260 research outputs found
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 and be given on the time interval ,
let there also be a multifunction (m/f) acting from to
and a finite set of moments from . The work deals with two
questions: the first one is the connection between the possibility of stepwise
construction (specified by ) of a value of for an
unknown step-by-step implemented argument and the existence
of a multiselector of the m/f with a non-anticipatory property
of special kind defined by ; and the second question is how to build
the above for a given pair . 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 can be carried out for any in steps
implemented argument if and only if the multiselector is
non-empty-valued. In this case, the desired value can be selected from
in step-by-step procedure for any unknown in advance argument
. The key point of the work is the procedure for calculation the
multiselector , 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
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 Π‘entral 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 Π‘entral 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.ΠΠΎΠΈΡΠΊ ΡΡΡΠΎΠΉΡΠΈΠ²ΠΎΠΉ ΠΊ Π½Π΅ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΠΎΡΡΠΈ ΡΠΈΡΠΊΠ°Π»ΡΠ½ΠΎΠΉ ΠΈ ΠΌΠΎΠ½Π΅ΡΠ°ΡΠ½ΠΎΠΉ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠΈ, Π½Π΅ ΠΏΡΠΈΠ²ΠΎΠ΄ΡΡΠ΅ΠΉ ΠΊ ΠΎΡΡΠΈΡΠ°ΡΠ΅Π»ΡΠ½ΡΠΌ ΠΏΠΎΡΠ»Π΅Π΄ΡΡΠ²ΠΈΡΠΌ ΠΏΡΠΈ Π»ΡΠ±ΡΡ
Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΡΡ
ΠΈΡΠΊΠ°ΠΆΠ΅Π½ΠΈΡΡ
ΡΠΏΠ΅ΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ, ΡΠ²Π»ΡΠ΅ΡΡΡ ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎ Π°ΠΊΡΡΠ°Π»ΡΠ½ΡΠΌ ΠΏΡΠΈ ΡΠ°Π·ΡΠ°Π±ΠΎΡΠΊΠ΅ Π΄ΠΈΠ½Π°ΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ. ΠΡΠΈ ΡΡΠΎΠΌ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»ΡΠ΅Ρ Π½Π°ΡΡΠ½ΡΠΉ ΠΈ ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΈΠΉ ΠΈΠ½ΡΠ΅ΡΠ΅Ρ Π²Π»ΠΈΡΠ½ΠΈΠ΅ ΡΡΠ΅ΠΏΠ΅Π½ΠΈ Π΄ΠΎΠΌΠΈΠ½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΌΠΎΠ½Π΅ΡΠ°ΡΠ½ΡΡ
