To formulate a single-leg seat inventory control problem in an airline ticket sales system, the concept and techniques of revenue management are applied in this research. In this model, it is assumed the cabin capacity is stochastic and hence its exact size cannot be forecasted in advance, at the time of planning. There are two groups of early-reserving and late-purchasing customers demanding t...

The clustering problem as a problem of set function optimization with constraints is considered. The behavior of quasi-concave functions on antimatroids and on convex geometries is investigated. The duality of these two set function optimizations is proved. The greedy type Chain algorithm, which allows to find an optimal cluster, both as the “most distant” group on antimatroids and as a dense c...

The object of this paper is to revisit the results of P. Bernhard (J. Optim. Theory Appl. 27 (1979), 51–69) on two-person zero-sum linear quadratic differential games and generalize them to utility functions without positivity assumptions on the matrices acting on the state variable and to linear dynamics with bounded measurable data matrices. The paper specializes to state feedback via Lebesgu...

Let di(m) denote the coefficients of the Boros-Moll polynomials. Moll’s minimum conjecture states that the sequence {i(i+1)(di (m)−di−1(m)di+1(m))}1≤i≤m attains its minimum at i = m with 2−2mm(m + 1) ( 2m m )2 . This conjecture is stronger than the log-concavity conjecture proved by Kauers and Paule. We give a proof of Moll’s conjecture by utilizing the spiral property of the sequence {di(m)}0≤...

Winning bids in reverse auctions are efficient solutions (providing that fairly weak assumptions about the bidders are met). The auctions are efficient, un‐der the assumption that the utilities of all participants are quasi‐linear. This assumption is often unrealistic. Typically then, auctions are inefficient mechanisms. This paper presents the limitations and impracticability of the quasi‐ lin...

Simion had a unimodality conjecture concerning the number of lattice paths in a rectangular grid with the Ferrers diagram of a partition removed. Hildebrand recently showed the stronger result that these numbers are log concave. Here we present a simple proof of Hildebrand’s result.

In this paper we give estimates of tails and moments of multidimensional chaoses P ai1,...,idX (1) i1 · · ·X id (ai1,...,id ≥ 0) generated by positive random variables X (1) i1 , . . . , X (d) id with logarithmically concave tails. The estimates are exact up to constants depending only on the dimension d.

We study a simple model of factor saving technological innovation in a concave framework. Capital can be used either to reproduce itself or, at additional cost, to produce a higher quality of capital that requires less labor input. If higher quality capital can be produced quickly, we get a model of exogenous balanced growth as a special case. If, however, higher quality capital can be produced...

In this note we make several observations concerning symplectic cobordisms. Among other things we show that every contact 3-manifold has in nitely many concave symplectic llings and that all overtwisted contact 3-manifolds are \symplectic cobordism equivalent".