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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:
    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:
    Dual quaternions for the kinematic description of a fish-like propulsion system
    Autorzy:
    Kitowski, Zygmunt
    Piskur, Paweł
    Orłowski, Mateusz
    Powiązania:
    https://bibliotekanauki.pl/articles/11542693.pdf
    Data publikacji:
    2023
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    dual quaternion
    artificial fish
    underwater vehicle
    undulating propulsion system
    kwaternion dualny
    sztuczna ryba
    pojazd podwodny
    układ napędowy
    Opis:
    This study discusses the use of quaternions and dual quaternions in the description of artificial fish kinematics. The investigation offered here illustrates quaternion and dual quaternion algebra, as well as its implementation in the software chosen. When it comes to numerical stability, quaternions are better than matrices because a normalised quaternion always shows the correct rotation, while a matrix more easily loses its orthogonality due to rounding errors and oversizing. Although quaternions are more compact than rotation matrices, using quaternions does not always provide less numerical computation and the amount of memory needed. In this paper, an algebraic form of quaternion representation is provided which is less memory-demanding than the matrix representation. All the functions that were used to prepare this work are presented, and they can be employed to conduct more research on how well quaternions work in a specific assignment.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2023, 33, 2; 171--181
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the spectra of a quaternion singular integral operator and its components on spatial surfaces
    O spektrum kwaternionowego osobliwego operatora całkowego i jego składowe na powierzchniach przestrzennych
    Autorzy:
    Gerus, Oleg F.
    Powiązania:
    https://bibliotekanauki.pl/articles/1837643.pdf
    Data publikacji:
    2021-08-12
    Wydawca:
    Łódzkie Towarzystwo Naukowe
    Tematy:
    quaternion
    differentiable function
    hyperholomorphic function
    singular integral Cauchy operator
    spectrum
    kwaternion
    funkcja różniczkowalna
    hiperholomorficzna funkcja
    osobliwy całkowy operator Cauchy’ego
    spektrum
    Opis:
    On the spectra of a quaternion singular integral operator and its components on spatial surfaces.
    Źródło:
    Bulletin de la Société des Sciences et des Lettres de Łódź, Série: Recherches sur les déformations; 2020, 70, 1; 153-167
    1895-7838
    2450-9329
    Pojawia się w:
    Bulletin de la Société des Sciences et des Lettres de Łódź, Série: Recherches sur les déformations
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-15 z 15

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