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Tytuł:
On split r-Jacobsthal quaternions
Autorzy:
Bród, Dorota
Powiązania:
https://bibliotekanauki.pl/articles/1395923.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
Tematy:
Jacobsthal numbers
quaternion
split quaternion
split Jacobsthal quaternion
Binet formula
Opis:
In this paper we introduce a one-parameter generalization of the split Jacobsthal quaternions, namely the split r-Jacobsthal quaternions. We give a generating function, Binet formula for these numbers. Moreover, we obtain some identities, among others Catalan, Cassini identities and convolution identity for the split r-Jacobsthal quaternions.
Źródło:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2020, 74, 1
0365-1029
2083-7402
Pojawia się w:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On a new generalization of split Pell quaternions
O nowym uogólnieniu kokwaternionów Pella
Autorzy:
Bród, Dorota
Powiązania:
https://bibliotekanauki.pl/articles/953280.pdf
Data publikacji:
2019
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Pell numbers
quaternion
split quaternion
split Pell quaternion
split r-Pell quaternion
kwaternion
kokwaternion
kokwaternion pella
kokwaternion r-pella
liczby Pella
Opis:
In this paper we introduce and study a generalization of the split Pell quaternions - split r-Pell quaternions. We give some identities, among others Binet's formula, Catalan's, Cassini's and d'Ocagne's identity for these numbers.
W artykule wprowadzono pewne jednoparametrowe uogólnienie kokwaternionów Pella - kokwaterniony r-Pella. Przedstawione zostały różne tożsamości dla tych liczb m.in. wzór Bineta, Catalana i Cassiniego.
Źródło:
Mathematica Applicanda; 2019, 47, 2
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal reorientation of spacecraft orbit
Autorzy:
Chelnokov, Yu. N.
Pankratov, I. A.
Sapunkov, Y. G.
Powiązania:
https://bibliotekanauki.pl/articles/229458.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
spacecraft
optimal control
quaternion
Opis:
The problem of optimal reorientation of the spacecraft orbit is considered. For solving the problem we used quaternion equations of motion written in rotating coordinate system. The use of quaternion variables makes this consideration more efficient. The problem of optimal control is solved on the basis of the maximum principle. An example of numerical solution of the problem is given.
Źródło:
Archives of Control Sciences; 2014, 24, 2; 119-128
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Structure fractals and para-quaternionic geometry
Autorzy:
Ławrynowicz, Julian
Vaccaro, Massimo
Powiązania:
https://bibliotekanauki.pl/articles/747163.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
Tematy:
Fractal
quaternion
para-quaternion
Clifford structure
para-quaternionic structure
bilinear form
quadratic form
Opis:
It is well known that starting with real structure, the Cayley-Dickson process gives complex, quaternionic, and octonionic (Cayley) structures related to the Adolf Hurwitz composition formula for dimensions \(p = 2, 4\) and \(8\), respectively, but the procedure fails for \(p = 16\) in the sense that the composition formula involves no more a triple of quadratic forms of the same dimension; the other two dimensions are \(n = 2^7\). Instead, Ławrynowicz and Suzuki (2001) have considered graded fractal bundles of the flower type related to complex and Pauli structures and, in relation to the iteration process \(p \to p + 2 \to p + 4 \to ...\), they have constructed \(2^4\)-dimensional “bipetals” for \(p = 9\) and \(2^7\)-dimensional “bisepals” for \(p = 13\). The objects constructed appear to have an interesting property of periodicity related to the gradating function on the fractal diagonal interpreted as the “pistil” and a family of pairs of segments parallel to the diagonal and equidistant from it, interpreted as the “stamens”. The first named author, M. Nowak-Kepczyk, and S. Marchiafava (2006, 2009a, b) gave an effective, explicit determination of the periods and expressed them in terms of complex and quaternionic structures, thus showing the quaternionic background of that periodicity. In contrast to earlier results, the fractal bundle flower structure, in particular petals, sepals, pistils, and stamens are not introduced ab initio; they are quoted a posteriori, when they are fully motivated. Physical concepts of dual and conjugate objects as well as of antiparticles led us to extend the periodicity theorem to structure fractals in para-quaternionic formulation, applying some results in this direction by the second named author. The paper is concluded by outlining some applications.
