Structure of 3-(3,5-Dimethylpiperidino)-\u3cem\u3eN\u3c/em\u3e-(\u3cem\u3ep\u3c/em\u3e-Chlorophenyl)Succinimide

In the title molecule, 3-(3,5-dimethylpiperidino )-1-(4-chlorophenyl)-2,5-pyrrolidinedione (1), the N-(p-chlorophenyl) substituent is rotated by 68.8° relative to the succinimide plane. The piperidinyl ring has a chair conformation with all substituents in equatorial positions; the conformation around the piperidino-succinimide C--N bond is staggered

\u3cem\u3eβ\u3c/em\u3e-Homopipitzolone

The structure of β-homopipitzolone (one of the two isomers of an intermediate product in the homocedrole synthesis) has been unequivocally established as 1 O-hydroxy-2,6,9-trimetbyltricyclo[6.3.1.01,6] dodeca-9-ene-5, II, 12-trione with relative IR,2R,6R,8S configuration

Synthesis and Characterization of Large Stereoregular Organosiloxane Cycles

The large stereoregular phenyltrimethylsiloxysiloxane macrocycles of general formula [PhSi(OSiMe3)O]n (n=6 and 12) have been selectively obtained with high yields by trimethylsilylation of cage-like oligophenylmetallasiloxanes (OPMS) which we described earlier. The compounds 3 (n=6) and 4 (n=12) have been characterized by NMR-spectroscopy method and by single crystal X-ray analysis. This investigation showed unambiguously that the siloxane macrocycles keep their size and configuration (the same as in the initial OPMS) during the trimethylsilylation. Thus a synthetic route for obtaining large stereoregular siloxane macrocycles has been developed

Miura-type transformations for lattice equations and Lie group actions associated with Darboux-Lax representations

Miura-type transformations (MTs) are an essential tool in the theory of integrable nonlinear partial differential and difference equations. We present a geometric method to construct MTs for differential-difference (lattice) equations from Darboux–Lax representations (DLRs) of such equations. The method is applicable to parameter-dependent DLRs satisfying certain conditions. We construct MTs and modified lattice equations from invariants of some Lie group actions on manifolds associated with such DLRs. Using this construction, from a given suitable DLR one can obtain many MTs of different orders. The main idea behind this method is closely related to the results of Drinfeld and Sokolov on MTs for the partial differential KdV equation. Considered examples include the Volterra, Narita–Itoh–Bogoyavlensky, Toda, and Adler–Postnikov lattices. Some of the constructed MTs and modified lattice equations seem to be new

Conservation laws for multidimensional systems and related linear algebra problems

We consider multidimensional systems of PDEs of generalized evolution form with t-derivatives of arbitrary order on the left-hand side and with the right-hand side dependent on lower order t-derivatives and arbitrary space derivatives. For such systems we find an explicit necessary condition for existence of higher conservation laws in terms of the system's symbol. For systems that violate this condition we give an effective upper bound on the order of conservation laws. Using this result, we completely describe conservation laws for viscous transonic equations, for the Brusselator model, and the Belousov-Zhabotinskii system. To achieve this, we solve over an arbitrary field the matrix equations SA=A^tS and SA=-A^tS for a quadratic matrix A and its transpose A^t, which may be of independent interest.Comment: 12 pages; proof of Theorem 1 clarified; misprints correcte

Algebraic properties of Gardner's deformations for integrable systems

An algebraic definition of Gardner's deformations for completely integrable bi-Hamiltonian evolutionary systems is formulated. The proposed approach extends the class of deformable equations and yields new integrable evolutionary and hyperbolic Liouville-type systems. An exactly solvable two-component extension of the Liouville equation is found.Comment: Proc. conf. "Nonlinear Physics: Theory and Experiment IV" (Gallipoli, 2006); Theor. Math. Phys. (2007) 151:3/152:1-2, 16p. (to appear

(Non)local Hamiltonian and symplectic structures, recursions, and hierarchies: a new approach and applications to the N=1 supersymmetric KdV equation

Using methods of math.DG/0304245 and [I.S.Krasil'shchik and P.H.M.Kersten, Symmetries and recursion operators for classical and supersymmetric differential equations, Kluwer, 2000], we accomplish an extensive study of the N=1 supersymmetric Korteweg-de Vries equation. The results include: a description of local and nonlocal Hamiltonian and symplectic structures, five hierarchies of symmetries, the corresponding hierarchies of conservation laws, recursion operators for symmetries and generating functions of conservation laws. We stress that the main point of the paper is not just the results on super-KdV equation itself, but merely exposition of the efficiency of the geometrical approach and of the computational algorithms based on it.Comment: 16 pages, AMS-LaTeX, Xy-pic, dvi-file to be processed by dvips. v2: nonessential improvements of exposition, title change

Homological evolutionary vector fields in Korteweg-de Vries, Liouville, Maxwell, and several other models

We review the construction of homological evolutionary vector fields on infinite jet spaces and partial differential equations. We describe the applications of this concept in three tightly inter-related domains: the variational Poisson formalism (e.g., for equations of Korteweg-de Vries type), geometry of Liouville-type hyperbolic systems (including the 2D Toda chains), and Euler-Lagrange gauge theories (such as the Yang-Mills theories, gravity, or the Poisson sigma-models). Also, we formulate several open problems.Comment: Proc. 7th International Workshop "Quantum Theory and Symmetries-7" (August 7-13, 2011; CVUT Prague, Czech Republic), 20 page

Situational Awareness and Problems of Its Formation in the Tasks of UAV Behavior Control

Situational awareness formation is one of the most critical elements in solving the problem of UAV behavior control. It aims to provide information support for UAV behavior control according to its objectives and tasks to be completed. We consider the UAV to be a type of controlled dynamic system. The article shows the place of UAVs in the hierarchy of dynamic systems. We introduce the concepts of UAV behavior and activity and formulate requirements for algorithms for controlling UAV behavior. We propose the concept of situational awareness as applied to the problem of behavior control of highly autonomous UAVs (HA-UAVs) and analyze the levels and types of this situational awareness. We show the specifics of situational awareness formation for UAVs and analyze its differences from situational awareness for manned aviation and remotely piloted UAVs. We propose the concept of situational awareness as applied to the problem of UAV behavior control and analyze the levels and types of this situational awareness. We highlight and discuss in more detail two crucial elements of situational awareness for HA-UAVs. The first of them is related to the analysis and prediction of the behavior of objects in the vicinity of the HA-UAV. The general considerations involved in solving this problem, including the problem of analyzing the group behavior of such objects, are discussed. As an illustrative example, the solution to the problem of tracking an aircraft maneuvering in the vicinity of a HA-UAV is given. The second element of situational awareness is related to the processing of visual information, which is one of the primary sources of situational awareness formation required for the operation of the HA-UAV control system. As an example here, we consider solving the problem of semantic segmentation of images processed when selecting a landing site for the HA-UAV in unfamiliar terrain. Both of these problems are solved using machine learning methods and tools. In the field of situational awareness for HA-UAVs, there are several problems that need to be solved. We formulate some of these problems and briefly describe them