140 research outputs found
Behavioural Characteristics of Children with Developmental Disorder Risks
The article is devoted to the study of the temperament and behaviour of children with developmental disorder risks. Early age is most significant in terms of early identifying deviant development markers for implementing effective programmes for early intervention. The article deals with the peculiarities of using the Infant Behaviour Questionnaire - Revised (IBQ-R) and its application in scientific research; the results of domestic and foreign research into temperament as a marker/predictor of deviant behaviour are presented. The paper describes the results of a pilot study of differences in behaviour in a sample of 49 children aged 5.6 months. The research involved two groups of test children, a reference group (typically developing children) and the children of developmental risk groups (which included prematurity, family risk of autism spectrum disorders (ASD)/attention deficit and hyperactivity disorder (ADHD), paediatric arterial ischemic stroke). The significant impact of developmental disorder risks on the Perceptual Sensitivity Scale (IBQ-R) as well as the effect of sexand risks on the Approach, Vocal Reactivity (IBQ-R) scale were discovered. There are suggestions that prematurity may have a negative impact on the development of temperament in children aged 6 months. However, in comparison with such factors as the genetic predisposition to atypical development or local brain damage due to paediatric arterial ischemic stroke, prematurity (excluding extremely premature) probably has less influence on the development of temperament and behavioural characteristics. There is a significant heterotypic continuity of individual differences in temperament indicators at an early age, which highlights the need for further research into the issue and the formation of large cohorts of children.
Keywords: deviant development markers, behaviour, IBQ-R questionnaire
Developmental psychology: Parent responsiveness and its role in neurocognitive and socioemotional development of one-year-old preterm infants
