A Minty variational principle for set optimization

Extremal problems are studied involving an objective function with values in (order) complete lattices of sets generated by so called set relations. Contrary to the popular paradigm in vector optimization, the solution concept for such problems, introduced by F. Heyde and A. L\"ohne, comprises the attainment of the infimum as well as a minimality property. The main result is a Minty type variational inequality for set optimization problems which provides a sufficient optimality condition under lower semicontinuity assumptions and a necessary condition under appropriate generalized convexity assumptions. The variational inequality is based on a new Dini directional derivative for set-valued functions which is defined in terms of a "lattice difference quotient": A residual operation in a lattice of sets replaces the inverse addition in linear spaces. Relationships to families of scalar problems are pointed out and used for proofs: The appearance of improper scalarizations poses a major difficulty which is dealt with by extending known scalar results such as Diewert's theorem to improper functions

Organ Procurement, Values and Public Policy

The success of organ transplants in recent years has created a shortage of transplantable cadaver organs. Voluntarism, the primary mode of organ procurement currently in use nationwide, appears to be no longer successful. Policy makers and others are examining alternatives to the current system, namely, presumed consent (routine salvaging) and required request. In this process, there is a danger in considering only the effectiveness of the means and neglecting the value and belief commitments that underlie them. These need to be brought to the surface because they ultimately contribute toward shaping the moral character of society. In this light, required request might be a preferable public policy option because it balances the values of voluntarism (autonomy, individual rights, and charity) with those of presumed consent (community, social well-being, and justice). It also promises to be more effective than either of the other two alternatives

Where should livestock graze? Integrated modeling and optimization to guide grazing management in the Cañete basin, Peru

Integrated watershed management allows decision-makers to balance competing objectives, for example agricultural production and protection of water resources. Here, we developed a spatially-explicit approach to support such management in the Cañete watershed, Peru. We modeled the effect of grazing management on three services – livestock production, erosion control, and baseflow provision – and used an optimization routine to simulate landscapes providing the highest level of services. Over the entire watershed, there was a trade-off between livestock productivity and hydrologic services and we identified locations that minimized this trade-off for a given set of preferences. Given the knowledge gaps in ecohydrology and practical constraints not represented in the optimizer, we assessed the robustness of spatial recommendations, i.e. revealing areas most often selected by the optimizer. We conclude with a discussion of the practical decisions involved in using optimization frameworks to inform watershed management programs, and the research needs to better inform the design of such programs

Electrodeposition of alloys or compounds in molten salts and applications

This article deals with the different modes of preparation of alloys or intermetallic compounds using the electrodeposition in molten salts, more particularly molten alkali fluorides. The interest in this process is to obtain new materials for high technology, particularly the compounds of reactive components such as actinides, rare earth and refractory metals. Two ways of preparation are considered: (i) electrocoating of the more reactive metal on a cathode made of the noble one and reaction between the two metals in contact, and (ii) electrocoating on an inert cathode of the intermetallic compound by coreduction of the ions of each elements. The kinetic is controlled by the reaction at the electrolyte interface. A wide bibliographic survey on the preparation of various compounds (intermetallic compounds, borides, carbides…) is given and a special attention is paid to the own experience of the authors in the preparation of these compounds and interpretation of their results

Scalar Representation and Conjugation of Set-Valued Functions

To a function with values in the power set of a pre-ordered, separated locally convex space a family of scalarizations is given which completely characterizes the original function. A concept of a Legendre-Fenchel conjugate for set-valued functions is introduced and identified with the conjugates of the scalarizations. Using this conjugate, weak and strong duality results are proven.Comment: arXiv admin note: substantial text overlap with arXiv:1012.435

Metaplectic Ice

Spherical Whittaker functions on the metaplectic n-fold cover of GL(r+1) over a nonarchimedean local field containing n distinct n-th roots of unity may be expressed as the partition functions of statistical mechanical systems that are variants of the six-vertex model. If n=1 then in view of the Casselman-Shalika formula this fact is related to Tokuyama's deformation of the Weyl character formula. It is shown that various properties of these Whittaker functions may be expressed in terms of the commutativity of row transfer matrices for the system. Potentially these properties (which are already proved by other methods, but very nontrivial) are amenable to proof by the Yang-Baxter equation

Group Support Systems (GSS)

Groupware is a term describing an emerging computer software technology enhancing the ability of people to work together as a group, (a software driven 'group support system'). This project originated at the beginning of 1992 and reports were issued describing the activity through May 1995. These reports stressed the need for process as well as technology. That is, while the technology represented a computer assisted method for groups to work together, the Group Support System (GSS) technology als required an understanding of the facilitation process electronic meetings demand. Even people trained in traditional facilitation techniques did not necessarily aimlessly adopt groupware techniques. The latest phase of this activity attempted to (1) improve the facilitation process by developing training support for a portable groupware computer system, and (2) to explore settings and uses for the portable groupware system using different software, such as Lotus Notes

Space market model development project, phase 3

The results of a research project investigating information needs for space commercialization is described. The Space Market Model Development Project (SMMDP) was designed to help NASA identify the information needs of the business community and to explore means to meet those needs. The activity of the SMMDP is reviewed and a report of its operation via three sections is presented. The first part contains a brief historical review of the project since inception. The next part reports results of Phase 3, the most recent stage of activity. Finally, overall conclusions and observations based on the SMMDP research results are presented