The area A inside a simple closed curve C can be estimated graphically by drawing a square lattice of sides 1/M. The number of lattice points inside C is approximately AM. If C has continuous non-zero radius of curvature, then the number of lattice points is accurate to order of magnitude at most M for any a> §. We show that if the radius of curvature of C is continuously differentiate, then th...

Cluster Deletion and Cluster Editing ask to transform a graph by at most k edge deletions or edge edits, respectively, into a cluster graph, i.e., disjoint union of cliques. Equivalently, a cluster graph has no conflict triples, i.e., two incident edges without a transitive edge. We solve the two problems in time O∗(1.415k) and O∗(1.76k), respectively. These results round off our earlier work b...

Classicaly, the Hilbert class polynomial P∆ ∈ Z[X] of an imaginary quadratic discriminant ∆ is computed using complex analytic techniques. In 2002, Couveignes and Henocq [5] suggested a p-adic algorithm to compute P∆. Unlike the complex analytic method, it does not suffer from problems caused by rounding errors. In this paper we complete the outline given in [5] and we prove that, if the Genera...

P and time are integral dimensions of virtually any decision. To treat them together, we consider the prospect of receiving outcome x with a probability p at time t. We define risk and time distance, and show that if these two distances are traded off linearly, then preferences are characterized by three functions: a value function, a probability discount rate function, and a psychological dist...

In this paper, we present a genetic algorithm (GA) for optimization of a multi-mode resource constrained time cost trade off (MRCTCT) problem. The proposed GA, each activity has several operational modes and each mode identifies a possible executive time and cost of the activity. Beyond earlier studies on time-cost trade-off problem, in MRCTCT problem, resource requirements of each execution mo...

We show that any real matrix can be rounded to an integer matrix in such a way that the rounding errors of all row sums are less than one, and the rounding errors of all column sums as well as all sums of consecutive row entries are less than two. Such roundings can be computed in linear time. This extends and improves previous results on rounding sequences and matrices in several directions. I...

zinc-nickel electrodeposits have been widely adopted for surface treatment of automobile steel sheet for high corrosion resistance. in this work the effect of pulse parameters on the zn-ni alloy electrodeposits was investigated. the hardness, thickness, corrosion resistance and composition of deposits thus produced were investigated. the surface topography of the deposits was also observed in s...

cumin (cuminum cyminum) is an annual suitable for the dry and semi-dry areas of iran. recently, farmers have chosen to plant cumin because it requires less water and growth time. however, at harvest time, the resistance of cumin seed to shatter is low and, if careful attention is not paid to this fact, a major portion of the crop can be lost. when the connection force of the seed decreases, see...