United States. National Aeronautics and Space Administration. Physical Oceanography Program

ECCO version 4: an integrated framework for non-linear inverse modeling and global ocean state estimation

Complete stability robustness of third-order LTI multiple time-delay systems

Parsing the Turing Test is a landmark exploration of both the philosophical and methodological issues surrounding the search for true artificial intelligence. Will computers and robots ever think and communicate the way humans do? When a computer crosses the threshold into self-consciousness, will it immediately jump into the Internet and create a World Mind? Will intelligent computers someday recognize the rather doubtful intelligence of human beings? Distinguished psychologists, computer scientists, philosophers, and programmers from around the world debate these weighty issues and, in effect, the future of the human race in this important volume.

Parsing the Turing Test: Philosophical and Methodological Issues in the Quest for the Thinking Computer

Brief A practical method for analyzing the stability of neutral type LTI-time delayed systems

A two-level procedure for heat-exchanger network synthesis problems, which is related to structural optimization, is carried out by a simulated-annealing procedure. The main control parameters, that is, the initial annealing temperature, the temperature length, and the temperature-decreasing scheme, are extensively studied on the well-known 10SP1 problem, and their values are used for solving a 5SP1 problem with forbidden matches and a larger scale problem, the 20SP1. In all cases, the structural search is initialized with the network involving only utilities. For each generated network, the operating conditions (temperatures and split rates) are optimized by an NLP procedure to minimize the sum of investment and operating costs. Particular attention is given to the size reduction of the NLP problem. The proposed procedure leads to a reduction by a factor of 3 of the problem size in terms of number of variables and constraints. This slave problem is solved by an SQP procedure from the IMSL Library.

Synthesis of heat‐exchanger network by simulated annealing and NLP procedures

This dictionary of numbers, arranged in order of magnitude, exposes the fascinating facts about certain numbers and number sequences. The aim of the book is to entertain and enthral the reader, which it certainly does.

