mathematical model

SIMULATION AND RESEARCH OF THE SEPARATION OF TWO TYPES OF SUSPENDED PARTICLES IN A DISPERSED MIXTURE UNDER THE INFLUENCE OF AN ACOUSTIC FIELD

A mathematical model of the process of separating suspended microparticles in a dispersed mixture within a 2-branched channel of a microfluidic lab-chip under the influence of an acoustic field has been developed. The model is implemented in the environment of COMSOL Multiphysics, using thermoviscous acoustics, creeping flow, particle tracking in a fluid flow, and fluid-particle interaction multiphysics interfaces.

RESEARCH OF VIBRATION OSCILLATIONS OF MEMS RESONATORS DURING THEIR OPERATION

 A mathematical model has been developed to study the amplitude-frequency characteristics of the resonator beam. Nonlinear mechanics methods were used in the modeling process. The model takes into account the influence of changes in the elastic properties of the beam material on its oscillation amplitude and frequency. To analyze the internal processes in the material, Voigt's and Bolotin's laws were applied.

Mathematical Model of Logistic Regression for Binary Classification. Part 2. Data Preparation, Learning and Testing Processes

This article reviews the theoretical aspects of logistic regression for binary data classification, including data preparation processes, training, testing, and model evaluation metrics.

Requirements for input data sets are formulated, methods of coding categorical data are described, methods of scaling input features are defined and substantiated.

Mathematical Model of Logistic Regression for Binary Classification. Part 1. Regression Models of Data Generalization

In this article, the mathematical justification of logistic regression as an effective and simple to implement method of machine learning is performed.

A review of literary sources was conducted in the direction of statistical processing, analysis and classification of data using the logistic regression method, which confirmed the popularity of this method in various subject areas.

Model and tools of the navigation system between educational institution buildings using augmented reality technology

A problem of navigation within large educational complexes has been identified, which poses a particular challenge for new students, visitors, and staff. It has been established that the implementation of augmented reality technologies considerably enhances the intuitiveness and usability of the navigation system. A comprehensive structural and mathematical model of the navigation system based on augmented reality technologies has been meticulously developed.

Investigation of Changes in Natural Gas Parameters along a Damaged Gas Pipeline

The paper presents a mathematical model of the stationary flow of natural gas in an inclined gas pipeline, which makes it possible to calculate the gas parameters (pressure, temperature, compressibility factor) in every cross-section of gas pipeline. An improved mathematical model is also proposed by the authors, which considers the change in the gas flowrate along the gas pipeline. Complex 1 characterizing the effect of frictional forces and pressure losses and Complex 2 determining the effect of flow velocity were proposed to confirm the need to use an improved mathematical model.

Stability of the medication distribution model in the body as an open system formed by subsystems

In the paper, the spread of medicine (toxin) in the body which is assumed to be an open system carrying out exchange with the environment is considered. The system itself is considered as a combination of two subsystems: blood and muscle. It is shown that the model can be unstable under some conditions and for a certain range of parameters. Solutions obtained with such parameter values do not correspond to the actual amount of the substance during intravenous injections.

USE OF MICROWAVE RADIATION FOR EFFECTIVE PURIFICATION OF WASTEWATER FROM ORGANIC COMPOUNDS

This article is devoted to the problem of using microwave radiation as a potentially effective method of cleaning wastewater from organic compounds. The problem of cleaning wastewater from organic contaminants in the food industry requires highly effective methods since protein compounds in wastewater can cause environmental hazards and complicate the cleaning process.

Multi-agent modeling of traffic organization in urban agglomerations

The authors consider the features of multi-agent modeling for traffic optimization in the central areas of cities. While evaluating the unique challenges associated with the high concentration of vehicles, pedestrians and historical buildings, the potential of multi-agent systems to effectively solve the problem of congestion, safety and quality of life in urban areas is investigated. The potential of multi-agent modeling in the context of traffic management in the central areas of the city allows us to identify the key challenges and opportunities.

MATHEMATICAL MODELS OF MEMS CONTROL DEVICES

This article discusses MEMS actuators of various types (electrostatic, magnetic, piezoelectric, thermal actuators). The features of their designs are considered. Methods for constructing mathematical models of these actuators and possibilities of their application in the design of complex technical systems using such actuators are analyzed. An example of calculating the characteristic of the inductance of a nano-solenoid, which is a component of an electromagnetic actuator, is provided.