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K. V. Zhukovsky - One of the best experts on this subject based on the ideXlab platform.
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Quark mixing and Exponential Form of the Cabibbo-Kobayashi-Maskawa matrix
Physics of Atomic Nuclei, 2008Co-Authors: K. V. Zhukovsky, D. DattoliAbstract:Various Forms of representation of the mixing matrix are discussed. An Exponential parametrization e ^  of the Cabibbo-Kobayashi-Maskawa matrix is considered in the context of the unitarity requirement, this parametrization being the most general Form of the mixing matrix. An explicit representation for the Exponential mixing matrix in terms of the first and second degrees of the matrix  exclusively is obtained. This representation makes it possible to calculate this Exponential mixing matrix readily in any order of the expansion in the small parameter λ . The generation of new unitary parametric representations of the mixing matrix with the aid of the Exponential matrix is demonstrated.
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Neutrino mixing and the Exponential Form of the Pontecorvo-Maki-Nakagawa-Sakata matrix
The European Physical Journal C, 2008Co-Authors: G. Dattoli, K. V. ZhukovskyAbstract:The Form of the neutrino mixing matrix is discussed. The Exponential parameterisation of the Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrix is proposed and the generation of the new unitary parameterisation of the neutrino mixing matrix by the Exponential Form is demonstrated. The CP violating phase and the Majorana phases in the PMNS matrix are accounted for by a special term, separated from the rotational one. The O(3) rotation matrix in the angle-axis Form is discussed in the context of such a representation of the mixing matrix. Its properties are reviewed in the context of the unitarity requirement.
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Quark flavour mixing and the Exponential Form of the Kobayashi–Maskawa matrix
The European Physical Journal C, 2007Co-Authors: G. Dattoli, K. V. ZhukovskyAbstract:The Form of the mixing matrix of quarks is discussed. The Exponential parameterisation of the Cabibbo–Kobayashi–Maskawa (CKM) matrix is identified as the most general Form of the mixing matrix. Its properties are reviewed in the context of the unitarity requirement. A recurrence series representation of the Exponential Form of the mixing matrix that is easy to handle is obtained, allowing for a direct and simple method of calculation of the CKM matrix. The generation of the new parameterisations of the CKM matrix by the Exponential Form is demonstrated.
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quark flavour mixing and the Exponential Form of the kobayashi maskawa matrix
European Physical Journal C, 2007Co-Authors: G. Dattoli, K. V. ZhukovskyAbstract:The Form of the mixing matrix of quarks is discussed. The Exponential parameterisation of the Cabibbo–Kobayashi–Maskawa (CKM) matrix is identified as the most general Form of the mixing matrix. Its properties are reviewed in the context of the unitarity requirement. A recurrence series representation of the Exponential Form of the mixing matrix that is easy to handle is obtained, allowing for a direct and simple method of calculation of the CKM matrix. The generation of the new parameterisations of the CKM matrix by the Exponential Form is demonstrated.
G. Dattoli - One of the best experts on this subject based on the ideXlab platform.
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Neutrino mixing and the Exponential Form of the Pontecorvo-Maki-Nakagawa-Sakata matrix
The European Physical Journal C, 2008Co-Authors: G. Dattoli, K. V. ZhukovskyAbstract:The Form of the neutrino mixing matrix is discussed. The Exponential parameterisation of the Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrix is proposed and the generation of the new unitary parameterisation of the neutrino mixing matrix by the Exponential Form is demonstrated. The CP violating phase and the Majorana phases in the PMNS matrix are accounted for by a special term, separated from the rotational one. The O(3) rotation matrix in the angle-axis Form is discussed in the context of such a representation of the mixing matrix. Its properties are reviewed in the context of the unitarity requirement.
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Quark flavour mixing and the Exponential Form of the Kobayashi–Maskawa matrix
The European Physical Journal C, 2007Co-Authors: G. Dattoli, K. V. ZhukovskyAbstract:The Form of the mixing matrix of quarks is discussed. The Exponential parameterisation of the Cabibbo–Kobayashi–Maskawa (CKM) matrix is identified as the most general Form of the mixing matrix. Its properties are reviewed in the context of the unitarity requirement. A recurrence series representation of the Exponential Form of the mixing matrix that is easy to handle is obtained, allowing for a direct and simple method of calculation of the CKM matrix. The generation of the new parameterisations of the CKM matrix by the Exponential Form is demonstrated.