Źródło:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2011, 65, 2
0365-1029
2083-7402
Pojawia się w:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Robust dual color images watermarking scheme with hyperchaotic encryption based on quaternion DFrAT and genetic algorithm
Autorzy:
Luo, Hui-Xin
Gong, Li-Hua
Chen, Su-Hua
Powiązania:
https://bibliotekanauki.pl/articles/27310094.pdf
Data publikacji:
2023
Wydawca:
Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Tematy:
color image watermarking
hyperchaotic encryption
quaternion discrete fractional angular transform
quaternion singular value decomposition
genetic algorithm
Opis:
A robust dual color images watermarking algorithm is designed based on quaternion discrete fractional angular transform (QDFrAT) and genetic algorithm. To guarantee the watermark security, the original color watermark image is encrypted with a 4D hyperchaotic system. A pure quaternion matrix is acquired by performing the discrete wavelet transform (DWT), the block division and the discrete cosine transform on the original color cover image. The quaternion matrix is operated by the QDFrAT to improve the robustness and the security of the watermarking scheme with the optimal transform angle and the fractional order. Then the singular value matrix is obtained by the quaternion singular value decomposition (QSVD) to further enhance the scheme’s stability. The encryption watermark is also processed by DWT and QSVD. Afterward, the singular value matrix of the encryption watermark is embedded into the singular value matrix of the host image by the optimal scaling factor. Moreover, the values to balance imperceptibility and robustness are optimized with a genetic algorithm. It is shown that the proposed color image watermarking scheme performs well in imperceptibility, security, robustness and embedding capacity.
Źródło:
Optica Applicata; 2023, 53, 2; 261--280
0078-5466
1899-7015
Pojawia się w:
Optica Applicata
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An FPGA-oriented fully parallel algorithm for multiplying dual quaternions
Autorzy:
Cariow, A.
Cariowa, G.
Witczak, M.
Powiązania:
https://bibliotekanauki.pl/articles/114212.pdf
Data publikacji:
2015
Wydawca:
Stowarzyszenie Inżynierów i Techników Mechaników Polskich
Tematy:
dual quaternion product
fast algorithms
hardware complexity reduction
FPGA
Opis:
This paper presents a low multiplicative complexity fully parallel algorithm for multiplying two dual quaternions. The “pen-and-paper” multiplication of two dual quaternions requires 64 real multiplications and 56 real additions. More effective solutions still do not exist. We show how to compute a product of two dual quaternions with 24 real multiplications and 64 real additions. During synthesis of the discussed algorithm we use the fact that the product of two dual quaternions can be represented as a matrix–vector product. The matrix multiplicand that participates in the product calculating has unique structural properties that allow performing its advantageous factorization. Namely this factorization leads to significant reducing of the multiplicative complexity of dual quaternion multiplication. We show that by using this approach, the computational process of calculating dual quaternion product can be structured so that eventually requires only half the number of multipliers compared to the direct implementation of matrix-vector multiplication.
Źródło:
Measurement Automation Monitoring; 2015, 61, 7; 370-372
2450-2855
Pojawia się w:
Measurement Automation Monitoring
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Totally real minimal submanifolds in a quaternion projective space
Autorzy:
Liu, Ximin
Powiązania:
https://bibliotekanauki.pl/articles/1294373.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
totally real submanifold
quaternion projective space
curvature pinching
Opis:
We prove some pinching theorems with respect to the scalar curvature of 4-dimensional conformally flat (concircularly flat, quasi-conformally flat) totally real minimal submanifolds in QP⁴(c).
Źródło:
Annales Polonici Mathematici; 1998, 69, 1; 31-36
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Quaternion-based filtering for gyroless attitude estimation without an attitude dynamics model
Autorzy:
Zhang, S.
Xing, F.
Sun, T.
You, Z.
Powiązania:
https://bibliotekanauki.pl/articles/220655.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
quaternion-based filtering
gyroless attitude estimation
angular velocity determination
Kalman filter
Opis:
Conventionally, the filtering technique for attitude estimation is performed using gyros or attitude dynamics models. In order to extend the application range of an attitude filter, this paper proposes a quaternion-based filtering framework for gyroless attitude estimation without an attitude dynamics model. The attitude estimation system is established based on a quaternion kinematic equation and vector observation models. The angular velocity in the system is determined through observation vectors from attitude sensors and the statistical properties of the angular velocity error are analysed. A Kalman filter is applied to estimate the attitude error such that the effect from the angular velocity error is compensated with its statistical properties at each sampling moment. A numerical simulation example is presented to illustrate the performance of the proposed algorithm.
Źródło:
Metrology and Measurement Systems; 2018, 25, 3; 631-643
0860-8229
Pojawia się w:
Metrology and Measurement Systems
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Hardware-Efficient Schemes of Quaternion Multiplying Units for 2D Discrete Quaternion Fourier Transform Processors
Autorzy:
Cariow, A.
Cariowa, G.
Chicheva, M.
