling working fluids, should be considered among the methods that are highly sought after. The methods for selecting a working fluid for ORC devices also have a significant impact on characteristics of the installation determining the range of cycle operating temperatures and pressures. The solution of the above problems can lead to a reduction in the cost of heat exchange equipment, and, consequently, to a decrease in costs for design of ORC generators. В статье рассмотрены вопросы утилизации низкопотенциальных энергетических ресурсов на объектах малой энергетики. Показана перспектива использования технологии органического цикла Ренкина (ОЦР) в качестве технологии утилизации или преобразования низкопотенциальной энергии.Приведены разработки в области реализации и утилизации бросового тепла. Наиболее перспективные из них представлены в применении ОЦР, который широко используется на геотермальных источниках, в водогрейных котельных, газотурбинных установках. За счёт постоянного растущего сортамента рабочих тел ОЦР может применяться в широком температурном диапазоне, начиная от 100°С и заканчивая свыше 350°С. Также ведутся разработки в области проектирования ОЦР-генераторов с целью повышения надёжности отдельных узлов системы, таких как турбины и детандеры. Исходя из вышеперечисленных факторов, можно сделать вывод, что при более глубоком исследовании проблем внедрения ОЦР-технологий они могут стать весьма перспективным направлением в развитии теплоэнергетики.Определено, что основным фактором, препятствующим широкому внедрению ОЦР-технологии, является высокая стоимость теплообменного оборудования из-за повышенных теплообменных поверхностей. Показано, что проектирование миниэлектростанций и энергокомплексов на основе использования низкопотенциальной энергии требует совершенствования методов математического моделирования для достоверного определения режимов работы и характеристик каждого из агрегатов. К востребованным следует отнести методы моделирования испарительных и конденсационных систем, в том числе турбин и детандеров, работающих на органических низкокипящих рабочих телах. Методики выбора рабочего тела для ОЦР-устройств также оказывают существенное влияние на характеристики установки, которые определяют диапазон эксплуатационных температур и давлений цикла. Решение вышеуказанных задач способно привести к удешевлению теплообменного оборудования, а, следовательно, снижению издержек на проектирование ОЦР-генераторов.

Kharlovka 1-6 on the Kola Peninsula: One of the Oldest Gressbakken House Sites in Northern Fennoscandia

The remains of a semi-subterranean house were discovered at the Kharlovka 1-6 site on the Barents Sea coast of the Kola Peninsula, Russia. Despite suffering from erosion, features such as a double stone-boarded hearth and chimney pipe together with diagnostic finds allow us to attribute the house to the so-called Gressbakken type. The artefact assemblage includes stone tools, bone and antler tools and adornments, asbestos-tempered pottery, an amber pendant and a copper tubular bead. Numerous faunal remains are primarily represented by marine species of mammals and birds. Radiocarbon dates on charcoal point to the period 2600–2300 calBC, which is also supported by the artefact types, elevation of the cultural layer and construction type of the house. When accounting for the early dates of Kharlovka 1-6 and several other dwellings, it can be assumed that the Gressbakken house tradition emerged around 2600–2300 calBC. This date is somewhat earlier than previously thought