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This paper is concerned by the concept of algebra up to homotopy for a structure defined by two operations . and [ , ] . An important example of such a structure is the Gerstenhaber algebra ( i.e. commutatitve structure with degree 0 and Lie structure with degree −1). The notion of Gerstenhaber algebra up to homotopy ( G ∞ algebra) is known: it is a codifferential bicogebra. Here, we give a definition of pre-Gerstenhaber algebra (pre-commutative and pre-Lie) allowing a similar construction for a pre G ∞ algebra. Given a structure of pre-commutative (Zinbiel) and pre-Lie algebra and working over the corresponding Koszul dual operads, we will give an explicit construction of the associated pre-Gerstenhaber algebra up to homotopy: it is a bicogebra (Leibniz and permutative) equipped with a codifferential which is a coderivation for the two coproducts. [ABSTRACT FROM AUTHOR]

We study the concept of algebra up to homotopy for a structure defined by two operations . and [ , ] . An important example of such a structure is the Gerstenhaber algebra (commutatitve and Lie). The notion of Gerstenhaber algebra up to homotopy ( G ∞ algebra) is known. In this paper, we give a Hom-Gerstenhaber algebra defined by a structure of commutative and Hom-associative algebra and a structure of a Hom-Lie algebra. We will give an explicit construction of the associated Hom-Gerstenhaber algebra up to homotopy, this is a bicoalgebra (Hom-coLie and Hom-coassociative) equipped with a codifferential which is a coderivation for the two coproducts allowing the construction of Hom G ∞ algebra. [ABSTRACT FROM AUTHOR]

Let F be a field of characteristic 2, and T ( F ) the set of totally singular F -quadratic forms up to isometry. The u ˆ -invariant of F is the maximal dimension of an anisotropic F -quadratic form. In this paper we introduce new invariants of F related to the u ˆ -invariant. The first one, called u ˜ -invariant, is the maximal dimension of an anisotropic not totally singular F -quadratic form. The motivation of introducing this invariant is to see how the values of the u ˆ -invariant can be given without the use of forms of T ( F ) , this is because most of the known values of the u ˆ -invariant are realized by the forms of T ( F ) (see [12] ). Also, for r , s ≥ 1 integers, we introduce the u r -invariant ( resp. the u ˜ s -invariant) which is the maximal dimension of an anisotropic F -quadratic form having a regular part of dimension 2 r ( resp. the maximal dimension of an anisotropic not totally singular F -quadratic form having a quasilinear part of dimension s ). We make a comparison between these new invariants by relating them to the u -invariant and the u ˆ -invariant, and we give a list of values that they can take. We also discuss the classical question, due to Baeza [3] , on the universality of some nonsingular F -quadratic forms when F has finite u -invariant. [ABSTRACT FROM AUTHOR]

Abstract: Let be an algebraically closed field of characteristic 0. In this paper, we prove the equivalence between stability and quasi-reductivity for parabolic subalgebras of exceptional Lie algebras. Therefore, and considering the results of [1], we give a positive answer to the assertion (ii) of the conjecture (5.6) in [11] for parabolic Lie algebras. [Copyright &y& Elsevier]

Abstract: In this paper a new method for computing the topological index of a vector field at Cohen–Macaulay curves is described. It is based on properties of regular meromorphic differential forms which are used for computing the homological index of vectors fields introduced by X. Gómez-Mont. In particular, we show how to compute the index at quasihomogeneous Gorenstein curves and complete intersections, at monomial curves, at Cohen–Macaulay space curves, and others. In contrast to previous articles on this subject we do not use the technique of spectral sequences, or computer algebra systems for symbolic calculations. [Copyright &y& Elsevier]

Abstract: In this paper, we prove the following result: let X be a complex manifold, hyperbolic for the Carathéodory distance and let U be an open set relatively compact in X. Then, there exists such that we get, for the Carathéodory infinitesimal metric, . We also get results concerning fixed points of holomorphic mappings from X to U. [Copyright &y& Elsevier]

