A semi-Markov process with an inverse Gaussian distribution as sojourn time

Let X_n denote the state of a device after n repairs. We assume that the time between two repairs is the time τ taken by a Wiener process {W(t), t ? 0}, starting from w₀ and with drift μ < 0, to reach c ∈ [0, w₀). After the nth repair, the process takes on either the value X_n?1 + 1 or X_n?1 + 2. The probability that X_n = X_n?1 + j, for j = 1, 2, depends on whether τ ? t₀ (a fixed constant) or τ > t₀. The device is considered to be worn out when X_n ? k, where k ∈ {1, 2, …}. This model is based on the ones proposed by Rishel (1991) [1] and Tseng and Peng (2007) [2]. We obtain an explicit expression for the mean lifetime of the device. Numerical methods are used to illustrate the analytical findings.     

An inventory-transportation system with stochastic demand

We study a logistic system in which a supplier has to deliver a set of products to a set of retailers to face a stochastic demand over a given time horizon. The transportation from the supplier to each retailer can be performed either directly, by expensive and fast vehicles, or through an intermediate depot, by less expensive but slower vehicles. At most one time period is required in the former case, while two time periods are needed in the latter case. A variable transportation cost is charged in the former case, while a fixed transportation cost per journey is charged in the latter case. An inventory cost is charged at the intermediate depot. The problem is to determine, for each time period and for each product, the quantity to send from the supplier to the depot, from the depot to each retailer and from the supplier to each retailer, in order to minimize the total expected cost. We first show that the classical benchmark policy, in which the demand of each product at each retailer is set equal to the average demand, can give a solution which is infinitely worse with respect to the optimal solution. Then, we propose two classes of policies to solve this problem. The first class, referred to as Horizon Policies, is composed of policies which require the solution of the overall problem over the time horizon. The second class, referred to as Reoptimization Policies, is composed of a myopic policy and several rolling-horizon policies in which the problem is reoptimized at each time period, once the demand of the time period is revealed. We evaluate the performance of each policy dynamically, by using Monte Carlo Simulation.     

Wavy graphene sheets from electrochemical sewing of corannulene

The presence of non-hexagonal rings in the honeycomb carbon arrangement of graphene produces rippled graphene layers with valuable chemical and physical properties. In principle, a bottom-up approach to introducing distortion from planarity of a graphene sheet can be achieved by careful insertion of curved polyaromatic hydrocarbons during the growth of the lattice. Corannulene, the archetype of such non-planar polyaromatic hydrocarbons, can act as an ideal wrinkling motif in 2D carbon nanostructures. Herein we report an electrochemical bottom-up method to obtain egg-box shaped nanographene structures through a polycondensation of corannulene that produces a new conducting layered material. Characterization of this new polymeric material by electrochemistry, spectroscopy, electron microscopy (SEM and TEM), scanning probe microscopy, and laser desorption-ionization time of flight mass spectrometry provides strong evidence that the anodic polymerization of corannulene, combined with electrochemically induced oxidative cyclodehydrogenations (Scholl reactions), leads to polycorannulene with a wavy graphene-like structure.

A bottom-up synthesis of wavy graphene structures obtained through an anodic polymerization process, combined with an electrochemically triggered oxidative cyclodehydrogenation, of the bowl-shaped polyaromatic hydrocarbon corannulene.     

Different Pathways in the Base-Promoted Isomerization of Benzyl Oxiranyl Ethers

The base-promoted isomerization of benzyl oxiranyl ethers was investigated. In particular it was shown that the reaction may proceed toward two main regioisomeric products: a benzyl vinyl ether or a 2-aryl-3-(hydroxyalkyl)oxetane, depending on subtle variations in the substitution on the phenyl ring. Disubstituted oxetanes were obtained in a stereoselective manner, thus providing a good entry to this class of synthetically useful compounds.     

Synthesis of Glycosylrifamycins,a new type of semisynthetic rifamycins

Glycosylrifamycins, a new type of semisynthetic rifamycin derivatives, can be easily obtained by reaction of 3-(2-aminoethylthio)rifamycin SV ( 2 ) with a glycosyl compound carrying a coupling group, such as isothicyanate or carboxy. We prepared O-acetylated and free glucopyranosyl and arabinopyranosyl derivatives of rifamycin S and SV (see 3–10 ). Additionally, derivatives with D -saccharo-1,4-lactone and with shikimic acid were obtained (see 11–15 ). Glycosylrifamycins show an interesting inhibitory power on Gram-positive bacteria (Table).     

