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## Taxing Congestion of the Space Commons

Satellites launched by independent spacefaring agencies and firms create space congestion and collision risk. Taking as benchmark the cost of a marginal reduction of the congestion rate, we discuss tax mechanisms financing a debris removal effort. We compare the non-cooperative equilibrium traffic when there is a tax on each new launch to recover cleanup costs, with the welfare optimal traffic under a centralized tax. We find that under the latter it is twice as easy to recover cleanup costs and increase traffic than under the former. We also show that a linear tax is twice as effective as a quadratic one.

The article substantiates the concept of quantitative assessment of knowledge uncertainty in accident reconstruction tasks based on application of mathematical tools of the fuzzy set theory allowing considering an uncertainty of initial data caused for instance by varying resistance to the motion of investigated objects at the apex stages of the contact–separation processes. The application of the mathematical tools of the fuzzy set theory can substantially expand the potential of applying the methodology to the automobile and technical expertise and provide the enhancement of authenticity and improve the accuracy of making conclusions about the accident reconstruction results.

In this paper, we study the Maximum Happy Vertices and the Maximum Happy Edges problems (MHV and MHE for short). Very recently, the problems attracted a lot of attention and were studied in Agrawal ’17, Aravind et al. ’16, Choudhari and Reddy ’18, Misra and Reddy ’17. Main focus of our work is lower bounds on the computational complexity of these problems. Established lower bounds can be divided into the following groups: NP-hardness of the above guarantee parameterization, kernelization lower bounds (answering questions of Misra and Reddy ’17), exponential lower bounds under the Set Cover Conjecture and the Exponential Time Hypothesis, and inapproximability results. Moreover, we present an O∗(ℓk)O∗(ℓk) randomized algorithm for MHV and an O∗(2k)O∗(2k) algorithm for MHE, where ℓℓ is the number of colors used and *k* is the number of required happy vertices or edges. These algorithms cannot be improved to subexponential taking proved lower bounds into account.

The paper deals with the Turkic-Mongol taxation institute of tamgha widely used in the Mongol Empire since the first half of the 13th century. Author characterizes the etymology of this term, its meanings, legal regulation of levy and rates, evolution of the tax in different states – successors of the Mongol Empire (the Golden Horde, Ilkhanate, etc.) as well as in these states even after fall of Chinggisid dynasties (such as Iran under Safavids, Central Asia under Timurids). As the author supposes, the long-term use of tamgha allows us to talk about the vitality and effectiveness of Chinggisid legal tradition, which survived after the end of “Chinggisid age”. Even the rulers and dynasties, which positioned themselves as rivals of Chinggisids, used tamgha in their taxation system. This tax was also borrowed by the Russians and was used for a long time becoming a base for custom system in Russia. Other subjects of the research are the struggle of Islamic theologians and jurists against tamgha in different countries of Inner Asia and reasons for this struggle. The author attempts to clarify reasons of this struggle, strict position of clergy against tamgha and measures of rulers who did not want to be in trouble with clergy, but at the same time tried to save tamgha as effective and profitable tax.

This book is devoted to game theory and its applications to environmental problems, economics, and management. It collects contributions originating from the 12th International Conference on “Game Theory and Management” 2018 (GTM2018) held at Saint Petersburg State University, Russia, from 27 to 29 June 2018.

This contributed volume presents the state-of-the-art of games and dynamic games, featuring several chapters based on plenary sessions at the ISDG-China Chapter Conference on Dynamic Games and Game Theoretic Analysis, which was held from August 3-5, 2017 at the Ningbo campus of the University of Nottingham, China. The chapters in this volume will provide readers with paths to further research, serving as a testimony to the vitality of the field. Experts cover a range of theory and applications related to games and dynamic games.

In the paper the problem of space debris. Describes the causes of debris in near-Earth space. Describes the distribution of debris in near-Earth space. Shown that the accumulation of debris consists of two rings. Analyzes the statistics of debris. We analyze the spatial distribution of debris. Conjectured form rings debris in near-Earth space.

We use the vertical differentiation framework to explore the quality - price competition in the insurance market.

Game theory has recently become a useful tool for modeling and studying various networks. The past decade has witnessed a huge explosion of interest in issues that intersect networks and game theory. With the rapid growth of data traffic, from any kind of devices and networks, game theory is requiring more intelligent transformation. Game theory is called to play a key role in the design of new generation networks that are distributed, self-organizing, cooperative, and intelligent. This book consists of invited and technical papers of GAMENETS 2018, and contributed chapters on game theoretic applications such as networks, social networks, and smart grid.

We study experimentally how optical, electrical, and physical properties of spacecraft surface elements (optical glasses, "metal-insulator-metal" structures, and solar arrays) change upon bombardment by high-speed particles of submicron and micron size. For particle acceleration, we use an electrodynamic accelerator. В© Pleiades Publishing, Ltd., 2013.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.