Optimal transshipments and reassignments under periodic or cyclic holding cost accounting

In a centrally managed system, inventory at a retailer can be transshipped to a stocked-out retailer to meet demand. As the inventory at the former retailer may be demanded by future customers of that retailer and transshipment time/cost is non-negligible, it can be more profitable to not transship in some situations. When unsatisfied demand is backordered, reassignment of inventory to a previously backordered demand can perhaps become profitable as demand uncertainty resolves over time. Despite this intuition, we prove that no reassignments are necessary for cost optimality under periodic holding cost accounting in a two-retailer system. This remains valid for multi-retailer systems according to numerical analyses. When holding costs are accounted for only at the end of each replenishment cycle, reassignments are necessary for optimality but insignificant in reducing the total cost. In most instances tested, the decrease in total cost from reassignments is below 2% for end of cycle holding cost accounting. These results simplify transshipment policies and facilitate finding good policies in both implementation and future studies, as reassignments can be omitted from consideration in optimization models under periodic holding cost accounting and in approximation models under cyclical cost accounting.     

Conley conjecture and local Floer homology

In this paper we connect algebraic properties of the pair-of-pants product in local Floer homology and Hamiltonian dynamics. We show that for an isolated periodic orbit, the product is non-uniformly nilpotent and use this fact to give a simple proof of the Conley conjecture for closed manifolds with aspherical symplectic form. More precisely, we prove that on a closed symplectic manifold, the mean action spectrum of a Hamiltonian diffeomorphism with isolated periodic orbits is infinite.     

Extending external rays throughout the Julia sets of rational maps

For polynomial maps in the complex plane, the notion of external rays plays an important role in determining the structure of and the dynamics on the Julia set. In this paper we consider an extension of these rays in the case of rational maps of the form Fλ(z) = z ⁿ + λ/z ⁿ where n > 1. As in the case of polynomials, there is an immediate basin of ∞, so we have similar external rays. We show how to extend these rays throughout the Julia set in three specific examples. Our extended rays are simple closed curves in the Riemann sphere that meet the Julia set in a Cantor set of points and also pass through countably many Fatou components. Unlike the external rays, these extended rays cross infinitely many other extended rays in a manner that helps determine the topology of the Julia set.     

Gamma ray shielding capabilities of rhenium-based superalloys

ABSTRACT

Because of the high radiation dose in applications involving nuclear reactors, medical treatments etc., it is important to reduce the exposure to radiation of areas and workers. In this study, we were examined gamma ray shielding parameters of the newly produced Re-based superalloys. Mass attenuation coefficient (µ/ρ) of the alloys were obtained experimentally at 81, 276, 302, 356, 383 keV photon energies emitted from ¹³³Ba radioactive source using Ultra Ge detector. The experimental results were compared with the values obtained by the WinXCOM program and were found to be in perfect agreement with each other. Additionally, effective atomic number (Z_eff) and electron density (N_eff) were determined for produced Rhenium (Re) based super alloys in the energy range 1 keV–100?GeV. S5 sample which has maximum Rhenium percentage own the largest µ/ρ and Z_eff values. Moreover, by using Geometric Progression (GP) approximation, EABF and EBF were computed for the superalloys depending on the energy and penetration depths. It has been deduced that the values of EABF and EBF are minimum in the medium energy region. EBF and EABF values of the alloys have changed depending on the equivalent atomic number. Among alloy samples under study, S5 superalloy is the best for gamma ray shielding. However, in general, considering the radiation energies used in many applications, all the alloys under study have satisfactory radiation absorption properties.     

C—H⃛O and C—H⃛π interactions in 1‐acetyl‐4‐(p‐chloro­benzyl­idene­amino)‐3‐ethyl‐4,5‐di­hydro‐1H‐1,2,4‐triazol‐5‐one

The title compound, C₁₃H₁₃ClN₄O₂, contains both a phenyl and a triazole ring, both of which are approximately coplanar with the entire mol­ecule. The triazole ring has substituents at the 1‐, 2‐ and 4‐positions. Intramolecular C—H⃛O and C—H⃛N interactions, together with intermolecular C—H⃛O and C—H⃛π interactions, help to stabilize the structure.     

