Form Of Mathematical Formulas Research Articles

DISSOLUTION OF A POLYDISPERSE SYSTEM OF PARTICLES IN A NO-FLOW APPARATUS

The processes of dissolution and crystallization are mass transfer phenomena that have a number of complex physicochemical features, and which are very difficult to theoretically describe in various mathematical models. During the dissolution process, the crystals may undergo various changes, such as grinding, combining and crystal growth. As a result of the process of mass dissolution of crystals, different speeds of movement of individual faces can be observed, which can lead to their disappearance. These phenomena are the result of complex dynamics of the dissolution process, which includes inter-actions between solvent molecules and the crystal surface. In this work, the process of mass dissolution was studied using the crystal size distribution density function. The task was set to obtain an analytical solution of the equation. The main object of the study was the diffusion law of movement of the radius of spherical crystals during a periodic process. As part of this study, analytical solutions were obtained for some interesting practical cases related to the process of mass dissolution of spherical crystals and the density function of crystal size distribution. These solutions were described in the article in the form of mathematical formulas and supplemented with graphical data characterizing the main parameters of the process. The use of these analytical solutions can be useful for a more accurate description and improvement of the mass dissolution process itself. Optimizing this process will improve its efficiency, provide more precise control and efficient use of reagents.

Mutable Observation Used by Television Drone Pilots: Efficiency of Aerial Filming Regarding the Quality of Completed Shots

Drones, as mobile media of the present day, increase the operational and narrative capabilities of television and accelerate the logistics of shooting. Unmanned aerial vehicles with a camera properly steered by a pilot are able, to some extent, to replace a jimmy jib/crane and a dolly; basic technical devices, used in the studios, enabling the creation of narrative systems of pictures in film and television. Television is more and more often using drone footage to report events, broadcast live, as well as create coverage and television documentaries. In many productions, the pilot of the drone simultaneously acts as the drone camera operator, which can improve the effectiveness of shooting, but also carries some risks related to flight safety. The article describes and presents in the form of processed footage the real conditional ties of a Visual Line of Sight (VLOS) flight faced by pilots filming with a drone. VLOS is a type of air operation, which requires maintaining eye contact with the drone. In many countries, a drone visibility flight is legally sanctioned as VLOS Operation. An experiment was conducted to investigate the interactions between a human and a machine in airspace steered using a controller with a touchscreen. The drone pilot was considered an integral part of the drone’s flight system control Experimental data was collected with the use of a mobile eye-tracker, video cameras, surveys, and pilot declarations. During the experiment, eight television drone pilot operators recaptured a model shot under the regime of VLOS flight at low altitudes. They all show that both advanced and beginner pilots did not look at the UAV for over half the time of shot execution. The experiment allowed establishing two coefficients related to the effectiveness of a VLOS flight aiming at filming from the drone. The results point to clear differences in screen perception styles used by drone television pilots. The coefficients were described in the form of mathematical formulas and their limit values were determined. The research also determines the limits of pilots’ perception, within which they can film with a drone. The outcomes may help to optimize the process of aerial filming with the use of a drone, carried out for television, film, and other media, as well as in a simulation of such a flight for research and training. From the perspective of media science and social communication, the presented study included a technological component that can be accessed through information science, using statistical models and variable distributions. Media scholars can study the impact of the media without having to look into the metaphorical black box. Computer science opens up this possibility.

Economic and mathematical models for forecasting the development of the space industry

The article examines a problem relevant to the national security of the state, the possibility of applying economic and mathematical models to predict the prospects for the development of the space industry. In modern conditions the, space industry is seen as the basis for innovative development and economic security of the state, which is the driving force of economic development.
 After all, in order to sustainably develop the economy and achieve the indicators planned by the government, it is necessary to have a clear idea of the mechanisms and function of the system as a whole and its individual parts.
 That is why competent forecasting of the main indicators of the development of the space industry with the identification of key factors influencing it is especially relevant at the present stage. Forecasting of indicators, based on the construction of economic and mathematical models of industry development.
 It is determined that the construction of this model begins with the development of a specification of the model, which includes a verbal description of the study, followed by a presentation of the process of its operation in the form of mathematical formulas. It is important to clearly formulate and define the problem, as well as to identify all the factors and patterns that characterize the functioning of the system. Economic and mathematical models can increase the efficiency of the planning system of the industry and increase the accuracy of the process of forecasting its development.
 The successful development of the space industry today becomes a necessary condition for preserving national sovereignty both in the military-political aspect and in the field of information security.