ΠΈ ΡΠΈΡΠΊΠ°Π»ΡΠ½ΡΡ
Π²Π»Π°ΡΡΠ΅ΠΉ Π΄ΡΡΠ³ Π½Π°Π΄ Π΄ΡΡΠ³ΠΎΠΌ Π½Π° ΡΡΡΠΎΠΉΡΠΈΠ²ΠΎΡΡΡ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠΈ. Π Π΄Π°Π½Π½ΠΎΠΉ ΠΏΡΠ±Π»ΠΈΠΊΠ°ΡΠΈΠΈ Π½Π° ΠΏΡΠΈΠΌΠ΅ΡΠ΅ Π½Π΅ΠΎΠΊΠ΅ΠΉΠ½ΡΠΈΠ°Π½ΡΠΊΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΎ Π²Π»ΠΈΡΠ½ΠΈΠ΅ ΡΡΠ΅ΠΏΠ΅Π½ΠΈ ΡΠΎΡΡΡΠ΄Π½ΠΈΡΠ΅ΡΡΠ²Π° Π¦Π΅Π½ΡΡΠΎΠ±Π°Π½ΠΊΠ° ΠΈ ΠΏΡΠ°Π²ΠΈΡΠ΅Π»ΡΡΡΠ²Π° Π½Π° ΡΡΡΠΎΠΉΡΠΈΠ²ΠΎΡΡΡ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠΈ. ΠΡΠΈ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΈ ΠΏΡΠΎΠ±Π»Π΅ΠΌΡ ΡΡΡΠΎΠΉΡΠΈΠ²ΠΎΡΡΠΈ ΠΊ Π½Π΅ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΠΎΡΡΡΠΌ ΡΠΈΡΠΊΠ°Π»ΡΠ½ΠΎΠΉ ΠΈ ΠΌΠΎΠ½Π΅ΡΠ°ΡΠ½ΠΎΠΉ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠΈ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π»ΠΈΡΡ ΡΠΊΠΎΠ½ΠΎΠΌΠΈΠΊΠΎ-ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΌΠ΅ΡΠΎΠ΄Ρ ΠΈ ΠΌΠ΅ΡΠΎΠ΄Ρ ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ½ΠΎΠ³ΠΎ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ. Π£ΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΎ, ΡΡΠΎ ΡΠΊΠΎΠΎΡΠ΄ΠΈΠ½ΠΈΡΠΎΠ²Π°Π½Π½ΠΎΠ΅ Π²Π·Π°ΠΈΠΌΠΎΠ΄Π΅ΠΉΡΡΠ²ΠΈΠ΅ ΡΠΈΡΠΊΠ°Π»ΡΠ½ΠΎΠΉ ΠΈ ΠΌΠΎΠ½Π΅ΡΠ°ΡΠ½ΠΎΠΉ Π²Π»Π°ΡΡΠΈ Π΄Π»Ρ ΡΠ΅ΠΆΠΈΠΌΠ° Ρ ΠΎΠ±ΡΠ·Π°ΡΠ΅Π»ΡΡΡΠ²Π°ΠΌΠΈ ΠΈ Π΄Π»Ρ Π΄ΠΈΡΠΊΡΠ΅ΡΠΈΠΎΠ½Π½ΠΎΠ³ΠΎ ΡΠ΅ΠΆΠΈΠΌΠ° ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎ Π»ΠΈΡΡ ΠΏΡΠΈ Π±ΠΎΠ»ΡΡΠ΅ΠΉ ΠΏΠ΅ΡΠ΅Π³ΠΎΠ²ΠΎΡΠ½ΠΎΠΉ ΡΠΈΠ»Π΅ Π¦Π΅Π½ΡΡΠ°Π»ΡΠ½ΠΎΠ³ΠΎ Π±Π°Π½ΠΊΠ°. ΠΡΠΎ ΡΠΏΡΠ°Π²Π΅Π΄Π»ΠΈΠ²ΠΎ ΠΊΠ°ΠΊ Π΄Π»Ρ ΠΌΠΎΠ΄Π΅Π»ΠΈ Ρ Π½Π°ΠΈΡ
ΡΠ΄ΡΠΈΠΌ ΡΡΠ΅Π½Π°ΡΠΈΠ΅ΠΌ, ΡΠ°ΠΊ ΠΈ Π΄Π»Ρ ΠΌΠΎΠ΄Π΅Π»ΠΈ Ρ ΡΡΡΠΎΠΉΡΠΈΠ²ΠΎΠΉ ΠΊ Π½Π΅ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΠΎΡΡΡΠΌ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠΈ. ΠΠ»Ρ ΡΠ΅ΠΆΠΈΠΌΠ° Ρ ΠΎΠ±ΡΠ·Π°ΡΠ΅Π»ΡΡΡΠ²Π°ΠΌΠΈ ΡΠ²Π΅Π»ΠΈΡΠ΅Π½ΠΈΠ΅ ΡΡΠ΅ΠΏΠ΅Π½ΠΈ Π΄ΠΎΠΌΠΈΠ½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΠ°Π²ΠΈΡΠ΅Π»ΡΡΡΠ²Π° ΠΏΡΠΈΠ²ΠΎΠ΄ΠΈΡ Π² ΠΎΡΠ½ΠΎΠ²Π½ΠΎΠΌ ΠΊ ΠΈΡΠΊΠ°ΠΆΠ΅Π½ΠΈΡΠΌ ΠΎΡΠΊΠ»ΠΈΠΊΠ° Π³ΠΎΡΡΠ°ΡΡ
