Product line selection and pricing under a share-of-surplus choice model

Product line selection and pricing decisions are critical to the profitability of many firms, particularly in today’s competitive business environment in which providers of goods and services are offering a broad array of products to satisfy customer needs.We address the problem of selecting a set of products to offer and their prices when customers select among the offered products according to a share-of-surplus choice model. A customer’s surplus is defined as the difference between his utility (willingness to pay) and the price of the product. Under the share-of-surplus model, the fraction of a customer segment that selects a product is defined as the ratio of the segment’s surplus from this particular product to the segment’s total surplus across all offered products with positive surplus for that segment.We develop a heuristic procedure for this non-concave, mixed-integer optimization problem. The procedure utilizes simulated annealing to handle the binary product selection variables, and a steepest-ascent-style procedure that relies on certain structural properties of the objective function to handle the non-concave, continuous portion of the problem involving the prices. We also develop a variant of our procedure to handle uncertainty in customer utilities. In computational studies, our basic procedures perform extremely well, producing solutions whose objective values are within about 5% of those obtained via enumerative methods. Our procedure to handle uncertain utilities also performs well, producing solutions with expected profit values that are roughly 10% higher than the corresponding expected profits from solutions obtained under the assumption of deterministic utilities.     

Highly planar amphiphilic porphyrins

A first synthesis of an asymmetric and amphiphilic β-substituted porphyrin is reported. The porphyrin can be integrated into various types of nanostructures with the amphiphilic characters in hydrophilic solvents. The one-dimensional integration may induce a magnetic interaction between the central metals.     

Dielectric properties and conductivity of styrene-methacrylic acid copolymers and partially neutralized salts

Dielectric and conductivity measurements have been carried out on styrene-methacrylic acid copolymers and their salts in the glass transition region, stressing the comparison of polymers neutralized to different extents. A simple monomer-dimer equilibrium between carboxylic acid groups is applicable to the pure acid polymers, which explains the increase of both the glass transition temperature and of the dielectric strength with concentration of methacrylic acid. The dielectric data indicate that very few sodium carboxylate groups can dissolve in the matrix of the pure salt, whereas the presence of carboxylic acid groups in partly neutralized polymers enhances the dissolution of the salt groups in the matrix. Considerable differences are observed between the partly neutralized polymer and the blend consisting of pure acid and pure salt copolymers, which suggests that exchange of cations between acid and salt groups is quite slow even at high temperatures. The conductivity of the ionomers appears to be related to the diffusion of carriers through the matrix.     

Synthesis of 7‐acetyloxy‐3,7‐dimethy1‐7,8‐dihydro‐6H‐isochromene‐6,8‐dione and its analogues

7‐Alkanoyloxy‐3,7‐dimefhyl‐7,8‐dihydro‐6H‐isochromene‐6,8‐diones 12‐15 were synthesized in 69‐16% yields from the reaction of 2,4‐dihydroxy‐3‐methyl‐6‐(2‐oxopropyl)benzaldehyde 11 with p‐toluenesulfonic acid in various carboxylic acids such as acetic acid, propionic acid, butyric acid and heptanoic acid followed by oxidation with lead tetraacetate. On the other hand, (±)‐daldinin A 5 (oleate) was not obtained using oleic acid as a medium. In the cases of heptanoic acid and oleic acid, esters 16 and 17 were produced in 23 and 9% yields, respectively. 6,8‐Dihydroxy‐3,7‐dimethyl‐2‐benzopyrylium p‐toluenesulfonate 31 is considered as the intermediate for the production of 12‐15. Overall yields of isochromenes 12‐15 were 26‐6% starting from 2‐methylresorcinol for seven steps.     