The synthesis of methyl 2-(benzyloxycarbonyl)amino-3-dimethylaminopropenoate. The synthesis of trisubstituted pyrroles, 3-amino-2H-pyran-2-ones,fused 2H-pyran-2-ones and 4H-pyridin-4-ones

Methyl 2-(benzyloxycarbonyl)aimno-3-dimemylaminopropenoate ( 2 ) was prepared from methyl N-(benzyloxycarbonyl)glycinate ( 1 ) and t-butoxybis(dimethylamino)methane, and used as a reagent for preparation of substituted 3-(benzyloxycarbonyl)amino-4H-quinolizin-4-ones 5 and 6 , ?2H-pyran-2-ones 17–19 , ?2H-1-benzopyran-2-ones 28–31 , and -naphthopyrans 32–35 , ?2H-pyrano[3,2-c]pyridine-2,5-dione 46 , -pyrano-[4,3-b]pyran-2,5-dione 47 , -pyrano[3,2-c]benzopyran-2,5-dione 48 , -pyrano[2,3-c]pyrazol-6-ones 49 and 50 , -pyrano[2,3-d]pyrirnidin-7-ones 51 and 52 derivatives. In the reaction of 2 with 1,3-diketones trisubsti tuted pyrroles 14–16 were formed. Selective removal of benzyloxycarbonyl group was achieved by cat alytic transfer hydrogenation with Pd/C in the presence of cyclohexene to afford free 3-amino compounds 7 , 8 , 20 , 36–38 and 53–57 in yields better than 80%.     

Self‐Sufficient Formaldehyde‐to‐Methanol Conversion by Organometallic Formaldehyde Dismutase Mimic

The catalytic networks of methylotrophic organisms, featuring redox enzymes for the activation of one‐carbon moieties, can serve as great inspiration in the development of novel homogeneously catalyzed pathways for the interconversion of C₁ molecules at ambient conditions. An imidazolium‐tagged arene–ruthenium complex was identified as an effective functional mimic of the bacterial formaldehyde dismutase, which provides a new and highly selective route for the conversion of formaldehyde to methanol in absence of any external reducing agents. Moreover, secondary amines are reductively methylated by the organometallic dismutase mimic in a redox self‐sufficient manner with formaldehyde acting both as carbon source and reducing agent.     

Characterisation of varnishes used in violins by pyrolysis-gas chromatography/mass spectrometry

The correct characterisation and a detailed knowledge of the materials originally used in violin varnishes, like natural resins, is crucial for the conservation in museums and for a suitable restoration technique. The study presented here reports on the potential of pyrolysis (Py) coupled with gas chromatography (GC) and mass spectrometry (MS) for the identification of chemical markers of each resin; this technique is very sensitive and selective, it needs a small quantity of sample and does not require chemical treatments. To improve the chromatographic behaviour of polar compounds the derivatising agent tetramethylammonium hydroxide (TMAH) in combination with pyrolysis has been used, in the so-called TMAH thermochemolysis or thermally assisted hydrolysis and methylation (THM), or more simply pyrolysis-methylation. The natural resins studied were colophony, sandarac, manila copal, elemi, amber and benzoin, mainly composed of terpenic compounds, with the exception of the latter, composed of aromatic compounds. Many compounds were identified; in particular, methyl esters of resinous acids that, individually or in a group, can be used as chemical markers. However, through this technique it was not possible to distinguish between the sandarac and manila copal resins because their chromatographic behaviour is very similar. Finally, the procedure applied has been employed in the characterisation of original varnish samples.     

Controlled Annealing in Adaptive Multicomponent Gels

We use a pH-driven annealing process to convert between co-assembled and self-sorted networks in multicomponent gels. The initially formed gels at low pH are co-assembled, with the two components coexisting within the same self-assembled structures. We use an enzymatic approach to increase the pH, resulting in a gel-to-sol transition, followed by a hydrolysis to lower the pH once again. As the pH decreases, a self-sorted network is formed by a two-stage gelation process determined by the pK_a of each component. This approach can be expanded to layered systems to generate many varied systems by changing composition and rates of pH change, adapting their microstructure and so allowing access to a far greater range of morphologies and complexity than can be achieved in single component systems.