Profit maximization in an inventory system with time-varying demand,partial backordering and discrete inventory cycle

In this paper, an inventory problem where the inventory cycle must be an integer multiple of a known basic period is considered. Furthermore, the demand rate in each basic period is a power time-dependent function. Shortages are allowed but, taking necessities or interests of the customers into account, only a fixed proportion of the demand during the stock-out period is satisfied with the arrival of the next replenishment. The costs related to the management of the inventory system are the ordering cost, the purchasing cost, the holding cost, the backordering cost and the lost sale cost. The problem is to determine the best inventory policy that maximizes the profit per unit time, which is the difference between the income obtained from the sales of the product and the sum of the previous costs. The modeling of the inventory problem leads to an integer nonlinear mathematical programming problem. To solve this problem, a new and efficient algorithm to calculate the optimal inventory cycle and the economic order quantity is proposed. Numerical examples are presented to illustrate how the algorithm works to determine the best inventory policies. A sensitivity analysis of the optimal policy with respect to some parameters of the inventory system is developed. Finally, conclusions and suggestions for future research lines are given.

     

On the applicability of the HSAB principle through the use of improved computational schemes for chemical hardness evaluation

Finite difference schemes, named Compact Finite Difference Schemes with Spectral-like Resolution, have been used for a less crude approximation of the analytical hardness definition as the second-order derivative of the energy with respect to the electron number. The improved computational schemes, at different levels of theory, have been used to calculate global hardness values of some probe bases, traditionally classified as hard and soft on the basis of their chemical behavior, and to investigate the quantitative applicability of the HSAB principle. Exchange acid-base reactions have been used to test the HSAB principle assuming the reaction energies as a measure of the stabilization of product adducts.     

Solvation properties of N-substituted cis and trans amides are not identical: significant enthalpy and entropy changes are revealed by the use of variable temperature 1H NMR in aqueous and chloroform solutions and ab initio calculations

The cis/trans conformational equilibrium of N-methyl formamide (NMF) and the sterically hindered tert-butylformamide (TBF) was investigated by the use of variable temperature gradient 1H NMR in aqueous solution and in the low dielectric constant and solvation ability solvent CDCl3 and various levels of first principles calculations. The trans isomer of NMF in aqueous solution is enthalpically favored relative to the cis (deltaH(o) = -5.79 +/- 0.18 kJ mol(-1)) with entropy differences at 298 K (298 x deltaS(o) = -0.23 +/- 0.17 kJ mol(-1)) playing a minor role. The experimental value of the enthalpy difference strongly decreases (deltaH(o) = -1.72 +/- 0.06 kJ mol(-1)), and the contribution of entropy at 298 K (298 x deltaS(o) = -1.87 +/- 0.06 kJ mol(-1)) increases in the case of the sterically hindered tert-butylformamide. The trans isomer of NMF in CDCl3 solution is enthalpically favored relative to the cis (deltaH(o) = -3.71 +/- 0.17 kJ mol(-1)) with entropy differences at 298 K (298 x deltaS(o) = 1.02 +/- 0.19 kJ mol(-1)) playing a minor role. In the sterically hindered tert-butylformamide, the trans isomer is enthalpically disfavored (deltaH(o) = 1.60 +/- 0.09 kJ mol(-1)) but is entropically favored (298 x deltaS(o) = 1.71 +/- 0.10 kJ mol(-1)). The results are compared with literature data of model peptides. It is concluded that, in amide bonds at 298 K and in the absence of strongly stabilizing sequence-specific inter-residue interactions involving side chains, the free energy difference of the cis/trans isomers and both the enthalpy and entropy contributions are strongly dependent on the N-alkyl substitution and the solvent. The significant decreasing enthalpic benefit of the trans isomer in CDCl3 compared to that in H2O, in the case of NMF and TBF, is partially offset by an adverse entropy contribution. This is in agreement with the general phenomenon of enthalpy versus entropy compensation. B3LY/6-311++G** and MP2/6-311++G** quantum chemical calculations confirm the stability orders of isomers and the deltaG decrease in going from water to CHCl3 as solvent. However, the absolute calculated values, especially for TBF, deviate significantly from the experimental values. Consideration of the solvent effects via the PCM approach on NMF x H2O and TBF x H2O supermolecules improves the agreement with the experimental results for TBF isomers, but not for NMF.     

Domain and hull-enclosed area distributions in two-dimensional coarsening

We obtain the exact distribution of the areas enclosed by domain boundaries (“hulls”) during the coarsening dynamics of a two-dimensional nonconserved scalar field. We prove that the number of hulls per unit area that enclose an area greater than A has the form N_h(A,t)=2c/(A+λt), where . This result is also a demonstration of the validity of the dynamical scaling hypothesis in this system. We also show that domain areas (regions of aligned spins) have a similar distribution.     

Evaluation of the mixed aggregate method as an alternative to the bismuth active substances and cobalt thiocyanate active substances procedures for the determination of nonionic surfactants in raw and treated sewage

The mixed aggregate (MA) method was evaluated for the routine determination of total ethoxylated nonionic surfactants in municipal raw and treated sewage. Nonionics in wastewater samples were enriched with a C8 solid-phase extraction cartridge, eluted with ethyl acetate-methanol, and separated from interferences with stacked strong anionic (quaternary ammonium form) and cationic (benzenesulfonic acid form) exchange columns. Sample extracts were evaporated to dryness and redissolved in distilled water. The total amount of ethoxylates, on a weight basis, was determined by measuring the critical micelle concentration of a mixed micelle made up of ethoxylates and the anionic surfactant sodium dodecyl sulfate, used as the reagent. The dye Coomassie Brilliant Blue G was used as a photometric probe. The minimum amount of ethoxylate required for a single determination was 1 microg. For raw sewage samples, mean recoveries and standard deviations were 98 +/- 6 and 98 +/- 4% at fortification levels of 0.3 and 0.6 microg/mL, respectively. For treated sewage samples, mean recoveries and standard deviations were 95 +/- 2 and 100 +/- 2% at fortification levels of 0.03 and 0.06 microg/mL, respectively. The MA method and the classical bismuth active substances and cobalt thiocyanate active substances procedures were compared. The former offers some significant advantages over the classical procedures in terms of sensitivity, selectivity, precision, simplicity, and rapidity; the type of response is independent of both the molecular weight and the chain length of the surfactant.     

