Although the idea of using discrete methods for modeling partial differential equations occurred very early, the actual statement that cellular automata techniques can approximate the solutions of hydrodynamic partial differential equations was first discovered by Frisch, Hasslacher, and Pomeau. Their description of the derivation, which assumes the validity of the Boltzmann equation, appeared in the Physical Review Letters in April 1986. It is the intent of this book to provide some overview of the directions that lattice gas research has taken from 1986 to early 1989.
Quantum computing promises to solve problems which are intractable on digital computers. Highly parallel quantum algorithms can decrease the computational time for some problems by many orders of magnitude. This important book explains how quantum computers can do these amazing things. Several algorithms are illustrated: the discrete Fourier transform, Shor's algorithm for prime factorization; algorithms for quantum logic gates; physical implementations of quantum logic gates in ion traps and in spin chains; the simplest schemes for quantum error correction; correction of errors caused by imperfect resonant pulses; correction of errors caused by the nonresonant actions of a pulse; and numerical simulations of dynamical behavior of the quantum Control-Not gate. An overview of some basic elements of computer science is presented, including the Turing machine, Boolean algebra, and logic gates. The required quantum ideas are explained.
As Americans have grown in size, the incidence of diabetes has increased to epidemic proportions, so that what was once an uncommon disease now seems to be everywhere. According to the American Diabetes Association, 25.8 million adults and children in the United States currently suffer from diabetes—that’s 8.3 percent of the population. Gary Null teaches that we each have the power to control diabetes through nutrition and dietary regimens, exercise, mental composure, and healthy living habits. Through cutting-edge research and clear instruction, Gary Null empowers readers to take control of their health without the use of drugs. Did you know that ginseng and aloe vera help to normalize blood glucose levels? Have you considered how vaccines may be contributing to the rise in diabetes among children? No More Diabetes offers surprising information that could save your life, along with practical advice for becoming the healthiest version of yourself. In addition, readers will find tips for convincing a loved one with diabetes to take charge of his or her weight; recipes to make healthy eating fun and appealing; and input from several other experts, including Dr. Martin Feldman, a pioneer in complementary medicine, and award-winning Dr. Richard Brown, who discusses how stress contributes to diabetes.
Although the idea of using discrete methods for modeling partial differential equations occurred very early, the actual statement that cellular automata techniques can approximate the solutions of hydrodynamic partial differential equations was first discovered by Frisch, Hasslacher, and Pomeau. Their description of the derivation, which assumes the validity of the Boltzmann equation, appeared in the Physical Review Letters in April 1986. It is the intent of this book to provide some overview of the directions that lattice gas research has taken from 1986 to early 1989.
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