The present paper deals with the non-real eigenvalues for singular indefinite Sturm–Liouville problems. The lower bounds on non-real eigenvalues for this singular problem associated with a special separated boundary condition are obtained.

Dans ce papier, nous traitons le problème de minimisation dumakespan dans un flow shop hybride à deux étages avec machinesdédiées. En premier lieu, nous présentons des propriétés de base, unensemble de bornes inférieures et deux cas polynomiaux. En secondlieu, nous proposons une nouvelle heuristique qui exploite cespropriétés, et cherche à placer les jobs, en tenant compte pourchaque instance du problème, de la valeur de la borne inférieure.La dernière partie de ce travail présente les résultatsexpérimentaux d'une étude comparative avec une heuristique de lalittérature. L'analyse de ces résultats permet d'apprécier laqualité de notre proposition.

Linear programming techniques can be used in constructing schedules but theirapplication is not trivial. This in particular holds true if a trade-offhas to be made between computation time and solution quality. However,it turns out that – whenhandled with care – mixed integer linear programs may provide effectivetools. This is demonstrated in the successful approach to the benchmarkconstructed for the 2007 ROADEF computation challenge on scheduling problemsfurnished by France Telecom.

We investigate well-structured graph-driven parity-FBDDs, which strictly generalize the two well-known models parity OBDDs and well-structured graph-driven FBDDs. The first main result is a characterization of the complexity of Boolean functions represented by well-structured graph-driven parity-FBDDs in terms of invariants of the function represented and the graph-ordering used. As a consequence, we derive a lower bound criterion and prove an exponential lower bound for certain linear code functions. The second main result of this paper is a polynomial time algorithm that minimizes the number of nodes in a graph-driven parity-FBDD.

We show that one-way Π2-alternating Turing machines cannotaccept unary nonregular languages in o(log n) space. This holdsfor an accept mode of space complexity measure, defined asthe worst cost of any accepting computation. This lower boundshould be compared with the corresponding bound for one-wayΣ2-alternating machines, that are able to accept unarynonregular languages in space O(log log n). Thus, Σ2-alternation is more powerful than Π2-alternationfor space bounded one-way machines with unary inputs.

Lower and upper bounds of degree m for the probability of the union of n not necessarily exchangeable events are established. These bounds may be constructed to improve the Bonferroni and the Sobel–Uppuluri bounds.

An application to equi-correlated multivariate normal distribution is given.

This paper develops another canonical form for (0, 1)-matrices which may be used in the same spirit as the nearly decomposable matrix [5] or the k-nearly decomposable matrix [1], This form is intrinsic in each fully indecomposable matrix and does not require the replacement of any of its non-zero entries by 0's.

Let Un(f) denote the class of all n × n (0, 1)-matrices with precisely r-ones, r≥3, in each row and column. Then