ΠΎΠ΄ΠΎΠ² Π½Π° ΡΠΎΠΊ ΠΈΠ½ΡΠ»ΡΡΠΈΠΎΠ½Π½ΡΡ
ΠΈΠ·Π΄Π΅ΡΠΆΠ΅ΠΊ. Π‘ ΡΠ²Π΅Π»ΠΈΡΠ΅Π½ΠΈΠ΅ΠΌ ΡΡΠ΅ΠΏΠ΅Π½ΠΈ Π΄ΠΎΠΌΠΈΠ½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΠ°Π²ΠΈΡΠ΅Π»ΡΡΡΠ²Π° Π² ΡΠΎΡΡΡΠ΄Π½ΠΈΡΠ΅ΡΡΠ²Π΅ Ρ Π¦Π΅Π½ΡΡΠ°Π»ΡΠ½ΡΠΌ Π±Π°Π½ΠΊΠΎΠΌ ΠΏΡΠΈ Π΄ΠΈΡΠΊΡΠ΅ΡΠΈΠΎΠ½Π½ΠΎΠΉ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠ΅ ΡΠΎΠ»Ρ ΠΈΡΠΊΠ°ΠΆΠ΅Π½ΠΈΠΉ, Π²Π½ΠΎΡΠΈΠΌΡΡ
Π² ΡΡΠ°Π½Π΄Π°ΡΡΠ½ΡΡ ΠΌΠΎΠ΄Π΅Π»Ρ, ΡΠΌΠ΅Π½ΡΡΠ°Π΅ΡΡΡ. ΠΡΠΈ ΡΠ΅ΠΆΠΈΠΌΠ΅ Ρ ΠΎΠ±ΡΠ·Π°ΡΠ΅Π»ΡΡΡΠ²Π°ΠΌΠΈ ΠΈ ΠΏΡΠΈ Π΄ΠΈΡΠΊΡΠ΅ΡΠΈΠΎΠ½Π½ΠΎΠΉ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠ΅ ΠΈΡΠΊΠ°ΠΆΠ΅Π½ΠΈΡ, Π²Π½ΠΎΡΠΈΠΌΡΠ΅ Π² ΡΡΠ°Π½Π΄Π°ΡΡΠ½ΡΡ ΠΌΠΎΠ΄Π΅Π»Ρ ΠΏΡΠΈ ΡΠΎΠΊΠ°Ρ
ΡΠΏΡΠΎΡΠ°, ΠΌΠΈΠ½ΠΈΠΌΠ°Π»ΡΠ½Ρ. ΠΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΌΠΎΠ³ΡΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°ΡΡΡΡ ΠΏΡΠΈ Π°Π½Π°Π»ΠΈΠ·Π΅ ΠΊΡΡΠΏΠ½ΠΎΠΌΠ°ΡΡΡΠ°Π±Π½ΡΡ
Π΄ΠΈΠ½Π°ΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΠΎΡ
Π°ΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ. Π‘Π΄Π΅Π»Π°Π½ Π²ΡΠ²ΠΎΠ΄, ΠΎ ΡΠΎΠΌ, ΡΡΠΎ ΠΏΡΠΈ Π°Π½Π°Π»ΠΈΠ·Π΅ ΠΌΠΎΠ½Π΅ΡΠ°ΡΠ½ΠΎΠΉ ΠΈ ΡΠΈΡΠΊΠ°Π»ΡΠ½ΠΎΠΉ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠΈ Π² ΠΌΠ°ΠΊΡΠΎΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
Π΄ΠΈΠ½Π°ΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΌΠΎΠ΄Π΅Π»ΡΡ
, ΡΠ»Π΅Π΄ΡΠ΅Ρ ΠΏΡΠΈΠ½ΠΈΠΌΠ°ΡΡ Π²ΠΎ Π²Π½ΠΈΠΌΠ°Π½ΠΈΠ΅ ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅ Π² Π΄Π°Π½Π½ΠΎΠΉ ΡΡΠ°ΡΡΠ΅ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΏΠΎ ΡΠ°Π·ΡΠ°Π±ΠΎΡΠΊΠ΅ ΡΡΡΠΎΠΉΡΠΈΠ²ΠΎΠΉ ΠΊ Π½Π΅ΡΡΡΡΠΊΡΡΡΠ½ΡΠΌ Π½Π΅ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΠΎΡΡΡΠΌ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠΈ
Enhanced chemical etch rate of borosilicate glass via spatially resolved laser-generated color centers
Β© 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
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
- β¦