The implicit compact finite-difference scheme was developed for evolutionary partial differential parabolic and Schrodinger-type equations and systems with a weak nonlinearity. To make a temporal step of the compact implicit scheme we need to solve a non-linear system. We use for this step a simple explicit difference scheme and then Newton - Raphson iterations, which are implemented by the double-sweep method. Numerical experiments confirm the 4-th order of an algorithm. The Richardson extrapolation improves it up to the 6-th order.     

Essential dimension of a family of complex manifolds is the dimension of the image of its base in the Kuranishi space of the fiber. We prove that any family of hyperk\"ahler manifolds over a compact simply connected base has essential dimension not greater than 1. A similar result about families of complex tori is also obtained.

We prove that any compact K\"ahler 3-dimensional manifold which has no non-trivial complex subvarieties is a torus. This is a very special case of a general conjecture on the structure of 'simple manifolds', central in the bimeromorphic classification of compact K\"ahler manifolds. The proof follows from the Brunella pseudo-effectivity theorem, combined with fundamental results of Siu and of the second author on the Lelong numbers of closed positive (1,1)-currents, and with a version of the hard Lefschetz theorem for pseudo-effective line bundles, due to Takegoshi and Demailly-Peternell-Schneider. In a similar vein, we show that a normal compact and K\"ahler 3-dimensional analytic space with terminal singularities and nef canonical bundle is a cyclic quotient of a simple non-projective torus if it carries no effective divisor. This is a crucial step to complete the bimeromorphic classification of compact K\"ahler 3-folds.

A locally conformally Kahler manifold is a Hermitian manifold (M,I,ω) satisfying dω=θ∧ω, where θ is a closed 1-form, called the Lee form of M. It is called pluricanonical if ∇θ is of Hodge type (2,0)+(0,2), where ∇ is the Levi-Civita connection, and Vaisman if ∇θ=0. We show that a compact LCK manifold is pluricanonical if and only if the Lee form has constant length and the Kahler form of its covering admits an automorphic potential. Using a degenerate Monge-Ampere equation and the classification of surfaces of Kahler rank one, due to Brunella, Chiose and Toma, we show that any pluricanonical metric on a compact manifold is Vaisman. Several errata to our previous work are given in the last Section.

In the era of the knowledge economy intangibles are recognized by investors as pivotal value drivers. Previous research of portfolio forming methods based on intangibles is limited by taking into account only the quantity of intangibles. We propose a tool to select companies able to create knowledge (in contrast to the absorption of knowledge), which is a quality of intangibles. To test whether these abilities are results of skill we implement a bootstrap procedure. It shows that only 22% of companies have the skills to create knowledge, but all of them are characterized by positive results of knowledge creation. To show the practical implications of the proposed approach selected companies are combined in a portfolio. This portfolio demonstrates a higher cumulative return, Sharpe ratio and drawdown than S&P500. We also find the increasing importance of intangibles for investors during the crisis. While exogenous shocks influenced both creators and absorbers, we found that intangibles create an obstacle to a sharp drop of market value.

This article focuses on the development of antitrust policy in transition economies in the context of preventing explicit and tacit collusion. Experience of BRICS, Kazakhstan, Ukraine and CEE countries (Bulgaria, Hungary, Latvia, Lithuania, Poland, Romania, Slovakia, Slovenia, Czech Republic, Estonia) in the creation of antitrust institutions was analyzed, including both legislation and enforcement practice. This article analyzes such enforcement problems as: classification problems (tacit vs explicit collusion, vertical vs horizontal agreements), flexibility of prohibitions (“per se” vs “rule of reason”), design of sanctions, private enforcement challenge, leniency program mechanisms, the role of antitrust authorities etc. Main challenges for policy effectiveness in this field were shown