Background. It has been demonstrated that preterm birth negatively affects the neurocognitive and socioemotional development of a child. It is therefore important to identify the factors that can decrease potential risks for atypical development in preterm infants. The social environment which surrounds a child is considered to be one such factor. We hypothesize that parent responsiveness positively influences the development of a preterm child. Objective. The purpose of this research is to reveal differences in the development of two one-year-old preterm children whose parents have exhibited opposite types of parent responsiveness. Design. Based on the analysis of video recordings of child-parent interactions, we identified two children whose parents registered opposite patterns of responsiveness. Parent responsiveness was measured based on Parent Responsiveness Markers Protocol methodology. The Bayley-III was used to assess the children's cognitive and socioemotional development. Results. We identified that the preterm child whose parent showed a high level of parental responsiveness had normative levels of neurocognitive development, socioemotional skills and adaptive behavior. The preterm child, whose parent showed a low level of parental responsiveness, scored lower on the Bayley-III. Conclusion. Preterm birth not only affects infant development, but also has a psychological impact on parents, evoking fear and anxiety for their child. This affects parental behavior and their responsiveness towards their child. This study showed that parent responsiveness has a positive effect on the neurocognitive and socioemotional development of a preterm child. Further research should focus on assessing the role of parent responsiveness in child development using a larger sample. Β© Lomonosov Moscow State University, 2019. Russian Psychological Society, 2019.19-513-92001\19The research was supported by the grant of the Russian Science Foundation RFBR β 19-513-92001\19
Via Hexagons to Squares in Ferrofluids: Experiments on Hysteretic Surface Transformations under Variation of the Normal Magnetic Field
We report on different surface patterns on magnetic liquids following the
Rosensweig instability. We compare the bifurcation from the flat surface to a
hexagonal array of spikes with the transition to squares at higher fields. From
a radioscopic mapping of the surface topography we extract amplitudes and
wavelengths. For the hexagon--square transition, which is complex because of
coexisting domains, we tailor a set of order parameters like peak--to--peak
distance, circularity, angular correlation function and pattern specific
amplitudes from Fourier space. These measures enable us to quantify the smooth
hysteretic transition. Voronoi diagrams indicate a pinning of the domains. Thus
