Abstract: Based on a metric that represents a value of a game of chance, a payout distribution is optimized with respect to the metric.

Abstract: The catalytic efficiency of supported catalysts containing metal nanoparticles is strongly related to the chemical softness at the surfaces of such nanoparticles. Supported catalysts containing platinum nanoparticles having average surface softness values (expressed in scaled units ranging from 0 to 1) between 0.07198 and 0.09247 exhibit high catalytic efficiency. The catalytic efficiency of such platinum nanoparticles for CO oxidation, expressed as the turn-over frequency (TOF), was observed to be on or above 0.03062 s?1. The supported catalysts containing platinum nanoparticles with tighter average surface softness ranges exhibit even higher catalytic efficiencies. The TOF for CO oxidation of platinum nanoparticles having average surface softness values between 0.08031 and 0.08679 was observed to be on or above 0.06554 s?1.

Abstract: The catalytic efficiency of supported catalysts containing metal nanoparticles is strongly related to the chemical softness at the surfaces of such nanoparticles. The chemical softness of a nanoparticle is obtained using results from Density Functional Theory modeling, an extended version of Embedded Atom Method modeling, and continuum modeling based on size and shape of the nanoparticle. A metal nanoparticle of a certain size and shape is first modeled using the extended EAM and EAM parameters that have been validated with results from DFT modeling, to obtain atomic energy densities at each atom location. The chemical softness value at each atom location is then calculated from the atomic energy densities and various parameters that are derived based on results from DFT modeling. The surface chemical softness value is derived from the local chemical softness values based on the geometry and atomistic structure of the metal nanoparticle.

Abstract: A set of data is received containing values associated with respective data points, the values associated with each of the data points being characterized by a distribution. The values for each of the data points are expressed in a form that includes information about a distribution of the values for each of the data points. The distribution information is used in clustering the set of data with at least one other set of data containing values associated with data points.

Abstract: Supported catalysts are produced with nanometer sized particles comprised of different metals dispersed throughout the catalyst support material. The supported catalysts reduce substantially or completely the amount of platinum that is required without sacrificing catalytic performance. In place of platinum, the supported catalysts employ palladium, silver, or copper, all of which costs significantly less than platinum.

Abstract: A method for producing highly dispersed catalysts is disclosed. The method includes contacting a support material with a solvent for a period of time, adding a metal salt to the solvent and support mixture, and then adding a reducing agent to the solution to reduce the metal salt to nanometer sized metal particles on the surface of the support. Excess solvent is used in the process, the volume of solvent being greater than two times the pore volume of the support.

Abstract: Historical information is stored about demand behavior associated with different sizes of styles of items of commerce. A size assortment recommendation is generated based on the stored historical information and on objectives with respect to purchase or allocation decisions about assortments of the different sizes.

Abstract: Price elasticity of sales of an item of commerce is estimated. Based on the price elasticity, a maximum gross margin for the item is determined. The maximum possible gross margin is then used in connection with setting or evaluating markdown scenarios for the item.

Abstract: Historical information is stored about demand behavior associated with different sizes of styles of items of commerce. A size assortment recommendation is generated based on the stored historical information and on objectives with respect to purchase or allocation decisions about assortments of the different sizes.

Abstract: Based on a metric that represents a value of a game of chance, a payout distribution is optimized with respect to the metric.

Abstract: A set of data is received containing values associated with respective data points, the values associated with each of the data points being characterized by a distribution. The values for each of the data points are expressed in a form that includes information about a distribution of the values for each of the data points. The distribution information is used in clustering the set of data with at least one other set of data containing values associated with data points.

Abstract: Price elasticity of sales of an item of commerce is estimated. Based on the price elasticity, a maximum gross margin for the item is determined. The maximum possible gross margin is then used in connection with setting or evaluating markdown scenarios for the item.

Abstract: Based on a metric that represents a value of a game of chance, a payout distribution is optimized with respect to the metric.

Abstract: A set of data is received containing values associated with respective data points, the values associated with each of the data points being characterized by a distribution. The values for each of the data points are expressed in a form that includes information about a distribution of the values for each of the data points. The distribution information is used in clustering the set of data with at least one other set of data containing values associated with data points.

Abstract: Historical information is stored about demand behavior associated with different sizes of styles of items of commerce. A size assortment recommendation is generated based on the stored historical information and on objectives with respect to purchase or allocation decisions about assortments of the different sizes.