Efficient aspect ratio of the wing with AT winglets

In the article, by the method of the system of equations of steady horizontal flight the effective aspect ratio of the wing with AT winglet wingtips is explored. The total aerodynamic force, created by all four parts of the wingtips is determined. The vector of the total aerodynamic force of the wingtips is represented in the form of components of a linked coordinate system. Equilibrium equations for the steady rectilinear motion of an aircraft with AT winglets type wing tips in a horizontal flight are recorded. From these equations it is obtained that, in the direction of motion, the longitudinal component of the vector of the total aerodynamic force of the tips reduces the force of the drag of the wing, the vertical component is added to the lifting force of the wing and increases it, and the lateral component, due to the symmetry of the wing, is zero. The coefficient of inductive drag of the wing with the tips is written in the form of the difference in the inductive drag of the wing without the tip and the coefficient of the longitudinal component of the total aerodynamic force of the tips. Writing the coefficient of inductive drag of the wing with the tips in the traditional form through the coefficient of lift and aspect ratio of the wing, the expression for the effective wing aspect ratio with the AT winglets, which is longer without aerodynamic termination. An important consequence is that at the constant weight of the aircraft, the product of the effective wing aspect ratio with aerodynamic wingtips to its coefficient of inductive resistance is a constant value, independent of the kind of the wingtips. It is shown that with increasing flight speed, and also by reducing the inductive speed, the aspect ratio of the wing decreases

Influence of Administrative Regulation on the Efficiency of Business Activities in the Region

The article discusses the theoretical issues of the formation of the administrative regulation mechanisms for business entities. The necessity of the further development of theoretical and methodological base and the application tools for the design of business environment is proved. This can stimulate the growth of business and investment activity in the Russian regions and municipalities. The authors identify two types of government structures influence on the business entities, differentiated by the nature of the targeting impact on the economic activity of business structures—the administrative pressure and administrative assistance. It is suggested that in practice, high cost implications for compliance with all regulation requirements as well as sanctions for the violation of these requirements create preconditions for the development of informal interaction between entrepreneurs and the representatives of regulatory bodies. Therefore, businessmen try to minimize the costs associated with the implementation of formal administrative requirements, rules and regulations by personal arrangements. A mathematical model for the assessment of the informal interaction between business entities and certain officials of control supervisory authorities is proposed. It allows to determine the range of benefits for economic entities from avoiding the implementation of administrative norms, requirements and rules. It is concluded that unreasonably high level of costs for the implementation of formal administrative requirements rules and regulations by business entities composes the economic basis for the reproduction of informal relations. This determines mutual benefits for a number of entrepreneurs and a part of bureaucracy from various schemes of informal interaction.The article has been prepared with the support of the Grant of the Russian Foundation for Humanities in the framework of the research and development project " Development of a favourable institutional configuration of the regional business environment as the factor to increase the competitiveness of business entities" No. 16–12–02007

Mirror symmetry in two steps: A-I-B

We suggest an interpretation of mirror symmetry for toric varieties via an equivalence of two conformal field theories. The first theory is the twisted sigma model of a toric variety in the infinite volume limit (the A-model). The second theory is an intermediate model, which we call the I-model. The equivalence between the A-model and the I-model is achieved by realizing the former as a deformation of a linear sigma model with a complex torus as the target and then applying to it a version of the T-duality. On the other hand, the I-model is closely related to the twisted Landau-Ginzburg model (the B-model) that is mirror dual to the A-model. Thus, the mirror symmetry is realized in two steps, via the I-model. In particular, we obtain a natural interpretation of the superpotential of the Landau-Ginzburg model as the sum of terms corresponding to the components of a divisor in the toric variety. We also relate the cohomology of the supercharges of the I-model to the chiral de Rham complex and the quantum cohomology of the underlying toric variety.Comment: 50 pages; revised versio

Multiloop Superstring Amplitudes from Non-Minimal Pure Spinor Formalism

Using the non-minimal version of the pure spinor formalism, manifestly super-Poincare covariant superstring scattering amplitudes can be computed as in topological string theory without the need of picture-changing operators. The only subtlety comes from regularizing the functional integral over the pure spinor ghosts. In this paper, it is shown how to regularize this functional integral in a BRST-invariant manner, allowing the computation of arbitrary multiloop amplitudes. The regularization method simplifies for scattering amplitudes which contribute to ten-dimensional F-terms, i.e. terms in the ten-dimensional superspace action which do not involve integration over the maximum number of $\theta$'s.Comment: 23 pages harvmac, added acknowledgemen

Universal Drinfeld-Sokolov Reduction and Matrices of Complex Size

We construct affinization of the algebra $gl_{\lambda}$ of ``complex size'' matrices, that contains the algebras $\hat{gl_n}$ for integral values of the parameter. The Drinfeld--Sokolov Hamiltonian reduction of the algebra $\hat{gl_{\lambda}}$ results in the quadratic Gelfand--Dickey structure on the Poisson--Lie group of all pseudodifferential operators of fractional order. This construction is extended to the simultaneous deformation of orthogonal and simplectic algebras that produces self-adjoint operators, and it has a counterpart for the Toda lattices with fractional number of particles.Comment: 29 pages, no figure

Конфликт как основа разрешения противоречий социальных интересов, заложенных в праве

Маликов Е. Ю. Конфликт как основа разрешения противоречий социальных интересов, заложенных в праве / Е. Ю. Маликов // Правове життя сучасної України : матеріали Міжнар. наук. конф. проф.-викл. та аспірант. складу (м. Одеса, 16-17 травня 2013 р.) / відп. за вип. В. М. Дрьомін ; НУ "ОЮА". Півд. регіон. центр НАПрН України. - Одеса : Фенікс, 2013. - Т. 1. - С. 11-13

Two-Dimensional Twisted Sigma Models, the Mirror Chiral de Rham Complex, and Twisted Generalised Mirror Symmetry

In this paper, we study the perturbative aspects of a "B-twisted" two-dimensional $(0,2)$ heterotic sigma model on a holomorphic gauge bundle $\mathcal E$ over a complex, hermitian manifold $X$. We show that the model can be naturally described in terms of the mathematical theory of ``Chiral Differential Operators". In particular, the physical anomalies of the sigma model can be reinterpreted as an obstruction to a global definition of the associated sheaf of vertex superalgebras derived from the free conformal field theory describing the model locally on $X$. In addition, one can also obtain a novel understanding of the sigma model one-loop beta function solely in terms of holomorphic data. At the $(2,2)$ locus, one can describe the resulting half-twisted variant of the topological B-model in terms of a $\it{mirror}$ "Chiral de Rham complex" (or CDR) defined by Malikov et al. in \cite{GMS1}. Via mirror symmetry, one can also derive various conjectural expressions relating the sheaf cohomology of the mirror CDR to that of the original CDR on pairs of Calabi-Yau mirror manifolds. An analysis of the half-twisted model on a non-K\"ahler group manifold with torsion also allows one to draw conclusions about the corresponding sheaves of CDR (and its mirror) that are consistent with mathematically established results by Ben-Bassat in \cite{ben} on the mirror symmetry of generalised complex manifolds. These conclusions therefore suggest an interesting relevance of the sheaf of CDR in the recent study of generalised mirror symmetry.Comment: 97 pages. Companion paper to hep-th/0604179. Published versio