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[Page generation failure. The bibliography processor requires a browser with Javascript enabled.] It is known that the smallest complete bipartite graph which is not 3-choosable has 14 vertices. We show that the extremal configuration is unique. |

[Page generation failure. The bibliography processor requires a browser with Javascript enabled.] The usual tight-binding (TB) approximation, employed in electronic structure calculations, is extended to include the more-distant neighbor sites than the first. In doing so, a simple power law is adopted to describe the bond and overlap contributions, which enables the energy dispersion relation to... |

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[Page generation failure. The bibliography processor requires a browser with Javascript enabled.] The following questions are studied: Under what conditions does the existence of a (nonzero) fixed point for every member of a semigroup of matrices imply a common fixed point for the entire semigroup? What is the smallest number k such that the existence of a common fixed point for every k members ... |

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[Page generation failure. The bibliography processor requires a browser with Javascript enabled.] An approximate solution of the Klein-Gordon equation for the general Hulthen-type potentials in D -dimensions within the framework of an approximation to the centrifugal term is obtained. The bound state energy eigenvalues and the normalized eigenfunctions are obtained in terms of hypergeometric pol... |

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[Page generation failure. The bibliography processor requires a browser with Javascript enabled.] The distance from an arbitrary rank-one projection to the set of nilpotent operators, in the space of k x k matrices with the usual operator norm, is shown to be sec(pi/(k+2))/2. This gives improved bounds for the distance between the set of all non-zero projections and the set of nilpotents in the ... |

[Page generation failure. The bibliography processor requires a browser with Javascript enabled.] We analyze the polynomial solutions of the linear differential equation p2(x)y″+p1(x)y′+p0(x)y=0 where pj(x) is a jth-degree polynomial. We discuss all the possible polynomial solutions and their dependence on the parameters of the polynomials pj(x). Special cases are related to known differenti... |

[Page generation failure. The bibliography processor requires a browser with Javascript enabled.] We prove that it is relatively consistent with ZFC that in any perfect Polish space, for every nonmeager set A there exists a nowhere dense Cantor set C such that A boolean AND C is nonmeager in C. We also examine variants of this result and establish a measure theoretic analog. |

[Page generation failure. The bibliography processor requires a browser with Javascript enabled.] We construct an irreducible multiplicative semigroup of non-negative square-zero operators acting on L-P[0, 1), for 1 less than or equal to p < infinity. |

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[Page generation failure. The bibliography processor requires a browser with Javascript enabled.] Let P be a poset, consisting of all sets X subset of or equal to [n] = {1, 2, ..., n} which contain at least one of a given collection F of 2-subsets of [n], ordered by inclusion. By modifying a construction of Greene and Kleitman, we show that if F is hamiltonian, that is, contains {1, 2}, {2, 3}, ... |

[Page generation failure. The bibliography processor requires a browser with Javascript enabled.] The asymptotic iteration method is used to find exact and approximate solutions of Schrödinger’s equation for a number of one-dimensional trigonometric potentials (sine-squared, double-cosine, tangent-squared, and complex cotangent). Analytic and approximate solutions are obtained by first using ... |

[Page generation failure. The bibliography processor requires a browser with Javascript enabled.] Recursive procedures are found for calculating the kth-order entropy of non-periodic sequences. These entropies are used as measures of disorder of the sequences and we treat: the Fibonacci sequence and generalizations; the Thue-Morse sequence together with generalizations and the period-doubling se... |