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.     

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.

     

Kinetic and thermodynamic stability of naphthalene oxide and related compounds. A comparative microcalorimetric and computational (DFT) study

The kinetics of the acid-catalyzed ring opening of naphthalene 1,2-oxide (5) in highly aqueous media to give naphthols has been measured by heat-flow microcalorimetry. The reaction enthalpy of this aromatization reaction was measured as DeltaH = -51.3 +/- 1.7 kcal mol(-)(1). The unexpectedly low reactivity of naphthalene oxide is suggested to be due to an unusually large thermodynamic stability. A crude estimate of the stabilization effect, approximately 1 kcal mol(-)(1)(not a significant stabilization), is obtained by using the measured reaction enthalpies of structurally related substrates as references. A larger value (2.7 kcal mol(-)(1)) was obtained by calculation using the B3LYP hybrid functional corrected with solvation energies derived from semiempirical AM1/SM2 calculations. The origin of this effect is discussed in terms of homoconjugative stabilization and homoaromaticity. There is a good linear correlation (with slope = 0.63) between the experimentally measured free energy of activation and the calculated enthalpy of carbocation formation in water.     

New Microphase‐Separated Diblock Copolymers Carrying Semifluorinated Side Groups Prepared by ROMP

We prepared new varied diblock copolymers by ring‐opening metathesis polymerization of functionalized norbornenes and cyclooctene in the presence of Schrock‐type initiators, either [Mo(CHCMe₂Ph)(N‐2,6‐iPr₂Ph)(OCCH₃(CF₃)₂)₂] or [Mo(CHCMe₂Ph)(N‐2,6‐iPr₂Ph)(OC(CH₃)₃)₂]. The block copolymers were microphase separated and presented the individual phases of each polymer block constituent, that were amorphous/amorphous, amorphous/semicrystalline, or semicrystalline/liquid‐crystalline. One example of such a block copolymer is shown.