Selling to the “Newsvendor” with a forecast update: Analysis of a dual purchase contract

We consider a supply chain in which a manufacturer sells to a procure-to-stock retailer facing a newsvendor problem with a forecast update. Under a wholesale price contract, the retailer waits as long as she can and optimally places her order after observing the forecast update. We show that the retailer’s wait-and-decide strategy, induced by the wholesale price contract, hinders the manufacturer’s ability to (1) set the wholesale price and maximize his profit, (2) hedge against excess inventory risk, and (3) reduce his profit uncertainty. To mitigate the adverse effect of wholesale price contract, we propose the dual purchase contract, through which the manufacturer provides a discount for orders placed before the forecast update. We characterize how and when a dual purchase contract creates strict Pareto improvement over a wholesale price contract. To do so, we establish the retailer’s optimal ordering policy and the manufacturer’s optimal pricing and production policies. We show how the dual purchase contract reduces profit variability and how it can be used as a risk hedging tool for a risk averse manufacturer. Through a numerical study, we provide additional managerial insights and show, for example, that market uncertainty is a key factor that defines when the dual purchase contract provides strict Pareto improvement over the wholesale price contract.     

Weighted cylindric partitions

Journal of Algebraic Combinatorics - Recently Corteel and Welsh outlined a technique for finding new sum-product identities by using functional relations between generating functions for cylindric...     

Solutions of the Schrödinger equation for Dirac delta decorated linear potential

We have studied bound states of the Schrödinger equation for a linear potential together with any finite number (P) of Dirac delta functions. Forx<-0, the potential is given as

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where 0<f; 0<x ₁<x ₂<...<x _P , theσ _i are arbitrary real numbers, and the potential is infinite forx<0.

     

Bose-Einstein condensate in a harmonic trap with an eccentric dimple potential

We investigate Bose-Einstein condensation of noninteracting gases in a harmonic trap with an offcenter dimple potential. We specifically consider the case of a tight and deep dimple potential, which is modeled by a point interaction. This point interaction is represented by a Dirac delta function. The atomic density, chemical potential, critical temperature and condensate fraction, and the role of the relative depth and the position of the dimple potential are analyzed by performing numerical calculations.     

Rotation barriers in N-substituted 2,4,6-trimethylpyridinium cations

The α-methyl and β-protons in ¹H-NMR spectra, the α-methyl, α-ring, and β-ring carbons in ¹³C-NMR spectra of N-substituted 2,4,6-trimethylpyridinium salts III are anisochronous. Dynamic NMR spectroscopy affords appreciably higher activation enthalpies ΔG≠ for rotation around the N(sp²)C(sp³) bond than ΔG≠ for the analogously substituted mesityl derivatives, in agreement with the shorter $\text{N}\text{+}$C than the CC bond.     

Chromenol Derivatives as Novel Antifungal Agents: Synthesis,In Silico and In Vitro Evaluation

Herein we report the synthesis of some new 1H-1,2,4-triazole functionalized chromenols (3a–3n) via tandem reactions of 1-(alkyl/aryl)-2-(1H-1,2,4-triazole-1-yl) with salicylic aldehydes and the evaluation of their antifungal activity. In silico prediction of biological activity with computer program PASS indicate that the compounds have a high novelty compared to the known antifungal agents. We did not find any close analog among the over 580,000 pharmaceutical agents in the Cortellis Drug Discovery Intelligence database at the similarity cutoff of 70%. The evaluation of antifungal activity in vitro revealed that the highest activity was exhibited by compound 3k, followed by 3n. Their MIC values for different fungi were 22.1–184.2 and 71.3–199.8 µM, respectively. Twelve from fourteen tested compounds were more active than the reference drugs ketoconazole and bifonazole. The most sensitive fungus appeared to be Trichoderma viride, while Aspergillus fumigatus was the most resistant one. It was found that the presence of the 2-(tert-butyl)-2H-chromen-2-ol substituent on the 4th position of the triazole ring is very beneficial for antifungal activity. Molecular docking studies on C. albicans sterol 14α-demethylase (CYP51) and DNA topoisomerase IV were used to predict the mechanism of antifungal activities. According to the docking results, the inhibition of CYP51 is a putative mechanism of antifungal activity of the novel chromenol derivatives. We also showed that most active compounds have a low cytotoxicity, which allows us to consider them promising antifungal agents for the subsequent testing activity in in vivo assays.     

