Divisor

About: Divisor is a research topic. Over the lifetime, 2462 publications have been published within this topic receiving 21394 citations. The topic is also known as: factor & submultiple.

Recording method and apparatus for control track

Abstract: A method and apparatus for recording control pulses on a control track are provided. The control pulses correspond to a number M (where M is an integer equal to or larger than four) of azimuthal tracks on the tape on which the number M of segmented data, obtained by dividing image data corresponding to one frame into the number M of segments, are recorded. One period of the control pulses corresponds to a number N (where N is a divisor of M) of azimuthal tracks, and a duty ratio pattern of the control pulses in a number L (L=M/N) of successive periods corresponding to one frame is different in each of a number K (where K is an integer equal to or larger than two) of successive frames.

Positivity of log canonical divisors and Mori/Brody hyperbolicity

Abstract: Let X be a complex projective variety of dimension n, D a reduced divisor with a decomposition D = D_1 + ... + D_r, where the D_i's are reduced Cartier but not necessarily irreducible. The pair (X, D) is called Brody hyperbolic, respectively Mori hyperbolic, with respect to the decomposition if neither X - D nor (\cap_{i \in I} D_i) - (\cup_{j \in J} D_j) contains a non constant holomorphic image, respectively algebraic image, of C for every partition of {1, ..., r} = I \cupprod J. Assuming that the singularities of the pair (X, D) are mildly singular, we show that the log canonical divisor K_X + D is numerically effective in the case of Mori hyperbolicity and that K_X + D is ample provided that either n < 4 and D is non-empty or at least n-2 of the D_i's are ample in the case of Brody hyperbolicity.

System, method, and apparatus for division coupled with truncation of signed binary numbers

Abstract: A system, method, and apparatus for efficient rounding of signed numbers is presented herein. If the divisor is positive, the dividend is added to one half of the magnitude of the divisor. If the divisor is negative, the complement of the dividend is added to one half of the magnitude of the divisor. If the dividend is negative, and the divisor is also negative, one is added to the sum of the inverted dividend and one-half of the magnitude of the divisor. If the dividend is negative and the divisor is positive, one is subtracted from the sum of the dividend and one-half the magnitude of the divisor. The result is then right shifted x times. If the signs of the divisor and dividend are different, a most-significant-bit(sign-bit) of the result is shifted in as the most significant bit during each right shift. Otherwise, a “0” is shifted in.

Vanishing theorems for Dolbeault cohomology of log homogeneous varieties

Abstract: We consider a complete nonsingular variety $X$ over $\bC$, having a normal crossing divisor $D$ such that the associated logarithmic tangent bundle is generated by its global sections. We show that $H^i\big(X, L^{-1} \otimes \Omega_X^j(\log D)\big) = 0$ for any nef line bundle $L$ on $X$ and all $i j$, and gives back a vanishing theorem of Broer when $X$ is a flag variety.