the smoothness of the transition is roughness on a small scale.Comment: 17 pages, 14 figure
Conformation of gem-diphenyl group in six-membered cyclic ethers of acids of sulfur, selenium, and arsenic
1. The sulfate, selenite, chloroarsenite, and bromoarsenite of 2,2-diphenyl-1,3-propanediol have been synthesized. 2. In the molecules of cyclic esters based on 2,2-diphenyl-l,3-propanediol, in the dissolved state, equivalent rotation of the phenyl groups relative to the ring symmetry plane is realized. Β© 1980 Plenum Publishing Corporation
ΠΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠ΅ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΠΏΠ΅ΡΠ΅Π½ΠΎΡΠΈΠΌΡΡ ΠΊΠ°ΠΏΠ΅Π»Ρ ΡΠ»Π΅ΠΊΡΡΠΎΠ΄Π½ΠΎΠ³ΠΎ ΠΌΠ΅ΡΠ°Π»Π»Π° ΠΌΠ΅ΡΠΎΠ΄ΠΎΠΌ ΠΈΠΌΠΈΡΠ°ΡΠΈΠΎΠ½Π½ΠΎΠ³ΠΎ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΈ Π²ΠΈΠ·ΡΠ°Π»ΠΈΠ·Π°ΡΠΈΠΈ
The nature of the molten electrode metal melting and transfer is the main process parameter of manual metal arc welding (MMA) with coated electrodes. It significantly affects the efficiency of the welding process. For this reason the relevant task is to identify the parameters of the transferred molten electrode metal drops and their further transfer into the weld pool with maximum accuracy. The aim of the given paper is to develop a method and visual representation of the form and the geometrics (volume, area, mass) of a molten electrode metal drop.We have developed the method of simulation modeling and visualization for molten electrode metal drops transfer and their parameters. It allows obtaining highly reliable input data to be used for developing and verification of mathematical models for the thermal fields distribution along the welded item surface. The algorithm is realized as the calculation programs for specifying the molten metal drop parameters and means of its geometrics and space form visualization.We used this method to specify a number of molten electrode metal drop parameters: volume, mass, center-of-gravity position, surface area.We have established that it is possible to conduct the measurements with maximumThe suggested method significantly decreases the labor intensity of experimental studies aimed at specifying the size of electrode metal drops in comparison to the standard methods. When we know the size of the drops under certain welding conditions we can control the drop transfer process, i. e. reduce the heat input into the welded item and produce weld joints with the tailored performance characteristics.ΠΡΠ½ΠΎΠ²Π½ΡΠΌ ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΠΌ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠΌ ΠΏΡΠΎΡΠ΅ΡΡΠ° ΡΡΡΠ½ΠΎΠΉ Π΄ΡΠ³ΠΎΠ²ΠΎΠΉ ΡΠ²Π°ΡΠΊΠΈ, ΠΏΠΎΠΊΡΡΡΡΠΌ ΡΠ»Π΅ΠΊΡΡΠΎΠ΄Π°ΠΌΠΈ, ΡΡΡΠ΅ΡΡΠ²Π΅Π½Π½ΠΎ Π²Π»ΠΈΡΡΡΠΈΠΌ Π½Π° ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΡΡΡ Π΅Π³ΠΎ ΠΏΡΠΎΡΠ΅ΠΊΠ°Π½ΠΈΡ, ΡΠ²Π»ΡΠ΅ΡΡΡ Ρ
