Abstract:
Anaerobic degradation of polycyclic aromatic hydrocarbons has been brought to the fore, but information on removal kinetics and anaerobic degrading bacteria is still lacking. In order to explore the organic micropollutants removal kinetics under anaerobic conditions in regard to the methane production kinetics, the removal rate of 12 polycyclic aromatic hydrocarbons was measured in two anaerobic batch reactors series fed with a highly loaded secondary sludge as growth substrate. The results underscore that organic micropollutants removal is coupled to the initial stages of anaerobic digestion (acidogenesis and acetogenesis). In addition, the organic micropollutants kinetics suggest that the main removal mechanisms of these hydrophobic compounds are biodegradation and/or sequestration depending on the compounds. 1. Introduction Polycyclic aromatic hydrocarbons (PAHs) are nowadays considered as environmental pollutants by environmental and health agencies because of their toxic, mutagenic, and carcinogenic effects on living organisms [1]. PAHs are mainly formed during human activities such as crude oil spillage, fossil fuel combustion, and gasoline leakage. Through the air and runoff after rainy events, the PAHs can deposit to soil, water bodies, and sewage system [2, 3]. Due to their low water solubility and high octanol-water partition coefficients, these organic micropollutants (μP) are mainly associated with hydrophobic compartments such as the organic matter in sewage sludge and river sediments or the lipids in biota, with levels between 0.001 and 10？μg/gDM for PAHs [4–6]. μP can be also sorbed irreversibly in a short time scale to the organic matter. This phenomenon named sequestration has been reported by different authors as one of the abiotic mechanisms of μP removal in digested sewage sludge and soils [7–9]. PAHs are known to be biodegraded under aerobic conditions [10, 11]. However, most contaminated environments are anaerobic. In these environments, the anaerobic digestion can occur. Anaerobic digestion is a process whereby organic matter is broken down in the absence of oxygen into methane and carbon dioxide by naturally occurring microorganisms. The anaerobic digestion consists of four stages where different microbial populations participate: (1) hydrolysis, (2) acidogenesis, (3) acetogenesis, and (4) methanogenesis. The digestion process begins with the hydrolysis of insoluble organic polymers into monomers that are available for microorganisms. Acidogenesis is the step where these monomers are converted to carbon dioxide, hydrogen, and

Abstract:
Pulling back the weight system associated with the spinor representation of the Lie algebra so(7) by the universal Vassiliev-Kontsevich invariant yields a numerical link invariant with values in formal power series. Computing some skein relations satisfied by this invariant, I derive a recursive algorithm for its evaluation. The values of this invariant belong to the ring Z[W,W^{-1}] of Laurent polynomials in one variable.

Abstract:
The theory of Vassiliev invariants deals with many modules of diagrams on which the algebra Lambda defined by Pierre Vogel acts. By specifying a quadratic simple Lie superalgebra, one obtains a character on Lambda. We show the coherence of these characters by building a map of graded algebras beetwen Lambda and a quotient of a ring of polynomials in three variables; all the characters induced by simple Lie superalgebras factor through this map. In particular, we show that the characters for the Lie superalgebra f(4) with dimension 40 and for sl(3) are the same. Resume: De nombreux modules de diagrammes sont utilises dans la theorie des invariants de Vassiliev. Pierre Vogel a definit une algebre Lambda qui agit sur ces espaces. Les superalgebres de Lie simples quadratiques fournissent des caracteres sur Lambda. On montre leur coherence en construisant un morphisme d'algebre graduee, entre Lambda et un quotient d'un anneau de polyneme en trois variables, qui factorise tous ces caracteres. En particulier, on montre que le caractere associe a la superalgebre de Lie f(4) de dimension 40 coincide avec celui associe a sl(3).

Abstract:
Kricker constructed a knot invariant Z^{rat} valued in a space of Feynman diagrams with beads. When composed with the so called "hair" map H, it gives the Kontsevich integral of the knot. We introduce a new grading on diagrams with beads and use it to show that a non trivial element constructed from Vogel's zero divisor in the algebra \Lambda\ is in the kernel of H. This shows that H is not injective.

Abstract:
The usual construction of link invariants from quantum groups applied to the superalgebra D_{2 1,alpha} is shown to be trivial. One can modify this construction to get a two variable invariant. Unusually, this invariant is additive with respect to connected sum or disjoint union. This invariant contains an infinity of Vassiliev invariants that are not seen by the quantum invariants coming from Lie algebras (so neither by the colored HOMFLY-PT nor by the colored Kauffman polynomials).

Abstract:
This paper generalize [7](math.GT/0601291): We construct new links invariants from g, a type I basic classical Lie superalgebra. The construction uses the existence of an unexpected replacement of the vanishing quantum dimension of typical module. Using this, we get a multivariable link invariant associated to any one parameter family of irreducible g-modules.

Abstract:
In this paper we give a re-normalization of the supertrace on the category of representations of Lie superalgebras of type I, by a kind of modified superdimension. The genuine superdimensions and supertraces are generically zero. However, these modified superdimensions are non-zero and lead to a kind of supertrace which is non-trivial and invariant. As an application we show that this new supertrace gives rise to a non-zero bilinear form on a space of invariant tensors of a Lie superalgebra of type I. The results of this paper are completely classical results in the theory of Lie superalgebras but surprisingly we can not prove them without using quantum algebra and low-dimensional topology.

Abstract:
We study various specializations of the colored HOMFLY-PT polynomial. These specializations are used to show that the multivariable link invariants arising from a complex family of sl(m|n) super-modules previously defined by the authors contains both the multivariable Alexander polynomial and Kashaev's invariants. We conjecture these multivariable link invariants also specialize to the generalized multivariable Alexander invariants defined by Y. Akutsu, T. Deguchi, and T. Ohtsuki.

Abstract:
We introduce the notion of a relative spherical category. We prove that such a category gives rise to the generalized Kashaev and Turaev-Viro-type 3-manifold invariants defined in arXiv:1008.3103 and arXiv:0910.1624, respectively. In this case we show that these invariants are equal and extend to what we call a relative Homotopy Quantum Field Theory which is a branch of the Topological Quantum Field Theory founded by E. Witten and M. Atiyah. Our main examples of relative spherical categories are the categories of finite dimensional weight modules over non-restricted quantum groups considered by C. De Concini, V. Kac, C. Procesi, N. Reshetikhin and M. Rosso. These categories are not semi-simple and have an infinite number of non-isomorphic irreducible modules all having vanishing quantum dimensions. We also show that these categories have associated ribbon categories which gives rise to re-normalized link invariants. In the case of sl(2) these link invariants are the Alexander-type multivariable invariants defined by Y. Akutsu, T. Deguchi, and T. Ohtsuki.