Players Indifferent to Cooperate and Characterizations of the Shapley Value

In this paper we provide new axiomatizations of the Shapley value for TU-games using axioms that are based on relational aspects in the interactions among players. Some of these relational aspects, in particular the economic or social interest of each player in cooperating with each other, can be found embedded in the characteristic function. We define a particular relation among the players that it is based on mutual indifference. The first newaxiom expresses that the payoffs of two playerswho are not indifferent to each other are affected in the same way if they become enemies and do not cooperate with each other anymore. The second new axiom expresses that the payoff of a player is not affected if players to whom it is indifferent leave the game. We show that the Shapley value is characterized by these two axioms together with the well-known efficiency axiom. Further, we show that another axiomatization of the Shapley value is obtained if we replace the second axiom and efficiency by the axiom which applies the efficiency condition to every class of indifferent players. Finally, we extend the previous results to the case of weighted Shapley values. © Springer-Verlag Berlin Heidelberg 2012

Majorana spin-flip transitions in a magnetic trap

Atoms confined in a magnetic trap can escape by making spin-flip Majorana transitions due to a breakdown of the adiabatic approximation. Several papers have studied this process for atoms with spin $F = 1/2$ or $F= 1$. The present paper calculates the escape rate for atoms with spin $F > 1$. This problem has new features because the perturbation $\Delta T$ which allows atoms to escape satisfies a selection rule $\Delta F_z = 0, \pm 1, \pm 2$ and multi-step processes contribute in leading order. When the adiabatic approximation is satisfied the leading order terms can be summed to yield a simple expression for the escape rate.Comment: 16page

Development and evaluation of the elastic recovery concept for expandable space structures

Elastic recovery of expandable space structure

Doping dependence of magnetic excitations of 1D cuprates as probed by Resonant Inelastic x-ray Scattering

We study the dynamical, momentum dependent two- and four-spin response functions in doped and undoped 1D cuprates, as probed by resonant inelastic x-ray scattering, using an exact numerical diagonalization procedure. In the undoped $t-J$ system the four-spin response vanishes at $\pi$, whereas the two-spin correlator is peaked around $\pi/2$, with generally larger spectral weight. Upon doping spectra tend to soften and broaden, with a transfer of spectral weight towards higher energy. However, the total spectral weight and average peak position of either response are only weakly affected by doping up to a concentration of 1/8. Only the two-spin response at $\pi$ changes strongly, with a large reduction of spectral weight and enhancement of excitation energy. At other momenta the higher-energy, generic features of the magnetic response are robust against doping. It signals the presence of strong short-range antiferromagnetic correlations, even after doping mobile holes into the system. We expect this to hold also in higher dimensions.Comment: 7 pages, 5 figure

On Some One-Parameter Families of Three-Body Problems in One Dimension: Exchange Operator Formalism in Polar Coordinates and Scattering Properties

We apply the exchange operator formalism in polar coordinates to a one-parameter family of three-body problems in one dimension and prove the integrability of the model both with and without the oscillator potential. We also present exact scattering solution of a new family of three-body problems in one dimension.Comment: 10 pages, LaTeX, no figur

A Comparison of Consumer\u27s Surplus and Monopoly Revenue Estimates of Recreational Value for Two Utah Waterfowl Marshes

Demand curves were estimated for waterfowl hunting and nonconsumptive recreational use from use rate and variable expenditure data collected at the Bear River Migratory Bird Refuge and the Farmington Bay Waterfowl Management Area during fiscal 1969. Consumer\u27s surplus and monopoly revenue estimates were then derived from the demand functions. Adjusted estimates of consumer\u27s surplus for waterfowl hunting amounted to $7,260 per year at Bear River and$11,400 per year at Farmington Bay. For nonconsumptive recreation annual consumer\u27s surplus was estimated to be $18,700 at Bear River and$3,760 at Farmington Bay. Monopoly revenue estimates were between one-half and one-fourth the corresponding consumer\u27s surplus estimates. The capitalized value (at 8 percent interest) of predicted annual consumer\u27s surplus for all recreation was $865,800 for Bear River and$299,000 for Farmington Boy. Capitalization of the corresponding monopoly revenue estimates gave $276,900 for Bear River and$92,100 for Farmington Bay. At 3 percent interest, the capitalized consumer\u27s surplus values increase to $4,242,000 for Bear River and$1,184,000 for Farmington Buy, while those for monopoly revenue increase to $1,330,000 for Bear River and$350,000 for Farmington Bay. The author believes that consumer\u27s surplus estimates are more valuable than monopoly revenue estimates for comparison with other values included in the benefit/cost analysis of water development projects because the needed values include more than a non-discriminating monopolist can extract. It will never be possible to make additive estimates of all of the relevant values of natural areas used for outdoor recreation. Allocation decisions must draw on several disciplines in addition to economics to determine where the balance will swing for the greatest net benefit to society, nevertheless, the author believes that exceptions exist where the native flora and fauna can be managed to attract visitors such than an area can remain in natural production in perpetuity and be competitive with potentially conflicting interests in terms of measurable economic values. It is believed that future research should concentrate on high-value sites and be directed toward sensitivity analysis, the simultaneous evaluation of alternative uses, the influence of the travel-time variable, marginal resource values, and off-site benefits

Atalanta: The Exception to Social Normality Presented in the Ancient World

This thesis is an analysis of two ancient authors: the Greek Apollodorus, and the Latin Ovid, and how they both handle the ancient views of societal gender roles. The two authors write more than one hundred years apart (the 2nd century BCE and the mid-1st century BCE - early 1st century CE respectively), yet the two of them write unique accounts of the myth of Ata-lanta. Atalanta is a heroine of Greek and Roman mythology, and is one of the few examples of strong women that survive to the present day. However, Apollodorus and Ovid portray a very different view of Atalanta (within The Library and The Metamorphoses respectively), and both of them reveal some interesting possibilities of how Atalanta may have been viewed by both an-cient men and women of Greece and Rome.Honors DiplomaHonors CollegeCunningham Memorial Library, Terre Haute, Indiana State UniversityUndergraduateTitle from document title page. Document formatted into pages: 27