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quark flavour mixing and the Exponential Form of the kobayashi maskawa matrix
European Physical Journal C, 2007Co-Authors: G. Dattoli, K. V. ZhukovskyAbstract:The Form of the mixing matrix of quarks is discussed. The Exponential parameterisation of the Cabibbo–Kobayashi–Maskawa (CKM) matrix is identified as the most general Form of the mixing matrix. Its properties are reviewed in the context of the unitarity requirement. A recurrence series representation of the Exponential Form of the mixing matrix that is easy to handle is obtained, allowing for a direct and simple method of calculation of the CKM matrix. The generation of the new parameterisations of the CKM matrix by the Exponential Form is demonstrated.
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Flavour mixing, supersymmetric Hamiltonians and Exponential Form of the Cabibbo-Kobayashi-Maskawa matrix
Il Nuovo Cimento A (1965-1970), 1996Co-Authors: G. Dattoli, A. TorreAbstract:It is suggested that the weak-mixing matrix can be viewed as an evolution operator for a three-level system interaction. The supersymmetric nature of the system Hamiltonian is discussed and the relevant coupling strengths are written as powers of a scale parameter recognized as the Cabibbo angle. The entries of the weak-mixing matrix are then reproduced using two input parameters, i.e. the Cabibbo angle and the CP -violating phase. General Forms of weak mass matrices, including CP -violating contributions, are derived and their physical meaning is discussed.
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Mass Matrices of Weak Interaction, Quark Flavour Mixing and Exponential Form of the Cabibbo-Kobayashi-Maskawa Matrix.
Il Nuovo Cimento A, 1995Co-Authors: G. Dattoli, A. TorreAbstract:The quark mixing matrix is diagonalized. The use of the Exponential parametrization leads to straightforward results, obtained in exact Form, without simplifying assumptions. We define weak-interaction eigenstates in the sense of Fritzch and Planckl. The relevant mass matrices are derived and are shown to belong to Barnhill canonical Forms. It is proven that, at lowest order, these matrices exhibit a democratic structure. The mechanism of democracy breaking is finally discussed.
Garth D Irwin - One of the best experts on this subject based on the ideXlab platform.
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Comparison of root-matching techniques for electromagnetic transient simulation
IEEE Transactions on Power Delivery, 2000Co-Authors: Neville R. Watson, Garth D IrwinAbstract:Electromagnetic transient simulation has become a very important tool in the design of electrical power systems. Dommel's trapezoidal integrator substitution, the standard method for electromagnetic transient simulations, often causes numerical oscillations due to truncation errors, particularly if some small time constants exist in the network. An alternative Exponential Form of the difference equation has been developed and demonstrated, using root-matching techniques. This Exponential Form of difference equation results in highly efficient and accurate time domain simulation with no tendency for numerical oscillation regardless of the time step used. In applying the root-matching techniques, an assumption is made as to the variation of the input between time steps. This paper looks at the perFormance of the various Exponential Forms of difference equation.
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Accurate and stable electromagnetic transient simulation using root-matching techniques
International Journal of Electrical Power & Energy Systems, 1999Co-Authors: Neville R. Watson, Garth D IrwinAbstract:The method of substituting the trapezoidal integrator, developed by Dommel, is generally applied in electromagnetic transient simulations. The trapezoidal rule is based on a truncated Taylor series and therefore contains truncation errors. These truncation errors cause numerical oscillations when the time step is large relative to some of the time constants in the network. Various techniques have been developed to reduce the numerical oscillations, each with strengths and drawbacks. In this paper an Exponential Form of the difference equation is developed, using root-matching techniques, that eliminates the truncation error and provides a highly efficient and accurate time domain regardless of the time step used. This Exponential Form of the difference equation generates a solution at each time point that is exact for the step response and a good approximation for an arbitrary forcing function. The Exponential Form is compatible with Dommel's method.
Neville R. Watson - One of the best experts on this subject based on the ideXlab platform.
