Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 bulk metallic glasses were prepared by cooling the melt with a rate of about 10 K/s and investigated with respect to their chemical and structural homogeneity by atom probe field ion microscopy and transmission electron microscopy. The measurements on these slowly cooled samples reveal that the alloy exhibits phase separation in the undercooled liquid state. Signi...

For each sequence P = (p1(t), p2(t), . . . ) of polynomials we define a characteristic series of groups, called the derived series localized at P. Given a knot K in S, such a sequence of polynomials arises naturally as the orders of certain submodules of a sequence of higher-order Alexander modules of K. These group series yield filtrations of the knot concordance group that refine the (n)-solv...

We present an algorithm to compute the primary decomposition of any ideal in a polynomial ring over a factorially closed algorithmic principal ideal domain R. This means that the ring R is a constructive PID and that we are given an algorithm to factor polynomials over fields which are finitely generated over R or residue fields of R. We show how basic ideal theoretic operations can be performe...

In this talk, we will present an algorithm that computes the local algebra of the roots of a zero-dimensional polynomial equations system, whose cost is polynomial in the number of variables, in the evaluation cost of the equations and in the Bézout number of the input system. Let K be a field of characteristic zero, and let f1, . . . , fm, g be polynomials in K[x1, . . . , xn] such that the sy...

in this paper, a boussinesq equation is solved by using the adomian's decomposition method, modified adomian's decomposition method and homotopy analysis method. the approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. the existence and uniqueness of the solution and the convergence of the propose...