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991.
I. T. Habibullin 《Theoretical and Mathematical Physics》2006,146(2):170-182
We find analogues of the generalized two-dimensional Toda chains of the CN and
series with three discrete independent variables and give Lax pairs for these chains.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 2, pp. 208–221, February, 2006. 相似文献
992.
Joël Merker 《Acta Appl Math》2006,92(2):125-207
We treat the problem of linearizability of a system of second order ordinary differential equations. The criterion we provide has applications to nonlinear Newtonian mechanics, especially in three-dimensional space. Let or , let , let , let and let
be a collection of m analytic second order ordinary differential equations, in general nonlinear. We obtain a new and applicable necessary and sufficient condition in order that this system is equivalent, under a point transformation
to the Newtonian free particle system .Strikingly, the explicit differential system that we obtain is of first order in the case , whereas according to a classical result due to Lie, it is of second order the case of a single equation . 相似文献
993.
Daniel Guan 《Annals of Global Analysis and Geometry》2006,30(2):139-167
This paper is the first of a series of papers in which we generalize our results in (Asian J. of Math. 4, 817–830 (2000); J. Geom. Anal. 12, 63–79 (2002); Intern. J. Math. 14, 259–287 (2003)) to the general complex compact almost homogeneous manifolds of real cohomogeneity one. In this paper we deal with the exceptional case of the G 2 action (Cf. Intern. J. Math. 14, 259–287 (2003), p. 285). In particular, we prove the existence of Kähler-Einstein metric on this manifold. 相似文献
994.
In this paper, we use the classical Lie group symmetry method to get the Lie point symmetries of the (2+1)-dimensional hyperbolic nonlinear Schr6dinger (HNLS) equation and reduce the (2+1)-dimensional HNLS equation to some (1 + 1 )-dimensional partial differential systems. Finally, many exact travelling solutions of the (2+1)-dimensional HNLS equation are obtained by the classical Lie symmetry reduced method. 相似文献
995.
Two new families of completely integrable perturbations of the N-dimensional isotropic harmonic oscillator Hamiltonian are presented. Such perturbations depend on arbitrary functions and N free parameters and their integrals of motion are explicitly constructed by making use of an underlying h6-coalgebra symmetry. Several known integrable Hamiltonians in low dimensions are obtained as particular specializations of the general results here presented. An alternative route for the integrability of all these systems is provided by a suitable canonical transformation which, in turn, opens the possibility of adding (N−1) ‘Rosochatius’ terms that preserve the complete integrability of all these models. 相似文献
996.
997.
Moiz Ahmad Yinan Liu Zachary W. Slavens Russell Low Elmar Merkle Ken-Pin Hwang Anthony Vu Jingfei Ma 《Magnetic resonance imaging》2010
Sampling water and fat signals symmetrically (i.e., at 0° and 180° relative phase angles) in a dual-echo Dixon technique offers high intrinsic tolerance to phase fluctuations in postprocessing and maximum signal-to-noise performance for the separated water and fat images. However, identification of which image is water and which image is fat after their separation is not possible based on the phase information alone. In this work, we proposed a semiempirical automatic image identification method that is based on the intrinsic asymmetry between the water and fat chemical shift spectra. Specifically, the approximately bimodal feature of the fat spectra and the observation that most in vivo tissues are either predominantly water or predominantly fat are used to construct a spectrum-based algorithm. Additional refinement is accomplished by considering the spatial distribution of the tissues that may have a coexistence of water and fat. The final improved algorithm was tested on a total of 131 three-dimensional patient datasets collected from different scanners and found to yield correct water and fat identification in all datasets. 相似文献
998.
Pabitra Kumar Pradhan Manoj Kumar Pandey 《Mathematical Methods in the Applied Sciences》2020,43(9):6081-6092
The system of generalized Chaplygin gas equations with a coulomblike friction term has been investigated by using the famous Lie symmetry method. A direct and systematic algorithm based on the adjoint transformation and invariants of the admitted Lie algebras is then used to construct one- and two-dimensional optimal system of the Chaplygin gas equations. Inequivalent classes of group invariant solutions are then obtained using the one-dimensional optimal system. Further, the evolutionary behaviour of the weak discontinuity wave within the state characterized by one of the group invariant solutions is investigated in detail, and certain observations are noted in respect to their contrasting behaviour. 相似文献
999.
Francis N. Castro Robin Chapman Luis A. Medina L. Brehsner Sepúlveda 《Discrete Mathematics》2018,341(7):1915-1931
Rotation symmetric Boolean functions are invariant under circular translation of indices. These functions have very rich cryptographic properties and have been used in different cryptosystems. Recently, Thomas Cusick proved that exponential sums of rotation symmetric Boolean functions satisfy homogeneous linear recurrences with integer coefficients. In this work, a generalization of this result is proved over any Galois field. That is, exponential sums over Galois fields of some rotation symmetric polynomials satisfy linear recurrences with integer coefficients. In the particular case of , an elementary method is used to obtain explicit recurrences for exponential sums of some of these functions. The concept of trapezoid Boolean function is also introduced and it is showed that the linear recurrences that exponential sums of trapezoid Boolean functions satisfy are the same as the ones satisfied by exponential sums of the corresponding rotations symmetric Boolean functions. Finally, it is proved that exponential sums of trapezoid and symmetric polynomials also satisfy linear recurrences with integer coefficients over any Galois field . Moreover, the Discrete Fourier Transform matrix and some Complex Hadamard matrices appear as examples in some of our explicit formulas of these recurrences. 相似文献
1000.
Tetsuya Sato 《Journal of Pure and Applied Algebra》2018,222(10):2888-2896
We show that the Giry monad is not strong with respect to the canonical symmetric monoidal closed structure on the category Meas of all measurable spaces and measurable functions. 相似文献