Powiązania:
https://bibliotekanauki.pl/articles/114724.pdf
Data publikacji:
2017
Wydawca:
Stowarzyszenie Inżynierów i Techników Mechaników Polskich
Tematy:
discrete quaternion Fourier transform
fast algorithms
implementation complexity reduction
FPGA implementation
Opis:
In this paper, we offer and discuss three efficient structural solutions for the hardware-oriented implementation of discrete quaternion Fourier transform basic operations with reduced implementation complexities. The first solution – a scheme for calculating sq product, the second solution – a scheme for calculating qt product, and the third solution – a scheme for calculating sqt product, where s is a so-called i -quaternion, t is an j - quaternion, and q – is an usual quaternion. The direct multiplication of two usual quaternions requires 16 real multiplications (or two-operand multipliers in the case of fully parallel hardware implementation) and 12 real additions (or binary adders). At the same time, our solutions allow to design the computation units, which consume only 6 multipliers plus 6 two input adders for implementation of sq or qt basic operations and 9 binary multipliers plus 6 two-input adders and 4 four-input adders for implementation of sqt basic operation.
Źródło:
Measurement Automation Monitoring; 2017, 63, 6; 206-208
2450-2855
Pojawia się w:
Measurement Automation Monitoring
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Graded Hilbert-symbol equivalence of number fields
Autorzy:
Koprowski, Przemysław
Powiązania:
https://bibliotekanauki.pl/articles/729195.pdf
Data publikacji:
2015
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Brauer group
Brauer-Wall group
Hilbert symbol equivalence
Witt equivalence
graded quaternion algebras
Opis:
We present a new criterion for the existence of Hilbert-symbol equivalence of two number fields. In principle, we show that the system of local conditions for this equivalence may be expressed in terms of Clifford invariants in place of Hilbert-symbols, shifting the focus from Brauer groups to Brauer-Wall groups.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2015, 35, 1; 105-113
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Zastosowanie algebr hiperzespolonych w przetwarzaniu sygnałów
Application of hypercomplex algebras in signal processing
Autorzy:
Błaszczyk, Ł.
Powiązania:
https://bibliotekanauki.pl/articles/134792.pdf
Data publikacji:
2016
Wydawca:
ADVSEO
Tematy:
hypercomplex algebras
quaternion Fourier transform
octonion Fourier transform
system analysis
partial differential equations
Opis:
The subject of this paper is the application of hypercomplex algebras (in particular quaternions and octonions) in the analysis of time-invariant linear systems. We present the Cayley-Dickson construction of hypercomplex algebras and its important properties. Moreover, we formulate the concept of quaternion and octonion Fourier transform and their properties important from the signal processing point of view. We present an overview of known quaternion Fourier transform applications in the analysis of systems and partial differential equations of two variables. We also point out the direction of further work in the subject of application of the octonion Fourier transform in system analysis and analysis of partial differential equations of three variables. Such considerations are possible thanks to recently proved properties of octonion Fourier transform, which are also stated in this paper.
Źródło:
Technical Issues; 2016, 3; 13-18
2392-3954
Pojawia się w:
Technical Issues
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The New Insight into the Theory of 2-D Complex and Quaternion Analytic Signals
Autorzy:
Snopek, K. M.
Powiązania:
https://bibliotekanauki.pl/articles/226235.pdf
Data publikacji:
2011
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
2-D Fourier transform
quaternion Fourier transforms
2-D Hilbert transforms
2-D analytic signals
Opis:
The paper presents the overview of the theory of 2-D complex and quaternion analytic signals with the 1st-quadrant spectrum support. Both signals are expressed as complex/hypercomplex sums of partial and total 2-D Hilbert transforms. Moreover, starting with the definition of 2-D complex and quaternion Fourier transforms, the 2-D Hilbert transforms are derived in the form of sums of parts of different parity with respect to signal-domain variables. Some new relations for Hilbert quaternion spectra have been derived. The paper is illustrated with the example of the 2-D separable Cauchy signal.
Źródło:
International Journal of Electronics and Telecommunications; 2011, 57, 3; 285-291
2300-1933
Pojawia się w:
International Journal of Electronics and Telecommunications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Dual quaternions as a tool for rigid body motion analysis: a tutorial with an application to biomechanics
Kwaterniony dualne jako narzędzie analizy ruchu ciał sztywnych. Przykład zastosowań w biomechanice
Autorzy:
Pennestri, E.
Valentini, P. P.
Powiązania:
https://bibliotekanauki.pl/articles/139472.pdf
Data publikacji:
2010
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
biomechanika
interpolacja z użyciem kwaternionów dualnych
ruch człowieka
biomechanics
dual quaternion interpolation
human motion
Opis:
Dual quaternions and dual quaternion interpolation are powerful mathematical tools for the spatial analysis of rigid body motions. In this paper, after a review of some basic results and formulas, it will be presented an attempt to use these tools for the kinematic modeling of human joints. In particular, the kinematic parameters extracted from experimentally acquired data are compared with those theoretically computed from dual quaternions rigid body motion interpolation.
