An improvement of discrete Tardos fingerprinting codes

It has been proven that the code lengths of Tardos’s collusion-secure fingerprinting codes are of theoretically minimal order with respect to the number of adversarial users (pirates). However, the code lengths can be further reduced as some preceding studies have revealed. In this article we improve a recent discrete variant of Tardos’s codes, and give a security proof of our codes under an assumption weaker than the original Marking Assumption. Our analysis shows that our codes have significantly shorter lengths than Tardos’s codes. For example, when c = 8, our code length is about 4.94% of Tardos’s code in a practical setting and about 4.62% in a certain limit case. Our code lengths for large c are asymptotically about 5.35% of Tardos’s codes. A part of this work was presented at 17th Applied Algebra, Algebraic Algorithms, and Error Correcting Codes (AAECC-17), Bangalore, India, December 16–20, 2007.     

Diastereoselective protonation on a radical anion in the photoallylation and photoreduction of 1,1-dicyano-2-methyl-3-phenyl-1-butene by allyltrimethylsilane

Diastereoselectivity in the photoallylation and photoreduction of 1,1-dicyano-2-methyl-3-phenyl-1-butene by allyltrimethylsilane in the presence of phenanthrene was dependent on the structures and stoichiometry of the added carboxylic acids. Diastereoselectivity increased up to 72% by the addition of equimolar amount of l-lactic acid based on the alkene.     

In vivo SNR in DENSE MRI; temporal and regional effects of field strength, receiver coil sensitivity and flip angle strategies

Aim

The influences on the signal-to-noise ratio (SNR) of Displacement ENcoding with Stimulated Echoes (DENSE) MRI of field strength, receiver coil sensitivity and choice of flip angle strategy have been previously investigated individually. In this study, all of these parameters have been investigated in the same setting, and a mutual comparison of their impact on SNR is presented.

Materials and methods

Ten healthy volunteers were imaged in a 1.5 T and a 3 T MRI system, using standard five- or six-channel cardiac coils as well as 32-channel coils, with four different excitation patterns. Variation of spatial coil sensitivity was assessed by regional SNR analysis.

Results

SNR ranging from 2.8 to 30.5 was found depending on the combination of excitation patterns, coil sensitivity and field strength. The SNR at 3 T was 53±26% higher than at 1.5 T (P<.001), whereas spatial differences of 59±26% were found in the ventricle (P<.001). Thirty-two-channel coils provided 52±29% higher SNR compared to standard five- or six-channel coils (P<.001). A fixed flip angle strategy provided an excess of 50% higher SNR in half of the imaged cardiac cycle compared to a sweeping flip angle strategy, and a single-phase acquisition provided a sixfold increase of SNR compared to a cine acquisition.

Conclusion

The effect of field strength and receiver coil sensitivity influences the SNR with the same order of magnitude, whereas flip angle strategy can have a larger effect on SNR. Thus, careful choice of imaging hardware in combination with adaptation of the acquisition protocol is crucial in order to realize sufficient SNR in DENSE MRI.     

A Copper(I)‐Catalyzed Enantioselective γ‐Boryl Substitution of Trifluoromethyl‐Substituted Alkenes: Synthesis of Enantioenriched γ,γ‐gem‐Difluoroallylboronates

The first catalytic enantioselective γ‐boryl substitution of CF₃‐substituted alkenes is reported. A series of CF₃‐substituted alkenes was treated with a diboron reagent in the presence of a copper(I)/Josiphos catalyst to afford the corresponding optically active γ,γ‐gem‐difluoroallylboronates in high enantioselectivity. The thus obtained products could be readily converted into the corresponding difluoromethylene‐containing homoallylic alcohols using highly stereospecific allylation reactions.     

Study on the surface density of surface-active substances through total-reflection X-ray absorption fine structure measurement

The total-reflection X-ray absorption fine structure (XAFS) method previously employed for the adsorption of dodecyltrimethylammonium bromide (DTAB) at the air/water interface was applied to that in the presence of NaBr. The surface concentration of the bromide ions Gamma(X)(B) of DTAB and NaBr was evaluated by using the Br K-edge absorption jump values of the total-reflection XAFS spectra and was compared to the corresponding value Gamma(H)(B) estimated from the dependence of surface tension on the bulk concentrations of DTAB m(1) and NaBr m(2). The Gamma(X)(B) values trace almost perfectly the Gamma(X)(B) versus m(1) curve up to a concentration near the critical micelle concentration (cmc) and deviate gradually above the concentration. This behavior is basically similar to that of the single DTAB system and ensures that the XAFS method is also applicable to the DTAB system, even in the presence of NaBr. In addition, this method was extended to the single nonionic amphiphile with covalently bonded bromine, and the surface concentrations of 6-bromo-1-hexanol (BrC6OH), Gamma(X)(1) and Gamma(H)(B), were evaluated and compared with each other. It was found that the Gamma(X)(1) value almost perfectly traces the Gamma(H)(1) versus m(1) curve, even at high surface concentrations. The excellent coincidence confirmed that the total-reflection XAFS method can be applied to the nonionic amphiphile system as well as a cationic surfactant with or without an added salt system. Finally, the difference between the Gamma(X)(B) and Gamma(H)(B) values observed in the DTAB with and without an added salt system is briefly described.     

Novel synthesis of 1,3-dienes from 1-alkenes via /ldene/rd reaction with pummerer rearrangement product: a short synthesis of the sex pheromone of the red bollworm moth

A Pummerer rearrangement product, 4-chlorophenylthiomethyl trifluoroacetate (6), obtained from 4-chlorophenyl methyl sulfoxide (5) and trifluoroacetic anhydride, reacted with 1-alkenes in trifluoroacetic acid to give the ene products 8, which were readily converted into the terminal 1,3-dienes 10 by oxidation and subsequent pyrolysis. Using this method, 9,11-dodecadien-1-yl acetate (12), a sex pheromone of the red bollworm moth, was synthesized.     

Extraction of alkali metal picrates by crown ethers having uncharged coordinating flexible side-chains

Crown ethers were synthesized which have a flexible, neutral side-chain capable of providing the crown ether-bound metal with an additional binding site from the axial direction. Liquid—liquid extraction of alkali metal picrates with these crown ethers was studied; the extraction is compared with that of the normal crown ethers as well as those crown ethers with a proton-dissociable side-chain. The neutral side-chain may assist or suppress the ease of metal extraction depending on the site of the ligating atom on the chain. An anionic ligating side-chain interacts favorably with the lighter metals, resulting in a net decrease in the metal extraction selectivity.