Π°ΡΠ°ΠΊΡΠ΅Ρ ΠΏΠ»Π°Π²Π»Π΅Π½ΠΈΡ ΠΈ ΠΏΠ΅ΡΠ΅Π½ΠΎΡΠ° ΡΠ°ΡΠΏΠ»Π°Π²Π»Π΅Π½Π½ΠΎΠ³ΠΎ ΡΠ»Π΅ΠΊΡΡΠΎΠ΄Π½ΠΎΠ³ΠΎ ΠΌΠ΅ΡΠ°Π»Π»Π°. ΠΠΎΡΡΠΎΠΌΡ Π°ΠΊΡΡΠ°Π»ΡΠ½ΡΠΌ ΡΠ²Π»ΡΠ΅ΡΡΡ Π²ΠΎΠΏΡΠΎΡ ΠΌΠ°ΠΊΡΠΈΠΌΠ°Π»ΡΠ½ΠΎ ΡΠΎΡΠ½ΠΎΠ³ΠΎ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΠΏΠ΅ΡΠ΅Π½ΠΎΡΠΈΠΌΡΡ
ΠΊΠ°ΠΏΠ΅Π»Ρ ΡΠ°ΡΠΏΠ»Π°Π²Π»Π΅Π½Π½ΠΎΠ³ΠΎ ΡΠ»Π΅ΠΊΡΡΠΎΠ΄Π½ΠΎΠ³ΠΎ ΠΌΠ΅ΡΠ°Π»Π»Π° ΠΈ ΠΈΡ
ΠΏΠΎΡΠ»Π΅Π΄ΡΡΡΠ΅Π³ΠΎ ΠΏΠ΅ΡΠ΅Ρ
ΠΎΠ΄Π° Π² ΡΠ²Π°ΡΠΎΡΠ½ΡΡ Π²Π°Π½Π½Ρ. Π¦Π΅Π»ΡΡ Π΄Π°Π½Π½ΠΎΠΉ ΡΠ°Π±ΠΎΡΡ ΡΠ²Π»ΡΠ»Π°ΡΡ ΡΠ°Π·ΡΠ°Π±ΠΎΡΠΊΠ° ΠΌΠ΅ΡΠΎΠ΄ΠΈΠΊΠΈ ΠΈ Π²ΠΈΠ·ΡΠ°Π»ΡΠ½ΠΎΠ³ΠΎ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½ΠΈΡ ΡΠΎΡΠΌΡ ΠΈ Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² (ΠΎΠ±ΡΡΠΌ, ΠΏΠ»ΠΎΡΠ°Π΄Ρ, ΠΌΠ°ΡΡΠ°) ΠΊΠ°ΠΏΠ»ΠΈ ΡΠ°ΡΠΏΠ»Π°Π²Π»Π΅Π½Π½ΠΎΠ³ΠΎ ΡΠ»Π΅ΠΊΡΡΠΎΠ΄Π½ΠΎΠ³ΠΎ ΠΌΠ΅ΡΠ°Π»Π»Π°.Π Π°Π·ΡΠ°Π±ΠΎΡΠ°Π½ ΠΌΠ΅ΡΠΎΠ΄ ΠΈΠΌΠΈΡΠ°ΡΠΈΠΎΠ½Π½ΠΎΠ³ΠΎ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΈ Π²ΠΈΠ·ΡΠ°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΠΏΠ΅ΡΠ΅Π½ΠΎΡΠ° ΠΊΠ°ΠΏΠ΅Π»Ρ ΡΠ°ΡΠΏΠ»Π°Π²Π»Π΅Π½Π½ΠΎΠ³ΠΎ ΡΠ»Π΅ΠΊΡΡΠΎΠ΄Π½ΠΎΠ³ΠΎ ΠΌΠ΅ΡΠ°Π»Π»Π° ΠΈ ΠΈΡ
ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ², ΡΡΠΎ ΠΏΠΎΠ·Π²ΠΎΠ»ΠΈΡ ΠΏΠΎΠ»ΡΡΠΈΡΡ Π²Ρ
ΠΎΠ΄Π½ΡΠ΅ Π΄Π°Π½Π½ΡΠ΅ Ρ Π²ΡΡΠΎΠΊΠΎΠΉ ΡΡΠ΅ΠΏΠ΅Π½ΡΡ Π΄ΠΎΡΡΠΎΠ²Π΅ΡΠ½ΠΎΡΡΠΈ Π΄Π»Ρ ΡΠ°Π·ΡΠ°Π±ΠΎΡΠΊΠΈ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΠ½ΡΡ
ΠΏΠΎΠ»Π΅ΠΉ ΠΏΠΎ ΠΏΠΎΠ²Π΅ΡΡ
Π½ΠΎΡΡΠΈ ΡΠ²Π°ΡΠΈΠ²Π°Π΅ΠΌΠΎΠ³ΠΎ ΠΈΠ·Π΄Π΅Π»ΠΈΡ ΠΈ Π΅Ρ Π²Π΅ΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ. ΠΠ»Π³ΠΎΡΠΈΡΠΌ ΡΠ΅Π°Π»ΠΈΠ·ΠΎΠ²Π°Π½ Π² Π²ΠΈΠ΄Π΅ ΡΠ°ΡΡΡΡΠ½ΡΡ
ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌ Π΄Π»Ρ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΠΊΠ°ΠΏΠ»ΠΈ ΡΠ°ΡΠΏΠ»Π°Π²Π»Π΅Π½Π½ΠΎΠ³ΠΎ ΠΌΠ΅ΡΠ°Π»Π»Π° ΠΈ ΡΡΠ΅Π΄ΡΡΠ² Π²ΠΈΠ·ΡΠ°Π»ΡΠ½ΠΎΠ³ΠΎ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½ΠΈΡ Π΅Ρ Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΠΈ ΠΈ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅Π½Π½ΠΎΠΉ ΡΠΎΡΠΌΡ. Π‘ ΠΏΠΎΠΌΠΎΡΡΡ Π΄Π°Π½Π½ΠΎΠ³ΠΎ ΠΌΠ΅ΡΠΎΠ΄Π° ΠΎΠΏΡΠ΅Π΄Π΅Π»ΡΠ½ ΡΡΠ΄ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΠΊΠ°ΠΏΠ΅Π»Ρ ΡΠ°ΡΠΏΠ»Π°Π²Π»Π΅Π½Π½ΠΎΠ³ΠΎ ΡΠ»Π΅ΠΊΡΡΠΎΠ΄Π½ΠΎΠ³ΠΎ ΠΌΠ΅ΡΠ°Π»Π»Π°: ΠΎΠ±ΡΡΠΌ, ΠΌΠ°ΡΡΠ°, ΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΠ΅ ΡΠ΅Π½ΡΡΠ° ΠΌΠ°ΡΡ, ΠΏΠ»ΠΎΡΠ°Π΄Ρ ΠΏΠΎΠ²Π΅ΡΡ
