Dynamic lot-sizing in sequential online retail auctions

Retailers often conduct non-overlapping sequential online auctions as a revenue generation and inventory clearing tool. We build a stochastic dynamic programming model for the seller’s lot-size decision problem in these auctions. The model incorporates a random number of participating bidders in each auction, allows for any bid distribution, and is not restricted to any specific price-determination mechanism. Using stochastic monotonicity/stochastic concavity and supermodularity arguments, we present a complete structural characterization of optimal lot-sizing policies under a second order condition on the single-auction expected revenue function. We show that a monotone staircase with unit jumps policy is optimal and provide a simple inequality to determine the locations of these staircase jumps. Our analytical examples demonstrate that the second order condition is met in common online auction mechanisms. We also present numerical experiments and sensitivity analyses using real online auction data.     

A new method for resolving combinatorial ambiguities at hadron colliders

We present a new method for resolving combinatorial ambiguities that arise in multi-particle decay chains at hadron colliders where the assignment of visible particles to the different decay chains has ambiguities. Our method, based on selection cuts favoring high transverse momentum and low invariant mass pairings, is shown to be significantly superior to the more traditional hemisphere method for a large class of decay chains, producing an increase in signal retention of up to a factor of 2. This new method can thus greatly reduce the combinatorial ambiguities of decay chain assignments.     

On the Two Species Asymmetric Exclusion Process with Semi-Permeable Boundaries

We investigate the structure of the nonequilibrium stationary state (NESS) of a system of first and second class particles, as well as vacancies (holes), on L sites of a one-dimensional lattice in contact with first class particle reservoirs at the boundary sites; these particles can enter at site 1, when it is vacant, with rate α, and exit from site L with rate β. Second class particles can neither enter nor leave the system, so the boundaries are semi-permeable. The internal dynamics are described by the usual totally asymmetric exclusion process (TASEP) with second class particles. An exact solution of the NESS was found by Arita. Here we describe two consequences of the fact that the flux of second class particles is zero. First, there exist (pinned and unpinned) fat shocks which determine the general structure of the phase diagram and of the local measures; the latter describe the microscopic structure of the system at different macroscopic points (in the limit L→∞) in terms of superpositions of extremal measures of the infinite system. Second, the distribution of second class particles is given by an equilibrium ensemble in fixed volume, or equivalently but more simply by a pressure ensemble, in which the pair potential between neighboring particles grows logarithmically with distance. We also point out an unexpected feature in the microscopic structure of the NESS for finite L: if there are n second class particles in the system then the distribution of first class particles (respectively holes) on the first (respectively last) n sites is exchangeable.     

Experimental and theoretical assessment of Fe-doped indium-oxide-based dilute magnetic semiconductors

Specimens of iron-doped indium oxide (In_1-xFe_x)₂O₃ with x?=?0.015, 0.03, 0.045 and 0.06, amalgamated through a traditional solid-state reaction method followed by H₂/air sintering, were characterised using an X-ray diffractometer (XRD), a vibrating sample magnetometer (VSM), and a scanning electron microscope (SEM) to investigate their structural, magnetic and morphological properties respectively. According to XRD plots, all the specimens exhibit cubic bixbyite structures along with ancillary phases. Magnetic assessment showed that In₂O₃ has a negative susceptibility, exhibiting diamagnetic behaviour at room temperature. The doping of Fe ions induces ferromagnetic (FM) ordering, which is enhanced with increasing doping content. The strength of the magnetisation increases when the specimens are exposed to H₂ but is reduced on further air sintering. A bound magnetic polaron (BMP) model is successfully fitted to the observed FM data involving localised carriers and magnetic cations. A multivariate assessment viz. a hierarchical cluster analysis (HCA) was used to corroborate and strengthen the experimental determined magnetic properties. A homogeneous particle distribution was observed in all SEM micrographs and is validated through MATLAB-based simulation by applying a watershed segmentation algorithm. Surface plots also confirm the change in magnetic properties with increase in doping concentration.     

Complexes containing phosphorus lignads—161: New phosphinite,phosphonite and phosphite derivatives of ruthenium,osmium and iridium

The complexes [MHCl(CO)(PPh₃)₃] (M = Ru or Os) readily undergo substitution at the site trans to the hydride ligand to afford phosphinite-, phosphonite-, or phosphite-containing products [MHCI(CO)(PPh₃)₂L] [L = P(OR)Ph₂, P(OR)₂Ph or P(OR)₃ respectively; R = Me or Et]. The ruthenium complexes alone undergo further substitution to afford complex cations [RuH(CO)(PPh₃)_nL_4?n]⁺ [n = 2, L = P(OMe)₃; n = 1, L = P(OR)₃; n = 0, L = P(OR)₂Ph or P(OR)Ph₂] which were isolated and characterised as their tetraphenylborate salts. Synthesis of the cationic complexes [IrHL₅][BPh₄]₂ [L = P(OR)₃, R = Me or Et] is also reported. Stereochemical assignments based on NMR data are given, and second order ³¹P and high field ¹H NMR patterns are analysed.     

Enrichment of Zinc and Iron Micronutrients in Lentil (Lens culinaris Medik.) through Biofortification

Biofortification of pulse crops with Zn and Fe is a viable approach to combat their widespread deficiencies in humans. Lentil (Lens culinaris Medik.) is a widely consumed edible crop possessing a high level of Zn and Fe micronutrients. Thus, the present study was conducted to examine the influence of foliar application of Zn and Fe on productivity, concentration, uptake and the economics of lentil cultivation (LL 931). For this, different treatment combinations of ZnSO₄·7H₂O (0.5%) and FeSO₄·7H₂O (0.5%), along with the recommended dose of fertilizer (RDF), were applied to the lentil. The results of study reported that the combined foliar application of ZnSO₄·7H₂O (0.5%) + FeSO₄·7H₂O (0.5%) at pre-flowering (S1) and pod formation (S2) stages was most effective in enhancing grain and straw yield, Zn and Fe concentration, and uptake. However, the outcome of this treatment was statistically on par with the results obtained under the treatment ZnSO₄·7H₂O (0.5%) + FeSO₄·7H₂O (0.5%) at S1 stage. A single spray of ZnSO₄·7H₂O (0.5%) + FeSO₄·7H₂O (0.5%) at S1 stage enhanced the grain and straw yield up to 39.6% and 51.8%, respectively. Similarly, Zn and Fe concentrations showed enhancement in grain (10.9% and 20.4%, respectively) and straw (27.5% and 27.6% respectively) of the lentil. The increase in Zn and Fe uptake by grain was 54.8% and 68.0%, respectively, whereas uptake by straw was 93.6% and 93.7%, respectively. Also the benefit:cost was the highest (1.96) with application of ZnSO₄·7H₂O (0.5%) + FeSO₄·7H₂O (0.5%) at S1 stage. Conclusively, the combined use of ZnSO₄·7H₂O (0.5%) + FeSO₄·7H₂O (0.5%) at S1 stage can contribute significantly towards yield, Zn and Fe concentration, as well as uptake and the economic returns of lentil to remediate the Zn and Fe deficiency.