? = 0(r = 0), i^=-F(i), (r=l) dr u dr where Fit) is an empirical function of t. In all cases, as far as the authors are aware, the differential coefficients in (1) are considered separately when replaced by differences, and the principal term in du the truncation error of any difference formula obtained in this way contains — and ö u —Z-. This can be seen by obtaining the time derivatives of u ...

In this paper we give a new proof of the universality of the Tutte polynomial for matroids. This proof uses appropriate characters of Hopf algebra of matroids, algebra introduced by Schmitt (1994). We show that these Hopf algebra characters are solutions of some differential equations which are of the same type as the differential equations used to describe the renormalization group flow in qua...

We study quantized dual graded graphs, which are graphs equipped with linear operators satisfying the relation DU − qUD = rI. We construct examples based upon: the Fibonacci differential poset, permutations, standard Young tableau, and plane binary trees.

Part 1. Geometry of Curves We assume that we are given a parametric space curve of the form (1) x(u) =   x 1 (u) x 2 (u) x 3 (u)   u 0 ≤ u ≤ u 1 and that the following derivatives exist and are continuous (2) x (u) = dx du x (u) = d 2 x du 2 1. Arc Length The total arc length of the curve from its starting point x(u 0) to some point x(u) on the curve is defined to be (3) s(u) = u u 0 √ x ·x...

After analysing the Wiener process characteristics of reservoir storage capacity in flood regulation, an Ito stochastic differential equation including a random input term is proposed to describe and estimate the stochastic reservoir level hydrograph in a flood routing process. An expression of risk for flood release is given and the probability density functions of the reservoir level hydrogra...

We present a framework that unifies several standard differential techniques. This unified view allows us to consider many, potentially all, output differences for a given input difference and to combine the information derived from them in an optimal way. We then propose a new attack that implicitly mounts several standard, truncated, impossible, improbable and possible future variants of diff...

The purpose of this study was to investigate the underlying mechanism of metallothionein (MT) protection from depleted uranium (DU) using a proteomics approach to search for a DU toxicity-differential protein. MT-/- and MT+/+ mice were administrated with a single dose of DU (10 mg/kg, i.p.) or equal volume of saline. After 4 days, protein changes in kidney tissues were evaluated using a proteom...