Π½ΠΎΡΡΠΈ.Π£ΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΎ, ΡΡΠΎ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎ Ρ ΠΌΠ°ΠΊΡΠΈΠΌΠ°Π»ΡΠ½ΠΎΠΉ Π΄ΠΎΡΡΠΎΠ²Π΅ΡΠ½ΠΎΡΡΡΡ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΠΈΡΡ ΠΈΠ·ΠΌΠ΅ΡΠ΅Π½ΠΈΡ, ΡΠ²Π΅Π»ΠΈΡΠΈΡΡ ΡΠΈΡΠ»ΠΎ ΠΈΠ·ΠΌΠ΅ΡΡΠ΅ΠΌΡΡ
ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ², Π° ΡΠ°ΠΊΠΆΠ΅ Π½Π°Π³Π»ΡΠ΄Π½ΠΎ ΠΏΡΠ΅Π΄ΡΡΠ°Π²ΠΈΡΡ ΠΏΡΠΎΠΈΡΡ
ΠΎΠ΄ΡΡΠΈΠ΅ ΠΏΡΠΎΡΠ΅ΡΡΡ.ΠΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π½ΡΠΉ ΠΌΠ΅ΡΠΎΠ΄ Π·Π½Π°ΡΠΈΡΠ΅Π»ΡΠ½ΠΎ ΡΠΏΡΠΎΡΠ°Π΅Ρ ΡΡΡΠ΄ΠΎΡΠΌΠΊΠΎΡΡΡ ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½ΠΈΡ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΡΡ
ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΉ ΠΏΠΎ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΡΠ°Π·ΠΌΠ΅ΡΠ° ΠΊΠ°ΠΏΠ΅Π»Ρ ΡΠ»Π΅ΠΊΡΡΠΎΠ΄Π½ΠΎΠ³ΠΎ ΠΌΠ΅ΡΠ°Π»Π»Π° Π² ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΈ ΡΠΎ ΡΡΠ°Π½Π΄Π°ΡΡΠ½ΡΠΌΠΈ ΠΌΠ΅ΡΠΎΠ΄Π°ΠΌΠΈ. ΠΠ½Π°Ρ ΡΠ°Π·ΠΌΠ΅Ρ ΠΊΠ°ΠΏΠ΅Π»Ρ ΠΏΡΠΈ ΠΎΠΏΡΠ΅Π΄Π΅Π»ΡΠ½Π½ΡΡ
ΡΠ΅ΠΆΠΈΠΌΠ°Ρ
ΡΠ²Π°ΡΠΊΠΈ, ΠΌΠΎΠΆΠ½ΠΎ ΡΠΏΡΠ°Π²Π»ΡΡΡ ΠΏΡΠΎΡΠ΅ΡΡΠΎΠΌ ΠΊΠ°ΠΏΠ»Π΅ΠΏΠ΅ΡΠ΅Π½ΠΎΡΠ°, Ρ. Π΅. ΡΠΌΠ΅Π½ΡΡΠ°ΡΡ ΡΠ΅ΠΏΠ»ΠΎΠ²Π»ΠΎΠΆΠ΅Π½ΠΈΠ΅ Π² ΡΠ²Π°ΡΠΈΠ²Π°Π΅ΠΌΠΎΠ΅ ΠΈΠ·Π΄Π΅Π»ΠΈΠ΅ ΠΈ ΠΏΠΎΠ»ΡΡΠ°ΡΡ ΡΠ²Π°ΡΠ½ΡΠ΅ ΡΠΎΠ΅Π΄ΠΈΠ½Π΅Π½ΠΈΡ Ρ Π·Π°Π΄Π°Π½Π½ΡΠΌΠΈ ΡΠΊΡΠΏΠ»ΡΠ°ΡΠ°ΡΠΈΠΎΠ½Π½ΡΠΌΠΈ ΡΠ²ΠΎΠΉΡΡΠ²Π°ΠΌΠΈ
Π Π°Π·ΡΠ°Π±ΠΎΡΠΊΠ° ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΈ ΠΈΡΠΏΠΎΠ»Π½ΠΈΡΠ΅Π»ΡΠ½ΠΎΠ³ΠΎ ΠΎΠ±ΠΎΡΡΠ΄ΠΎΠ²Π°Π½ΠΈΡ, ΡΠ΅Π°Π»ΠΈΠ·ΡΡΡΠ΅Π³ΠΎ ΠΏΡΠΎΡΠ΅ΡΡ Π³Π΅Π½Π΅ΡΠ°ΡΠΈΠΈ ΠΊΠ°ΠΏΠ΅Π»Ρ ΠΌΠΈΠΊΡΠΎ- ΠΈ Π½Π°Π½ΠΎΠ΄ΠΈΠ°ΠΏΠ°Π·ΠΎΠ½Π°
Modeling of velocities and temperatures processes distribution in the plasma-forming channel determining the design features and optimal parameters of the plasma torch nozzle is one of promising directions in development of plasma technologies. The aim of this work was to simulate the processes of velocities and temperature distribution in the plasma-forming channel and to determine the design features and optimal geometric parameters of the plasmatron nozzle Β which Β ensures Β the Β formation Β of Β necessary Β direction Β of Β plasma Β flows for generation of surface waves on the surface of a liquid metal droplet under the influence of the investigated instabilities.One of the main tasks is to consider the process of plasma jet formation and the flow of electric arc plasma. For obtaining small-sized particles one of the main parameters is the plasma flow Β velocity. Β It Β is necessary that the plasma outflow velocity be close to