Selection of Output Voltage Compensators Gains in Two Cascaded Boost Converters with Input Filters by Means of the \({\mathfrak{D}}\)-Decomposition Technique

In this paper, the D-decomposition technique is investigated as an intuitive method for finding the non-linear trajectories of PI-compensator gains. The trajectories reflect the desired dynamic properties at a system level specified by the gain and the phase margin (GMPM) in the frequency domain. They are presented as parametric curves in the proportional and the integral gains coordinates in form of KI=f(KP) functions. The curves are inscribed into global stability boundaries (GSB). The corresponding Nyquist plots are included for comparison. The analysis is based on a system consisting of two serial-connected boost converters. Each converter has its input filter. The major parasitic components of the system are taken into account during the mathematical and simulation modelling. The control circuit time delays and non-linear semiconductors characteristics are also included. A complete set of practically useful system-level transfer functions in form of mathematical formulas is included. Selected aspects, such as the control-to-output voltage and the control-to-input current of one sub-system of the simulation model, have been verified experimentally. The presented results clearly indicate the need for interactions between the sub-systems of a system to be taken into account during controller gains selection.

Yates Algorithm to Analyze the Performance of MANET Routing Protocol

To test the performance of any routing protocol in Mobile Ad hoc Network (MANET), the re-searchers simulate their scenarios several times with different simulators to get either positive or negative results. This operation of the simulation can last many hours and sometimes several days depending on the performance either of the software or the hardware, and the number of factors used to analyze. In this paper, we propose a new method reckons on the Yates algorithm that are considered as a solution to evaluate the performance of any MANET routing protocols under the effect of any number of factors. This approach allows creating a simulation model in the form of mathematical formulas. To check the efficiency of our proposed method we chose Optimized Link State Routing Protocol (OLSR) as MANET routing protocol and the effect of four factors which are: The Black Hole attack, Worm Hole attack, Node Speed and the Pause Time.

Mathematical models in cardiology: From formulas to real clinical practice

Aim. To develop and implement into clinical practice six calculators of risk for various cardiovascular diseases in the form of mobile application for iOS/Android and module for the 1C: Medicine software.Material and Methods. At the premises of Tyumen Cardiology Research Center (TCRC) of Tomsk NRMC, we developed the mobile application for iOS/Android and module for the 1C: Medicine software based on six mathematical models that were invented and patented in our center earlier.Results and Discussion. The use of mobile application improved the convenience of working with the mathematical formulas and reduces the time for obtaining results of calculations. Implementation of 1C as a programming environment allowed to perform automatic filling out the calculator fields with medical data from individual patients, which significantly simplified and accelerated the rate of work with mathematical models.Conclusion. The developed mobile application and external processing for 1C allowed to implement research products of TCRC in the form of mathematical formulas into real-life clinical practice. These developments contributed to speeding up the process for acquisition of results and partial automatization of filling out the form fields.

Air quality indices: A review of methods to interpret air quality status

Urban air pollution is rapidly increasing in Indian cities. Different methods have been designed to calculate the air quality index in form of mathematical formula. Many studies have shown association between exposure of the population to air pollutants and its adverse health impact. But the formula designed by CPCB in 2014 is more robust to find out the air quality category. To provide the public, information for air pollution dangers, several governmental and municipal agencies developed air quality indices, as a timely information about the potential changes in air quality. In this paper review of air quality index shows how AQI constitutes as an effective method to estimate air pollution levels and risks and help the government in effective pollution control measures adopted for reduction of emissions from various sources.

