The author's view on the historical significance of two events of 1961 - the flight of Yuri Gagarin and the testing of a hydrogen bomb - is described in the article.

We give a sharp bound for orders of elementary abelian 2-groups of birational automorphisms of rationally connected threefolds.

The work is related to the detection of key international and Russian economic journals in cross-citation networks. A list of international journals and information on their cross-citations were taken from Web of Science (WoS) database while information on Russian journals was taken from Russian Science Citation Index (RSCI). We calculated classical centrality measures, which are used for key elements detection in networks, and proposed new indices based on short-range and long-range interactions. A distinct feature of the proposed methods is that they consider individual attributes of each journal and take into account only the most significant links between them. An analysis of 100 main international and 29 Russian economic journals was conducted. As a result, we detected journals with large number of citations to important journals and also journals where the observed rate of selfcitation is a dominant in the total level of citation. The obtained results can be used as a guidance for researchers planning to publish a new paper and as a measure of importance of scientific journals.

We study the integral Bailey lemma associated with the A_n-root system and identities for elliptic hypergeometric integrals generated thereby. Interpreting integrals as superconformal indices of four-dimensional N = 1 quiver gauge theories with the gauge groups being products of SU(n + 1), we provide evidence for various new dualities. Further con rmation is achieved by explicitly checking that the `t Hooft anomaly matching conditions holds. We discuss a flavour symmetry breaking phenomenon for supersymmetric quantum chromodynamics (SQCD), and by making use of the Bailey lemma we indicate its manifestation in a web of linear quivers dual to SQCD that exhibits full s-confinement.

It is well known that the Fano scheme of lines on a cubic 4-fold is a symplectic variety. We generalize this fact by constructing a closed p-form with p=2n-4 on the Fano scheme of lines on a (2n-2)-dimensional hypersurface Y of degree n. We provide several definitions of this form - via the Abel-Jacobi map, via Hochschild homology, and via the linkage class, and compute it explicitly for n = 4. In the special case of a Pfaffian hypersurface Y we show that the Fano scheme is birational to a certain moduli space of sheaves on a p-dimensional Calabi--Yau variety X arising naturally in the context of homological projective duality, and that the constructed form is induced by the holomorphic volume form on X. This remains true for a general non Pfaffian hypersurface but the dual Calabi-Yau becomes non commutative.

Given n ≥ 1 and r ∈ [0, 1), we consider the set Rn, r of rational functions having at most n poles all outside of 1/rD, were D is the unit disc of the complex plane. We give an asymptotically sharp Bernstein-type inequality for functions in Rn, r in weighted Bergman spaces with “polynomially” decreasing weights. We also prove that this result can not be extended to weighted Bergman spaces with “super-polynomially” decreasing weights

A problem of choosing an optimal portfolio of projects from a set of *m* projects that are to be financed under a limited budget, along with a schedule for their implementation within a period of time [1,*T*], where each project can commence at moments 1,*T *and last for several consecutive time segments, is considered. Each project requires a certain volume of investment to be distributed within a period of time that is a subset of consecutive time segments from [1,*T*], some projects from the set can generate profit upon completion according to a certain schedule, and the generated profit can be reinvested in the other projects. In the basic problem, it is assumed that all the projects are equally important (so that there are no priorities for choosing a subset of projects that should commence or be completed earlier that the others), and there is no order for executing any projects from the set. These assumptions transform the basic problem into a problem of finding an optimal order (schedule) for commencing the projects, where optimality can be understood, for instance, in the sense of the number of projects that can be completed within the period [1,*T*]. A mathematical formulation of the basic problem in the form of a Boolean programming one is proposed, and some generalizations of the problem, including those obtained by imposing certain precedence conditions on the execution of the projects, are discussed.

We obtain a partial solution of the problem on the growth of the norms of exponential functions with a continuous phase in the Wiener algebra. The problem was posed by J.-P. Kahane at the International Congress of Mathematicians in Stockholm in 1962. He conjectured that (for a nonlinear phase) one can not achieve the growth slower than the logarithm of the frequency. Though the conjecture is still not confirmed, the author obtained first nontrivial results.

In this paper it is proved that every orientable surface admits an orientation-preserving Morse-Smale diffeomorphism with one saddle orbit. It is shown that these diffeomorphisms have exactly three node orbits. In addition, all possible types of periodic data for such diffeomorphisms are established.

Gross exports accounting is a novel sub-area of research that seeks to allocate the value added in gross trade flows to its true country and sector of origin and country or sector of destination. Various frameworks have been recently proposed to perform such decompositions. This paper presents another effort to generalise the accounting framework so that it may be easily interpreted, customised and implemented in matrix computation software. The principal contribution is therefore a relatively simple way to derive the formulae for the decomposition of cumulative value added flows embodied in international trade. The underlying accounting approach is found to be largely similar to that of [Koopman et al., 2012; Stehrer, 2013], but the block matrix formulation allows the user to simultaneously decompose all bilateral flows at the country and/or sectoral level. The refined framework is applied to describe Russia’s export performance from the global value chain perspective using the data from the World Input-Output Database (WIOD) for 2000 and 2010. According to the findings, the countries that directly receive most of Russia’s exports are not exactly those that use most of Russia’s value added. Russia’s mining sector is found to be an intrinsic part of a complex downstream value chain where it indirectly contributes value to partner exports.

