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  8. 41-4

Electronic modeling

Vol 41, No 4 (2019)

 

CONTENTS

Mathematical Modeling and Computation Methods

  KALINOVSKY J.A., BOYARINOVA Y.E., KHITSKO J.V.
Method of Selecting Hypercomplex Number Systems for Modeling Digital Reversing Filters of the 3rd and 4th Orders
3-18
  KLIPKOV S.I.
Some Features of the Matrix Representations of the Octonions
19-34
  OGIR E.A.
Method of Increasing the Quality of Reconstruction of Diagnostic Images Based on Integral Convertions
35-48

Computational Processes and systems

  EFANOV D.V., SAPOZHNIKOV V.V., SAPOZHNIKOV V.V.
Unit Bits and one Weighted Bit Sum Codes with Arbitrary Counting Modules
49-72

Application of Modeling Methods and Facilities

  MOKHOR V.V., HONCHAR S.F.
Research of Validity of Presentation of Risks by Vectors in the Euclide Space
73-84
  IATSYSHYN A.V., KUTSAN YU.G., ARTEMCHUK V.O., KAMENEVA I.P., POPOV O.O., KOVACH V.O.
The Principles and Methods of Ecological Safety Management Through the Data of Air Monitoring Network Analysis
85-102
  GODUN O.V.
Calculating Model for Rational Innovation Nuclear Fuel Cycle Configuration Identification
103-114

METHOD OF SELECTING HYPERCOMPLEX NUMBER SYSTEMS FOR MODELING DIGITAL REVERSING FILTERS OF THE 3RD AND 4th ORDERS

J.A. Kalinovsky, Y.E. Boyarinova , J.V. Khitsko

Èlektron. model. 2019, 41(4):03-17

ABSTRACT

The article presents themethod of selecting hypercomplex number systems (HNS) formodeling digitalThe article presents themethod of selecting hypercomplex number systems (HNS) formodeling digitalreversible filters based on the analysis of the expression of the norm of the hypercomplex transferfunction denominator. The selected HNS, allowing to obtain in the transfer function of the filter acomplete set of powers of the shift operator. These HNS have weakly filled isomorphisms, the transitionto which can significantly reduce the number of real operations in the operation of the filter.

KEYWORDS

hypercomplex number system, linear convolution, isomorphism, multiplication,hypercomplex number system, linear convolution, isomorphism, multiplication,bicomplex numbers, quadriplex numbers, computer algebra system.

REFERENCES

1. Kalinovsky, Y.A., Lande, D.V., Bojarinova, J.E. and Khitsko, Y.V. (2014), Giperkompleksnyye chislovyye sistemy i bystryye algoritmy tsifrovoy obrabotki informatsii [Hypercomplex numbers systems and fast algorithms for digital information processing], IPRI NANU, Kyiv, Ukraine.
2. Toyoshima, H. (2002), “Computationally Efficient Implementation of Hypercomplex Digital Filters”, Fundamentals, pp. 1870-1876.
3. Schutte, H.D. (1991), Digital filter for processing complex and hypercomplex signals, Paderborn, Germany.
4. Schulz, D., Seitz, J. and LustosadaCosta J.P. (2011), “Widely Linear SIMO Filtering for Hypercomplex Numbers”, IEEE Information Theory Workshop, pp. 390-394.
https://doi.org/10.1109/ITW.2011.6089486
5. Toyoshima, H. and Higuchi, S. (1999), “Design of Hypercomplex All-Pass Filters to Realize Complex Transfer Functions”, Conference proceedings of the second International conference on Information, Communications and Signal Processing, pp. 1-5.
6. Toyoshima, H. (1998), “Computationally Efficient Bicomplex Multipliers for Digital Signal Processing”, Inf. & Syst, pp. 236-238.
7. Bulow, T. and Sommer, G. (2001), “Hypercomplex Signals — A Novel Extension of the Analytic Signal to the Multidimensional Case”, IEEE Transactions on Signal Processing, Vol. 49, no. 11, pp. 2844-2852.
https://doi.org/10.1109/78.960432
8. Parfieniuk, M. and Petrovsky, A. (2004), “Quaternionic building block for paraunitary filter banks”, Proceeding of the 12th European Signal Processing Conference (EUSIPCO '04), Vienna, Austria, 2004, pp. 1237-1240.
9. Alfsmann, D. and Göckler, H. G. (2005), “Design of Hypercomplex Allpass-Based Paraunitary Filter Banks applying Reduced Biquaternions”, Proceeding of EUROCON 2005, Belgrade, Serbia & Montenegro, 2005, pp. 92-95.
https://doi.org/10.1109/EURCON.2005.1629866
10. Ueda, K. and Takahashi, S. (1993) “Digital Filtrs with hypercomplex Coefficients”, ISCAP, pp. 479-482.
11. Kalinovsky, Ya.O. (2007), “Development of methods of the theory of hypercomplex numbers systems for mathematical modeling and computer calculations”, Abstract of Cand. Sci. (Tech.) dissertation, Kyiv, Ukraine.
12. Kalinovsky, Y.A., Boyarinova, Y.E. and Khitsko, Y.V. (2015), “Reversible Digital Filters Total Parametric Sensitivity Optimization using Non-canonical Hypercomplex Number Systems”, available at: http://arxiv.org/abs/1506.01701 (accessed June 23, 2019).
13. Sinkov, Ì.V., Kalinovsky, Ya.A. and Boyarinova, Yu.E. (2010), Konechnomernyie giperkompleksnyie chislovyie sistemy [Finite-dimensional hypercomplex number systems], Infodruk,
Kyiv, Ukraine.
14. Mel'nikov O.V., Remeslennikov V.N. and Roman'kov V.A.(1990), “General algebra”,
Nauka, Vol. 1.
15. Drozd, Yu.A., Kirichenko, V.V. (1980), Konechnomernyye algebry [Finite-dimensional algebras],Vyshcha shkola, Kyiv, Ukraine.
16. Kalinovskiy, Ya.A., Boyarinova, Yu.Ye., Khitsko, Ya.V., Sukalo, A.S. (2017), “Software complexfor hypercomplex computing”, Elektronnoye. modelirovaniye, Vol. 39, no. 5, pp. 81-96.
https://doi.org/10.15407/emodel.39.05.081