Technological parameters for vehicles in the organization of cargo transportation in the agro-industrial complex

The result of the research conducted shows that cargo transportation is one of the components of successful activity and efficiency of the enterprise in the agro-industrial complex. The collected data have shown that economic efficiency is influenced by many process parameters. The data collected allowed to make a conclusion that. For the optimization of cargo transportation, the AIC needs careful choice of the number, type and brands of vehicles, taking into account the type of activity of the enterprise, its production volumes and range of cargo transportation. When collecting the data to choose the type and construction of motor vehicles with regard to the operating conditions it was found out that it is necessary to consider many parameters: the type of cargo, the nature and volume of transportation, the mode of operation of motor vehicles, organization of transportation, road and weather conditions. For this purpose, the following information was specified: necessary parameters of the cargo taking into account volume and weight, the choice diagram of the vehicle based on the properties of the cargo. The data received which were used for choosing are provided in tables and graphs. After choosing the type and the number of vehicles and determining the volume of transportation, one of the components of efficient use of vehicles is to optimize the transportation. Optimization of transportation is considered and provided in the form of mathematical formulas. Everything is presented as an example for one of the types of transportation. The issue studied and presented in this article is topical for the farms of the Mari El Republic in conditions of the market economy. That is why the data and calculations received are of practical application in the organization of cargo transportation in the agro-industrial complex enterprises and their optimization for maximum efficiency.

Evolving role of modeling and simulation in drug development.

Pharmacokinetic-pharmacodynamic model is a kind of language that quantitatively describes the drug-related outcomes in the form of mathematical formula. Various outcomes can be subjected to modeling analysis if they can be expressed in numbers. Empirical models have been widely and successfully applied in drug development and research. However, a more competitive drug development environment requires more accurate and predictive models in the early stages of drug development. Accordingly, the subjects of PK-PD modeling have been extended from clinical data to preclinical and in vitro data in the discovery stage. More mechanistic and predictive models, such as physiologically based pharmacokinetic and quantitative system-based pharmacology models, are being increasingly used owing to the growing need to characterize drugs more accurately at the earliest. This tutorial briefly introduces the essential concepts of PK-PD modeling and simulation and describes the recent changing roles of PK-PD model for application in novel drug development process.

Seasonal variation of air quality index and assessment.

Different methods have been designed to calculate the air quality index in form of mathematical formula. But the formula designed by Central Pollution Control Board in 2014 is more robust to find out the air quality category. The index has been calculated based upon four parameters like particulate matters (PM10, PM2.5), sulfur oxide and nitrogen oxide. The study area has affected by different sources like point, line and volume. Presence of different industries and mining activities polluting the natural environment of nearby areas more, although the industries taking mitigative measures proactively. In the present research, monitoring of ambient air quality has been carried out for a period from March 2013 to February 2016 for three years. It has been revealed from the study that the air quality status of the area has been declining from 2013 to 2016 i.e. 78.9 to 157.8 in summer, 49.4 to 84.3 in monsoon and 86.9 to 183.9 in winter season. It has also been found that, PM10 and PM2.5 were responsible for maximum sub-index as well as air quality index. During the study period 2015-16, out of the eight stations most comes under moderately polluted category especially in winter season followed by summer season. Statistical and Duncan’s multiple range test has been applied to the results with two-way and one-way analysis of variance based on different seasons and stations. In two-way analysis of variance, F-value was computed to be 30.105 based on seasons and stations and one-way analysis of variance test shows the F-values as 186.07 and 18.97 based on seasons and stations respectively which is found to be significant (P<0.01).The present research is important to assess the environmental quality of a mining- industrial complex area and can be a reference for similar study in other areas.