Despite of the fact that the history of Initial Coin Offering (ICO) is short, new modification of it has already suggested. According to the ICORating , in the second half of 2018, the profitability of investments in blockchain startups decreased by 22%, and 58% of ICO projects announced in Q4 2018 were not able to raise more than 100,000 USD. Moreover, in Q4 2018 40% of projects with previously announced ICOs have already deleted their social network accounts and websites. The founder of Ethereum Vitalik Buterin (2015), who started the first ICO, proposed a new way of decentralized fundraising called DAICO in 2018. This new model will include elements of Decentralized Autonomous Organizations (DAO), and its purpose will be to minimize the difficulties and risks associated with the ICO. At the same time, in 2018 another model of financing appeared called Initial Exchange Offering (IEO) in order to minimize risks, problems of liquidity and the postponement of the listing of the tokens at the end of tokensale step. More than 70 IEOs listed on ICObench with average rating of 3.6 and 42 IEOs have been ended and raised $266 million in total. Nevertheless, there three types of tokens 95% of ICO projects are utility-based token. This makes ICO comparable to crowfunding. In order to be more attractive for investors the focus on a new wave of ICO projects is on the security type of tokens. The security token is any cryptocurrency that pays dividends, profits, shares or interest or invests in any other asset that also generates profits. The U.S. Securities and Exchange Commission (SEC) use the Howey Test and concludes the securities token are securities in contract to classical utility token of ICO projects. In order to back by real assets and follow the SEC's guidance on compliance, issuance, and trading new model is called Security Token Offering (STO) and differs from ICO. All three new models are a new focus for small and medium-sized enterprises (SME) and investors. The absence of any type of academic works emphasizes the relevance and scientific novelty of the forthcoming research. The contribution to the existing literature is the systematization of information and comparison analyses of ICO, DAOICO, IEO and STO by method of case study.

Under the Basel II accord, improving probability of default models is a key risk-management priority. There are four main aspects of this research: suggesting the bank default classification; using a wide time horizon (quarterly Russian banking statistics from 1998 to 2011); investigating the macroeconomic and institutional characteristics of the banking sector environment and finally, testing the accuracy of the models developed. We have employed nonlinearity and automatic classification of the independent variables in our models, paying attention to the structure of the banking market as well as to the reliability of the models developed. We have compared several models for estimating default probabilities. From the results of this comparison, we have chosen the binary logit - regression with quasi panel data structure. Our key findings are: - There is a quadratic relationship between bank's capital adequacy ratio and its probability of default. - The "too big to fail" hypothesis does not hold for the Russian banking sector. - There is a negative relationship between the Lerner index and bank's PD. Macroeconomic, institutional and time factors significantly improve the model quality. We believe that these results will be useful for the national financial regulatory authorities as well as for risk-management in commercial banks. Moreover, we think that these models will be valuable for other emerging economies.

Regardless of all attempts to declare the end of modernity, contemporary political researchers still take its classical conception into account and attempt to redefine it with respect to present-day challenges. Nevertheless, it seems that there is little agreement on the definition of “modernity”. Consequently, a wide range of theories, devoted to modernity, have developed. One of the most popular is “multiple modernities” proposed by Shmuel Noah Eisenstadt. According to this conception, modern societies can be defined and institutionally organized in a variety of ways. The reason for this diversity concerns the tradition and history of a particular society. For instance, intellectual and political elites in non-Western countries can produce their own understanding of modernity, combining elements of traditional politics with some elements of the classical modern program. Therefore, the role of tradition in the contemporary world is ambivalent. In modern society, tradition does not continually determine all spheres of life, including politics. On the other hand, tradition still influences the way in which modern institutions are organized.  However, it is not clear to what extent tradition can vary the origin-program of modernity. To explore this question, we examine the alternative conception of modernity, known as compensation theory, proposed by Joachim Ritter, Hermann Lübbe and Odo Marquard. We employ a comparative analysis and demonstrate the differences between compensation theory and the conception of multiple modernities with regard to the role of tradition in modern society.The findings of this research illustrate the reasons behind the fact that tradition can influence the original program of modernity. It also contributes fruitfully to the discussion about modernization and modernity.

The paper aims to identify key ideas, terms and assumptions and also to trace the development of two most cited methodological approaches in international relations theory. In order to make the comparison profound and clear, the author deploys Ukrainian conflict 2014-2015, where constructivism and neorealism have faced each other both at analytical (theoretical) and policymaking levels.