Polarographic determination of herbicide thifensulfuron methyl/application to agrochemical pesticide,soil, and fruit juice

A novel, sensitive, simple, fast, and fully validated differential pulse polarographic (DPP) method for the determination of trace amounts of thifensulfuron-methyl in pesticide formulation, soil, and orange juice is reported. This procedure was based on a highly sensitive peak formed due to the reduction of thifensulfuron-methyl on a dropping mercury electrode over the pH range 1.00–10.00 in Britton–Robinson buffer. The polarographic reduction exhibits only a single peak in the pH ranges pH?≥?3.0 and pH?≤?6.0 and pH?=?10.0 located at potential values of ?1.010, ?1.350, and ?1.610?V (vs. SCE), respectively. The single peak appeared as a maximum at pH 3.0 (?1.010?V) was well resolved and suitable to be investigated for analytical use. This peak showed quantitative increments with the additions of standard thifensulfuron-methyl solution under the optimal conditions, and the cathodic peak current was linearity proportional to the thifensulfuron-methyl concentration in the range of 2?×?10^?7–5?×?10^?5?M. The limit of detection (LOD) and limit of quantification (LOQ) were obtained as 1.05?×?10^?7 and 3.50?×?10^?7?M, respectively, according to the relation k ?×?SD/b (where k?=?3 for LOD, k?=?10 for LOQ, SD is the standard deviation of the blank, and b is the slope of the calibration curve). The proposed method was applied to pesticide formulation (Harmony® Extra), and the average percentage recovery was in agreement with that obtained by the spectrophotometric comparison method, 97.82 and 102.6%, respectively. The method was extended to determination of thifensulfuron-methy in spiked soil and orange juice, showing a good reproducibility and accuracy with a relative standard deviation of 4.55 and 1.40%, and relative errors of +2.80 and +1.90%, respectively.     

Weighted Rogers–Ramanujan partitions and Dyson crank

In this paper, we refine a weighted partition identity of Alladi. We write formulas for generating functions for the number of partitions grouped with respect to a partition statistic other than the norm. We tie our weighted results as well as the different statistics with the crank of a partition. In particular, we prove that the number of partitions into even number of distinct parts whose odd-indexed parts’ sum is n is equal to the number of partitions of n with non-negative crank.     

Hindered rotation around the N(sp2)-C(sp3) single bond in 2,4,6-trimethyl-N-alkylpyridinium cations:H DNMR analysist

Pairwise chemical shift nonequivalence of the 2,6-methyl and 3,5-protons in ¹H NMR spectra, as well as of the 2,6-methyl, 2,6-ring and 3,5-ring carbons in ¹³C NMR spectra, was observed for N-alkyl-2,4,6-trimethylpyridinium salts 2. Dynamic NMR spectroscopy demonstrates appreciably higher activation free energies ΔG^# for rotation around the N(sp²)-C(sp³ bond than ΔG# for the analogously substituted mesityl derivatives, in agreement with the shorter N-C bond distance than for the C-C bond.     

Bose-Einstein Condensate in a Linear Trap with a Dimple Potential

We study Bose-Einstein condensation in a linear trap with a dimple potential where we model dimple potentials by Dirac δ function. Attractive and repulsive dimple potentials are taken into account. This model allows simple, explicit numerical and analytical investigations of noninteracting gases. Thus, the Schrdinger equation is used instead of the Gross-Pitaevski equation. We calculate the atomic density, the chemical potential, the critical temperature and the condensate fraction. The role of the relative depth of the dimple potential with respect to the linear trap in large condensate formation at enhanced temperatures is clearly revealed. Moreover, we also present a semi-classical method for calculating various quantities such as entropy analytically. Moreover, we compare the results of this paper with the results of a previous paper in which the harmonic trap with a dimple potential in 1D is investigated.