We present a new algorithm for the fast expansion of rational numbers into continued fractions. This algorithm permits to compute the complete set of integer Euler numbers of the sophisticate tree graph manifolds, whi...We present a new algorithm for the fast expansion of rational numbers into continued fractions. This algorithm permits to compute the complete set of integer Euler numbers of the sophisticate tree graph manifolds, which we used to simulate the coupling constant hierarchy for the universe with five fundamental interactions. Moreover, we can explicitly compute the integer Laplacian block matrix associated with any tree plumbing graph. This matrix coincides up to sign with the integer linking matrix (the main topological invariant) of the graph manifold corresponding to the plumbing graph. The need for a special algorithm appeared during computations of these topological invariants of complicated graph manifolds since there emerged a set of special rational numbers (fractions) with huge numerators and denominators;for these rational numbers, the ordinary methods of expansion in continued fraction became unusable.展开更多
Published accounts of beatific visions are extremely rare.However,three famous philosophers recorded their own experiences of this phenomenon.They were the Frenchman Blaise Pascal(1623-1662),the German Friedrich Nietz...Published accounts of beatific visions are extremely rare.However,three famous philosophers recorded their own experiences of this phenomenon.They were the Frenchman Blaise Pascal(1623-1662),the German Friedrich Nietzsche(1844-1900)and the Swiss Carl Jung(1875-1961).This article poses the question of whether such visions should be considered to be schizophrenic hallucinations.展开更多
文摘We present a new algorithm for the fast expansion of rational numbers into continued fractions. This algorithm permits to compute the complete set of integer Euler numbers of the sophisticate tree graph manifolds, which we used to simulate the coupling constant hierarchy for the universe with five fundamental interactions. Moreover, we can explicitly compute the integer Laplacian block matrix associated with any tree plumbing graph. This matrix coincides up to sign with the integer linking matrix (the main topological invariant) of the graph manifold corresponding to the plumbing graph. The need for a special algorithm appeared during computations of these topological invariants of complicated graph manifolds since there emerged a set of special rational numbers (fractions) with huge numerators and denominators;for these rational numbers, the ordinary methods of expansion in continued fraction became unusable.
文摘Published accounts of beatific visions are extremely rare.However,three famous philosophers recorded their own experiences of this phenomenon.They were the Frenchman Blaise Pascal(1623-1662),the German Friedrich Nietzsche(1844-1900)and the Swiss Carl Jung(1875-1961).This article poses the question of whether such visions should be considered to be schizophrenic hallucinations.
