Đang tải... (xem toàn văn)
Đây là bộ sách tiếng anh về chuyên ngành vật lý gồm các lý thuyết căn bản và lý liên quan đến công nghệ nano ,công nghệ vật liệu ,công nghệ vi điện tử,vật lý bán dẫn. Bộ sách này thích hợp cho những ai đam mê theo đuổi ngành vật lý và muốn tìm hiểu thế giới vũ trụ và hoạt động ra sao.
[...]... the parameters of interacting galaxies can be determined Another type of general purpose algorithm, the Monte Carlo method, is introduced along with several variants in the following chapter In the succeeding chapter the emphasis is on algorithms for spin glasses, which is a model that has been at the center of interest of statistical physicists over the last two decades In the twelfth chapter, a phase... from statistical physics, including phase transitions and finite-size scaling are given You can skip this chapter if you are familiar with the subject The main part of the book starts with the sixth chapter Many algorithms are presented along with sample problems from physics, which can be solved using the algorithms First, techniques to calculate the maximum flow in networks are exhibited They can be... solve the problem, it does not say anything about the elaborateness of the algorithms which are applied Additionally, within the class of hard or within the class of easy problcrns, there is no universal method Usually, even for each kind of problem there are many different ways t o obtain an optimum On the other hand, there are several universal algorithms, but they find only approximations of the true... observation that all reasonable machine models are equivalent has led t o the Church's thesis: "For any algorithm a program can be written on all reasonable machine models." Since the term algorithm cannot be defined exactly it is impossible t o prove Church's thesis Nobody has come up with an algorithm that cannot be transfered t o a computer Hence, it seems reasonable that this thesis is true In the... to A: It can be shown that SAT is NP-complete The proof is quite technical It requires an exact machine model for certificate-checking algorithms The basic idea is: each problem in NP has a certificate-checking algorithm For that algorithm, a given instance and a given certificate, an equivalent boolean formula is constructed which is only satisfiable if the algorithm answers "yes" given the instance... not is called the halting problem With a similar and related diagonalization argument as we have seen above, it can be shown that there is indeed no solution t o this problem It means that no universal algorithm exists which decides for all programs whether the program will halt with a given input or run forever On the other hand, if a test for the halting problem was available it would be easy t o... for the time complexity Again, in practice an algorithm with running time T3(n) = n3 may be faster for small input sizes than another with T4(n) = 100n2 But these kinds of examples are very rare and rather artificial In general, finding an algorithm which has a lower time complexity is always more effective than waiting for a computer t o arrive that is ten times faster Consider two algorithms with time... complexity theory are explained They are needed as a basis for understanding the rest of the book In the next chapter an introduction to graph theory is given Many physical questions can be mapped onto graph theoretical optimization problems Then, some simple algorithms from graph theory are explained, sample applications are from percolation theory are presented In the following chapter, the basic notions... problems in polynomial time A normal algorithm is deterministic, i.e from a given state of the algorithm, which consists of the values of all variables and the program line where the execution is at one moment, and the next state follows in a deterministic way Nondeterministic algorithms are able to choose the next state randomly Thus, a machine executing nondeterministic algorithms is just a theoretical... algorithm which answers "yes" with the instance as input Thus, both models are equivalent As we have stated above, different recognition problems can be mapped onto each other Since all algorithms which we encounter in this context are polynomial, only transformations are of interest which can be carried through in polynomial time as well (as a function of the length of an instance) The precise definition . class="bi x0 y0 w0 h0 " alt="" Alexander K. Hartmann, Heiko Rieger Optimization Algorithms in Physics