scholarly journals PROBLEMS OF STABILITY OF LINEAR NON-STATIONARY SYSTEMS ON A FINITE TIME INTERVAL

2020 ◽  
Vol 71 (3) ◽  
pp. 52-58
Author(s):  
K.S. Dalbekova ◽  
◽  
F.R. Gusmanova ◽  
S.B. Berkimbaeva ◽  
A.K. Iskakova ◽  
...  
Keyword(s):  
Real Life ◽  
Physical Reality ◽  
Time Interval ◽  
Russian Scientist ◽  
Infinite Time Interval ◽  
Finite Period ◽  
Stability And Stabilization ◽  
The Stability ◽  
Research Function ◽  
The Mathematical Model

When studying various processes taking place in real life, we have to deal with one of the most important concepts - the concept of stability of movement. The foundations of the theory of stability of motion were developed at the end of the last century by the great Russian scientist A. M. Lyapunov. As is known, Lyapunov stability is considered on an infinite time interval, which is a serious obstacle for many applications, since most of the objects of research function for a finite period of time. The concept of stability, introduced for an unlimited period of time, cannot be used to evaluate the properties of motion within a finite period of time. The study of motion stability by analyzing solutions of the corresponding equations is permissible and makes sense only if the mathematical model of physical reality is fully adequate. The purpose of this work is to study the stability and stabilization of the motion of linear non-stationary systems.

scholarly journals To stay or not to stay: The stability of choice perseveration in value-based decision making

2020 ◽  
Vol 74 (1) ◽  
pp. 199-217
Author(s):  
Ulrike Senftleben ◽  
Martin Schoemann ◽  
Matthias Rudolf ◽  
Stefan Scherbaum
Keyword(s):  
Decision Making ◽  
Stimulus Onset Asynchrony ◽  
Real Life ◽  
Stimulus Onset ◽  
Time Interval ◽  
Decision Task ◽  
Cognitive Stability ◽  
Inter Trial Interval ◽  
The Stability ◽  
Onset Asynchrony

In real life, decisions are often naturally embedded in decision sequences. In contrast, in the laboratory, decisions are oftentimes analysed in isolation. Here, we investigated the influence of decision sequences in value-based decision making and whether the stability of such effects can be modulated. In our decision task, participants needed to collect rewards in a virtual two-dimensional world. We presented a series of two reward options that were either quick to collect but were smaller in value or took longer to collect but were larger in value. The subjective value of each option was driven by the options’ value and how quickly they could be reached. We manipulated the subjective values of the options so that one option became gradually less valuable over the course of a sequence, which allowed us to measure choice perseveration (i.e., how long participants stick to this option). In two experiments, we further manipulated the time interval between two trials (inter-trial interval), and the time delay between the onsets of both reward options (stimulus onset asynchrony). We predicted how these manipulations would affect choice perseveration using a computational attractor model. Our results indicate that both the inter-trial interval and the stimulus onset asynchrony modulate choice perseveration as predicted by the model. We discuss how our findings extend to research on cognitive stability and flexibility.

scholarly journals TO THE QUESTION OF LEGAL CONDITIONS PLACE IN THE SYSTEM OF LEGAL FACTS

2020 ◽  
Vol 24 (1) ◽  
pp. 25-45
Author(s):  
Elena Yu. Tsukanova
Keyword(s):  
Social Relations ◽  
Legal Status ◽  
Real Life ◽  
Social Situation ◽  
Research Process ◽  
Physical Reality ◽  
Specific Situation ◽  
Functional Relationships ◽  
Long Time ◽  
The Stability