The Crystal and Molecular Structure of 2‐[(3,4‐dimethoxybenzylidene)amino]adamantane

The crystal structure of the title compound, C₁₉H₂₅NO₂ was determined by single crystal X‐ray diffraction technique. The crystal data are Orthorombic, space group Pbca, with a = 9.2119(4), b = 9.5555(4), c = 37.6049(5) Å, Z = 8, T = 293(2) K, MoKα radiation, λ = 0.71073 Å, Mr = 299.40, R = 0.0839 for 1945 reflections with I > 2σ(I). The title compound shows intermolecular C‐H…O type interactions.     

Comparative structural analysis of 4,5- and 3,6-dialkylsulfanylphthalonitriles of different bulkiness

Phthalonitriles disubstituted by alkylsulfanyl moieties of different bulkiness (tert-butyl, adamantly, cyclohexyl and hexyl) and in 4,5- or 3,6-positions, respectively, set A and set B, have been prepared for comparative structural analyses. Miscellaneous parameters such as melting points and related polarity of the compounds are summarized. Substituents position and bulkiness effects on NMR and IR spectroscopy as well as refined X-ray structural data were examined.     

Effect of fiber modification with carboxymethyl cellulose on the efficiency of a microparticle flocculation system

Carboxymethyl cellulose (CMC) has been used widely to enhance dry strength of paper and uniformity of sheet in the papermaking industry. Besides these positive effects, it may affect the fines retention and dewatering processes negatively. These negative effects are mainly seen when fiber modifications with high CMC dosages are studied in laboratory scale. In this paper, the effect of fiber modification with CMC on the deposition of precipitated calcium carbonate (PCC) and on the dewatering process in the presence of cationic polyacrylamide (CPAM)/bentonite microparticle flocculation system is examined. It was determined that fiber modification with 10 mg g⁻¹ of CMC decreased PCC deposition at the initial addition of CPAM and gave better PCC deposition at 2 mg g⁻¹ of CPAM. It was also observed that PCC deposition on unmodified fibers is higher at lower CPAM concentration. PCC deposition was found as almost stable after a maximum value obtained at 0.5 mg g⁻¹ of bentonite concentration for fiber modified with 40 mg g⁻¹ of CMC. This indicates that interaction between CPAM and bentonite particles changed due to higher surface charge and CMC conformation on fibers. Results of the dewatering experiments showed that CMC modification increased the drainage time due to a denser and more plugged sheet. This negative effect was compensated with higher concentrations of CPAM and bentonite. On the other hand, dewatering is also affected by the mass ratio of CMC and CPAM, which was not the optimum one in this study at lower of CPAM. Thus, the increase in the drainage time in the presence of CMC on the fiber surface could be also caused by incorrect ratios of chemicals because the effect of CMC on the drainage time was not observed at higher concentrations of CPAM.     

Effect of LiClO4 Salt on Dielectric Properties of Acrylonitrile-Methyl Methacrylate and Acrylonitrile-Isobutyl Methacrylate Copolymers

Poly(acrylonitrile-co-isobutyl methacrylate), PAN-co-PIBMA, and poly(acrylonitrile-co-methyl methacrylate), PAN-co-MMA copolymers are synthesized by emulsion polymerization. The structural characterization is done by FTIR and ¹H-NMR spectroscopy and thermal analyses are performed by thermogravimetric analysis (TGA). After various amounts of LiClO₄ salt loading into copolymer films, the dielectric properties of these films at different temperatures and frequencies are determined. The effects of different methacrylate groups and salt content on the dielectric properties of copolymers are investigated. It is found that the dielectric constant increases systematically with increasing MMA and IBMA content in the copolymer. The samples with higher salt content show higher ac-conductivities.