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Comparison of root-matching techniques for electromagnetic transient simulation
IEEE Transactions on Power Delivery, 2000Co-Authors: Neville R. Watson, Garth D IrwinAbstract:Electromagnetic transient simulation has become a very important tool in the design of electrical power systems. Dommel's trapezoidal integrator substitution, the standard method for electromagnetic transient simulations, often causes numerical oscillations due to truncation errors, particularly if some small time constants exist in the network. An alternative Exponential Form of the difference equation has been developed and demonstrated, using root-matching techniques. This Exponential Form of difference equation results in highly efficient and accurate time domain simulation with no tendency for numerical oscillation regardless of the time step used. In applying the root-matching techniques, an assumption is made as to the variation of the input between time steps. This paper looks at the perFormance of the various Exponential Forms of difference equation.
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Accurate and stable electromagnetic transient simulation using root-matching techniques
International Journal of Electrical Power & Energy Systems, 1999Co-Authors: Neville R. Watson, Garth D IrwinAbstract:The method of substituting the trapezoidal integrator, developed by Dommel, is generally applied in electromagnetic transient simulations. The trapezoidal rule is based on a truncated Taylor series and therefore contains truncation errors. These truncation errors cause numerical oscillations when the time step is large relative to some of the time constants in the network. Various techniques have been developed to reduce the numerical oscillations, each with strengths and drawbacks. In this paper an Exponential Form of the difference equation is developed, using root-matching techniques, that eliminates the truncation error and provides a highly efficient and accurate time domain regardless of the time step used. This Exponential Form of the difference equation generates a solution at each time point that is exact for the step response and a good approximation for an arbitrary forcing function. The Exponential Form is compatible with Dommel's method.
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The root-matching method
Power Systems Electromagnetic Transients Simulation, 1Co-Authors: Neville R. Watson, Jos ArrillagaAbstract:An alternative to the difference equation using the trapezoidal integration developed in Chapter 4 for the solution of the differential equations has been described in this chapter. It involves the Exponential Form of the difference equation and has been developed using the root-matching technique. The Exponential Form offers the following advantages: 1) Eliminates truncation errors, and hence numerical oscillations, regardless of the step length used. 2) Can be applied to both electrical networks and control blocks. 3) Can be viewed as a Norton equivalent in exactly the same way as the difference equation developed by the numerical integration substitution (NIS) method. 4) It is perfectly compatible with NIS and the matrix solution technique remains unchanged. 5) Provides highly efficient and accurate time domain simulation. The Exponential Form can be implemented for all series and parallel RL, RC, LC and RLC combinations, but not arbitrary components and hence is not a replacement for NIS but a supplement.
C. J. Schinas - One of the best experts on this subject based on the ideXlab platform.
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Study of the asymptotic behavior of the solutions of three systems of difference equations of Exponential Form
Applied Mathematics and Computation, 2012Co-Authors: Garyfalos Papaschinopoulos, M. A. Radin, C. J. SchinasAbstract:In this paper we study the boundedness, the persistence and the asymptotic behavior of the positive solutions of the following systems of two difference equations of Exponential Form: xnþ1 ¼ a þ be � yn c þ yn� 1 ; y nþ1 ¼ d þ � e � xn f þ xn� 1 ;
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on the system of two difference equations of Exponential Form xn 1 a bxn 1e yn yn 1 c dyn 1e xn
Mathematical and Computer Modelling, 2011Co-Authors: Garyfalos Papaschinopoulos, M. A. Radin, C. J. SchinasAbstract:Abstract It is the goal of this paper to study the boundedness, the persistence and the asymptotic behavior of the positive solutions of the system of two difference equations of Exponential Form x n + 1 = a + b x n − 1 e − y n , y n + 1 = c + d y n − 1 e − x n , where a , b , c , d are positive constants, and the initial values x − 1 , x 0 , y − 1 , y 0 are positive real values.
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On the system of two difference equations of Exponential Form: xn+1=a+bxn−1e−yn,yn+1=c+dyn−1e−xn
Mathematical and Computer Modelling, 2011Co-Authors: Garyfalos Papaschinopoulos, M. A. Radin, C. J. SchinasAbstract:Abstract It is the goal of this paper to study the boundedness, the persistence and the asymptotic behavior of the positive solutions of the system of two difference equations of Exponential Form x n + 1 = a + b x n − 1 e − y n , y n + 1 = c + d y n − 1 e − x n , where a , b , c , d are positive constants, and the initial values x − 1 , x 0 , y − 1 , y 0 are positive real values.