supersonic. An increase of Β the Β supersonic Β speed Β is possible due to design of the plasmatron nozzle especially the design feature and dimensions of the gas channel in which the plasma is formed. Also the modeling took into account dimensions of the plasma torch nozzle, i. e. the device should provide a supersonic plasma flow with the smallest possible geometric dimensions.As a result models of velocities and temperatures distribution in the plasma-forming channel at the minimum and maximum diameters of the channel were obtained. The design features and optimal geometric parameters of the plasmatron have been determined: the inlet diameter is 3 mm, the outlet diameter is 2 mm.The design of the executive equipment has been developed and designed which implements the investigated process of generating droplets of the micro- and nanoscale range. A plasmatron nozzle was manufactured which forms the necessary directions of plasma flows for the formation of surface waves on the metal droplet surface under the influence of instabilities. An algorithm has been developed for controlling of executive equipment that implements the process of generating drops of micro- and nanoscale range.ΠΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΠΏΡΠΎΡΠ΅ΡΡΠΎΠ² ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΡΠΊΠΎΡΠΎΡΡΠ΅ΠΉ ΠΈ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡ Π² ΠΏΠ»Π°Π·ΠΌΠΎΠΎΠ±ΡΠ°Π·ΡΡΡΠ΅ΠΌ ΠΊΠ°Π½Π°Π»Π΅, ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠ΅ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠ²Π½ΡΡ
ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎΡΡΠ΅ΠΉ ΠΈ ΠΎΠΏΡΠΈΠΌΠ°Π»ΡΠ½ΡΡ
ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΡΠΎΠΏΠ»Π° ΠΏΠ»Π°Π·ΠΌΠΎΡΡΠΎΠ½Π° ΡΠ²Π»ΡΠ΅ΡΡΡ ΠΎΠ΄Π½ΠΈΠΌ ΠΈΠ· ΠΏΠ΅ΡΡΠΏΠ΅ΠΊΡΠΈΠ²Π½ΡΡ
Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½ΠΈΠΉ Π² ΡΠ°Π·Π²ΠΈΡΠΈΠΈ ΠΏΠ»Π°Π·ΠΌΠ΅Π½Π½ΡΡ
ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΠΈΠΉ. Π¦Π΅Π»ΡΡ Π΄Π°Π½Π½ΠΎΠΉ ΡΠ°Π±ΠΎΡΡ ΡΠ²Π»ΡΠ»ΠΎΡΡ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΠΏΡΠΎΡΠ΅ΡΡΠΎΠ² ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΡΠΊΠΎΡΠΎΡΡΠ΅ΠΉ ΠΈ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡ Π² ΠΏΠ»Π°Π·ΠΌΠΎΠΎΠ±ΡΠ°Π·ΡΡΡΠ΅ΠΌ ΠΊΠ°Π½Π°Π»Π΅ ΠΈ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠ΅ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠ²Π½ΡΡ
ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎΡΡΠ΅ΠΉ ΠΈ ΠΎΠΏΡΠΈΠΌΠ°Π»ΡΠ½ΡΡ
Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΡΠΎΠΏΠ»Π° ΠΏΠ»Π°Π·ΠΌΠΎΡΡΠΎΠ½Π°, ΠΊΠΎΡΠΎΡΠΎΠ΅ Π΄ΠΎΠ»ΠΆΠ½ΠΎ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠΈΠ²Π°ΡΡ ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΡΡ
Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½ΠΈΠΉ ΠΏΠ»Π°Π·ΠΌΠ΅Π½Π½ΡΡ
ΠΏΠΎΡΠΎΠΊΠΎΠ² Π΄Π»Ρ ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡ Π½Π° ΠΏΠΎΠ²Π΅ΡΡ
Π½ΠΎΡΡΠΈ ΠΊΠ°ΠΏΠ»ΠΈ ΠΆΠΈΠ΄ΠΊΠΎΠ³ΠΎ ΠΌΠ΅ΡΠ°Π»Π»Π° ΠΏΠΎΠ²Π΅ΡΡ
Π½ΠΎΡΡΠ½ΡΡ
Π²ΠΎΠ»Π½ ΠΏΠΎΠ΄ Π΄Π΅ΠΉΡΡΠ²ΠΈΠ΅ΠΌ ΠΈΡΡΠ»Π΅Π΄ΡΠ΅ΠΌΡΡ
Π½Π΅ΡΡΡΠΎΠΉΡΠΈΠ²ΠΎΡΡΠ΅ΠΉ.ΠΠ΄Π½ΠΎΠΉ ΠΈΠ· Π³Π»Π°Π²Π½ΡΡ
Π·Π°Π΄Π°Ρ ΡΠ²Π»ΡΠ΅ΡΡΡ ΡΠ°ΡΡΠΌΠΎΡΡΠ΅Π½ΠΈΠ΅ ΠΏΡΠΎΡΠ΅ΡΡΠ° ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΏΠ»Π°Π·ΠΌΠ΅Π½Π½ΠΎΠΉ ΡΡΡΡΠΈ ΠΈ ΡΠ΅ΡΠ΅Π½ΠΈΡ ΡΠ»Π΅ΠΊΡΡΠΎΠ΄ΡΠ³ΠΎΠ²ΠΎΠΉ ΠΏΠ»Π°Π·ΠΌΡ. ΠΠ»Ρ ΠΏΠΎΠ»ΡΡΠ΅Π½ΠΈΡ ΠΌΠ΅Π»ΠΊΠΎΡΠ°Π·ΠΌΠ΅ΡΠ½ΡΡ
ΡΠ°ΡΡΠΈΡ ΠΎΠ΄Π½ΠΈΠΌ ΠΈΠ· Π³Π»Π°Π²Π½ΡΡ
ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΡΠ²Π»ΡΠ΅ΡΡΡ ΡΠΊΠΎΡΠΎΡΡΡ ΡΠ΅ΡΠ΅Π½ΠΈΡ ΠΏΠ»Π°Π·ΠΌΡ. ΠΠ΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΠΎ, ΡΡΠΎΠ±Ρ ΡΠΊΠΎΡΠΎΡΡΡ ΠΈΡΡΠ΅ΡΠ΅Π½ΠΈΡ ΠΏΠ»Π°Π·ΠΌΡ Π±ΡΠ»Π° Π±Π»ΠΈΠ·ΠΊΠ° ΠΊ ΡΠ²Π΅ΡΡ
Π·Π²ΡΠΊΠΎΠ²ΠΎΠΉ. Π£Π²Π΅Π»ΠΈΡΠ΅Π½ΠΈΠ΅ ΡΠΊΠΎΡΠΎΡΡΠΈ Π΄ΠΎ ΡΠ²Π΅ΡΡ
Π·Π²ΡΠΊΠΎΠ²ΠΎΠΉ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎ Π΄ΠΎΠ±ΠΈΡΡΡΡ Π·Π° ΡΡΡΡ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΈ ΡΠΎΠΏΠ»Π° ΠΏΠ»Π°Π·ΠΌΠΎΡΡΠΎΠ½Π°, Π° ΠΈΠΌΠ΅Π½Π½ΠΎ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠ²Π½ΠΎΠΉ ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎΡΡΡΡ ΠΈ ΡΠ°Π·ΠΌΠ΅ΡΠ°ΠΌΠΈ Π³Π°Π·ΠΎΠ²ΠΎΠ³ΠΎ ΠΊΠ°Π½Π°Π»Π°, Π² ΠΊΠΎΡΠΎΡΠΎΠΌ ΠΎΠ±ΡΠ°Π·ΡΠ΅ΡΡΡ ΠΏΠ»Π°Π·ΠΌΠ°. Π’Π°ΠΊΠΆΠ΅ ΠΏΡΠΈ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΠΈ ΡΡΠΈΡΡΠ²Π°Π»ΠΈΡΡ ΡΠ°Π·ΠΌΠ΅ΡΡ ΡΠΎΠΏΠ»Π° ΠΏΠ»Π°Π·ΠΌΠΎΡΡΠΎΠ½Π°, Ρ. Π΅. ΡΡΡΡΠΎΠΉΡΡΠ²ΠΎ Π΄ΠΎΠ»ΠΆΠ½ΠΎ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠΈΠ²Π°ΡΡ ΡΠ²Π΅ΡΡ
Π·Π²ΡΠΊΠΎΠ²ΠΎΠ΅ ΡΠ΅ΡΠ΅Π½ΠΈΠ΅ ΠΏΠ»Π°Π·ΠΌΡ ΠΏΡΠΈ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎ ΠΌΠ΅Π½ΡΡΠΈΡ
Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠ°Π·ΠΌΠ΅ΡΠ°Ρ
.Π ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΉ ΠΏΠΎΠ»ΡΡΠ΅Π½Ρ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΏΡΠΎΡΠ΅ΡΡΠΎΠ² ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΡΠΊΠΎΡΠΎΡΡΠ΅ΠΉ ΠΈ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡ Π² ΠΏΠ»Π°Π·ΠΌΠΎΠΎΠ±ΡΠ°Π·ΡΡΡΠ΅ΠΌ ΠΊΠ°Π½Π°Π»Π΅ ΠΏΡΠΈ ΠΌΠΈΠ½ΠΈΠΌΠ°Π»ΡΠ½ΡΡ
ΠΈ ΠΌΠ°ΠΊΡΠΈΠΌΠ°Π»ΡΠ½ΡΡ
Π΄ΠΈΠ°ΠΌΠ΅ΡΡΠ°Ρ
ΠΊΠ°Π½Π°Π»Π°. ΠΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Ρ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠ²Π½ΡΠ΅ ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎΡΡΠΈ ΠΈ ΠΎΠΏΡΠΈΠΌΠ°Π»ΡΠ½ΡΠ΅ Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΡ ΡΠΎΠΏΠ»Π° ΠΏΠ»Π°Π·ΠΌΠΎΡΡΠΎΠ½Π°: Π΄ΠΈΠ°ΠΌΠ΅ΡΡ Π½Π° Π²Ρ