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SOME FEATURES OF THE MATRIX REPRESENTATIONS OF THE OCTONIONS

S.I. Klipkov

Èlektron. model. 2019, 41(4):19-34

ABSTRACT

The problems of matrix representations of normalized octonions with division, as well as splitThe problems of matrix representations of normalized octonions with division, as well as splitoctonions due to non-associative multiplication are considered. An algorithm for matrix multiplicationis proposed, which makes it possible to formulate a new approach to the matrix representationof octonions, which can equally be used to represent both ordinary and split octonions. Theexamples illustrating the issues raised in the article are given.

KEYWORDS

octonions, split octonions, nonassociative, matrix representations of numberoctonions, split octonions, nonassociative, matrix representations of numbersystems.

REFERENCES

1. Gamba, A. (1998), “Maxwell’s equations in octonion form”, IL Nuovo Cimento A, Vol. 111, no. 3, pp. 293-299.
2. Gogberashvili, M. (2006), “Octonionic electrodynamics”, Journal of Physics A: Mathematical and Theoretical, Vol. 39, mo. 22, pp. 7099-7104.
https://doi.org/10.1088/0305-4470/39/22/020
3. Nurowski, P. (2009), “Split Octonions and Maxwell Equations”, Acta Physica Polonica A, Vol. 116, no. 6, pp. 992-993.
https://doi.org/10.12693/APhysPolA.116.992
4. Chanyal, B.C. (2015), “Octonion generalization of Pauli and Dirac matrices”, International Journal of Geometric Methods in Modern Physics, Vol. 12, no. 1, pp. 1550007-1- 1550007-24.
https://doi.org/10.1142/S0219887815500073
5. Baez, J.C. (2001), “The octonions”, Bulletin of the American Mathematical Society, Vol. 39, no. 2, pp. 145-205.
https://doi.org/10.1090/S0273-0979-01-00934-X
6. Rozenfeld B.A. (1955), Neyevklidovy geometrii [Non-Euclidean Geometries], GITTL, Moscow, SSSR.
7. Sinkov, M. V., Kalinovsky, Ya.A. and Boyarinova, Yu.E., (2010), “Matrix Representations of Isomorphic Hypercomplex Numerical Systems”, Reyestratsiya, zberihannya i obrobka. Danykh, Vol. 12, no. 4. pp. 43-53.
8. Klipkov, S.I. (2014), “The generalized analysis of matrix representations of associative hypercomplex numerical systems used in problems of power engineering”, Reyestratsiya, zberihannya i obrobka. Danykh, Vol. 16, no. 2. pp. 28-41.
9. Tian, Y. (2000), “Matrix Representations of Octonions and their Applications”, Advances in Applied Clifford Algebras, Vol. 10, no. 1, pp. 61-90.
https://doi.org/10.1007/BF03042010
10. Zorn, M. (1933), “Treatises from the Mathematical”, Seminar of the University of Hamburg, no. 9, pp. 395-402.
https://doi.org/10.1007/BF02940661
11. Daboul, J. and Delbourgo, R. (1999) “Matrix representation of octonions and generalizations”, Journal of Mathematical Physics, no. 40, pp. 4134-4150.
https://doi.org/10.1063/1.532950

