다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms in current use. DE operates through similar computational steps as employed by a standard evolutionary algorithm (EA). However, unlike traditional EAs, the DE-variants perturb the current-generation population members with the scaled differences of randomly selected and distinct population members. Therefore, no separate probability distribution has to be used for generating the offspring. Since its inception in 1995, DE has drawn the attention of many researchers all over the world resulting in a lot of variants of the basic algorithm with improved performance. This paper presents a detailed review of the basic concepts of DE and a survey of its major variants, its application to multiobjective, constrained, large scale, and uncertain optimization problems, and the theoretical studies conducted on DE so far. Also, it provides an overview of the significant engineering applications that have benefited from the powerful nature of DE.

/pdf/differential-evolution-a-survey-of-the-state-of-the-art-3lz840pz2t.pdf

Differential Evolution: A Survey of the State-of-the-Art

Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

We introduce a mechanism for generating higher-order rogue waves (HRWs) of the nonlinear Schrodinger (NLS) equation: the progressive fusion and fission of n degenerate breathers associated with a critical eigenvalue λ(0) creates an order-n HRW. By adjusting the relative phase of the breathers in the interacting area, it is possible to obtain different types of HRWs. The value λ(0) is a zero point of an eigenfunction of the Lax pair of the NLS equation and it corresponds to the limit of the period of the breather tending to infinity. By employing this mechanism we prove two conjectures regarding the total number of peaks, as well as a decomposition rule in the circular pattern of an order-n HRW.

/pdf/generating-mechanism-for-higher-order-rogue-waves-tbe1fvral1.pdf

Generating mechanism for higher-order rogue waves.

The determinant representation of the $n$-fold Darboux transformation of the Hirota equation is given. Based on our analysis, the 1-soliton, 2-soliton, and breathers solutions are given explicitly. Further, the first order rogue wave solutions are given by a Taylor expansion of the breather solutions. In particular, the explicit formula of the rogue wave has several parameters, which is more general than earlier reported results and thus provides a systematic way to tune experimentally the rogue waves by choosing different values for them.

/pdf/multisolitons-breathers-and-rogue-waves-for-the-hirota-3roo7p6w29.pdf

Multisolitons, breathers, and rogue waves for the Hirota equation generated by the Darboux transformation.

The n-fold Darboux transformation (DT) is a 2 × 2 matrix for the Kaup–Newell (KN) system. In this paper, each element of this matrix is expressed by a ratio of the (n + 1) × (n + 1) determinant and n × n determinant of eigenfunctions. Using these formulae, the expressions of the q[n] and r[n] in the KN system are generated by the n-fold DT. Further, under the reduction condition, the rogue wave, rational traveling solution, dark soliton, bright soliton, breather solution and periodic solution of the derivative nonlinear Schrodinger equation are given explicitly by different seed solutions. In particular, the rogue wave and rational traveling solution are two kinds of new solutions. The complete classification of these solutions generated by one-fold DT is given.

https://iopscience.iop.org/article/10.1088/1751-8113/44/30/305203/pdf

The Darboux transformation of the derivative nonlinear Schrödinger equation

The n-fold Darboux transformation (DT) is a 2\times2 matrix for the Kaup-Newell (KN) system. In this paper,each element of this matrix is expressed by a ratio of $(n+1)\times (n+1)$ determinant and $n\times n$ determinant of eigenfunctions. Using these formulae, the expressions of the $q^{[n]}$ and $r^{[n]}$ in KN system are generated by n-fold DT. Further, under the reduction condition, the rogue wave,rational traveling solution, dark soliton, bright soliton, breather solution, periodic solution of the derivative nonlinear Schrodinger(DNLS) equation are given explicitly by different seed solutions. In particular, the rogue wave and rational traveling solution are two kinds of new solutions. The complete classification of these solutions generated by one-fold DT is given in the table on page.

/pdf/the-darboux-transformation-of-the-derivative-nonlinear-schr-5em3how0g2.pdf

The Darboux transformation of the derivative nonlinear Schr\"odinger equation

A Wronskian formulation leading to rational solutions is presented for the Boussinesq equation. It involves third-order linear partial differential equations, whose representative systems are systematically solved. The resulting solutions formulas provide a direct but powerful approach for constructing rational solutions, positon solutions and complexiton solutions to the Boussinesq equation. Various examples of exact solutions of those three kinds are computed. The newly presented Wronskian formulation is different from the one previously presented by Li et al., which does not yield rational solutions.

Jingsong He

Papers

Generating mechanism for higher-order rogue waves.

Multisolitons, breathers, and rogue waves for the Hirota equation generated by the Darboux transformation.

The Darboux transformation of the derivative nonlinear Schrödinger equation

The Darboux transformation of the derivative nonlinear Schr\"odinger equation

A second Wronskian formulation of the Boussinesq equation