Localization of toric code defects

We explore the possibility of passive error correction in the toric code model. We first show that even coherent dynamics, stemming from spin interactions or the coupling to an external magnetic field, lead to logical errors. We then argue that Anderson localization of the defects, arising from unavoidable fluctuations of the coupling constants, provides a remedy. This protection is demonstrated by using general analytical arguments that are complemented with numerical results which show that self-correcting memory can in principle be achieved in the limit of a nonzero density of identical defects.     

Retention of regiochemistry and chirality in the ruthenium catalyzed allylic alkylation of disubstituted allylic esters

The regiospecific nucleophilic substitution during the ruthenium catalyzed allylic alkylation of 1,3-unsymmetrical disubstituted allylic esters was demonstrated. The nucleophile was selectively introduced at the position originally substituted with leaving group in the 2-DPPBA or ip-pybox ligated [RuCl(2)(p-cymene)](2) catalyzed allylic alkylation of 1,3-unsymmetrical disubstituted allylic esters. The chirality of the optically active allylic esters was also transferred to the alkylated products.     

An economic order quantity model for deteriorating item in a purchasing system with multiple prepayments

In the classic economic order quantity model the purchasing cost of an order should be paid at the time of its receipt. Sometimes, retailers ask purchasers to pay all or a fraction of the purchasing cost in advance and sometimes allow them to divide the prepayment into several equal-sized parts. In this paper, economic order quantity model for a deteriorating product with and without shortage under consecutive prepayments are developed. Numerical examples illustrate the proposed models and solution method and sensitivity analysis provides some managerial insights for managers.     

Study of Solution Polymerization of Styrene in the Presence of Poly(ethylene glycol)-RAFT Agents Possessing Benzoyl Xanthate Derivatives

In this work, Macro-Reversible addition fragmentation termination (RAFT) agents based on poly(ethylene glycol) (PEG) possessing different molecular weights and bearing benzoyl xanthate moieties were synthesized by the reaction of PEG potassium xanthate salts with benzoyl chloride, 4-methyl benzoyl chloride and 4-chloro benzoyl chloride. Controlled free radical polymerization of the styrene were carried out in the presence of these macro-RAFT agents using 2,2′-azobisizsobutyronitrile (AIBN) as an initiator to yield PS-b-PEG-b-PS block copolymers. The linear kinetic plot ln [M]_o/[M] vs. polymerization time indicated that was first order with reference to monomer concentration. The block copolymerization possessed controlled/living character. The controlled character of the RAFT polymerization of the styrene was confirmed by the formation of narrow polydispersity of the polymers, linear increases in the molecular weight with polymerization time and molecular weight of the products that agreed well with theoretical values. Polymers having relatively narrow molecular weight distributions and predetermined number average molecular weights were obtained by the RAFT polymerization of the styrene. However, molecular weights of the polymers deviated from the theoretical values when low molecular weight RAFT agents are used. The results indicate that PEG benzoyl xanthate RAFT agents can more efficiently control the polymerization comparing methyl or chlorobenzoyl derivatives. The block copolymers were characterized by spectroscopic and GPC methods.     

High‐rate crystallization of polycarbonate in spincast thin film

Surface morphology of bisphenol‐A polycarbonate (BAPC) thin films, with thickness ranging from 30 to 1000 nm on silicon substrates was studied by atomic force microscopy. The films were prepared by spincasting from 1,2‐dichloroethane solutions of 0.25–5.0 wt % BAPC. Even though longer annealing than 250 h was necessary for complete crystallization for bulk BAPC, high crystallinity was observed for 30 nm thick film after annealing at 200 °C for 48 h in vacuum. Positron annihilation lifetime spectroscopy measurements showed that the free volume hole size in 30 nm thick film was larger than that of bulk at 200 °C. Comparison of the BAPC concentration in the precursor solution with the overlap concentration suggests that the high crystallinity of the 30 nm BAPC film is due to less entangled chains caused by rapid removal of the solvent from the dilute solution. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

The characterization of plasma-polymerized C60 thin films

Plasma-polymerized C₆₀ thin films were investigated in the form of a field effect transistor (FET) structure. In the FET device, the C₆₀ polymer acts as a p-type semiconductor, whereas C₆₀ is an n-type semiconductor. Its conduction mechanism can be described as due to variable range hopping. As a sensing device, the C₆₀ polymer can behave as a gas sensor for electrophoric gases and can also be operated as a photo-sensing device in air. Received: 21 April 2001 / Accepted: 23 July 2001 / Published online: 2 October 2001     

When is ‘nearest neighbour’ meaningful: A converse theorem and implications

Beyer et al. gave a sufficient condition for the high dimensional phenomenon known as the concentration of distances. Their work has pinpointed serious problems due to nearest neighbours not being meaningful in high dimensions. Here we establish the converse of their result, in order to answer the question as to when nearest neighbour is still meaningful in arbitrarily high dimensions. We then show for a class of realistic data distributions having non-i.i.d. dimensions, namely the family of linear latent variable models, that the Euclidean distance will not concentrate as long as the amount of ‘relevant’ dimensions grows no slower than the overall data dimensions. This condition is, of course, often not met in practice. After numerically validating our findings, we examine real data situations in two different areas (text-based document collections and gene expression arrays), which suggest that the presence or absence of distance concentration in high dimensional problems plays a role in making the data hard or easy to work with.     

Multiple-buyer multiple-vendor multi-product multi-constraint supply chain problem with stochastic demand and variable lead-time: A harmony search algorithm

In this paper, a multi-buyer multi-vendor supply chain problem is considered in which there are several products, each buyer has limited capacity to purchase products, and each vendor has warehouse limitation to store products. In this chain, the demand of each product is stochastic and follows a uniform distribution. The lead-time of receiving products from a vendor to a buyer is assumed to vary linearly with respect to the order quantity of the buyer and the production rate of the vendor. For each product, a fraction of the shortage is backordered and the rest are lost. The ordered product quantities are placed in multiple of pre-defined packets and there are service rate constraints for the buyers. The goal is to determine the reorder points, the safety stocks, and the numbers of shipments and packets in each shipment of the products such that the total cost of the supply chain is minimized. We show that the model of this problem is of an integer nonlinear programming type and in order to solve it a harmony search algorithm is employed. To validate the solution and to compare the performance of the proposed algorithm, a genetic algorithm is utilized as well. A numerical illustration and sensitivity analysis are given at the end to show the applicability of the proposed methodology in real-world supply chain problems.     

Hydrogen adsorption and desorption in carbon nanotube systems and its mechanisms

The hydrogen physisorption properties in single-walled carbon nanotube (SWNT) based materials were characterized. The SWNTs were highly purified and three useful pores for hydrogen physisorption were activated. Hydrogen was physisorbed in intra-tube pores at room temperature and the capacity was estimated to be about 0.3–0.4 wt.% at room temperature. The adsorption capacity can be explained by the Langmuir model. The intra-tube pores have large adsorption potential and this induces hydrogen physisorption at comparatively higher temperatures. This fact indicates the importance of fabricating sub-nanometer ordered pores for this phenomena. PACS 51.30.+i; 51.90.+r; 81.05.Tp; 81.07.De