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METHOD OF INCREASING THE QUALITY OF RECONSTRUCTION OF DIAGNOSTIC IMAGES BASED ON INTEGRAL CONVERTIONS

E.A. Ogir

Èlektron. model. 2019, 41(4):35-47

ABSTRACT

A computational method was developed based on the filtering of reverberation signals-interferencesA computational method was developed based on the filtering of reverberation signals-interferencesand secondary diffraction maxima of the Fourier transform - the conversion when playingdiagnostic images, improves the spatial resolution of the system more than 6 times. The method isintended for use: in medical diagnostics to increase the detection efficiency of low-contrastneoplasms of the initial stage of development and in non-destructive testing tasks to detect thesmallest defects in materials and media (in the construction, energy and fuel industries).

KEYWORDS

reconstruction, interference signals, filtering, spatial resolution, echo signal,reconstruction, interference signals, filtering, spatial resolution, echo signal,hologram.

REFERENCES

1. Bamber, J., Dickinson, R. and Eckersley. (2008), Ul'trazvuk v meditsine. Fizicheskiye osnovy primeneniya [Ultrasound in medicine. Physical bases of application], FIZMALIT, Moscow, Russia.
2. Ermolov, I.N. (1981), Teoriya i praktika ul'trazvukovogo kontrolya [Theory and practice of ultrasonic testing], Mashinostroyeniye.
3. Falkevich, S.A. (1984), “Phased arrays in ultrasonic flaw detection”, Defektoskopiya, no. 3, pp. 3-16.
4. Evdokimov, V.F. and Ogir, A.S. (1996), “Mathematical modeling of signals and processes in acoustic holography: problems and prospects”, Elektronnoye modelirovaniye, Vol. 18, no. 4, pp. 29-33.
5. Evdokimov, V.F. and Ogir, A.S. (2001), “On building an ultrasonic inspection system for structural materials of energy and engineering facilities”, Elektronnoye modelirovaniye, Vol. 23, no. 5, pp. 85-90.
6. Evdokimov, V.F. and Ogir, A.S. (2000), “On the discrete mathematical model of the sound hologram”, Elektronnoye modelirovaniye, Vol. 22, no. 1, pp. 3-8.
7. Ogir, A.S. (1997), “Investigation of computer-aided reconstruction of acoustic images”, Metody i sredstva komp'yuternogo modelirovaniya. Sb. nauch. trudov IPME NANU, pp. 41-44.
8. Ogir, A.S. (2002), “On the construction of a quasi-holographic system of acoustic control of materials”, Modelyuvannya ta informatsiyni tekhnolohiyi. 36. nauk. prats' IPME NANU, Vol. 13, pp. 76-81.

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UNIT BITS AND ONE WEIGHTED BIT SUM CODES WITH ARBITRARY COUNTING MODULES

D.V. Efanov, V.V. Sapozhnikov, V.V. Sapozhnikov

Èlektron. model. 2019, 41(4):48-72

ABSTRACT

A new codes class focused on the error detection in information vectors is presented. The newA new codes class focused on the error detection in information vectors is presented. The newcodes building principles are based on weighing all bits in the data vectors, except for one, withunit weights and one bit—non-unit weights with further calculation of the smallest non-negativededuction of the total on-bits weight in a predetermined module. The description of this codesclass and the classification of code families depending on the check vectors lengths are given.The power of modular codes set is determined with the unit bits and one weighted bit sum foreach value of the length of the data vector. Some error detection features in data vectors by codesfrom the considered class are considered, which is important when solving the detecting faultsproblem in hardware implementations of automatic control systems logic devices.

KEYWORDS

redundant code; error detection codes; sum codes; controllable automation devices;redundant code; error detection codes; sum codes; controllable automation devices;check vector; technical diagnostic; fault-tolerance.

REFERENCES

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