The article is devoted to the problems of the formation and positioning of the legal status category in legal science. The relevance of this phenomenon in law is due to the lack of its unambiguous perception, which does not allow to fully determine its place and purpose in the theory of legal facts. The purpose of this article is to determine the philosophical and dialectical basis for the inclusion of this concept in the scientific categorical apparatus of jurisprudence. This will allow with sufficient certainty to identify its main characteristics, place in the classification of legal facts, as well as functional relationships with other elements of the legal-factual system. The methodological basis of the article was made by modern achievements of the theory of knowledge. In the research process, theoretical, general philosophical (dialectic, analysis, synthesis, deduction, systemic method,), as well as traditional legal methods (formal-logical, normative-dogmatic and others) were used. In the process of research, based on the ratio of the dialectic categories of movement and rest, the conclusion was formulated that physical reality is a series of static and dynamic situations. Static circumstances characterizing the stability and sustainability of a phenomenon or object are states. The variability of social relations is due to dynamic circumstances, which serve as the basis for a change of state. This approach allowed us to formulate the conclusion that states are natural elements of physical being. They can be qualified as real life circumstances and, provided that the rule of law associates a certain legal consequence with them, they should be recognized as legal facts. An analysis of the place of the state in the system of legal facts allowed us to conclude that the length of time cannot be considered as qualifying it. States are characterized by length in time, and it is precisely the “fluidity” of the phenomenon that matters for a specific situation. When a certain process takes a long time, but as applied to the social situation, it matters as a single whole, then it should be considered as an instantaneous fact.

scholarly journals Problems of Optimal Control for a Class of Linear and Nonlinear Systems of the Economic Model of a Cluster

2020 ◽  
Vol 07 (02) ◽  
pp. 109-127
Author(s):  
Zainelkhriet Murzabekov ◽  
Marek Milosz ◽  
Kamshat Tussupova ◽  
Gulbanu Mirzakhmedova
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Control Object ◽  
Quadratic Functional ◽  
Time Interval ◽  
Infinite Time ◽  
Optimal Stabilization ◽  
Infinite Time Interval ◽  
The Mathematical Model ◽  
Linear And Nonlinear Systems

For the mathematical model of a three-sector economic cluster, the problem of optimal control with fixed ends of trajectories is considered. An algorithm for solving the optimal control problem for a system with a quadratic functional is proposed. Control is defined on the basis of the principle of feedback. The problem is solved using the Lagrange multipliers of a special form, which makes it possible to find a synthesizing control. The problem of optimal stabilization for a class of nonlinear systems with coefficients that depend on the state of the control object is considered. The results obtained for nonlinear systems are used in the construction of control parameters for a three-sector economic cluster on an infinite time interval.

Statistical Management of Food Production Processes

2020 ◽  
pp. 30-35
Author(s):  
N.A. Jurk ◽  
Keyword(s):  
Production Process ◽  
Control Chart ◽  
Food Production ◽  
Time Interval ◽  
Bakery Products ◽  
Shewhart Control ◽  
Manufactured Products ◽  
Mnemonic Technique ◽  
The Stability

The article presents scientific research in the field of statistical controllability of the food production process using the example of bakery products for a certain time interval using statistical methods of quality management. During quality control of finished products, defects in bakery products were identified, while the initial data were recorded in the developed form of a checklist for registering defects. It has been established that the most common defect is packaging leakage. For the subsequent statistical assessment of the stability of the production process and further analysis of the causes of the identified defect, a Shewhart control chart (p-card by an alternative feature) was used, which allows you to control the quality of manufactured products by the number of defects detected. Analyzing the control chart, it was concluded that studied process is conditionally stable, and the emerging defects are random. At the last stage of the research, the Ishikawa causal diagram was used, developed using the 6M mnemonic technique, in order to identify the most significant causes that affect the occurrence of the considered defect in bakery products. A more detailed study will allow the enterprise to produce food products that meet the established requirements.

scholarly journals On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

scholarly journals Sliding Mode Control and Geometrization Conjecture in Seismic Response

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 353
Author(s):  
Ligia Munteanu ◽  
Dan Dumitriu ◽  
Cornel Brisan ◽  
Mircea Bara ◽  
Veturia Chiroiu ◽  
...  
Keyword(s):  
Sliding Mode Control ◽  
Ricci Flow ◽  
Lyapunov Functions ◽  
Seismic Waves ◽  
Sliding Mode ◽  
Flow Process ◽  
Mode Control ◽  
Finite Period ◽  
The Stability ◽  
Story Building

The purpose of this paper is to study the sliding mode control as a Ricci flow process in the context of a three-story building structure subjected to seismic waves. The stability conditions result from two Lyapunov functions, the first associated with slipping in a finite period of time and the second with convergence of trajectories to the desired state. Simulation results show that the Ricci flow control leads to minimization of the displacements of the floors.

scholarly journals Research on feeder network design: a case study of feeder service for the port of Kotka

