The Most Critical Path in a PERT Network

The classical PERT approach uses the path with the largest expected duration as the critical path to estimate the probability of completing a project by a given deadline. However, in general, such a path is not the ‘most critical’ path and does not provide the smallest estimate for the probability of completion time. This paper studies the ‘most critical path’ problem and formulates it as an optimal path problem in a deterministic network with a two-attribute fractional objective function. An exact solution approach is presented for the optimal path problem which also gives the solution to the most critical path problem. The illustrative examples as well as our computational results demonstrate that the proposed algorithm provides estimates for the probabilities of completion time that are much more accurate than those of the classical approach.     

The significance of reducing setup times/setup costs

Scheduling with setup times or setup costs plays a crucial role in todays modern manufacturing and service environments where reliable products/services are to be delivered on time. Scheduling activities profoundly depend on the times/costs required to prepare the facility for performing the activities. However, the vast majority of existing scheduling literature ignores this fact. We define and emphasize the importance, applications, and benefits of explicitly considering setup times/costs in scheduling research. Moreover, a review of the latest research on scheduling problems with setup times/costs is provided.     

Tributylammonium Halochromates/silica Gel:Simple Reagents for Oxidative Coupling of Thiols to Symmetrical Disulfides

New orange solid tributylammonium halochromates, (C₄H₉)₃N⁺CrO₃X^?, TBAXC (X=F, Cl) are easily synthesized by the reaction of tributylammonium fluoride and chloride with CrO₃ in a 1:1 molar ratio in the presence of HF and HCl. Tributylammonium halochromates(VI) are versatile reagent for the effective and selective oxidation of organic substrates. Silica gel supported TBAFC and TBACC are versatile reagents for the effective and selective oxidation of organic substrates, in particular, thiols, under mild conditions. Considerable improvements are observed in the presence of the absorbent, making the work‐up much more convenient.     

An ionic 2D inorganic-organic hybrid of tris[((1H-tetrazol-5-yl)methyl)morpholine] dodecatungstophosphate(Ⅴ) pentahydrate:Synthesis X-ray crystal structure and spectroscopic characterizations

<正>A unique ionic hybrid material[C_6H_(12)N_5O]_3[(PO_4)W__(12)O_(36)]·5H_2O has been synthesized from the reaction of((1H-tetrazole-5- yl)methyl)morpholine andα-H_3[(PO_4)W_(12)O_(36)]·21H_2O.It has successfully been characterized by elemental analysis,IR and ~1H NMR spectroscopies,TGA and single-crystal X-ray diffraction method.The title compound is constructed from the three [C_6H_(12)N_5O]~+ cations andα-Keggin[(PO_4)W_(12)O_(36)]~(3-) polyoxoanion.The most remarkable structural feature of this hybrid can be described as two-dimensional inorganic infinite plane-like(2D/∞)[(PO_4)W_(12)O_(36)]~(3-)) which forming via van der Waals interactions along the x axis.     

Minimizing the weighted number of early and tardy jobs in a stochastic single machine scheduling problem

We study a static stochastic single machine scheduling problem in which jobs have random processing times with arbitrary distributions, due dates are known with certainty, and fixed individual penalties (or weights) are imposed on both early and tardy jobs. The objective is to find an optimal sequence that minimizes the expected total weighted number of early and tardy jobs. The general problem is NP-hard to solve; however, in this paper, we develop certain conditions under which the problem is solvable exactly. An efficient heuristic is also introduced to find a candidate for the optimal sequence of the general problem. Our illustrative examples and computational results demonstrate that the heuristic performs well in identifying either optimal sequences or good candidates with low errors. Furthermore, we show that special cases of the problem studied here reduce to some classical stochastic single machine scheduling problems including the problem of minimizing the expected weighted number of early jobs and the problem of minimizing the expected weighted number of tardy jobs which are both solvable by the proposed exact or heuristic methods.     

The effect of fractional calculus on the formation of quantum-mechanical operators

In this paper, the deformation of the ordinary quantum mechanics is formulated based on the idea of conformable fractional calculus. Some properties of fractional calculus and fractional elementary functions are investigated. The fractional wave equation in 1 + 1 dimension and fractional version of the Lorentz transformation are discussed. Finally, the fractional quantum mechanics is formulated; infinite potential well problem, density of states for the ideal gas, and quantum harmonic oscillator problem are discussed.     

Poly(styrene-co-butyl acrylate)/mesoporous diatomaceous earth mineral nanocomposites by in situ AGET ATRP

Journal of Thermal Analysis and Calorimetry - Mesoporous diatomite platelets were used for in situ copolymerization of styrene and butyl acrylate by activators generated by electron transfer for...     

Enhancement of immune response and protection in BALB/c mice immunized with liposomal recombinant major surface glycoprotein of Leishmania (rgp63): The role of bilayer composition

Development of new generation vaccines requires adjuvants to elicit the type and intensity of immune response needed for protection. Liposomes have been shown to be an effective adjuvant formulation. In this study, the role of liposome bilayer composition with different phase transition temperature (T_c) to induce a T helper 1 (Th1) type of immune response and protection against leishmaniasis in BALB/c mice was assessed. Liposome formulations with different bilayer compositions consisting of egg phosphatidylcholine (EPC, T_c < 0 °C), dipalmitoylphosphatidylcholine (DPPC, T_c 41 °C), or distearoylphosphatidylcholine (DSPC, T_c 54 °C) were prepared. All liposomes were contained rgp63 as a recombinant antigen and used to immunize mice subcutaneously 3 times in 3-week intervals. Evaluation of lesion development and splenic parasite burden after challenge with L. major, evaluation of Th1 cytokine (IFN-γ) and Th2 cytokine (IL-4), and titration of IgG isotypes were carried out to assess the type of generated immune response and extent of protection. The results indicated the generated immune response in mice was influenced by the bilayer composition of liposomes, so that mice immunized with liposomes consisting of EPC induced a Th2 type of immune response while liposome consisting of DPPC or DSPC induced Th1 type of immune response. It seems that liposomes prepared with higher Tm phospholipids are suitable formulation to induce Th1 type of immune response and protection, and so might be used for further investigations to develop an effective vaccine against leishmaniasis.     

Joint control of production,remanufacturing, and disposal activities in a hybrid manufacturing–remanufacturing system

To generate insights into how production of new items and remanufacturing and disposal of returned products can be effectively coordinated, we develop a model of a hybrid manufacturing–remanufacturing system. Formulating the model as a Markov decision process, we investigate the structure of the optimal policy that jointly controls production, remanufacturing, and disposal decisions. Considering the average profit maximization criterion, we show that the joint optimal policy can be characterized by three monotone switching curves. Moreover, we show that there exist serviceable (i.e., as-new) and remanufacturing (i.e., returned) inventory thresholds beyond which production cannot be optimal but disposal is always optimal. We also identify conditions under which idling and disposal actions are always optimal when the system is empty. Using numerical comparisons between models with and without remanufacturing and disposal options, we generate insights into the benefit of utilizing these options. To effectively coordinate production, remanufacturing, and disposal activities, we propose a simple, implementable, and yet effective heuristic policy. Our extensive numerical results suggest that the proposed heuristic can greatly help firms to effectively coordinate their production, remanufacturing, and disposal activities and thereby reduce their operational costs.