A sorbent tube for oral malodour monitoring

Volatile sulphur compounds (VSCs) and particularly hydrogen sulphide are considered as the predominant gases causing oral malodour. In this paper, a simple alarm sensor has been developed for VSCs determination in mouth air. The device consists of a glass tube packed with a solid sensing phase. The VSCs react with the sensing phase to produce a change in the colour of the sensor visible with a naked eye.Different “reagents” were investigated to develop the sensing phase (neocuproine + Cu(II), bathocuproine + Cu(II), resazurin, 2,6-dichlorophenolindophenol and lead acetate), finding the neocuproine + Cu(II) as the best for our purposes. Also, different substrates such as Amberlite XAD-4 and XAD-7 and different trademarks of silica gel were tested as solid supports, being selected the silica gel.A device consisting of a glass tube packed with the sensing phase was optimized and tested with halitosis patients as a rapid illness test and the results compared with those obtained with a commercially available instrument, the Halimeter™, used for the determination of VSCs in mouth air. The results exhibited acceptable agreement between the proposed “qualitative” alarm sensor and a commercially available technique selected as reference, showing the possibility of using this “visual sensor” to control the halitosis and its evolution with an eventual treatment, by the own patient.     

Mechanism of Thyroxine Deiodination by Naphthyl‐Based Iodothyronine Deiodinase Mimics and the Halogen Bonding Role: A DFT Investigation

This paper deals with a systematic density functional theory (DFT) study aiming to unravel the mechanism of the thyroxine (T4) conversion into 3,3′,5‐triiodothyronine (rT3) by using different bio‐inspired naphthyl‐based models, which are able to reproduce the catalytic functions of the type‐3 deiodinase ID‐3. Such naphthalenes, having two selenols, two thiols, and a selenol–thiol pair in peri positions, which were previously synthesized and tested in their deiodinase activity, are able to remove iodine selectively from the inner ring of T4 to produce rT3. Calculations were performed including also an imidazole ring that, mimicking the role of the His residue, plays an essential role deprotonating the selenol/thiol moiety. For all the used complexes, the calculated potential energy surfaces show that the reaction proceeds via an intermediate, characterized by the presence of a X?I?C (X=Se, S) halogen bond, whose transformation into a subsequent intermediate in which the C?I bond is definitively cleaved and the incipient X?I bond is formed represents the rate‐determining step of the whole process. The calculated trend in the barrier heights of the corresponding transition states allows us to rationalize the experimentally observed superior deiodinase activity of the naphthyl‐based compound with two selenol groups. The role of the peri interactions between chalcogen atoms appears to be less prominent in determining the deiodination activity.     

Pt-Ag clusters and their neutral mononuclear Pt(II) starting complexes: structural and luminescence studies

The mononuclear complexes [Pt(bzq)(S^S)] [S^S = pyrrolidinedithiocarbamate (pdtc 1), dimethyldithiocarbamate (dmdtc 2)] were prepared by reaction of [Pt(bzq)(NCMe)(2)]ClO(4) with an equimolecular amount of [NH(4)(pdtc)] and [Na(dmdtc)·2H(2)O] respectively in MeOH. Reactions of 1 and 2 with AgClO(4) in 1 : 1 and 2 : 1 molar ratios rendered the heteropolinuclear compounds [{Pt(bzq)(S^S)Ag}(2)](ClO(4))(2) (S^S = pdtc 3, dmdtc 4) and [{Pt(bzq)(S^S)}(2)Ag](ClO(4)) (S^S = pdtc 5, dmdtc 6) respectively. The X-ray studies on single crystals of 3 and 4 showed that both consist of tetranuclear [Pt(2)Ag(2)] clusters with the Pt-Ag and the Ag-Ag distances in the range of those corresponding to Pt-Ag dative bonds and argentophilic interactions. In 3 the tetranuclear [Pt(2)Ag(2)] clusters are connected into infinite polymeric chains by Pt···Pt metallophilic interactions (Pt···Pt = 3.1890(7) ?). The X-ray study on a single crystal of 5 showed that it is a polymer based on trinuclear [Pt(2)Ag] clusters containing two unsupported Pt-Ag dative bonds and connected by Ag-S bonds in such a way that the "Pt-Ag-S-Pt-Ag-S" atoms draw a zigzag polymeric chain. TD-DFT calculations carried out for 1 indicate that the lowest energy absorption band in CH(2)Cl(2) can be described as a mixture of (1)MLCT, (1)IL and (1)L'LCT transitions. Powdered samples of 1 at 298 K and 77 K show a green-yellow emission band coming mainly from a (3)LC excited state. However complex 2 shows "luminescence thermochromism": the colour of its luminescence changes from green-yellow at 77 K to orange-red at 298 K. The emission of the Pt-Ag clusters, 3-6, in the solid state, are due to excimeric (3)ππ and/or (3)MMLCT (dσ* →π*) low-lying excited states, indicating that the presence of silver in the clusters makes the "Pt(bzq)(S^S)" fragments interact to a large extent through Pt···Pt and/or π-π interactions. Solid 3 is a highly selective vapochromic compound towards acetonitrile although this behaviour is not fully reversible.