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

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

Convergence of probability measures

We propose a definition of entropy production in the framework of algebraic quantum statistical mechanics. We relate our definition to heat flows through the system. We also prove that entropy production is non-negative in natural non-equilibrium steady states.

/pdf/on-entropy-production-in-quantum-statistical-mechanics-12wqwgfzar.pdf

On Entropy Production in Quantum Statistical Mechanics

1 Zentrum Mathematik M5, Technische Universitat Munchen, D-85747 Garching, Germany e-mail: hbar@ma.tum.de 2 Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, QC, H3A 2K6, Canada e-mail: jaksic@math.mcgill.co 3 Laboratoire de Mathematiques, Universite Paris-Sud, 91405 Orsay cedex, France e-mail: yan.pautrat@math.u-psud.fr 4 CPT-CNRS, UMR 6207, Universite du Sud, Toulon-Var, B.P. 20132, 83957 La Garde Cedex, France e-mail: pillet@univ-tln.fr

/pdf/topics-in-non-equilibrium-quantum-statistical-mechanics-36jl636jdb.pdf

Topics in non-equilibrium quantum statistical mechanics

In this paper we study the dynamics of fermionic mixed states in the mean-field regime. We consider initial states that are close to quasi-free states and prove that, under suitable assumptions on the initial data and on the many-body interaction, the quantum evolution of such initial data is well approximated by a suitable quasi-free state. In particular, we prove that the evolution of the reduced one-particle density matrix converges, as the number of particles goes to infinity, to the solution of the time-dependent Hartree-Fock equation. Our result holds for all times and gives effective estimates on the rate of convergence of the many-body dynamics towards the Hartree-Fock evolution.© 2015 Wiley Periodicals, Inc.

/pdf/mean-field-evolution-of-fermionic-mixed-states-1vk1m19laf.pdf

Mean‐Field Evolution of Fermionic Mixed States

We consider a class of models in which a Hamiltonian system A, with a finite number of degrees of freedom, is brought into contact with an infinite heat reservoir B. We develop the formalism required to describe these models near thermal equilibrium. Using a combination of abstract spectral techniques and harmonic analysis we investigate the singular spectrum of the Liouvillean L of the coupled system A+B. We provide a natural set of conditions which ensure that the spectrum of L is purely absolutely continuous except for a simple eigenvalue at zero. It then follows from the spectral theory of dynamical systems (Koopmanism) that the system A+B is strongly mixing. From a probabilistic point of view, we study a new class of random processes on finite dimensional manifolds: non-Markovian Ornstein-Uhlenbeck processes. The paths of such a process are solutions of a random integro-differential equation with Gaussian noise which is a natural generalization of the well known Langevin equation. In this context we establish that, under appropriate conditions, the OU process is strongly mixing even when the Langevin equation has memory and is driven by non-white noise.

/pdf/ergodic-properties-of-classical-dissipative-systems-i-3d9a2nm7ge.pdf

Ergodic properties of classical dissipative systems I

These notes are an expanded and revised version of the lectures given by the second and fourth autor in the summer school "Open Quantum System" held in Grenoble, June 16-July 4, 2003. They provide an introduction to recent developments in non-equilibrium statistical mechanics of open quantum systems, including a completely worked out (simple) example. We discuss non-equilibrium steady states (NESS) and their structural properties, entropy production, linear response theory and weak coupling limit. The emphasis is on Ruelle's scattering approach to the construction of NESS.

/pdf/topics-in-nonequilibrium-quantum-statistical-mechanics-8zvqrpthch.pdf

Vojkan Jaksic

Papers

On Entropy Production in Quantum Statistical Mechanics

Topics in non-equilibrium quantum statistical mechanics

Mean‐Field Evolution of Fermionic Mixed States

Ergodic properties of classical dissipative systems I

Topics in nonequilibrium quantum statistical mechanics