This empirical paper adds to competition and industrial organization literature by exploring the interplay between industry structure and competitiveness on local, rather than nation-wide, markets. We use micro-level statistical data for banks in two Russian regions (Bashkortostan and Tatarstan) to estimate Herfindahl-Hirschman index, Lerner index, and Panzar-Rosse model. We estimate Panzar-Rosse model in two ways: via the widely used price-equation that accounts for scale effects and then via a revenue-equation that disregards scale effects as suggested by Bikker et al. (2009). We find both regional markets to be ruled by monopolistic competition, although estimation by revenue-equation does not reject monopoly hypothesis for Tatarstan. Existence of sizeable locally-owned and operated institutions does not necessarily lead to higher competitiveness of the given regional market, and the results from non-structural methods of estimation suggest that bank competition in Bashkortostan is stronger than in Tatarstan. Going further away from aggregated analysis we compute Lerner indices in two product segments of Tatarstan – retail and corporate loans – and find that retail segment is significantly more competitive. Local banks exert more market power in corporate loans, while federal branches – in retail loans.

Larger cities typically give rise to two effects working in opposite directions: tougher competition among firms and higher production costs. Using an urban model with substitutability of production factors and pro-competitive effects, we study how market outcome responds to city population size, land-use regulation and commuting costs. For industries with small input of land, larger cities host more firms which set lower prices whereas larger cities accommodate more firms which charge higher prices in industries with intermediate land share in production. Furthermore, for industries with high input share of land, larger cities allocate fewer firms with higher product prices. We show that softer land-use regulation and/or lower commuting costs reinforce pro-competitive effects making larger cities more attractive for residents via lower product prices and broader variety for a larger number of industries.

Larger cities typically give rise to two opposite effects: tougher competition among firms and higher production costs. Using an urban model with substitutability of production factors and pro-competitive effects, I study the response of the market outcome to city size, land-use regulations, and commuting costs. For industries with low input shares of land, larger cities host more firms setting lower prices whereas for sectors with intermediate land shares larger cities accommodate more firms charging higher prices. Softer land-use regulations and/or lower commuting costs reinforce pro-competitive effects, making larger cities more attractive for residents via lower prices and broader product diversity.

A mixed manna contains goods (that everyone likes), bads (that everyone dislikes), as well as items that are goods to some agents, but bads or satiated to others. If all items are goods and utility functions are homothetic, concave (and monotone), the Competitive Equilibrium with Equal Incomes maximizes the Nash product of utilities: hence it is welfarist (determined utility-wise by the feasible set of profiles), single-valued and easy to compute. We generalize the Gale-Eisenberg Theorem to a mixed manna. The Competitive division is still welfarist and related to the product of utilities or disutilities. If the zero utility profile (before any manna) is Pareto dominated, the competitive profile is unique and still maximizes the product of utilities. If the zero profile is unfeasible, the competitive profiles are the critical points of the product of disutilities on the efficiency frontier, and multiplicity is pervasive. In particular the task of dividing a mixed manna is either good news for everyone, or bad news for everyone. We refine our results in the practically important case of linear preferences, where the axiomatic comparison between the division of goods and that of bads is especially sharp. When we divide goods and the manna improves, everyone weakly benefits under the competitive rule; but no reasonable rule to divide bads can be similarly Resource Monotonic. Also, the much larger set of Non Envious and Efficient divisions of bads can be disconnected so that it will admit no continuous selection.

We study the closure of the cubic Principal Hyperbolic Domain and its intersection $\mathcal{P}_\lambda$ with the slice $\mathcal{F}_\lambda$ of the space of all cubic polynomials with fixed point $0$ defined by the multiplier $\lambda$ at $0$. We show that any bounded domain $\mathcal{W}$ of $\mathcal{F}_\lambda\setminus\mathcal{P}_\lambda$ consists of $J$-stable polynomials $f$ with connected Julia sets $J(f)$ and is either of \emph{Siegel capture} type (then $f\in \mathcal{W}$ has an invariant Siegel domain $U$ around $0$ and another Fatou domain $V$ such that $f|_V$ is two-to-one and $f^k(V)=U$ for some $k>0$) or of \emph{queer} type (then at least one critical point of $f\in \mathcal{W}$ belongs to $J(f)$, the set $J(f)$ has positive Lebesgue measure, and carries an invariant line field).

