Temat: quaternion - Prolib Integro

Skocz do pozycji: 1.

Tytuł:: On split r-Jacobsthal quaternions
Autorzy:: Bród, Dorota
Tematy:: Jacobsthal numbers
quaternion
split quaternion
split Jacobsthal quaternion
Binet formula; Pokaż więcej
Wydawca:: Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
Powiązania:: https://bibliotekanauki.pl/articles/1395923.pdf Link otwiera się w nowym oknie
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.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: On a new generalization of split Pell quaternions
O nowym uogólnieniu kokwaternionów Pella
Autorzy:: Bród, Dorota
Tematy:: Pell numbers
quaternion
split quaternion
split Pell quaternion
split r-Pell quaternion
kwaternion
kokwaternion
kokwaternion pella
kokwaternion r-pella
liczby Pella; Pokaż więcej
Wydawca:: Polskie Towarzystwo Matematyczne
Powiązania:: https://bibliotekanauki.pl/articles/953280.pdf Link otwiera się w nowym oknie
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.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: Optimal reorientation of spacecraft orbit
Autorzy:: Chelnokov, Yu. N.
Pankratov, I. A.
Sapunkov, Y. G.
Tematy:: spacecraft
optimal control
quaternion; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Czytelnia Czasopism PAN
Powiązania:: https://bibliotekanauki.pl/articles/229458.pdf Link otwiera się w nowym oknie
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.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: Structure fractals and para-quaternionic geometry
Autorzy:: Ławrynowicz, Julian
Vaccaro, Massimo
Tematy:: Fractal
quaternion
para-quaternion
Clifford structure
para-quaternionic structure
bilinear form
quadratic form; Pokaż więcej
Wydawca:: Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
Powiązania:: https://bibliotekanauki.pl/articles/747163.pdf Link otwiera się w nowym oknie
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.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 5.

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
Tematy:: color image watermarking
hyperchaotic encryption
quaternion discrete fractional angular transform
quaternion singular value decomposition
genetic algorithm; Pokaż więcej
Wydawca:: Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Powiązania:: https://bibliotekanauki.pl/articles/27310094.pdf Link otwiera się w nowym oknie
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.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 6.

Tytuł:: Totally real minimal submanifolds in a quaternion projective space
Autorzy:: Liu, Ximin
Tematy:: totally real submanifold
quaternion projective space
curvature pinching; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Powiązania:: https://bibliotekanauki.pl/articles/1294373.pdf Link otwiera się w nowym oknie
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).
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 7.

Tytuł:: An FPGA-oriented fully parallel algorithm for multiplying dual quaternions
Autorzy:: Cariow, A.
Cariowa, G.
Witczak, M.
Tematy:: dual quaternion product
fast algorithms
hardware complexity reduction
FPGA; Pokaż więcej
Wydawca:: Stowarzyszenie Inżynierów i Techników Mechaników Polskich
Powiązania:: https://bibliotekanauki.pl/articles/114212.pdf Link otwiera się w nowym oknie
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.
Dostawca treści:: Biblioteka Nauki

Artykuł

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Skocz do pozycji: 8.

Tytuł:: On Balancing Quaternions and Lucas-Balancing Quaternions
Autorzy:: Bród, Dorota
Tematy:: balancing number
Lucas-balancing number
quaternion
Binet formula
generating function; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/55795681.pdf Link otwiera się w nowym oknie
Opis:: In this paper we define and study balancing quaternions and Lucas-balancing quaternions. We give the generating functions, matrix generators and Binet formulas for these numbers. Moreover, the well-known properties e.g. Catalan, d’ Ocagne identities have been obtained for these quaternions.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 9.

Tytuł:: Quaternion-based filtering for gyroless attitude estimation without an attitude dynamics model
Autorzy:: Zhang, S.
Xing, F.
Sun, T.
You, Z.
Tematy:: quaternion-based filtering
gyroless attitude estimation
angular velocity determination
Kalman filter; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Czytelnia Czasopism PAN
Powiązania:: https://bibliotekanauki.pl/articles/220655.pdf Link otwiera się w nowym oknie
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.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 10.

Tytuł:: Hardware-Efficient Schemes of Quaternion Multiplying Units for 2D Discrete Quaternion Fourier Transform Processors
Autorzy:: Cariow, A.
Cariowa, G.
Chicheva, M.
Tematy:: discrete quaternion Fourier transform
fast algorithms
implementation complexity reduction
FPGA implementation; Pokaż więcej
Wydawca:: Stowarzyszenie Inżynierów i Techników Mechaników Polskich
Powiązania:: https://bibliotekanauki.pl/articles/114724.pdf Link otwiera się w nowym oknie
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.
Dostawca treści:: Biblioteka Nauki

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