UNLOCKING of PREDICATE: APPLICATION to CONSTRUCTING A NON-ANTICIPATING SELECTION

We consider an approach to constructing a non-anticipating selection of a multivalued mapping; such a problem arises in control theory under conditions of uncertainty. The approach is called "unlocking of predicate'' and consists in the reduction of finding the truth set of a predicate to searching fixed points of some mappings. Unlocking of predicate gives an extra opportunity to analyze the truth set and to build its elements with desired properties. In this article, we outline how to build "unlocking mappings" for some general types of predicates: we give a formal definition of the predicate unlocking operation, the rules for the construction and calculation of "unlocking mappings" and their basic properties. As an illustration, we routinely construct two unlocking mappings for the predicate "be non-anticipating mapping" and then on this base we provide the expression for the greatest non-anticipating selection of a given multifunction

ON A DYNAMIC GAME PROBLEM WITH AN INDECOMPOSABLE SET OF DISTURBANCES

For an abstract dynamic system, a game problem of retention of the motions in a given set of the motion histories is considered. The case of an indecomposable set of disturbances is studied. The set of successful solvability and a construction of a resolving quasistrategy based on the method of programmed iterations is proposed

On a construction of a partially non-anticipative multiselector and its applications to dynamic optimization problems

Let the sets of functions $Z$ and $\Omega$ be given on the time interval $T$, let there also be a multifunction (m/f) $\alpha$ acting from $\Omega$ to $Z$ and a finite set of moments $\Delta$ from $T$. The work deals with two questions: the first one is the connection between the possibility of stepwise construction (specified by $\Delta$) of a value $z$ of $\alpha(\omega)$ for an unknown step-by-step implemented argument $\omega\in\Omega$ and the existence of a multiselector $\beta$ of the m/f $\alpha$ with a non-anticipatory property of special kind defined by $\Delta$; and the second question is how to build the above $\beta$ for a given pair $(\alpha,\Delta)$. The consideration of these questions is motivated by the presence of similar step-by-step procedures in the differential game theory, for example, in the alternating integral method, in pursuit-evasion problems posed with use of counter-strategies, and in the method of guide control. It is shown that the step-by-step construction of the value $z\in\alpha(\omega)$ can be carried out for any in steps implemented argument $\omega$ if and only if the multiselector $\beta$ is non-empty-valued. In this case, the desired value $z$ can be selected from $\beta(\omega)$ in step-by-step procedure for any unknown in advance argument $\omega$. The key point of the work is the procedure for calculation the multiselector $\beta$, for which a constructive and finite-step description is given. Illustrative examples are considered that include, in particular, problems of a guaranteed result optimization under functional constraints on control and/or disturbance implementations.Comment: 27 pages, 3 figure

Enhanced chemical etch rate of borosilicate glass via spatially resolved laser-generated color centers

© 2020 IOP Publishing Ltd. In this work, it is shown that controllable increases in chemical reactivity of borosilicate glass can be induced through spatially resolved femtosecond laser irradiation at fluence values significantly lower than the damage threshold. The hydrofluoric acid etch rate has been found to be closely correlated to the reduction in optical transmission of the glass at 488 nm, which is, in turn, governed by the production of boron-oxygen hole centers. The combination of laser irradiation below the ablation threshold followed by chemical etching is shown to yield surfaces that have a roughness lower than those achieved by either laser or chemical etching alone. Application of this effect to the manufacture of freeform Laplacian optics is demonstrated

The analysis steady to not structural uncertaintya monetary and fiscal policy at their cooperation interaction

