Nilpotent fusion categories

In this paper we extend categorically the notion of a finite nilpotent group to fusion categories. To this end, we first analyze the trivial component of the universal grading of a fusion category C, and then introduce the upper central series of C. For fusion categories with commutative Grothendieck rings (e.g., braided fusion categories) we also introduce the lower central series. We study arithmetic and structural properties of nilpotent fusion categories, and apply our theory to modular categories and to semisimple Hopf algebras. In particular, we show that in the modular case the two central series are centralizers of each other in the sense of M. Müger.     

Analysis of thermal phases in calcareous Iron Age pottery using FT-IR and Raman spectroscopy

The work deals with the FT-IR and micro-Raman spectroscopy study of the pseudo-amorphous and crystalline thermal phases in the composition of calcareous Iron Age pottery from the Galilee. The application of second-derivative and curve-fitting techniques improves the identification of the thermal phases in the composition of the pottery and makes it possible to analyze the pseudo-amorphous phases which are formed during the firing of the clayey raw material to pottery. This technique makes it possible to distinguish between meta-smectite and meta-kaolinite and to estimate the firing temperature of the pottery. The Micro-Raman spectroscopy is sensitive to the structural degree of ordering of the thermal phases and enables point analysis of peculiar components in the composition of the pottery. Based on the spectroscopic study, it is concluded that the calcareous pottery contained large amounts of microcrystalline-recarbonated calcite mixed with the meta-clay. The large amount of recarbonated calcite in the pottery material and the relatively low firing temperature indicates that instead of sintering the clay, lime technology was used for the cementation of the calcareous vessels. This process took place after the firing by recarbonation of the decomposed calcite which leads to cementation of the vessels with microcrystalline calcite.     

Response times in gated M/G/1 queues: The processor-sharing case

A class of single server queues with Poisson arrivals and a gated server is considered. Whenever the server becomes idle the gate separating it from the waiting line opens, admitting all the waiting customers into service, and then closes again. The batch admitted into service may be served according to some arbitrary scheme. The equilibrium waiting time distribution is provided for the subclass of conservative schemes with arbitrary service times and the processor-sharing case is treated in some detail to produce the equilibrium time-in-service and response time distributions, conditional on the length of required service. The LIFO and random order of service schemes and the case of compound Poisson arrivals are treated briefly as examples of the effectiveness of the proposed method of analysis. All distributions are provided in terms of their Laplace transforms except for the case of exponential service times where the L.T. of the waiting time distribution is inverted. The first two moments of the equilibrium waiting and response times are provided for most treated cases and in the exponential service times case the batch size distribution is also presented.     

Whole‐Genome Sequencing of a Single Viral Species from a Highly Heterogeneous Sample

Metagenomic studies suggest that only a small fraction of the viruses that exist in nature have been identified and studied. Characterization of unknown viral genomes is hindered by the many genomes populating any virus sample. A new method is reported that integrates drop‐based microfluidics and computational analysis to enable the purification of any single viral species from a complex mixed virus sample and the retrieval of complete genome sequences. By using this platform, the genome sequence of a 5243 bp dsDNA virus that was spiked into wastewater was retrieved with greater than 96 % sequence coverage and more than 99.8 % sequence identity. This method holds great potential for virus discovery since it allows enrichment and sequencing of previously undescribed viruses as well as known viruses.     

Antibacterial and antifungal LDPE films for active packaging

Active antimicrobial packaging is a promising form of active packaging that can kill or inhibit microorganism growth in order to maintain product quality and safety. One of the most common approaches is based on the release of volatile antimicrobial agents from the packaging material such as essential oils. Due to their highly volatile nature, the challenge is to preserve the essential oils during the high‐temperature melt processing of the polymer, while maintaining high antimicrobial activity for a desired shelf life. This study suggests a new approach in order to achieve this goal. Antimicrobial active films are developed based on low‐density polyethylene (LDPE), organo‐modified montmorillonite clays (MMT) and carvacrol (used as an essential oil model). In order to minimize carvacrol loss throughout the polymer compounding, a pre‐compounding step is developed in which clay/carvacrol hybrids are produced. The hybrids exhibit a significant increase in the d‐spacing of clay and enhanced thermal stability. The resulting LDPE/(clay/carvacrol) films exhibit superior and prolonged antibacterial activity against Escherichia coli and Listeria innocua, while polymer compounded with pure carvacrol loses the antibacterial properties within days. The films also present an excellent antifungal activity against Alternaria alternata, used as a model plant pathogenic fungus. Furthermore, infrared spectroscopy analysis of the LDPE/(clay/carvacrol) system displayed significantly higher carvacrol content in the film as well as a slower out‐diffusion of the carvacrol molecules in comparison to LDPE/carvacrol films. Thus, these new films have a high potential for antimicrobial food packaging applications due to their long‐lasting and broad‐spectrum antimicrobial efficacy. Copyright © 2014 John Wiley & Sons, Ltd.     

Saint-Venant's principle in nonlinear plane elasticity with sufficiently small strains

A homogeneous, isotropic cylinder in an equilibrium state of plane strain, whose cross-section is a rectangle R : [0 < y ₁ < 2L; 0 < y ₂ < h] with h/L 1, is considered. There are no body forces and the long sides are stress free. At y ₁ = 0 and y ₁ = 2L, there are arbitrary loadings, each statically equivalent to a uniformly distributed tensile or compressive stress c. Within the theory of nonlinear elasticity and with the strains and strain gradients assumed to be sufficiently small (but with no such assumptions on the displacement gradients), it is proved that if (,=1,2) represents the Cauchy stress tensor and the Kronecker delta, then |–c₁₁| decays exponentially to zero in R with distance from the nearer end, and the decay constant depends only upon the material but is independent of L.     

Autoinductive exponential signal amplification: a diagnostic probe for direct detection of fluoride

A new example of an exponential signal amplification strategy for the direct detection of fluoride is demonstrated. The amplification occurred through reaction of fluoride with a responsive chromogenic probe. The probe activity is based on a unique dendritic chain reaction that generates a fluoride anion, which is the analyte of interest, during the disassembly pathway of the dendritic probe. This autoinductive amplification mechanism may be applied for detection of other analytes by coupling activity of a modified probe with that of the fluoride amplifier.