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.

Arithmetic unit and information processor

Abstract: PROBLEM TO BE SOLVED: To speed up dividing process at the time of quantization by using the quotient obtained by dividing 1st data by 2nd data as the result of a comparison of large/small relation between each multiplication result and the 1st data. SOLUTION: Respective multipliers 18 to 25 multiply given divisors by specified multipliers. Respective comparators 26 to 33 inputs tmp as a DCT coefficient and a divisor which is multiplied as specified and compare the both with each other, thereby outputting '1' as their comparison results when tmp is less than the divisor which is multiplied as specified. When tmp is larger than the divisor, on the other hand, the comparators 26 to 33 output '0' as their comparison results. The comparators 26 to 32 supply their output values to a counter 34. Further, the comparator 33 supplies the output value as its comparison result to a computing element 14. Namely, the comparator 33 informs the computing element 14 of the result of the comparison between tmp and the multiplied divisor as a decision result showing whether or not tmp meets specific requirements.

On The Period of Sequences Modulo a Prime Satisfying A Second order Recurrence

Abstract: Let u n be an integer sequence satisfying u n+2=u n+1+u n and y be a, divisor of x 2 + x = 1 for an integer x. Juan Pla proved in [5] that the sequence w n defined by w n = xu n + 1 - u n satisfies one of the following two cases.

Random number generation system

Abstract: PURPOSE:To make it possible to generate various random numbers of a high random number property by dividing a counted value by an indicated divisor at a time indicated by a divisor controller and taking out the remainder to generate random numbers smaller than the divisor CONSTITUTION:Noise from noise generation source 1 is converted to a square wave by amplitude limiter 2, and the number of square waveforms of a random period is always counted by counter 3 Progress of this counting is random in respect to time, and the counter is reset to start counting from 0 again when the counted value reaches a maximum counted value The counted value is divided by an indicated divisor at a time indicated by divisor controller 5 in divider 4, and the remainder is taken out from remainder output terminal 6 of divider 4, thus generating random numbers smaller than the remainder Thus, various random numbers of a high random number property can be generated

Branched projective structures, branched $$\mathrm{SO}(3,{\mathbb {C}})$$ SO ( 3 , C ) -opers and logarithmic connections on jet bundle

Abstract: We study the branched holomorphic projective structures on a compact Riemann surface X with a fixed branching divisor $$S\, =\, \sum _{i=1}^d x_i$$ , where $$x_i \,\in \, X$$ are distinct points. After defining branched $$\mathrm{SO}(3,{\mathbb C})$$ -opers, we show that the branched holomorphic projective structures on X are in a natural bijection with the branched $$\mathrm{SO}(3,{\mathbb C})$$ -opers singular at S. It is deduced that the branched holomorphic projective structures on X are also identified with a subset of the space of all logarithmic connections on $$J^2((TX)\otimes {\mathcal O}_X(S))$$ singular over S, satisfying certain natural geometric conditions.

Equidistribution of Hodge loci II

Abstract: Let $H\subset G$ be semisimple Lie groups, $\Gamma\subset G$ a lattice and $K$ a compact subgroup of $G$. For $n \in \mathbb N$, let $\mathcal O_n$ be the projection to $\Gamma \backslash G/K$ of a finite union of closed $H$-orbits in $\Gamma \backslash G$. In this very general context of homogeneous dynamics, we prove an equidistribution theorem for intersections of $\mathcal O_n$ with an analytic subvariety $S$ of $G/K$ of complementary dimension: if $\mathcal O_n$ is equidistributed in $\Gamma \backslash G/K$, then the signed intersection measure of $S \cap \mathcal O_n$ normalized by the volume of $\mathcal O_n$ converges to the restriction to $S$ of some $G$-invariant closed form on $G/K$. We give general tools to determine this closed form and compute it in some examples. As our main application, we prove that, if $\mathbb V$ is a polarized variation of Hodge structure of weight $2$ and Hodge numbers $(q,p,q)$ over a base $S$ of dimension $rq$, then the (non-exceptional) locus where the Picard rank is at least $r$ is equidistributed in $S$ with respect to the volume form $c_q^r$, where $c_q$ is the $q^{\textrm{th}}$ Chern form of the Hodge bundle. This generalizes a previous work of the first author which treated the case $q=r=1$. We also prove an equidistribution theorem for certain families of CM points in Shimura varieties, and another one for Hecke translates of a divisor in $\mathcal A_g$.