We consider a class of nonlinear singular perturbation problems of the form [ ] β = α = ∈ = + ′ + ′ ′ ε ) ( , ) ( ]; , [ ), ( ) , ( )) ( ( ) ( b y a y b a x x r y x q x y p x y with a boundary layer at one end point. Using the theory of singular perturbations, the original problem is reduced to an asymptotically equivalent first order initial value problem. Then, a variable step size in itial v...

We have devised one 160 bits improved hash algorithm based on MD5 and SHA1. And in additional, we also introduce four assistant functions named:F(X,Y,Z), G(X,Y,Z), H(X,Y,Z), and I(X,Y,Z) to do 4 rounds of 16 steps iterative operation with 32-bit data as input and 32-bit as output, saving in A, B, C, D respectively. Then we use one new extending function K(X,Y,Z) to expand 32-bit A, B, C, D to 4...

An interior path-following algorithm is proposed for solving the nonlinear saddle point problem minimax c T x + (x) + b T y ? (y) ? y T Ax subject to (x; y) 2 X Y R n R m ; where (x) and (y) are smooth convex functions and X and Y are boxes (hyper-rectangles). This problem is closely related to models in stochastic programming and optimal control studied by Rockafellar and Wets. Existence condi...

and Applied Analysis 3 min y f ( x, y ) s.t. g ( x, y ) ≥ 0, 2.1 where F x, y and f x, y are the upper level and the lower level objective functions, respectively. G x, y and g x, y denote the upper level and the lower level constraints, respectively. Let S { x, y | G x, y ≥ 0, g x, y ≥ 0}, X {x | ∃y, G x, y ≥ 0, g x, y ≥ 0}, S x {y | g x, y ≥ 0}, and for the fixed x ∈ X, let S X denote the wea...

Some time ago, Shpilrain and Yu reported an algorithm for deciding whether or not a polynomial p ∈ K[x, y] is a coordinate, or, equivalently, whether or not a plane curve p(x, y) = 0 is isomorphic to a line. Here K is any constructible field of characteristic 0. In this paper, we show that their algorithm requires O(n log2 n) field operations, where n is the degree of a given polynomial. We als...

In blind source separation measurement noise introduces biases in the esti mated coe cients of the separation matrix In this letter a simple modi cation to an adaptive algorithm for blind source separation is derived that mitigates these bi ases for reasonable signal to noise ratios when the correlations of the noises are known Index Terms adaptive algorithm bias removal blind source separation...

In this paper, we address the following problems: Given a sequence A of n real numbers, and four parameters I, J,X and Y with I ≤ J and X ≤ Y , find the longest (or shortest) subsequence of A such that its length is between I and J and its sum is between X and Y . We present an online and an offline algorithm for the problems, both run in O(n logn) time, which are optimal. key words: length con...

A digraph D is unilateral if for every pair x, y of its vertices there exists a directed path from x to y, or a directed path from y to x, or both. A mixed graph M = (V,A,E) with arc-set A and edgeset E accepts a unilateral orientation, if its edges can be oriented so that the resulting digraph is unilateral. In this paper, we present the first linear-time recognition algorithm for unilaterally...

The centrepiece of this paper is a normal form for primitive elements which facilitates the use of induction arguments to prove properties of primitive elements. The normal form arises from an elementary algorithm for constructing a primitive element p in F(x, y) with a given exponent sum pair (X, Y ), if such an element p exists. Several results concerning the primitive elements of F(x, y) are...