Assortment planning for vertically differentiated products under a consider-then-choose model

Consider-then-choose models, borne out by empirical literature in marketing and psychology, note that customers follow a two-stage procedure to choose among alternatives. In this paper, we consider the assortment optimization problem of a retailer who manages a category of vertically differentiated products under customers’ consider-then-choose behavior. We characterize some structural results of the optimal assortment and find that the problem can be solved as the shortest path problem. Also, we develop an efficient algorithm to identify an optimal assortment.     

Weight enumerators of reducible cyclic codes and their dual codes

Let ${\mathbb{F}}_q$ be a finite field and $n$ a positive integer. In this paper, we find a new combinatorial method to determine weight enumerators of reducible cyclic codes and their dual codes of length $n$ over ${\mathbb{F}}_q$, which just generalize results of Zhu et al. (2015); especially, we also give the weight enumerator of a cyclic code, which is viewed as a partial Melas code. Furthermore, weight enumerators obtained in this paper are all in the form of power of a polynomial.     

Automorphism groups of designs with λ=1

If $G$ is a finite group and $k=q>2$ or $k=q+1$ for a prime power $q$ then, for infinitely many integers $v$, there is a 2-$(v,k,1)$-design $\mathbf{D}$ for which $\mathrm{Aut}\mathbf{D}?G$.     

Molecular structure and conformation of gaseous bromoacetyl chloride and bromoacetyl bromide as determined by electron diffraction

Bromoacetyl chloride and bromoacetyl bromide are studied by gas phase electron diffraction at nozzle-tip temperatures of 70°C and 77°C, respectively. Both compounds exist as mixtures of anti and gauche conformers. The mole fraction anti, with uncertainties estimated at 2σ, was found to be 0.474(0.080) for bromoacetyl chloride and 0.615(0.069) for bromoacetyl bromide. The results for the distance (r_a)and angle (∠α) parameters, with parenthesized uncertainties of 2σ including estimated uncertainty in the electron wave length and correlation effects are as follows: (1) bromoacetyl chloride, r(C-H) = 1.086(0.062) Å, r(CO) = 1.188(0.009) Å, r(C-C) = 1.519(0.018) Å, r(C-Cl) = 1.789(0.011) Å, r(C-Br) = 1.935(0.012) Å, ∠C-CO = 127.6(1.3)°, ∠C-C-Cl = 111.3(1.1)°, ∠C-C-Br = 111.0(1.5)°, ∠H-C-H = 109.5°(assumed), $\text{}\text{?}$/o (gauche torsion angle relative to 0° for the anti form) = 110.0°(assumed); (2) bromoacetyl bromide, r(C-H) =1.110(0.088) Å, r(C=O) = 1.175(0.013) Å, r(C-C) = 1.513(0.020) Å, r(CO-Br) = 1.987(0.020) Å, r(CH₂-Br) = 1.915(0.020) Å, ∠C-CO = 129.4(1.7)°, ∠CH₂-CO-Br = 110.7(1.5)°, ∠CO-CH₂-Br = 111.7(1.8)°, ∠H-C-H = 109.5°(assumed), ∠ø (gauche torsion angle relative to 0° for the anti form) = 105.0°(assumed). The structural results are discussed in connection with the structures of related molecules.     

Vibrational studies in aqueous solutions: Part II. The acid oxalate ion and oxalic acid

Assignments for oxalic acid in solution are re-examined. A detailed assignment of the IR and Raman spectra of the acid oxalate ion is presented for the first time. Raman spectroscopy is used to study the first ionization of oxalic acid.     

Ionic conductivity in Na+, K+, and Ag+ β″-alumina

This paper presents measurements of the ionic conductivity in single crystals of β″-alumina (0.84 M₂O · 0.67 MgO · 5.2 Al₂O₃, M = Na, K, Ag). Single crystals of sodium β″-alumina were grown from a melt of Na₂O, MgO, and Al₂O₃ at 1660 to 1730°C. Selected crystals were converted to the other isomorphs by ion exchange. The conductivity of sodium β″-alumina varies from 0.18 to 0.01 (ohm · cm)^?1 at 25°C depending upon crystal growth conditions. Potassium β″-alumina has the unusually high room temperature conductivity of 0.13 (ohm · cm)^?1. Silver β″-alumina has a slightly lower conductivity, 4 × 10^?3 (ohm · cm)^?1 at 25°C. The activation energies of sodium and potassium β″-alumina decrease with increasing temperature, while that of silver β″-alumina is constant from ?80 to 450°C.     

Investigation of m-nitroaniline formation during the Zimmermann reaction

The Zimmermann reaction for the determination of 17-ketosteroids was tested under both room-temperature and steam-distillation reaction conditions. meta-Nitroaniline was isolated from the residue of the steam distillation by ether extraction and thin-layer chromatography. Conclusive identification was by infrared spectroscopy. In contrast, m-nitroaniline was not formed under room-temperature reaction conditions, even when allowed to react for 24 hr. Similar results were also obtained for the reaction between acetone and m-dinitrobenzene under alkaline conditions. In conclusion, the results indicate that m-nitroaniline formation cannot account for the conversion of structure I to structure II under room-temperature reaction conditions as investigated herein.     

The crystal structure of bicyclo [3.3.3]undecane-1,5-diol and the conformation of bicyclo[3.3.3]undecane (manxane)

The crystal structure of bicyclo [3.3.3]undecane-1,5-diol has been determined. It is monoclinic, P2₁/c, a = 12.99(2), b = 14.16(2), c = 12.50(1)A,β = 112.42(2)°, with two independent molecules in the asymmetric unit. One of these is disordered, but the other has almost exact C_3h symmetry and its conformation and precise molecular geometry agree well with previous calculations by molecular mechanics. The molecule shows considerable angle strain, having bridge angles in the range 118–121°     

A theoretical approach to substituent effects: Interaction between directly bonded groups in the isoelectronic series XNH3+, XCH3, and XBH3−

Ab initio molecular orbital theory including full geometry optimization at the 4-31G level is used to examine the interactions between substitutents X(X = Li, BeH, BH₂, CH₃, NH₂, OH and F) and substrates Y(Y = NH₃⁺, CH₃, BH₃^?) in the isoelectronic series XNH₃⁺, XCH₃ and XBH₃^?. The results indicate that the interaction energies are dominated by σ-effects. NH₃⁺ is found to interact favorably with the σ-donors (e.g. Li, BeH and BH₂) and unfavorably with the σ-acceptors (e.g. F, OH, NH₂). The reverse pattern a observed for XBH₃^?. The range of interaction energies for XCH₃ is considerably smaller than for XNH₃⁺ and XBH₃^?.     

Elektronenstoss-induzierter zerfall von benzol-tricarbonyl-chrom- und -wolfram-derivaten; ein vergleich

The Electron impact mass spectra of (CO)₃ MC₆H₅—X complexes (M = Cr, W; X = OCH₃, OC₄H₉, CO₂CH₃, CO₂C₄H₉) were recorded. From metastable transitions and by high-resolution measurements complete fragmentation diagrams were obtained; in some cases comparative structure determinations of fragment ions were carried out by collisional activation. The fragmentation of the tungsten complexes considerably differs from that of the chromium compounds. The differences may be attributed to the stronger-electrophilic character as well as to the more pronounced tendency of tungsten to attain higher oxidation states.