2020 ◽  
Vol 12 (1) ◽  
Author(s):  
Yisong Lin ◽  
Xuefeng Wang ◽  
Hao Hu ◽  
Hui Zhao
Keyword(s):  
Control System ◽  
Numerical Experiment ◽  
Network Design ◽  
Evaluation System ◽  
Real Life ◽  
Objective Evaluation ◽  
Multi Objective Optimization ◽  
Real Life Data ◽  
The Mathematical Model

Abstract By exemplifying the feeder service for the port of Kotka, this study proposed a multi-objective optimization model for feeder network design. Innovative for difference from the single-objective evaluation system, the objective of feeder network design was proposed to include single allocation cost, intra-Europe cargo revenue, equipment balance, sailing cycle, allocation utilization, service route competitiveness, and stability. A three-stage control system was presented, and numerical experiment based on container liner’s real life data was conducted to verify the mathematical model and the control system. The numerical experiment revealed that the three-stage control system is effective and practical, and the research ideas had been applicable with satisfactory effect.

scholarly journals A Pot-Like Vibrational Microfluidic Rotational Motor

Micromachines ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 177
Author(s):  
Suzana Uran ◽  
Matjaž Malok ◽  
Božidar Bratina ◽  
Riko Šafarič
Keyword(s):  
Mathematical Model ◽  
Rotational Speed ◽  
Mechanical Energy ◽  
Real Life ◽  
Frequency Region ◽  
Theoretical Research ◽  
Practical Challenge ◽  
The Mathematical Model ◽  
Motor Structure ◽  
Proper Balance

Constructing a micro-sized microfluidic motor always involves the problem of how to transfer the mechanical energy out of the motor. The paper presents several experiments with pot-like microfluidic rotational motor structures driven by two perpendicular sine and cosine vibrations with amplitudes around 10 μm in the frequency region from 200 Hz to 500 Hz. The extensive theoretical research based on the mathematical model of the liquid streaming in a pot-like structure was the base for the successful real-life laboratory application of a microfluidic rotational motor. The final microfluidic motor structure allowed transferring the rotational mechanical energy out of the motor with a central axis. The main practical challenge of the research was to find the proper balance between the torque, due to friction in the bearings and the motor’s maximal torque. The presented motor, with sizes 1 mm by 0.6 mm, reached the maximal rotational speed in both directions between −15 rad/s to +14 rad/s, with the estimated maximal torque of 0.1 pNm. The measured frequency characteristics of vibration amplitudes and phase angle between the directions of both vibrational amplitudes and rotational speed of the motor rotor against frequency of vibrations, allowed us to understand how to build the pot-like microfluidic rotational motor.

scholarly journals Pre-Drawn Syringes of Comirnaty for an Efficient COVID-19 Mass Vaccination: Demonstration of Stability

Pharmaceutics ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1029
Author(s):  
Francesca Selmin ◽  
Umberto M. Musazzi ◽  
Silvia Franzè ◽  
Edoardo Scarpa ◽  
Loris Rizzello ◽  
...  
Keyword(s):  
Mechanical Stress ◽  
Real Life ◽  
Storage Conditions ◽  
Lipid Nanoparticles ◽  
Mass Vaccination ◽  
Hydrodynamic Diameter ◽  
The Us ◽  
Real Mass ◽  
The Stability ◽  
And Storage

Moving towards a real mass vaccination in the context of COVID-19, healthcare professionals are required to face some criticisms due to limited data on the stability of a mRNA-based vaccine (Pfizer-BioNTech COVID-19 Vaccine in the US or Comirnaty in EU) as a dose in a 1 mL-syringe. The stability of the lipid nanoparticles and the encapsulated mRNA was evaluated in a “real-life” scenario. Specifically, we investigated the effects of different storing materials (e.g., syringes vs. glass vials), as well as of temperature and mechanical stress on nucleic acid integrity, number, and particle size distribution of lipid nanoparticles. After 5 h in the syringe, lipid nanoparticles maintained the regular round shape, and the hydrodynamic diameter ranged between 80 and 100 nm with a relatively narrow polydispersity (<0.2). Samples were stable independently of syringe materials and storage conditions. Only strong mechanical stress (e.g., shaking) caused massive aggregation of lipid nanoparticles and mRNA degradation. These proof-of-concept experiments support the hypothesis that vaccine doses can be safely prepared in a dedicated area using an aseptic technique and transferred without affecting their stability.

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