This paper describes the competition of complementation strategies of Russian verbs of request. We conducted a corpus-based study of six strategies of compelement encoding: infinitive, nominalisation, prepositional phrase with nominalisation, finite clause introduced with complementizer čtoby, non-finite clause introduced with complementizer čtoby (i.e. čtoby + infinitive), prepositional phrase with čtoby and expletive pronoun to (o tom čtoby). The results suggest that there are several factors influencing the competition under consideration (such as coreference of different participants, request dictance, etc.) and that these factors belong to different language domains, including semantics. This challenges the classic point of view according to which complementation studies should be focused primarily on syntax. 

Moment-angle manifolds provide a wide class of examples of non-Kaehler compact complex manifolds. A complex moment-angle manifold Z is constructed via certain combinatorial data, called a complete simplicial fan. In the case of rational fans, the manifold Z is the total space of a holomorphic bundle over a toric variety with fibres compact complex tori. In general, a complex moment-angle manifold Z is equipped with a canonical holomorphic foliation F and a C*-torus action transitive in the transverse direction. Examples of moment-angle manifolds include Hopf manifolds of Vaisman type, Calabi-Eckmann manifolds, and their deformations. We construct transversely Kaehler metrics on moment-angle manifolds, under some restriction on the combinatorial data. We prove that all Kaehler submanifolds (or, more generally, Fujiki class C subvarieties) in such a moment-angle manifold lie in a compact complex torus contained in a fibre of the foliation F. For a generic moment-angle manifold Z in its combinatorial class, we prove that all subvarieties are moment-angle manifolds of smaller dimension. This implies, in particular, that the algebraic dimension of Z is zero.

We investigate the notion of complex rotation number which was introduced by V.I.Arnold in 1978. Let f: R/Z \to R/Z be an orientation preserving circle diffeomorphism and let {\omega} \in C/Z be a parameter with positive imaginary part. Construct a complex torus by glueing the two boundary components of the annulus {z \in C/Z | 0< Im(z)< Im({\omega})} via the map f+{\omega}. This complex torus is isomorphic to C/(Z+{\tau} Z) for some appropriate {\tau} \in C/Z. According to Moldavskis (2001), if the ordinary rotation number rot (f+\omega_0) is Diophantine and if {\omega} tends to \omega_0 non tangentially to the real axis, then {\tau} tends to rot (f+\omega_0). We show that the Diophantine and non tangential assumptions are unnecessary: if rot (f+\omega_0) is irrational then {\tau} tends to rot (f+\omega_0) as {\omega} tends to \omega_0. This, together with results of N.Goncharuk (2012), motivates us to introduce a new fractal set, given by the limit values of {\tau} as {\omega} tends to the real axis. For the rational values of rot (f+\omega_0), these limits do not necessarily coincide with rot (f+\omega_0)$ and form a countable number of analytic loops in the upper half-plane.

The transformation of traditional childbearing patterns of early family formation to later family formation characterized recent fertility trends in Russia. These were intrinsically interwoven with fundamental changes in all aspects of life of young people in the 1990s and the 2000s. The past quarter century was also marked by concern with low fertility and attempts to increase fertility in the early 1980s and the late 2000s. The family policies of the 1980s failed to raise fertility. Preliminary analyses indicate that the fate of the 2007 policies could be similar. In both cases the main emphasis was on material birth and child benefits, parental leaves and child care. Presumably insufficient attention was devoted to improving living conditions of young people and promoting gender equality. Will government efforts to raise fertility during the 2010s be sufficiently effective to offset economic and social forces challenging childbearing? As of 2012 the outlook for a future fertility increase does not appear hopeful.