# Mathematical Modeling - Springer Nature

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###### Last Updated: 19 September 2022

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##### Mathematical Modeling of Air Distribution in a Non-stationary Mode by Swirled-Compact Air Jets

In a non-stationary mode, the mathematical model of air supply with swirled-compact air jets has been updated. The room's dynamic parameters have been determined, as well as the establishment of a dynamic indoor climate. The dynamic evolution of the velocity plot is established by the method of intricate 4D numerical simulation of air velocities in the room as a function of time and coordinates at the same time.

##### Mathematical Modeling for Evaluation Reliability of a Bleaching System

The subsystem A contains only one unit, while subsystem B and C have two identical units that are connected in parallel configuration with each other. Working, partially working, and failure are all examples of states that can be described in the assumed bleaching framework, i. e. , working, partially working, and failing. By means of a new variable approach and the Markov process, the designed framework's mathematical model is solved. A Laplace transform of many differential equations is obtained. Several reliability parameters, including reliability, availability, mean time to failure, and estimated cost are also evaluated, as shown by a graph of the chosen system.

##### Mathematical Modeling as a Tool for Selecting a Rational Logistical Route in Multimodal Transport Systems

The paper seeks to perform mathematical simulation of the products delivery process from China to Ukraine, utilizing existing company alternatives and the benefits of new routes that use various modes of transportation. Based on parameter analysis of orders flow for trade enterprises in Kharkiv, cargo transportation volume in the current batch, risk assessment factor using similar methods of transport, and product delivery time for each option, it has been discovered that the order delivery times for each option has decreased.

##### Mathematical Modeling: A Conceptual Approach of Linear Algebra as a Tool for Technological Applications

Mathematical modeling is the branch of applied mathematics in charge of mathematically modeling problems, conditions, and phenomena of the world where we live. These models are a set of equations that describe the behavior of these phenomena, such as equations that describe planet movement and the behavior of atoms and charged particles, economic models of industry sectors, or how to manage a eucalyptus forest more sustainably and profitably, among others. The equations can be of physical description, such as the equations that characterize the movement of planets and the behavior of atoms and charged particles, socioeconomic factors, such as physical appearance.

##### Mathematical Modeling of an Air Flow Leakage with the Jets Interaction at the Variable Mode

The article is dedicated to the determination of the true task of air distribution effectiveness, which has increased with the use of flat air jets to create standardized air in the production apartments. The mathematical representation of air delivery with the presence of air jets in the premises is enhanced. The results of experimental investigations into air flow in the room by air distribution system with integration of flat air jets for more effective turbulence air flow in the room are presented.

##### Mathematical Model Identification of Self-Excited Systems Using Experimental Bifurcation Analysis Data

Compared to linear methods, the detection of such non-linear dynamical framework from data is more challenging. In this article, we propose two new mathematical model identification techniques for self-excited systems that use experimental bifurcation analysis results. The first method uses an empirical graphical system whose coefficients are determined to match the measured bifurcation diagram. The second approach considers a basic Hopf normal form model and learns a data-driven coordinate transformation mapping the normal form state-space to physical coordinates.

##### Mathematical Modelling of Integer Order PID and FOPID Controller for DC-DC Boost Converter

The comprehensive mathematical specifications are used to create integer order PID as well as fractional order PID under characteristic control legislation. In this paper, the method for computing the design requirements of integer order PID and FOPID controller is explained. For FOPID, a discretized control algorithm based on a finite approximation algorithm is also discussed, as well as conditions surrounding conditions inherent in control law characterization. The results show that the resulting controller can be superior to a standard integer order PID-type controller. PID-type controllers are also characterized by the results.

##### Mathematical Model for Determining Kinematic Parameters of a Bulldozer Ripper Mechanism

The engineering process is the primary step in creating any machine or system. determining the mechanism's kinematic parameters is a critical engineering problem during the development and design of any device that allows to determine its kinematic parameters. Of all available kinematic analysis software packages, the graphic, semigraphical, and analytical approaches are the most popular, since mathematical equations interlinking the basic kinematic and geometrical device parameters enable us to develop a computer for automating computations, where any accuracy of calculations can be adjusted. The paper provides step by step by using the kinematic analysis approach, a mathematical model for determining the kinematic parameters of a bulldozer ripper mechanism used in opencast mining, and steps by step.