1. Machines Extend Proposition 151. 1(the Perfect Folk Theorem with discounting)to arbitrary mixtures of payoff profiles of the original game G=(N, (Ai, lilieN Allow for both rational and real weights on the set of profiles u(a): aE A]; note that the statement of the result will involve an approximation of the payoff profile Construct a machine that implements the strategies in your proof

Chapter 1：前史——Isaac Newton Chapter 2 ：量子力学预备 Chapter 3：前量子论中的原子 Chapter 4 Max Planck——The Birth of the Quantum Adventure Chapter 5 ：Light——Wave or Projectile? Chapter 6：Einstein Enters the Scene Chapter 7：Niels Bohr Introduces the Quantum into Atomic Physics Chapter 8 Werner Heisenberg——An Equation for Uncertainty Chapter 9 Louis de Broglie——Matter Waves Chapter 10 Erwin Schrodinger——Wave Mechanics Chapter 11 Eigenstates——The Theory of the Seen and Unseen Chapter 12 Eigenstates in the Subnuclear World Chapter 13 Paul Dirac——Tying Things Together Chapter 14 Richard Feynman——The Strange Theory of Light and Matter Chapter 15 Quantum Reality——The World of the Absurd

Non-Inertial Reference Frame Gravitational attraction The Law of Universal Attraction was already introduced in lecture D1. The law postulates that the force of attraction between any two particles, of masses M and m, respectively, has a magnitude, F, given by F= (1) where r is the distance between the two particles, and G is the universal constant of gravitation. The value of G is empirically determined to be

Textures in different layers of superconductors based on YBGO system are analyzed using the methods of pole figure and conventional Φ scans. It is shown that the Φ scanning technology has only 1-dimensional description and could omit some information of 3-dimensional orientation distribution, which will in-fluence the superconductor quality. The pole figure method, in contrast, demonstrates the orientation distribution 2-dimensionally and gives a comprehensive view of thin film texture, which is a much better method for texture analysis in superconducting films,in which there is commonly an unique high sharpness texture com-ponent

So far we have used Newton's second law= ma to establish the instantaneous relation between the sum of the forces acting on a particle and the acceleration of that particle. Once the acceleration is known,the velocity (or position) is obtained by integrating the expression of the acceleration (or velocity). There are two situations in which the cumulative effects of unbalanced forces acting on a particle are of interest to us. These involve:

In addition to the equations of linear impulse and momentum considered in the previous lecture, there is a parallel set of equations that relate the angular impulse and momentum. Angular Momentum We consider a particle of mass, m, with velocity v, moving under the influence of a force F. The angular momentum about point O is defined as the \moment\ of the particle's linear

In this lecture we will consider the equations that result from integrating Newtons second law, F=ma, in time. This will lead to the principle of linear impulse and momentum. This principle is very useful when solving problems in which we are interested in determining the global effect of a force acting on a particle over a time interval Linear momentum We consider the curvilinear motion of a particle of mass, m, under the influence of a force F. Assuming that

In this lecture we will look at some other common systems of coordinates. We will present polar coordinates in two dimensions and cylindrical and spherical coordinates in three dimensions. We shall see that these systems are particularly useful for certain classes of problems Like in the case of intrinsic coordinates presented in the previous lecture, the reference frame changes from point to point. However, for the coordinate systems to be presented below, the reference frame depends only on the position of the particle. This is in contrast with the intrinsic coordinates, where the reference frame is a function of the position, as well as the path

Gene mutation and evolution Gradual accumulation of mutations over long periods of time results in new biological species, each with a unique DNA sequence. Mutations and stabilization of mutations to new species. Charles Darwin: Unifying evolution theory-the origin of species from a common ancestor

Definition: intra-articular and extra-articular processes may restrictjaw motion severely. Ankylosis of the TMJ is an intra-articular process characterized by fibrous,fibo- -osseous, or osseous obliteration(消失) of the joint space. Extracapsular causes of restricted jaw motion (pseudoankylosis) include but are not limited to coronoid-zygomatic fusion(融合), coronoid hypertropy, and muscular fibrosis