A k-path is a hypergraph Pk = {e1, e2, . . . , ek} such that |ei ∩ ej | = 1 if |j − i| = 1 and ei ∩ ej = ∅ otherwise. A k-cycle is a hypergraph Ck = {e1, e2, . . . , ek} obtained from a (k − 1)path {e1, e2, . . . , ek−1} by adding an edge ek that shares one vertex with e1, another vertex with ek−1 and is disjoint from the other edges. Let exr(n,G) be the maximum number of edges in an r-graph wi...

Workflow Management Systems (WFMS) coordinate execution of logically related multiple tasks in an organization. Each workflow that is executed on such a system is an instance of some workflow schema. A workflow schema is defined using a set of tasks that are coordinated using dependencies. Workflows generated from the same schema may differ with respect to the tasks executed. An important issue...

We prove that if a paratopological group G is a continuous image of an arbitrary product of regular Lindelöf Σ-spaces, then it is R-factorizable and has countable cellularity. If in addition, G is regular, then it is totally ω-narrow and satisfies celω(G) ≤ ω, and the Hewitt–Nachbin completion of G is again an R-factorizable paratopological group.

Some stochastic models for the copy number of plasmids in a cell line are studied. When considering the behavior of copy number in the whole cell line, the theory of multitype branching processes is appropriate. Attention is paid to the cure rate in the cell line, and the asymptotic fractions of cells containing a given number of plasmids. These quantities are used to compare the models numeric...

vVe prove lower bounds on the competitive ratio of randomized algorithms for several on-line scheduling problems. The main result is a bound of ej(e 1) for the on-line problem with objective minimizing the sum of completion times of jobs that arrive over time at their release times and are to be processed on a single machine. This lower bound shows that a randomized algorithm designed in [Cheku...

We study a problem of optimal scheduling and lot-sizing a number of products on m unrelated parallel machines to satisfy given demands. A sequence dependent setup time is required between lots of different products. The products are assumed to be all continuously divisible or all discrete. The criterion is to minimize the time, at which all the demands are satisfied, Cmax, or the maximum latene...

We study a problem of optimal scheduling and lot-sizing a number of products on m unrelated parallel machines to satisfy given demands. A sequence dependent setup time is required between lots of different products. The products are assumed to be all continuously divisible or all discrete. The criterion is to minimize the time, at which all the demands are satisfied, Cmax, or the maximum latene...