Kwaterniony dualne i interpolacja z użyciem kwaternionów dualnych stanowią silne narzędzia matematyczne wykorzystywane do analizy ruchu przestrzennego ciał sztywnych. W artykule przedstawiono przegląd podstawowych wzorów i wyników, a następnie zaprezentowano próbę użycia tych narzędzi do modelowania kinematyki stawów w ciele człowieka. W szczególności, parametry kinematyczne wyznaczone na podstawie danych eksperymentalnych porównano z wyliczonymi teoretycznie na podstawie interpolacji ruchu ciał sztywnych z użyciem kwaternionów dualnych.
Źródło:
Archive of Mechanical Engineering; 2010, LVII, 2; 187-205
0004-0738
Pojawia się w:
Archive of Mechanical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Color image encryption scheme based on quaternion discrete multi-fractional random transform and compressive sensing
Autorzy:
Ye, Huo-Sheng
Dai, Jing-Yi
Wen, Shun-Xi
Gong, Li-Hua
Zhang, Wen-Quan
Powiązania:
https://bibliotekanauki.pl/articles/2033985.pdf
Data publikacji:
2021
Wydawca:
Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Tematy:
color image encryption
quaternion discrete multi-fractional random transform
compressive sensing
confusion-diffusion strategy
Opis:
A color image compression-encryption algorithm by combining quaternion discrete multi-fractional random transform with compressive sensing is investigated, in which the chaos-based fractional orders greatly improve key sensitivity. The original color image is compressed and encrypted with the assistance of compressive sensing, in which the partial Hadamard matrix adopted as a measurement matrix is constructed by iterating Chebyshev map instead of utilizing the entire Guassian matrix as a key. The sparse images are divided into 12 sub-images and then represented as three quaternion signals, which are modulated by the quaternion discrete multi-fractional random transform. The image blocking and the quaternion representation make the proposed cryptosystem avoid additional data extension existing in many transform-based methods. To further improve the level of security, the plaintext-related key streams generated by the 2D logistic-sine-coupling map are adopted to diffuse and confuse the intermediate results simultaneously. Consequently, the final ciphertext image is attained. Simulation results reveal that the proposed cryptosystem is feasible with high security and has strong robustness against various attacks.
Źródło:
Optica Applicata; 2021, 51, 3; 349-364
0078-5466
1899-7015
Pojawia się w:
Optica Applicata
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Aspekty algorytmiczne redukcji liczby bloków mnożących w układzie do obliczania iloczynu dwóch kwaternionów
Algorithmic aspects of multiplication block number reduction in a two quaternion hardware multiplier
Autorzy:
Tariova, G.
Tariov, A.
Powiązania:
https://bibliotekanauki.pl/articles/154591.pdf
Data publikacji:
2010
Wydawca:
Stowarzyszenie Inżynierów i Techników Mechaników Polskich
Tematy:
iloczyn kwaternionów
liczby hiperzespolone
algorytmy i układy obliczeniowe
hypercomplex numbers
quaternion product
computation algorithms and units
Opis:
W pracy został przedstawiony zracjonalizowany algorytm mnożenia dwóch kwaternionów wymagający wykonania mniejszej liczby operacji mnożenia i dodawania, niż dowolny ze znanych autorom "szybkich" algorytmów tego typu. Pozwala to przy implementacji zmniejszyć nakłady obliczeniowe lub zapotrzebowanie na zasoby sprzętowe oraz stworzyć dogodne warunki do efektywnej realizacji operacji mnożenia dwóch kwaternionów w dowolnym sprzętowo-programowym środowisku implementacyjnym.
In the paper the rationalised algorithm for two quaternion product calculating with the reduced number of arithmetic operations (or multipliers and adders - in hardware implementation case) is presented. The computing of quaternion product in the naive way, using the definition, takes 16 multiplications and 12 additions, while the proposed algorithm can compute the same result in only 8 multiplications and 28 additions. This approach allows lowering hardware expenses and creates favorable conditions for effective convolution realisation on the reprogrammable platform. The computational procedure for quaternion multiplication is described in matrix notation. This notation enables adequate representation of the space-time structures of an implemented computational process and directly maps these structures into the hardware realisation space. The proposed structure can be successfully applied to accelerate calculations on FPGA based platforms as well as enhance the efficiency of hardware in general.
Źródło:
Pomiary Automatyka Kontrola; 2010, R. 56, nr 7, 7; 688-690
0032-4140
Pojawia się w:
Pomiary Automatyka Kontrola
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 17

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