• • • Part of the book series (NAII, volume 72) Abstract The name of the technique takes its origin in 1964 paper of L. Among the earlier closely related approaches, one should mention J. Schwinger [ ] and R. Feynman and F. Classical counterparts of the Keldysh technique are extremely useful and interesting on their own. I shall mention Wyld diagrammatic technique [ ], which is the basis of the modern theory of turbulence; Martin-Siggia-Rose-DeDominics method [ ] for stochastic systems; and Doi-Peliti technique [, ] for reaction-diffusion systems and cellular automata.

Despite the unique power and wide popularity of the technique its pedagogical presentations are rare. One may find some in books [, ] or in a review [ ]. This lecture is not an alternative for the existing literature. Using the simplest possible example, I try to explain the general structure of the theory, its relation to other approaches, its potential for novel applications and open problems. Technicalities of the numerous practical applications may be found in the literature and left outside the scope of the lecture.

I tried hard, however, to mention possible traps and silent points which are rarely exposed explicitly. Cite this chapter as: Kamenev A. (2002) Keldysh and DOI-Peliti Techniques for Out-of-Equilibrium Systems. In: Lerner I.V., Althsuler B.L., Fal’ko V.I., Giamarchi T. (eds) Strongly Correlated Fermions and Bosons in Low-Dimensional Disordered Systems. NATO Science Series (Series II: Mathematics, Physics and Chemistry), vol 72. Springer, Dordrecht • DOI • Publisher Name Springer, Dordrecht • Print ISBN 978-1-4020-0749-1 • Online ISBN 978-94-010-0530-2 • eBook Packages • •.

Created Date: 2/14/2017 3:45:37 PM. PDF File (290 KB) Abstract; Article info and citation; First page; References; Abstract. Let (X ) be a separable Banach space, (Y ) a Banach space and (f:X to Y ) a Lipschitz function. Shadow of mordor free. We show that the set of all G ^ ateaux non-differentiability points at which (f ) has all one-sided or two-sided directional derivatives can be covered.

The Orthodox Jewish community of Berlin celebrated a welcoming of a Torah Scroll into the local synagogue at the beginning of the week. During the ceremony, led by Rabbi Yehuda Teichtal, rabbi of the Jewish community of Berlin, torches were held by children of the local Jewish community and by Syrian refugee children. 'We seek to live our lives in peace' stated Rabbi Teichtal in his speech, referring to endless arguments and debates before the upcoming Berlin election day. 'The Torah teaches us to love humanity as a whole and to always reach out to those in need', were the opening words in Rabbi Teichtal's speech. 'Unfortunately, we have been witnessing those who try and spread out hate while taking advantage of the fear and disorderly feelings at this time.

This kind of manner is one far from the Jewish customs and Jewish values. We mustn't forget that regardless of the time, and no matter what the political arguments are, we must unite as a whole and together look forward to a time of peace'. Later in his speech, Rabbi Teichtal directed his words to the Syrian refugee children 'It is an honor for me that you joined us today and celebrated with us. God has brought us all to this part of the world. I wish that we all do our best to allow us all to live in love and peace together'. 'Despite the tension in the air in Berlin before the upcoming elections on September 18th, this parade was walking to the beat of a different drummer.

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