scholarly journals Performance of arithmetical operations on mobile gadgets using axioms of classical and nonstandard interval analysis

2021 ◽  
Vol 5 (3) ◽  
pp. 128-136
Author(s):  
Valeriy Dubnitskiy ◽  
Anatolii Kobylin ◽  
Oleg Kobylin
Keyword(s):  
Interval Analysis ◽  
Interval Arithmetic ◽  
Programming System ◽  
Interval Mathematics ◽  
Touch Input ◽  
Banking Activity ◽  
Business Negotiations ◽  
Efficiency Comparison ◽  
Comparison Of The Results ◽  
Relative Change

We propose a programming system for calculation of economical standards of regulating banking activity by means of Euclidian and interval arithmetic using mobile gadgets. The program was created by means of Microsoft Visual Studio 2017 Express for Windows Phone using C#.  The feature of this programming system is the possibility to be used anywhere: during business negotiations, in the absence of PCs and WiFi, etc. For its application, one needs a smartphone with Android operation system. The smartphone needs to have a capacitive screen with multi-touch input with the possibility of more than four touches at once. The size of the screen can vary, but the resolution must be 480*480 pixels. During the progress, the system calculates the indicators of banking activity approved by National bank of Ukraine. Using of the interval arithmetic gives the possibility to analyse the financial status of the bank under any conditions. The comparison of the results of arithmetical operations by using the axioms of classical and nonstandard interval analysis was carried out. The criterion of the efficiency is the value of the relative change of the final interval of the calculations that were carried out using the axioms of the nonstandard interval analysis related to the same calculations that were carried out using the axioms of the classical interval analysis. For efficiency comparison we choose standard indicators that define the financial safety of the bank. The results of the calculations show that the intervals defined according to the rules of the nonstandard interval mathematics have the size of the interval 12-90% less than the intervals calculated according to the rules of the classical interval mathematics.

scholarly journals Interval arithmetic in calculations

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Gaziza Bairbekova ◽  
Talgat Mazakov ◽  
Sholpan Djomartova ◽  
Salima Nugmanova
Keyword(s):  
Interval Analysis ◽  
Interval Arithmetic ◽  
Mathematical Structure ◽  
Rounding Errors ◽  
Math Model ◽  
Interval Mathematics ◽  
Integral Analysis ◽  
Data Objects ◽  
Definition Of ◽  
The Given

Abstract Interval arithmetic is the mathematical structure, which for real intervals defines operations analogous to ordinary arithmetic ones. This field of mathematics is also called interval analysis or interval calculations. The given math model is convenient for investigating various applied objects: the quantities, the approximate values of which are known; the quantities obtained during calculations, the values of which are not exact because of rounding errors; random quantities. As a whole, the idea of interval calculations is the use of intervals as basic data objects. In this paper, we considered the definition of interval mathematics, investigated its properties, proved a theorem, and showed the efficiency of the new interval arithmetic. Besides, we briefly reviewed the works devoted to interval analysis and observed basic tendencies of development of integral analysis and interval calculations.

scholarly journals The Efficiency Comparison of Hydro Turbines for Micro Power Plant from Free Vortex

Energies ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 7961
Author(s):  
Piyawat Sritram ◽  
Ratchaphon Suntivarakorn
Keyword(s):  
Power Plant ◽  
Key Factors ◽  
Generator System ◽  
Free Vortex ◽  
Water Head ◽  
Micro Power ◽  
Pond Size ◽  
Overall Efficiency ◽  
Efficiency Comparison ◽  
Comparison Of The Results

In this research paper, the relationship between a crossflow turbine and propeller turbine size changes and the pond size in a free vortex power generation system was investigated. This relationship can be written in the form of a new mathematical equation using the principles of the response surface methodology (RSM) method. This study aimed to compare the efficiency of a crossflow turbine and propeller turbine to enhance a micro power plant from free vortex. The pond size in a micro power plant from free vortex was 1 m in diameter and 0.5 m in height with a 0.2 m outlet drain at the bottom. All turbines were tested at different water flowrates of 0.2, 0.3, 0.4, 0.5, and 0.6 m3/s to identify the rpm, water head, voltage, and electric current to access the waterpower, power output, and overall efficiency. At a 0.02 m3/s water flowrate, the crossflow turbine had greater overall efficiency than the propeller turbine, reaching 9.09% efficiency. From the comparison of the results of the two turbines used in the 0.5 m high cylinder-shaped generator pond, the turbine type, turbine size (height and diameter), number of blades, and water flowrate are key factors that affect the overall efficiency. The crossflow turbine can achieve greater efficiency than the propeller turbine in this generator system.

Evaluation of computational algorithms for the Associated Legendre Polynomials by interval analysis

1971 ◽  
Vol 61 (2) ◽  
pp. 375-381
Author(s):  
Ralph A. Wiggins ◽  
Masanori Saito
Keyword(s):  
Recurrence Relation ◽  
Interval Analysis ◽  
Legendre Polynomial ◽  
Interval Arithmetic ◽  
Legendre Polynomials ◽  
Computational Scheme ◽  
Computational Algorithms ◽  
Good Estimator ◽  
Arithmetic Scheme ◽  
Significant Figures

abstract An interval arithmetic that consists of tracing the number of significant figures during each calculation is applied to computational algorithms for the Associated Legendre Polynomial, Pnm(cos ϑ). The results indicate that the interval arithmetic scheme is a good estimator for the propagation of round-off errors and that one particular algorithm [a recurrence relation that relates Pnm (cos ϑ) to Pnn(cos ϑ)] is by far the superior computational scheme.

scholarly journals Interval Arithmetic for Nonlinear Problem Solving

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Benito A. Stradi-Granados
Keyword(s):  
Hydrogen Sulfide ◽  
Problem Solving ◽  
Nonlinear Problem ◽  
Critical Points ◽  
Interval Arithmetic ◽  
Specific Volume ◽  
Nonlinear Problems ◽  
Interval Mathematics ◽  
Computing Platform

Implementation of interval arithmetic in complex problems has been hampered by the tedious programming exercise needed to develop a particular implementation. In order to improve productivity, the use of interval mathematics is demonstrated using the computing platform INTLAB that allows for the development of interval-arithmetic-based programs more efficiently than with previous interval-arithmetic libraries. An interval-Newton Generalized-Bisection (IN/GB) method is developed in this platform and applied to determine the solutions of selected nonlinear problems. Cases 1 and 2 demonstrate the effectiveness of the implementation applied to traditional polynomial problems. Case 3 demonstrates the robustness of the implementation in the case of multiple specific volume solutions. Case 4 exemplifies the robustness and effectiveness of the implementation in the determination of multiple critical points for a mixture of methane and hydrogen sulfide. The examples demonstrate the effectiveness of the method by finding all existing roots with mathematical certainty.

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