The search for a fiscal and monetary policy that is robust to uncertainty and does not lead to negative consequences for any possible distortion specifications of the economic model, is particularly relevant to the development of dynamic models. It is of scientific and practical interest to study the effect of the degree of the dominance of monetary and fiscal authorities over each other on policy stability. In this article, a neo-Keynesian model is used as a case to study the effect of the degree of cooperation between the Сentral Bank and the government on policy stability. Analysis is performed of robustness to non-structural uncertainties of fiscal and monetary policies with cooperative interaction between the monetary and fiscal authorities for the regime with the obligations and discretionary policy regime. Recommendations are offered for the development of robustness of non-structural policy uncertainties. Economic-mathematical methods and computer simulation methods were used in the study of sustainability issues to the uncertainties of fiscal and monetary policy. It was found that the coordinated interaction of fiscal and monetary authorities to the regime with obligations and discretionary mode is effective only in the case of a greater negotiating power of the Сentral Bank. This is true for the model with the worst-case scenario, and for models resistant to policy uncertainty. For the regime with obligations, the growing degree dominance of the government leads to distortions in the main response of government spending on inflation shock. With an increasing degree of government dominance in cooperation with the Central Bank under a discretionary policy the role of the distortions introduced by the standard model is reduced. In the case of a policy with commitments and under a discretionary policy the distortions brought to the standard model at a shock of demand, are minimal. It is concluded that that the analysis of monetary and fiscal policy in the macroeconomic dynamic models should take into account the obtained results outlined in this paper when developing a policy that is resistant to non-structural uncertainties.Поиск устойчивой к неопределенности фискальной и монетарной политики, не приводящей к отрицательным последствиям при любых возможных искажениях спецификации экономической модели, является особенно актуальным при разработке динамических моделей. При этом представляет научный и практический интерес влияние степени доминирования монетарных и фискальных властей друг над другом на устойчивость политики. В данной публикации на примере неокейнсианской модели исследовано влияние степени сотрудничества Центробанка и правительства на устойчивость политики. При исследовании проблемы устойчивости к неопределенностям фискальной и монетарной политики использовались экономико-математические методы и методы компьютерного моделирования. Установлено, что скоординированное взаимодействие фискальной и монетарной власти для режима с обязательствами и для дискреционного режима эффективно лишь при большей переговорной силе Центрального банка. Это справедливо как для модели с наихудшим сценарием, так и для модели с устойчивой к неопределенностям политики. Для режима с обязательствами увеличение степени доминирования правительства приводит в основном к искажениям отклика госрасходов на шок инфляционных издержек. С увеличением степени доминирования правительства в сотрудничестве с Центральным банком при дискреционной политике роль искажений, вносимых в стандартную модель, уменьшается. При режиме с обязательствами и при дискреционной политике искажения, вносимые в стандартную модель при шоках спроса, минимальны. Полученные результаты могут использоваться при анализе крупномасштабных динамических стохастических моделей. Сделан вывод, о том, что при анализе монетарной и фискальной политики в макроэкономических динамических моделях, следует принимать во внимание полученные в данной статье результаты по разработке устойчивой к неструктурным неопределенностям политики

Influence of the gap and the friction on trajectory reproduction accuracy in a multiaxis machine with CNC

Precision multiaxis machining centers with CNC and industrial robots are the base of modern mechanical engineering. The requirements of reproduction accuracy of the motion trajectory of operative parts of the NCaided manufacturing equipment are constantly increasing. Gaps and a friction in drives are a main factor affecting the accuracy of trajectory reproduction. The results of the investigation into the influence of gaps and a friction in drive mechanisms covered and not covered by position feedback loop on the accuracy of trajectory reproduction by the imitation modeling method are described

Causal analysis of the interinfluence of workforce productivity and rail freight intensity in the regions of the Ural Federal District

Relevance. The development of the railway industry has a significant positive impact on socio-economic dynamics at both the state and regional levels, which has been confirmed by numerous domestic and foreign studies. However, the issue of mutual influence of such categories as regional labour productivity and rail freight intensity has been little studied. At the same time, the most important task today is to find effective incentives for the growth of regional labour productivity.Research Objective. This study aims to econometric analysis of the relationship between rail freight intensity and workforce productivity in the Ural Federal District (UFD).Data and Methods. The study uses official statistical data on Russian regions provided by the Federal State Statistics Service. The methods of Vector Error Correction Models (VECM) and pooled mean group estimates (PMG method) formed the methodological basis of the study.Results. The study has shown that there is a relationship between workforce productivity and rail freight intensity. At that point, in a short-term period growth of rail freight intensity leads to an increase in workforce productivity, which in a long-term period itself becomes an incentive to increase the shipped commodity mass and rail freight intensity.Conclusions. The findings can be of interest to public authorities at the national and regional levels, for heads of industrial structures and functional institutions, representatives of business and scientific communities interested in the development and modernization of transport infrastructure, being a basic condition for the increased intensity of cargo transportation in the region

On a condition of existence of non-anticipating selections

The hereditary selections of multi-functions play an important role in the theory of diferential games in connection with the construction of resolving quasi-strategies. The existence of a non-anticipating selection of a non-anticipating multi-function is considered. In most cases important for applications, it is known that any non-anticipating multi-function with non-empty compact values has a non-anticipating selection. Namely, the result is valid when the non-anticipation property is defined by a totally ordered family in the domain of ”time” variable. In this note, we show that the condition is essential: when the family is not totally ordered, there exists a hereditary multi-function with non-empty compact values that has no non-anticipating selections. © 201