Students' ability to solve word problems has an essential role in learning mathematics. However, some junior high school students still have difficulty solving problems. The difficulties experienced by cause errors when mathematical This qualitative study aims analyze students' the Least Common Multiple and Greatest Divisor Fifty-nine of Integrated Islamic Junior High School Al-Fahmi Palu were ...

Dear Charlie, I promised to write to you about the "characteristic-free" extension of Richard Brauer's Lemma: if a row permutation and a column permutation have the same effect on a nonsingular matrix, the two permutations must have the same number of cycles of any given length. Differently put: if two permutation matrices are conjugate in the general linear group, they are already conjugate in...

The problem of approximating the greatest common divisor(GCD) for polynomials with inexact coefficients can be formulated as a low rank approximation problem with Sylvester matrix. This paper presents a method based on Structured Total Least Norm(STLN) for constructing the nearest Sylvester matrix of given lower rank. We present algorithms for computing the nearest GCD and a certified 2-GCD for...

We give a reduction of the irregular case for the effective non-vanishing conjecture by virtue of the Fourier-Mukai transform. As a consequence, we reprove that the effective non-vanishing conjecture holds on algebraic surfaces. In this note we consider the following so-called effective non-vanishing conjecture, which has been put forward by Ambro and Kawamata [Am99, Ka00]. Conjecture 1 (ENn). ...

The interplay between the topology of cortical circuits and synchronized activity modes in distinct cortical areas is a key enigma in neuroscience. We present a new nonlocal mechanism governing the periodic activity mode: the greatest common divisor (GCD) of network loops. For a stimulus to one node, the network splits into GCD-clusters in which cluster neurons are in zero-lag synchronization. ...

(1) D(α) = D(K)(I(α))2, where I(α) = [OK : Z[α]], the index of the ring generated by α in the full ring of integers OK of K. Classically, the index of the field K is the greatest common divisor of all indices I(α) for α ∈ OK with K = Q(α). Dedekind was the first to show that the index may not be 1 by exhibiting certain cubic and quartic fields with this property. By results of Bauer and von Żyl...

We comment on the set of visible points of a lattice and its Fourier transform, thus continuing and generalizing previous work by Schroeder [1] and Mosseri [2]. A closed formula in terms of Dirichlet series is obtained for the Bragg part of the Fourier transform. We compare this calculation with the outcome of an optical Fourier transform of the visible points of the 2D square lattice. Recently...