Theoretical Analysis of Velocity and Position Loop Behaviour of Nonlinear Cascade Feedforward Controller for Positioning of XY Table Ballscrew Drive System

The trend in machine tools and positioning systems nowadays are demanding for accuracy, precision and robustness attributes. In addition to those characteristics, a low-cost and adaptive control systems towards various disturbance forces also add a significant advantage to control engineers who can fulfill those needs. The objective of this paper is to introduce a newly improved control strategy named as Nonlinear Cascade Feedforward. It is basically, a cascade control structure with the additional of two add on modules called Nonlinear function plus independent feedforward function. Secondly, the aim of this article is to focus on the fundamental aspect on how to analyze the open loop and closed loop behavior for both velocity and position loop in the control structure by extracting the mathematical formulation of the controller. The outcome from this paper which is in the form of mathematical formula is beneficial and exceptionally significant during the validation and verification stage. The theoretical analysis involved are analysis on gain and phase margin, bandwidth frequency, sensitivity function, position error and finally analysis on dynamic stiffness of the system which is in this case the XY Table Ballscrew drive system. The strength of this controller is the self-adjusting mechanism towards variable disturbance cutting forces. Based on mathematical formulation, it is observed that the designed nonlinear cascade feedforward offer more flexibility and robustness in terms of the ability to compensate the tracking errors at variable disturbances.

Theoretical Analysis of Close Loop Behaviour of Ideal Cascade Controller Structure for Positioning of XY Table Ballscrew Drive System

The implementation of Classical Cascade Controller for the purpose of controlling various type of engineering appliances has been vastly utilized by control engineer community. Cascade controller provides a simple structure of controller but yet functional and have the ability to satisfy the control design requirement. In general, the controller consists of two loops, namely velocity loop and position loop. This paper is focused on the fundamental aspect on how to analyzed the close loop behaviour for both velocity and position loop and to extract the mathematical formulation of the controller. The outcome from this paper which is in the form of mathematical formula is useful and very significant in order to validate the theoretical result with the simulation result. To be more precise, the result from this research work are in the form of transfer function for both velocity and position loop of the position output, position error, dynamic stiffness of the controller and the damping ratio of the system which is in this case the XY Table Ballscrew drive system.

Handling Valuation Models

Valuation models are useful tools, but they need to be handled with care. When taking the form of mathematical formulas, they can easily be made to convey a false sense of precision. In particular, selective choice of long‐term growth rates and discount rates can be used to justify almost any desired valuation.The author shows how relatively simple valuation models can be applied by active investors in a way that honors the fundamentalist dictum of building valuations on the foundation of “what we know” and avoiding speculation about long‐term growth rates. The article also emphasizes the role of accounting in discovering what we know, and shows how to use accounting results in a way that not only minimizes speculation about growth rates and discount rates, but actually challenges the speculation about those rates that is implicit in current stock prices. Accounting‐based valuation models are “reverse‐engineered” to discover the forecasts of future operating performance that are effectively built into current prices, so the plausibility of such forecasts can be evaluated with fundamental analysis. In this sense, valuation models are used not so much to discover the “right” price as to identify, and then subject to critical examination, the market's current expectations about future performance.

The influence of radapertization upon some sensory properties of black pepper.

Radapertization may be used as an effective method for sterilization of spices. A possible influence of irradiation upon the sensoric qualities should be considered in this context. Therefore the objectives of the work were: --to determine the influence of the irradiation of pepper upon its sensoric quality --to determine the qualitative changes of volatile chemical substances under the influence of the irradiation of pepper --to determine correlation between changes resulting from irradiation and the sensoric quality of pepper. The spice was irradiated with doses of 10, 20, 40 and 60 kGy. Thresholds of recognition and difference were determined. It was established that the quantity of the dose is related to the values of thresholds mentioned above. The larger the dose was the less intensive the flavour became and the higher the thresholds. These interdependences were written in a form of mathematical formulas. A significant influence of irradiation upon the decrease of the quantity of essential oils and carbohydrates was noticed. These relations were also presented in a form of mathematical formulas. The work provides evidence for the fact that there is a relation between the results of sensoric assessments and the chemical characteristics (the content of volatile carbonyl, sulphuric and nitrogenic substances). Correlation between these factors was determined on the basic statistical analysis of the results obtained during our investigations.

Design theory and experiment for silicon computer diodes

The quantitative information available in the form of mathematical formulas and some of the considerations necessary in designing an alloyed silicon computer diode are analytically studied. The results of some preliminary work to develop a silicon computer diode are shown in the graphs. The prediction of the characteristics of a silicon computer diode from the mathematical expressions is discussed on the basis of the preliminary results.