Antimicrobial active packaging combining essential oils mixture: Migration and odor control study

Thymol is an essential oil (EO), known to have excellent antimicrobial (AM) properties and can potentially be used as an active agent in AM food packages. Mixing Thymol with other EOs may help to reduce the organoleptic impact of its strong odor. In the present study, the effect of thymol, carvacrol, citral, and eugenol binary mixtures on the AM activity, migration over time, and sensory properties of polypropylene (PP)/polyamide (PA)/nanoclays composite blends active package (AP) films was examined. The release of different EOs from the polymer film was found to have a direct correlation with the odor perception of thymol. Varied EOs bearing films have shown different capacity to inhibit bacterial growth over time (Escherichia coli). Lastly, the inhibition of fungal growth on food sample using EO‐loaded films was obtained for over 50 days, indicating the potential use of the developed films as active food packaging.     

Characterization of heat recirculation effects on the stabilization of edge flames in the near-wake of a mixing layer

A fundamental study aimed at investigating the stabilization characteristics of edge flames established in the near-wake of two merging streams, one containing fuel and the other oxidizer, is presented, with the main focus placed on the effects of the thermal interaction between the flame and the splitter plate. To this end, a diffusive-thermal model characterized by constant gas density and transport coefficients is used for conditions at which flame liftoff is likely to occur. It is assumed that the incoming streams are of equal strain rates, that the fuel and oxidizer are supplied in stoichiometric proportion, and that the mass diffusivities of the reactants are equal, such that the resulting combustion field is symmetric with respect to the centerline extending from the splitter plate. The results indicate that the plate has a negligible effect on the edge flame unless the tip of the plate intrudes into the preheat zone of the curved premixed flame segment forming the edge flame. In an overall adiabatic system, the heat conducted from the flame to the plate is completely recirculated back to the reactants via the lateral surfaces of the plate, thus supporting an excess enthalpy flame in the near-wake. The average output heat flux, defined as the total heat output through the lateral surfaces of the plate divided by the characteristic length associated with the temperature variation along the plate, is identified as an appropriate measure to characterize the heat recirculation efficiency.     

Galois stratification over Frobenius fields

New first-order conformally covariant differential operators P_k on spinor-k-forms, i.e., tensor products of contravariant spinors with k-forms, in an arbitrary n-dimensional pseudo-Riemannian spin manifold, are introduced. This provides a series of generalizations of the Dirac operator $\text{?}\text{?}$, in analogy with the series of generalizations (introduced by the author in [1]) of the Maxwell operator and the conformally covariant Laplacian $\text{□}$ on functions. In particular, new intertwining operators for representations of SU(2, 2) and SO(p + 1, q + 1) are found. Related nonlinear covariant operators are also introduced, and mixed nonlinear covariant systems are obtained by coupling to the Yang-Mills-Higgs-Dirac system in dimension 4. The spinor-form bundle is isomorphic with E⁽³⁾ = E ? E ? E, where E is the spin bundle, and the P_k give a covariant operator on sections of E⁽³⁾. This is generalized to a covariant operator on E^{(2l + 1)}. The relation of powers of these operators to higher-order covariant operators on lower spin bundles (analogous to the relation between $\text{?}\text{?}$ and $\text{□}$) is discussed.     

Capacitary estimates of solutions of a class of nonlinear elliptic equations

Let $\text{Ω}$ be a smooth bounded domain in $\text{R}{}^{\mathrm{N}}$ and K a compact subset of $\text{?Ω}$. Assume that q?(N+1)/(N?1) and denote by U_K the maximal solution of ?Δu+u^q=0 in $\text{Ω}$ which vanishes on $\text{?Ω?K}$. We obtain sharp upper and lower estimates for U_K in terms of the Bessel capacity C_2/q,q′ and prove that U_K is σ-moderate. In addition we relate the strong ‘blow-up’ points of U_K on $\text{?Ω}$ to the ‘thick’ points of K in the fine topology associated with C_2/q,q′ and characterize these points by a path integral condition on U_K. To cite this article: M. Marcus, L. Véron, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

On Zsigmondy primes

We present simple proofs of Walter Feit's results on large Zsigmondy primes.

     

Two competing discrete-time queues with priority

This paper considers a class of two discrete-time queues with infinite buffers that compete for a single server. Tasks requiring a deterministic amount of service time, arrive randomly to the queues and have to be served by the server. One of the queues has priority over the other in the sense that it always attempts to get the server, while the other queue attempts only randomly according to a rule that depends on how long the task at the head of the queue has been waiting in that position. The class considered is characterized by the fact that if both queues compete and attempt to get the server simultaneously, then they both fail and the server remains idle for a deterministic amount of time. For this class we derive the steady-state joint generating function of the state probabilities. The queueing system considered exhibits interesting behavior, as we demonstrate by an example.     

On the normalizer of finitely generated subgroups of absolute galois groups of uncountable hilbertian fields of characteristic 0

For a fieldK and a positive integere let N _e (K) be the set of alle-tuplesσ = (σ ₁, …,σ _e)εG(K) ^e that generate a selfnormalizer closed subgroup ofG(K). Chatzidakis proved, that ifK is Hilbertian and countable, then N _e (K) has Haar measure 1. IfK is Hilbertian and uncountable, this need not be the case. Indeed, we prove that ifK ₀ is a field of characteristic 0 that contains all roots of unity,T is a set of cardinality ℵ₁ which is algebraically independent overK ₀ andK =K ₀(T), then neither N _e (K) nor its complement contain a set of positive measure. In particular N _e (K) is a nonmeasurable set. This work was partially supported by an NSF grant #DMS-H603187, while the second author enjoyed the hospitality of Rutgers University.     

Pairs of edge disjoint Hamiltonian circuits in 5-connected planar graphs

Summary A variety of examples of 4-connected 4-regular graphs with no pair of disjoint Hamiltonian circuits were constructed in response to Nash-Williams conjecture that every 4-connected 4-regular graph is Hamiltonian and also admits a pair of edge-disjoint Hamiltonian circuits. Nash-Williams's problem is especially interesting for planar graphs since 4-connected planar graphs are Hamiltonian. Examples of 4-connected 4-regular planar graphs in which every pair of Hamiltonian circuits have edges in common are included in the above mentioned examples.B. Grünbaum asked whether 5-connected planar graphs always admit a pair of disjoint Hamiltonian circuits. In this paper we introduce a technique that enables us to construct infinitely many examples of 5-connected planar graphs, 5-regular and non regular, in which every pair of Hamiltonian circuits have edges in common.