Explore the vast range of titles available.

In the study of the joint spectral radius of linear operators, an important role is played by invariant norms and invariant convex bodies. It is known that they are dual to each other in the sense of the polar transform and conjugation of operators. This property is used in studying the highest growth rate of trajectories of discrete-time linear dynamical systems. In the case of continuous-time systems, an analog of joint spectral radius is Lyapunov exponent. For such systems, invariant norms have been defined and their existence has been proved. However, there are no results concerning the invariant bodies of continuous-time systems in the literature. This paper is devoted to the duality of continuous-time systems. It is shown that there exists no natural notion of an invariant body for such systems and, therefore, the duality of systems is defined in terms of invariant norms.

Future radio surveys will generate catalogs of tens of millions of radio sources, for which redshift estimates will be essential to achieve many of the science goals. However, spectroscopic data will be available for only a small fraction of these sources, and in most cases even the optical and infrared photometry will be of limited quality. Furthermore, radio sources tend to be at higher redshift than most optical sources (most radio surveys have a median redshift greater than 1) and so a significant fraction of radio sources hosts differ from those for which most photometric redshift templates are designed. We therefore need to develop new techniques for estimating the redshifts of radio sources. As a starting point in this process, we evaluate a number of machine-learning techniques for estimating redshift, together with a conventional template-fitting technique. We pay special attention to how the performance is affected by the incompleteness of the training sample and by sparseness of the parameter space or by limited availability of ancillary multiwavelength data. As expected, we find that the quality of the photometric-redshift degrades as the quality of the photometry decreases, but that even with the limited quality of photometry available for all-sky-surveys, useful redshift information is available for the majority of sources, particularly at low redshift. We find that a template-fitting technique performs best in the presence of high-quality and almost complete multi-band photometry, especially if radio sources that are also X-ray emitting are treated separately, using specific templates and priors. When we reduced the quality of photometry to match that available for the EMU all-sky radio survey, the quality of the template-fitting degraded and became comparable to some of the machine-learning methods. Machine learning techniques currently perform better at low redshift than at high redshift, because of incompleteness of the currently available training data at high redshifts.

A multifactorial stationary field experiment on water infiltration and the rates of irrigation erosion of mountainous chernozems on slopes of 0.02 to 0.06 at the foothills of the Kyrgyz Range was conducted. The studied chernozems contained 6–8% of humus, 0.25–3.0% of nitrogen, 0.22–0.3% of phosphorus, and 2.6–3% of potassium. The parent material was loess-like, non-solonetzic loam with a slightly alkaline reaction and varied particle size distribution. Geographic information systems and remote sensing technologies were used to collect, process, analyze, and map spatial data. The experiment included various slopes of agricultural plots with varying configurations and furrow irrigation of row crops (sugar beets, grain corn, and perennial grasses). Soil erosion losses were assessed by collecting irrigation water samples in various experimental setups and subsequently determining the soil solids content of the water. The data obtained indicate that protective measures such as seeded furrows and reinforced pipes increase infiltration and reduce soil erosion. During precipitation without slope tillage, the maximum water absorption rate averaged 7.3 cm/h, while with transverse autumn plowing, the absorption rate increased to 18.2 cm/h. This made it possible to increase (due to atmospheric precipitation) the moisture capacity of the 0–80 cm soil layer by 560 m3/ha, creating the necessary reserves of soil moisture.

— We have studied phase equilibria in the quaternary system NaF–NaCl–NaBr–Na 2 CrO 4 . The results demonstrate that the continuous series of NaCl x Br 1 – x solid solutions persists in the system. The chemical composition and melting point (507°C) of a mixture with the composition corresponding to the quaternary minimum have been determined by differential thermal analysis, and its enthalpy of fusion (232 J/g) has been determined by differential scanning calorimetry. Its phase composition has been confirmed by X-ray diffraction. Theoretical and experimental techniques have been used to identify phase equilibria and the phase crystallization sequence and construct a 3D computer model of phase relations, which makes it possible to predict phase transformations for arbitrary representative points in the system studied.

AbstractThis study is devoted to variational methods for solving the problem of simultaneous determination of the unknown complex-valued coefficients multiplying the lower and nonlinear terms of a nonstationary Schrödinger-type equation generalizing the well-known quantum mechanical Schrödinger equation. The sought coefficient of the lower term is a complex-valued quantum potential. Problems of this type arise in nonlinear optics, in the study of processes in quantum waveguides, and in other areas. The solvability of the variational statement of the problem under consideration is proved, a necessary condition for its solution is established, and an expression for the gradient of the cost functional based on the final observation is obtained. These results are used to develop and justify an iterative algorithm for solving the problem. An example of the instability of its solution is given, and an iterative regularizing algorithm for solving the problem is described.

A study has been made of the inverse problem on determining the thermophysical characteristics of multiply connected structures with heterogeneous materials, that are taken as the sign of their diagnostics. The procedure of diagnostics is based on solution of the inverse problem on determining the thermophysical characteristics of objects in a variational formulation. The quality functional for this formulation is new, not used before in the theory of inverse problems and diagnostics. The theorem of singe-valued solvability of the inverse problem in question has been proved, the iterative algorithm of its solution has been presented, and the extreme properties of the quality functional have been established. The proposed procedure is based on observations beyond an object and allows diagnostics in a nondestructive noncontact regime. Initial data with an error and the influence of the standard on solution are discussed.

The application of inverse problems to thermal diagnostics of homogeneous structures is outlined, variational formulations of the problems under study are considered, their solvability is proven, and an iterative solution algorithm is described. The results are applied to the thermal diagnostics of thermoelastic structures, a theorem of existence and uniqueness of the solution to the problem of determining the inhomogeneous thermal characteristics of the medium, which is used to restore the physical and technical image of the diagnosed object, is proved, and the necessary condition for the extremum is formulated in the form of a variational inequality. An example of a numerical solution to the problem under consideration is given and an analysis of the calculation results on the application of the proposed diagnostic technique is given.

Internal control in accordance with international and federal standards is a process that is organized and implemented by the management of an enterprise, its employees and representatives of the owner. Model of development of the internal control system.

The paper considers the influence of low-frequency pulsed force of an electromagnetic field on the formation of a solidifying metal structure, investigated experimentally. Pulses in the range from 0.1 to 10 Hz were applied to the melt, during the ingots growth in the cylindrical volume, to create the conditions of the forced convection. The final metal structure and deformation of the samples free surface, solidified in different conditions was analyzed. The reduction of porosity in metal ingots was stated for the cases of forced convection under the pulsed frequencies from 0.1 to 1 Hz, in comparison to the structure, formed by permanent electromagnetic stirring. The specimens, grown under the pulsed forcing with equal time of the pulses and the pauses have concave free surface, as well as in the cases of natural convection and permanent stirring. A flatter form of the free surface was obtained during the solidification process under the short pulses of electromagnetic force. Intorduction

The aim of this study was to improve the processability and to investigate the resistance of polyethylene to thermal oxidation in the presence of different mineral fillers. It was shown that the presence in crosslinked polyethylene of 5-10 parts aluminium powder promotes a 2-3-fold increase in thermal oxidation resistance by comparison with unfilled polyethylene.