A celebrated result of Dol'nikov, and of \v{Z}ivaljevi\'c and Vre\'cica, asserts that for every collection of $m$ measures $\mu_1,\dots,\mu_m$ on the Euclidean space $\mathbb R^{n + m - 1}$ there exists a projection onto an $n$-dimensional vector subspace $\Gamma$ with a point in it at depth at least $\tfrac{1}{n + 1}$ with respect to each associated $n$-dimensional marginal measure $\Gamma_*\mu_1,\dots,\Gamma_*\mu_m$.

In this paper we consider a natural extension of this result and ask for a minimal dimension of a Euclidean space in which one can require that for any collection of $m$ measures there exists a vector subspace $\Gamma$ with a point in it at depth slightly greater than $\tfrac{1}{n + 1}$ with respect to each $n$-dimensional marginal measure. In particular, we prove that if the required depth is $\tfrac{1}{n + 1} + \tfrac{1}{3(n + 1)^3}$ then the increase in the dimension of the ambient space is a linear function in both $m$ and $n$.

In this paper we present new formulas, which represent commutators and anticommutators of Clifford algebra elements as sums of elements of different ranks. Using these formulas we consider subalgebras of Lie algebras of pseudo-unitary groups. Our main techniques are Clifford algebras. We have found 12 types of subalgebras of Lie algebras of pseudo-unitary groups.

We present a new class of multifractal process on R, constructed using an embedded branching process. The construction makes use of known results on multitype branching random walks, and along the way constructs cascade measures on the boundaries of multitype Galton–Watson trees. Our class of processes includes Brownian motion subjected to a continuous multifractal time-change. In addition, if we observe our process at a fixed spatial resolution, then we can obtain a finite Markov representation of it, which we can use for on-line simulation. That is, given only the Markov representation at step n, we can generate step n+1 in O(log n) operations. Detailed pseudo-code for this algorithm is provided.R

A full closed mathematical model to describe and calculate Kondratiev’s long wave (LW) of economic development is presented for the first time. The innovative process that generates a new long wave in the economy is described as a stochastic Poisson process. The key role in constructing production functions during both the upward and downward trends of the LW is played by the self-similarity property of the innovative process, which is determined by its fractal structure. The role of the switch from an upward wave to a downward one is played by entrepreneurial profit; this article places primary emphasis on calculation of it. The practical effect of the model developed is illustrated through predictive calculations of GDP movement paths and the number of employees in the economy and the dynamics of fixed physical capital formation and growth of labor productivity by the example of the development of the US economy during the coming sixth Kondratiev LW (2018–2050).

We introduce a unital associative algebra associated with degenerate CP1. We show that is a commutative algebra and whose Poincare' series is given by the number of partitions. Thereby, we can regard as a smooth degeneration limit of the elliptic algebra introduced by Feigin and Odesskii [Int. Math. Res. Notices 11, 531 (1997)]. Then we study the commutative family of the Macdonald difference operators acting on the space of symmetric functions. A canonical basis is proposed for this family by using and the Heisenberg representation of the commutative family studied by Shiraishi [ Commun. Math. Phys. 263, 439 (2006)]. It is found that the Ding-Iohara algebra [Lett. Math. Phys. 41, 183 (1997)] provides us with an algebraic framework for the free field construction. An elliptic deformation of our construction is discussed, showing connections with the Drinfeld quasi-Hopf twisting [Leningrad Math. J. 1, 1419 (1990)] in the sence of Babelon-Bernard-Billey [Phys. Lett. B. 375, 89 (1996)], the Ruijsenaars difference operator [Commun. Math. Phys. 110, 191 (1987)], and the operator M(q,t1,t2) of Okounkov-Pandharipande [e-print arXiv:math-ph/0411210].

The paper deals with cyclostationarity as a natural extension of stationarity as the key property in designing the widely-used models of random processes. The comparative example of two processes, one is wide-sense stationary and the other is wide-sense cyclostationary, is given in the paper and reveals the lack of the conventional stationary description based on one-dimensional autocorrelation functions. It is shown that two significantly different random processes appear to be characterized by exactly the same autocorrelation function while their two-dimensional autocorrelation functions provide outlook where the difference between processes of two above-mentioned classes becomes much clearer. More concise representation by expanding the two-dimensional autocorrelation function to its Fourier series where the cyclic frequency appears as the transform parameter is illustrated. The closed-form expression for the components of the cyclic autocorrelation function is also given for the random process which is an infinite pulse train made of rectangular pulses with randomly varying amplitudes.