ΠΎΠ΄Π΅ 3 ΠΌΠΌ, Π΄ΠΈΠ°ΠΌΠ΅ΡΡ Π²ΡΡ
ΠΎΠ΄Π½ΠΎΠΉ 2 ΠΌΠΌ.Π Π°Π·ΡΠ°Π±ΠΎΡΠ°Π½Π° ΠΈ ΡΠΏΡΠΎΠ΅ΠΊΡΠΈΡΠΎΠ²Π°Π½Π° ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΡ ΠΈΡΠΏΠΎΠ»Π½ΠΈΡΠ΅Π»ΡΠ½ΠΎΠ³ΠΎ ΠΎΠ±ΠΎΡΡΠ΄ΠΎΠ²Π°Π½ΠΈΡ, ΡΠ΅Π°Π»ΠΈΠ·ΡΡΡΠ°Ρ ΠΈΡΡΠ»Π΅Π΄ΡΠ΅ΠΌΡΠΉ ΠΏΡΠΎΡΠ΅ΡΡ Π³Π΅Π½Π΅ΡΠ°ΡΠΈΠΈ ΠΊΠ°ΠΏΠ΅Π»Ρ ΠΌΠΈΠΊΡΠΎ- ΠΈ Π½Π°Π½ΠΎΡΠ°Π·ΠΌΠ΅ΡΠ½ΠΎΠ³ΠΎ Π΄ΠΈΠ°ΠΏΠ°Π·ΠΎΠ½Π°. ΠΠ·Π³ΠΎΡΠΎΠ²Π»Π΅Π½ΠΎ ΡΠΎΠΏΠ»ΠΎ ΠΏΠ»Π°Π·ΠΌΠΎΡΡΠΎΠ½Π°, ΡΠΎΡΠΌΠΈΡΡΡΡΠ΅Π΅ Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΡΠ΅ Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ ΠΏΠ»Π°Π·ΠΌΠ΅Π½Π½ΡΡ
ΠΏΠΎΡΠΎΠΊΠΎΠ² Π΄Π»Ρ ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡ Π½Π° ΠΏΠΎΠ²Π΅ΡΡ
Π½ΠΎΡΡΠΈ ΠΊΠ°ΠΏΠ»ΠΈ ΠΆΠΈΠ΄ΠΊΠΎΠ³ΠΎ ΠΌΠ΅ΡΠ°Π»Π»Π° ΠΏΠΎΠ²Π΅ΡΡ
Π½ΠΎΡΡΠ½ΡΡ
Π²ΠΎΠ»Π½ ΠΏΠΎΠ΄ Π΄Π΅ΠΉΡΡΠ²ΠΈΠ΅ΠΌ ΠΈΡΡΠ»Π΅Π΄ΡΠ΅ΠΌΡΡ
Π½Π΅ΡΡΡΠΎΠΉΡΠΈΠ²ΠΎΡΡΠ΅ΠΉ. Π Π°Π·ΡΠ°Π±ΠΎΡΠ°Π½ Π°Π»Π³ΠΎΡΠΈΡΠΌ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ ΠΈΡΠΏΠΎΠ»Π½ΠΈΡΠ΅Π»ΡΠ½ΡΠΌ ΠΎΠ±ΠΎΡΡΠ΄ΠΎΠ²Π°Π½ΠΈΠ΅ΠΌ, ΡΠ΅Π°Π»ΠΈΠ·ΡΡΡΠ΅ΠΌ ΠΏΡΠΎΡΠ΅ΡΡ Π³Π΅Π½Π΅ΡΠ°ΡΠΈΠΈ ΠΊΠ°ΠΏΠ΅Π»Ρ ΠΌΠΈΠΊΡΠΎ- ΠΈ Π½Π°Π½ΠΎΡΠ°Π·ΠΌΠ΅ΡΠ½ΠΎΠ³ΠΎ Π΄ΠΈΠ°ΠΏΠ°Π·ΠΎΠ½Π°
Time-Fractional Optimal Control of Initial Value Problems on Time Scales
We investigate Optimal Control Problems (OCP) for fractional systems
involving fractional-time derivatives on time scales. The fractional-time
derivatives and integrals are considered, on time scales, in the
Riemann--Liouville sense. By using the Banach fixed point theorem, sufficient
conditions for existence and uniqueness of solution to initial value problems
described by fractional order differential equations on time scales are known.
Here we consider a fractional OCP with a performance index given as a
delta-integral function of both state and control variables, with time evolving
on an arbitrarily given time scale. Interpreting the Euler--Lagrange first
order optimality condition with an adjoint problem, defined by means of right
Riemann--Liouville fractional delta derivatives, we obtain an optimality system
for the considered fractional OCP. For that, we first prove new fractional
integration by parts formulas on time scales.Comment: This is a preprint of a paper accepted for publication as a book
chapter with Springer International Publishing AG. Submitted 23/Jan/2019;
revised 27-March-2019; accepted 12-April-2019. arXiv admin note: substantial
text overlap with arXiv:1508.0075
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