Convergence of Archimedean Copulas

Convergence of a sequence of bivariate Archimedean copulas to another Archimedean copula or to the comonotone copula is shown to be equivalent with convergence of the corresponding sequence of Kendall distribution functions.No extra differentiability conditions on the generators are needed.Archimedean copula;generator;Kendall distribution function

Lower Tail Dependence for Archimedean Copulas: Characterizations and Pitfalls

Tail dependence copulas provide a natural perspective from which one can study the dependence in the tail of a multivariate distribution.For Archimedean copulas with continuously differentiable generators, regular variation of the generator near the origin is known to be closely connected to convergence of the corresponding lower tail dependence copulas to the Clayton copula.In this paper, these characterizations are refined and extended to the case of generators which are not necessarily continuously differentiable.Moreover, a counterexample is constructed showing that even if the generator of a strict Archimedean copula is continuously differentiable and slowly varying at the origin, then the lower tail dependence copulas do not need to converge to the independent copula.Archimedean copula;regular variation;tail dependence;de Haan class

Convergence of Archimedean Copulas

Convergence of a sequence of bivariate Archimedean copulas to another Archimedean copula or to the comonotone copula is shown to be equivalent with convergence of the corresponding sequence of Kendall distribution functions.No extra differentiability conditions on the generators are needed.

2-[(Dodecylsulfanyl)carbonothioyl­sulfanyl]­propanoic acid

In the title compound, C16H30O2S3, the decyl chain adopts an extended zigzag conformation. Two mol­ecules are disposed about a center of inversion, forming an O—H⋯O hydrogen-bonded dimer

Réduction et contrôle du foisonnement filamenteux des boues activées par application d'un régime turbulent

Le foisonnement filamenteux des boues activées est un problème important dans les stations d'épuration du type Boues Activées, car il peut entraîner des pertes de biomasse avec l'eau épurée. Les techniques de lutte utilisées actuellement sont, soit des techniques dites « biologiques » (sélecteurs), soit des techniques chimiques (floculants, biocides). L'objectif de notre travail a été la mise au point d'un procédé original basé sur la création d'une zone de turbulence pour casser les réseaux filamenteux. La réduction et le contrôle du bulking sont obtenus par passage (de durée limitée T1) de la biomasse dans un système venturi, équipée d'une prise d'air. L'efficacité du procédé dépend principalement de la turbulence due à l'auto-aspiration d'air au niveau du rétrécissement du venturi. Cette turbulence contribue d'une part au mécanisme de « cisaillement » des filaments, et d'autre part à la qualité de l'effluent sortant. Une gestion adaptée (aération séquentielle en procédé à faible charge) permet d'obtenir, outre une amélioration de la décantation, une amélioration de l'élimination de l'azote. De plus, le contrôle de la biomasse optimise l'élimination de la pollution carbonée.The loss of biomass in a waste water plant as a result of sludge bulking is an important problem. Biological (ex.: selector configuration) or chemical (ex. : floculating reagents, biocides...) methods habe been used in order to control bulking. A new process based on the generation of turbulence to break the filaments is described. To reduce and control sludge bulking, the biomass is pumped through a venturi equipped with an air inlet. Figure 1 represents the pilot scheme. Two processes can be used : the emulsor with air is introduced on recycling of sludge or is placed in an independent loop. Here, it is the latter that has been used.We tried to reduce bulking by mechanical treatment. The hydrodynamic efficiency of the process depends mostly on the degree of turbulence generated by the waters speed and by the suction of air in the constricted part of the venturi.During the first trials on the plant, we defined the maximum turbulence allowed in order not to break the floc. We could not use a big aeration to prevent defloculation.The main factors to reduce bulking are :- the sequences of usage of the emulsor venturi (the periodicity of the treatment is T),- the speed of the water in the nozzle of the venturi (we can refer to the Reynolds Number Re = Ud/ʋ; but this number can’t really represent the turbulence created),- the duration of the emulsor's application. The emulsor venturi is used during a period T1 with a periodicity T (T>T1), with T1 : n X (VR/qv) where VR/qv is the contact time in the venturi and n is the frequence of recycling.During the period T, it is possible to use continuous aeration or to work with sequential aeration.a) continuous aeration|_________________________| TTime between two applications of the venturi|_______________| T1Venturi durationThe process is the same as the aeration of activated sludge. COD is reduced but only with low load, significant nitrification occurs. Figure 5 shows the efficiency of the continuous aeration process especially versus the sludge index parameter.b) sequential aerationAs we try to remove nitrogen, the sequential aeration is more useful than continuous aeration. A cycle is divided in two periods (T2, T3 with T = T2 + T3), and of course, the duration of the venturi use equal to T1.|_________________________| TTime between two applications of the venturi|_____________| T1Venturi duration|_________________| T2Aeration duration          |_____| T3Anoxic periodFigures 6 and 7 show the efficiency of the emulsor if we consider lB (sludge index) as the main parameter for the sequential operation (T2, T3) and it's also possible to obtain a good removal of nitrogen pollution.Our operations parameters were for these experiments :T = 8 or 12 hoursT1 between 20 min. and 1 hourT2 between 4 and 5 hoursThis process is now patiented and the first industrial applications are now defined

Quantum nature of the critical points of substances

Thermodynamics of chemical elements, based on the two-component electron-nuclear plasma model shows that the critical parameters for the liquid-vapor transition are the quantum values for which the classical limit is absent.Comment: 4 pages, no figure