A minimax distribution-free procedure for a newsvendor problem with free shipping

In this paper, we study the optimal policies of retailers who operate their inventory with a single period model (i.e., newsvendor model) under a free shipping offer where a fixed shipping fee is exempted if an order quantity is greater than or equal to a given minimum quantity. Zhou et al. (2009) have explored this model, and we further investigate their analysis for the optimal ordering policies which they did not sufficiently develop. Based on the investigation, we extend the base model in order to deal with the practically important aspect of inventory management when the exact distribution function of demand is not available. We incorporate the aspect into the base model and present the optimal policies for the extended model with a numerical example. Finally, we conduct extensive numerical experiments to evaluate the performance of the extended model and analyze the impacts of minimum free shipping quantity and the fixed shipping fee on the performance.     

Controlled synthesis of Sb<Subscript>2</Subscript>O<Subscript>3</Subscript> nanoparticles by chemical reducing method in ethylene glycol

Antimony trioxide (Sb₂O₃) nanoparticles with particle size range from 2 to 12 nm were successfully synthesized by chemical reducing method. Antimony trichloride was reduced by hydrazine with the presence of sodium hydroxide (NaOH) as catalyst in ethylene glycol at 120 °C for 1 h. Effects of hydrazine concentration ([N₂H₅OH]/[Sb³⁺] = 0.75, 5, 10, 20, and 30, when concentration of NaOH was fixed [NaOH]/[Sb³⁺] = 3) and NaOH concentration ([NaOH]/[Sb³⁺] = 0, 1, 3, and 5, when concentration of hydrazine was fixed [N₂H₅OH]/[Sb³⁺] = 10) on the particle size and shape of the Sb₂O₃ nanoparticles were investigated. Transmission electron microscope, selected area electron diffraction pattern, and high resolution electron microscope were employed to study the morphology and crystallinity of the nanoparticles. It was observed that the particle size decreased and remained constant when [N₂H₅OH]/[Sb³⁺]) ≥ 10 and [NaOH]/[Sb³⁺] = 3. Further study on the crystallinity and phase of the nanoparticles was assisted by X-ray diffractometer (XRD). XRD revealed a cubic phase of Sb₂O₃ (ICDD file no. 00-043-1071) with preferred plane of (622) and lattice spacing of 1.68 Å. Correlation between UV–visible absorption wavelengths of the nanoparticles and their sizes was established.     

Strain-dependent splitting of the double-resonance Raman scattering band in graphene

Under homogeneous uniaxial strains, the Raman 2D band of graphene involving two-phonon double-resonance scattering processes splits into two peaks and they altogether redshift strongly depending on the direction and magnitude of the strain. Through polarized micro-Raman measurements and first-principles calculations, the effects are shown to originate from significant changes in resonant conditions owing to both the distorted Dirac cones and anisotropic modifications of phonon dispersion under uniaxial strains. Quantitative agreements between the calculation and experiment enable us to determine the dominant double-resonance Raman scattering path, thereby answering a fundamental question concerning this key experimental analyzing tool for graphitic systems.     

Coupled magnetic cycloids in multiferroic TbMnO3 and Eu3/4Y1/4MnO3

Based on the detailed Mn L(2,3)-edge x-ray resonant scattering results, we report a new complexity in the magnetic order of multiferroic orthomangnites, which has been considered as the simple A-type cycloid order inducing ferroelectricity. The Dzyaloshinskii-Moriya interaction involved in the orthorhombic distortion brings on F-type canting from the A type, and the ordering type becomes the off-phase synchronized bc cycloid in TbMnO(3) or the tilted antiphase ab cycloid in Eu(3/4)Y(1/4)MnO(3). The F-type canting is responsible for the magnetic field-driven multiferroicity to weak ferromagnetism transition.     

Fragile magnetic ground state in half-doped LaSr2Mn2O7

We investigated the orbital and antiferromagnetic ordering behaviors of the half-doped bilayer manganite La(2-2x)Sr(1+2x)Mn2O7 (x ? 0.5) by using Mn L(2,3)-edge resonant soft x-ray scattering. Resonant soft x-ray scattering reveals the CE-type orbital order below T(oo) ? 220 K, which shows partial melting behavior below T(m) ? 165 K. We also found coexistence CE- and A-type antiferromagnetic orders. Both orders involve the CE-type orbital order with nearly the same orbital character and are coupled with each other. These results manifest that the ground state with the CE-type antiferromagnetic order is easily susceptible to destabilization into the A-type one even with a small fluctuation of the doping level, as suggested by the extremely narrow magnetic phase boundaries at x ? 0.5±0.005.     

Thermoresponsive copolymers of methacrylic acid and poly(ethylene glycol) methyl ether methacrylate

Copolymers of methacrylic acid (MAA) and poly(ethylene glycol) methyl ether methacrylate (PEGMA) were prepared and their cloud points in aqueous solution were studied as a function of comonomer ratio, solution pH, and presence of hydrophobic comonomers. Under acidic conditions, the cloud point falls below 0 °C for copolymers with between 25% to 60% ether content, because of the formation of hydrophobic H‐bonded ether–acid complexes. The cloud point also decreases with solution pH. For equivalent ether to acid ratios, the cloud point decreases with decreasing PEG chain length, because of the presence of a larger number of hydrophobic methyl and methacrylate groups. Similarly, the cloud point decreases upon incorporation of hydrophobic comonomers such as butyl, lauryl, or glycidyl methacrylates. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 6095–6104, 2005     

Multiple optical line traps using a single phase-only rectangular ridge

An optical line trap has the ability to simultaneously trap and align microparticles in line formation due to its intensity profile. In this paper, we demonstrate a straightforward means to generate multiple optical line traps by simply placing a phase-only rectangular ridge in the path of a laser beam. By carefully positioning the rectangular ridge, we were able to control the separation between the optical trapping lines, which were then used to create multiple line formations of trapped particles. The simplicity of the proposed technique lends itself to the realization of a highly efficient optical line trap converter for easy modification of existing optical microscopes.     

The entrainment of air by water jet impinging on a free surface

High-speed cine and video photographs were used to capture the flow patterns of a column of water jet impinging into a pool of water. The impact results in air entrainment into water in the form of a void with no mixing between the water in the jet and the surrounding water. Conservation of fluid momentum shows that the rate of increase of the height of the air void depends on the drag coefficient of the jet front. By neglecting the frictional losses, the application of energy conservation yields an expression that relates the maximum height of the air void with the properties of the water jet.