The Penguin Dictionary of Curious and Interesting Numbers

Acknowledgments. Author's Note. Introduction. Entries A to Z. abc conjecture. abundant number. AKS algorithm for primality testing. aliquot sequences (sociable chains). almost-primes. amicable numbers. amicable curiosities. Andrica's conjecture. arithmetic progressions, of primes. Aurifeuillian factorization. average prime. Bang's theorem. Bateman's conjecture. Beal's conjecture, and prize. Benford's law. Bernoulli numbers. Bernoulli number curiosities. Bertrand's postulate. Bonse's inequality. Brier numbers. Brocard's conjecture. Brun's constant. Buss's function. Carmichael numbers. Catalan's conjecture. Catalan's Mersenne conjecture. Champernowne's constant. champion numbers. Chinese remainder theorem. cicadas and prime periods. circle, prime. circular prime. Clay prizes, the. compositorial. concatenation of primes. conjectures. consecutive integer sequence. consecutive numbers. consecutive primes, sums of. Conway's prime-producing machine. cousin primes. Cullen primes. Cunningham project. Cunningham chains. decimals, recurring (periodic). the period of 1/13. cyclic numbers. Artin's conjecture. the repunit connection. magic squares. deficient number. deletable and truncatable primes. Demlo numbers. descriptive primes. Dickson's conjecture. digit properties. Diophantus (c. AD 200 d. 284). Dirichlet's theorem and primes in arithmetic series. primes in polynomials. distributed computing. divisibility tests. divisors (factors). how many divisors? how big is d(n)? record number of divisors. curiosities of d(n). divisors and congruences. the sum of divisors function. the size of sigma(n). a recursive formula. divisors and partitions. curiosities of sigma(n). prime factors. divisor curiosities. economical numbers. Electronic Frontier Foundation. elliptic curve primality proving. emirp. Eratosthenes of Cyrene, the sieve of. Erdos, Paul (1913-1996). his collaborators and Erdos numbers. errors. Euclid (c. 330-270 BC). unique factorization. &Radic 2 is irrational. Euclid and the infinity of primes. consecutive composite numbers. primes of the form 4n +3. a recursive sequence. Euclid and the first perfect number. Euclidean algorithm. Euler, Leonhard (1707-1783). Euler's convenient numbers. the Basel problem. Euler's constant. Euler and the reciprocals of the primes. Euler's totient (phi) function. Carmichael's totient function conjecture. curiosities of phi(n). Euler's quadratic. the Lucky Numbers of Euler. factorial. factors of factorials. factorial primes. factorial sums. factorials, double, triple ... factorization, methods of. factors of particular forms. Fermat's algorithm. Legendre's method. congruences and factorization. how difficult is it to factor large numbers? quantum computation. Feit-Thompson conjecture. Fermat, Pierre de (1607-1665). Fermat's Little Theorem. Fermat quotient. Fermat and primes of the form x 2 + y 2 . Fermat's conjecture, Fermat numbers, and Fermat primes. Fermat factorization, from F 5 to F 30 . Generalized Fermat numbers. Fermat's Last Theorem. the first case of Fermat's Last Theorem. Wall-Sun-Sun primes. Fermat-Catalan equation and conjecture. Fibonacci numbers. divisibility properties. Fibonacci curiosities. Edouard Lucas and the Fibonacci numbers. Fibonacci composite sequences. formulae for primes. Fortunate numbers and Fortune's conjecture. gaps between primes and composite runs. Gauss, Johann Carl Friedrich (1777-1855). Gauss and the distribution of primes. Gaussian primes. Gauss's circle problem. Gilbreath's conjecture. GIMPS-Great Internet Mersenne Prime Search. Giuga's conjecture. Giuga numbers. Goldbach's conjecture. good primes. Grimm's problem. Hardy, G. H. (1877-1947). Hardy-Littlewood conjectures. heuristic reasoning. a heuristic argument by George Polya. Hilbert's 23 problems. home prime. hypothesis H. illegal prime. inconsummate number. induction. jumping champion. k-tuples conjecture, prime. knots, prime and composite. Landau, Edmund (1877-1938). left-truncatable prime. Legendre, A. M. (1752-1833). Lehmer, Derrick Norman (1867-1938). Lehmer, Derrick Henry (1905-1991). Linnik's constant. Liouville, Joseph (1809-1882). Littlewood's theorem. the prime numbers race. Lucas, Edouard (1842-1891). the Lucas sequence. primality testing. Lucas's game of calculation. the Lucas-Lehmer test. lucky numbers. the number of lucky numbers and primes. "random" primes. magic squares. Matijasevic and Hilbert's 10th problem. Mersenne numbers and Mersenne primes. Mersenne numbers. hunting for Mersenne primes. the coming of electronic computers. Mersenne prime conjectures. the New Mersenne conjecture. how many Mersenne primes? Eberhart's conjecture. factors of Mersenne numbers. Lucas-Lehmer test for Mersenne primes. Mertens constant. Mertens theorem. Mills' theorem. Wright's theorem. mixed bag. multiplication, fast. Niven numbers. odd numbers as p + 2a 2 . Opperman's conjecture. palindromic primes. pandigital primes. Pascal's triangle and the binomial coefficients. Pascal's triangle and Sierpinski's gasket. Pascal triangle curiosities. patents on prime numbers. Pepin's test for Fermat numbers. perfect numbers. odd perfect numbers. perfect, multiply. permutable primes. pi, primes in the decimal expansion of. Pocklington's theorem. Polignac's conjectures. Polignac or obstinate numbers. powerful numbers. primality testing. probabilistic methods. prime number graph. prime number theorem and the prime counting function. history. elementary proof. record calculations. estimating p(n). calculating p(n). a curiosity. prime pretender. primitive prime factor. primitive roots. Artin's conjecture. a curiosity. primordial. primorial primes. Proth's theorem. pseudoperfect numbers. pseudoprimes. bases and pseudoprimes. pseudoprimes, strong. public key encryption. pyramid, prime. Pythagorean triangles, prime. quadratic residues. residual curiosities. polynomial congruences. quadratic reciprocity, law of. Euler's criterion. Ramanujan, Srinivasa (1887-1920). highly composite numbers. randomness, of primes. Von Sternach and a prime random walk. record primes. some records. repunits, prime. Rhonda numbers. Riemann hypothesis. the Farey sequence and the Riemann hypothesis. the Riemann hypothesis and sigma(n), the sum of divisors function. squarefree and blue and red numbers. the Mertens conjecture. Riemann hypothesis curiosities. Riesel number. right-truncatable prime. RSA algorithm. Martin Gardner's challenge. RSA Factoring Challenge, the New. Ruth-Aaron numbers. Scherk's conjecture. semi-primes. sexy primes. Shank's conjecture. Siamese primes. Sierpinski numbers. Sierpinski strings. Sierpinski's quadratic. Sierpinski's phi(n) conjecture. Sloane's On-Line Encyclopedia of Integer Sequences. Smith numbers. Smith brothers. smooth numbers. Sophie Germain primes. safe primes. squarefree numbers. Stern prime. strong law of small numbers. triangular numbers. trivia. twin primes. twin curiosities. Ulam spiral. unitary divisors. unitary perfect. untouchable numbers. weird numbers. Wieferich primes. Wilson's theorem. twin primes. Wilson primes. Wolstenholme's numbers, and theorems. more factors of Wolstenholme numbers. Woodall primes. zeta mysteries: the quantum connection. Appendix A: The First 500 Primes. Appendix B: Arithmetic Functions. Glossary. Bibliography. Index.

Prime Numbers: The Most Mysterious Figures in Math

The appeal of games and puzzles is timeless and universal. In this unique book, David Wells explores the fascinating connections between games and mathematics, proving that mathematics is not just about tedious calculation but imagination, insight and intuition. The first part of the book introduces games, puzzles and mathematical recreations, including knight tours on a chessboard. The second part explains how thinking about playing games can mirror the thinking of a mathematician, using scientific investigation, tactics and strategy, and sharp observation. Finally the author considers game-like features found in a wide range of human behaviours, illuminating the role of mathematics and helping to explain why it exists at all. This thought-provoking book is perfect for anyone with a thirst for mathematics and its hidden beauty; a good high school grounding in mathematics is all the background that is required, and the puzzles and games will suit pupils from 14 years.

/pdf/games-and-mathematics-subtle-connections-1agn1poqsn.pdf

Games and Mathematics: Subtle Connections

Preamble: Young on The Teaching of Mathematics Introduction: Motivation and Mathematics Teaching Demotivating and Demotivated Pupils Motivating and Motivated Pupils Appreciating = Knowing About Mathematics Motivating Emotions: Beauty and Aesthetics Proof in School Classrooms Ways of Seeing Mathematics Euclidean Geometry as Game-Like The Scientific Approach to Mathematics Mathematics as Perception Mathematics Applied to Science Classrooms in Other Countries Rich Complexity False Simplicity Appendix: Jennifer Kano's Letter

Motivating Mathematics: Engaging Teachers And Engaged Students

A collection of strange mathematical facts and stories. This anthology covers a whole range of ages, maths and mathematicians, and includes probability paradoxes, jumbled Shakespearean sonnets, record-breaking monkeys and typewriters, and theories of big game hunting. Also featured are stories of people who looked for logical loopholes in the American Constitution, calmed their nerves with algebra or used sextants to measure the buttocks of Hottentot women.

The Penguin Book of Curious and Interesting Mathematics

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