First-principles energy band calculation for undoped and N-doped InTaO4 with layered wolframite-type structure

The electronic structures of undoped and N-doped InTaO₄ with optimized structures are calculated within the framework of the density functional theory. Calculated lattice constants are in excellent agreement with experimental values, within a difference of 2%. The valence band maximum (VBM) is located near the middle point on the ZD line and the conduction band minimum (CBM) near the middle point on the DX line. This means that InTaO₄ is an indirect-gap material and a minimum theoretical gap between VBM and CBM is ca. 3.7 eV. The valence band in the range from −6.0 to 0 eV mainly consists of O 2p orbitals, where In 4d5s5p and Ta 5d orbitals are slightly hybridized with O 2p orbitals. On the other hand, the conduction band below 5.5 eV is mainly composed of the Ta 5d orbitals and the contributions of In and O orbitals are small. The band gap of N-doped InTaO₄ decreases by 0.3 eV than that of undoped InTaO₄, because new gap states originating from N 2p orbitals appear near the top of the valence band. This result indicates that doping of N atoms into metal oxides is a useful method to develop photocatalysts sensitive to visible light.     

Preconcentration and determination of cadmium by GFAAS after solid-phase extraction with synthetic zeolite.

The solid-phase extraction (SPE) method for the preconcentration of trace amounts of cadmium using synthetic zeolite A-4 and its determination by graphite furnace atomic absorption spectrometry (GFAAS) was investigated. The preconcentration conditions, such as the optimum pH range of the sample solution for the adsorption of cadmium and the kind of acid solution for dissolving the cadmium-adsorbed synthetic zeolite A-4, as well as the measurement conditions for the determination of cadmium by GFAAS, e.g., the ashing and atomizing temperature, were investigated. Quantitative recovery of cadmium onto zeolite A-4 from the sample solution over the pH range 2.0 - 9.0 was achieved by the batch method. After the solid-phase (cadmium-adsorbed zeolite A-4) was separated from the sample solution by a membrane filter, it was dissolved in 2.0 cm(3) of 2.0 mol dm(-3) nitric acid. An aliquot of the resulting solution was injected into the graphite furnace. In GFAAS measurements an alternate gas (Ar, 90%; O(2), 10%) was used as a sheath gas, and the ashing temperature and atomizing temperature were 400 degrees C and 1600 degrees C, respectively. The detection limit (3 sigma) for cadmium was 0.002 microg dm(-3). The relative standard deviation at 0.010 microg dm(-3) was 3.5 - 4.5% (n = 5). The proposed method has been successfully applied to the analysis of trace cadmium in environmental water samples.     

Determination of 36Cl in environmental samples collected in the JCO by AMS

Long-lived chlorine, ³⁶Cl (T_1/2 = 301,000 y) in environmental samples has been measured by the AMS system installed in Tandem Accelerator Center, University of Tsukuba. A tri-carbon-molecular ¹²C₃ ^- pilot beam method is used to stabilize the terminal voltage of the tandem. A small amount of pure carbon graphite is well mixed into a AgCl target material for creating Cl^- and ¹²C₃ ^- in the ion source. A ³⁶S isobaric interference in the system is eliminated to determine ³⁶Cl in environmental samples by chemical procedure. Some samples containing chlorine such as soil, chemical reagents and table salt have been collected in the JCO criticality accident site and analyzed to detect neutron-induced ³⁶Cl. The experimental result has been compared with a theoretical calculation.     

A non-commutative version of the minimal supersymmetric standard model

A minimal supersymmetric standard model on non-commutative space-time (NC MSSM) is proposed. The model fulfills the requirements of non-commutative gauge invariance and the absence of anomaly. The existence of supersymmetry with a scale of its breaking lower than the non-commutative scale is crucial in order to achieve consistent gauge symmetry breaking.     

Sorption and partial molar volume of gases in poly (dimethyl siloxane)

Sorption of N₂, O₂, Ar, CH₄, CO₂, C₂H₄, and C₂H₆ in poly (dimethyl siloxane) liquid and rubber and the dilation of the polymers due to sorption of the gases are studied at 25°C under pressures up to 50 atm. In the liquid, the sorption isotherms for low-solubility and high-solubility gases are described by Henry's law and the Flory–Huggins equation, respectively. Gas sorption in the rubber, which contains a 29 wt % silica filler, follows the dual-mode sorption model, though marked hysteresis is observed in the sorption of O₂ and CH₄. The dilation isotherms increase linearly or exponentially in both polymers with increasing pressure. Considering that gas molecules adsorbed into micropores of the filler particles do not participate in the dilation, partial molar volumes of the dissolved gases in the rubber are determined from data of sorption and dilation. The values are nearly equal to the partial molar volumes in the liquid (48–60 cm³/mol).