Approximate nucleolus-based revenue sharing in airline alliances

Alliances allow the airlines to extend their networks and increase the number of destinations they can access. Different from the traditional single airline approach, in an alliance, partner airlines may sell tickets for the same itinerary. In addition, one itinerary may consist of several flight legs, each of which may be operated by a different airline. A major issue that needs to be addressed is how to share the revenue generated from selling a ticket for a product among the individual airlines in a fair way. The fair allocation of the revenue has a critical importance for the long-term stability of the alliance. We model the problem as a cooperative game and show that the core of the game is non-empty. We propose to use a revenue proration scheme based on the concept of the nucleolus. The numerical studies reveal that the revenue shares can effectively be computed even for large alliance networks.     

The beauties of calorimetry An overview

This paper gives a short overview of direct and indirect calorimetric experiments to determine the heat production or at least the metabolic turnover of whole plants or their blossoms. A special emphasis is placed on thermogenic plants because of their high specific heat production rates equal to those of mammals or birds and sometimes even surpassing them.     

Infrared thermography and thermometry of phototropic plants

Thermal investigations using infrared (IR) thermometry and false colour thermography were carried out on flowering plants in the Botanical Garden of Berlin and in a private garden. Special interest went to phototropic plants that orient their blossoms towards a light source (mainly the sun) and within this group to solar trackers (heliotropism) that follow the path of the sun during the day. Best known among the latter is the sunflower. Bowl shaped flowers comparable to satellite disks focus the solar radiation effectively on their centre, resulting in a warming of the female organs at that point. Temperature differences above ambient can be as high as 10.7 K with a mean value of 6.0 K. Pollinating insects were often observed sun-basking in the bowls or on the flower disks attracted by energetic rewards in form of nectar and heat.     

Zyklische Erweiterungen arithmetischer Funktionenkörper

Ohne ZusammenfassungHerrnFriedrich Karl Schmidt zum 60. Geburtstag am 22. 9. 1961 gewidmet     

A second-quantization framework for the unified treatment of relativistic and nonrelativistic molecular perturbations by response theory

A formalism is presented for the calculation of relativistic corrections to molecular electronic energies and properties. After a discussion of the Dirac and Breit equations and their first-order Foldy-Wouthuysen [Phys. Rev. 78, 29 (1950)] transformation, we construct a second-quantization electronic Hamiltonian, valid for all values of the fine-structure constant alpha. The resulting alpha-dependent Hamiltonian is then used to set up a perturbation theory in orders of alpha(2), using the general framework of time-independent response theory, in the same manner as for geometrical and magnetic perturbations. Explicit expressions are given to second order in alpha(2) for the Hartree-Fock model. However, since all relativistic considerations are contained in the alpha-dependent Hamiltonian operator rather than in the wave function, the same approach may be used for other wave-function models, following the general procedure of response theory. In particular, by constructing a variational Lagrangian using the alpha-dependent electronic Hamiltonian, relativistic corrections can be calculated for nonvariational methods as well.     

Construction and properties of quasi-linear functionals

Quasi-linear functionals are shown to be uniformly continuous and decomposable into a difference of two quasi-integrals. A predual space for the quasi-linear functionals inducing the weak*-topology is given. General constructions of quasi-linear functionals by solid set-functions and q-functions are given.

     

A refinement of Vietoris' inequality for sine polynomials

Let where In 1958, Vietoris proved that σ_n (x) is positive for all n ≥ 1 and x ∈ (0, π). We establish the following refinement. The inequalities hold for all natural numbers n and real numbers n ≥ 1 and x ∈ (0, π) if and only if