Abstract: Starting from an ethnographic enquiry and with examples from Haitian literary authors, this paper offers a pragmatic analysis of greetings, rites of interaction, and acts of language within a Haitian context which is imbued with symbolism. Indeed, in Haiti, respect for others is the concern of everyone and each person is responsible for their own behaviour, and must be careful to avoid causing offence to any member of this cosmos either by what they say or what they do. Controlling one''s body and one''s speech is a guarantee of harmony and friendly relations within the community and helps to maintain the balance between the visible and the invisible. These principles form the whole basis of the way children are brought up. A foray into studies devoted to forms of address and courtesy in seventeenth century Europe and into manuals concerning the education of children in France from bygone days allows us to see that these Haitian forms of address are vestiges of the forms of courtesy used by the French gentleman of the sixteenth and seventeenth centuries. These were codes which prescribed the acquisition of bodily as well as linguistic self control. However, the length of these greetings seems more African than French in origin, which would indicate that these exchanges should be placed on a continuum moving from Europe to Africa, and this independently of the actual language used by the speakers. [Copyright &y& Elsevier]

Abstract: This paper provides us two types of results. In a first part we obtain an asymptotic expansion of the terms for α in and , , and where is a sufficiently smooth function. These expressions are given by two different integral kernels or according to or . In the other hand we give an asymptotic expansion of the orthogonal polynomials on the unit circle with respect to the weight for the same values of α. We denote by these polynomials. With this notation our result concern the coefficients with . We can remark that the expression is the same for all the reals α in . When α goes to we obtain the quantities and that proves a conjecture of Harry Kesten and that allows us to obtain the trace of . [Copyright &y& Elsevier]

Abstract: In a recent work [P.G. Lemarié-Rieusset, Uniqueness for the Navier–Stokes problem: Remarks on a theorem of Jean-Yves Chemin, Nonlinearity 20 (2007) 1475–1490], P.G. Lemarié-Rieusset proved the uniqueness of solution to the Navier–Stokes equations in the space provided that and . In this paper, we prove a local version of this result which covers the limit case . Precisely, we prove the uniqueness of solution to the Navier–Stokes equations in the space for every and where is the closure of the test functions in the Morrey–Campanato space . The prove of our result relies on an extension of the Comparison Theorem of P.G. Lemarié-Rieusset (Theorem 21.1 in [P.G. Lemarié-Rieusset, Recent developments in the Navier–Stokes problem, Chapman & Hall/CRC, 2002]). Moreover, this extension allows us to prove the uniqueness of solution to the Navier–Stokes equations in a functional space closed to the critical space . [Copyright &y& Elsevier]

Abstract: This paper reports on a simplified approach for analysing the temperature evolution in a semi-transparent thin membrane of the amorphous polyethylene terephtalate type (PET) exposed to a radiative source. It is based on a 3D finite elements method. The thermophysical properties of the PET are assumed independent of temperature while the internal radiative intensity absorption is taken as one-dimensional and is governed by the Beer–Lambert law. To avoid the difficult problem of computing the shape factors, a semi-analytical approach is used. Finally, the numerical simulations have allowed to validate the analytical and experimental results. In the first place, we have written the energy conservation equation in absence of convection (based on the first law of thermodynamics) (1.a), the radiative source term (1.b) and the boundary conditions (2). As for the finite elements method, the Galerkin approach is used for the formulation of the 3D heat transfer equation (3) and the diagonalisation of the heat capacity matrix, “lumped matrix”, is adopted [M.A. Dokainish, K. Subbaraj, A survey of direct time-integration methods in computational structural dynamics, Comput. Struct. 32 (6) (1989) 1371–1386]. A single step implicit time integration scheme is used for the computation [M.A. Dokainish, K. Subbaraj, A survey of direct time-integration methods in computational structural dynamics, Comput. Struct. 32 (6) (1989) 1371–1386]. After recalling the classical expressions for the radiative flux divergence (5) and the flux itself (6), we have rewritten the radiative source term for an homogeneous medium as a function of spectral intensity (7) and given the integro-differential equation of radiative transfer [R. Siegel, J.R. Howel, Thermal Radiation Heat Transfer, Hemisphere Publishing Corporation, Washington, 1992], Eq. (8). The spectral relations linking coefficients of extinction, absorption, scattering and scattering albedo are given by Eqs. (9) and (10), while Eq. (11) expresses the boundary conditions. In the second place, on the basis of the non-scattering behaviour of amorphous PET [K. Esser, E. Haberstroh, U. Hüsgen, D. Weinand, Infrared radiation in the processing of plastics: Precise adjustment-the key to productivity, Adv. Polymer Technol. 7 (2) (1987) 89–128; M.D. Shelby, Effects of infrared lamp temperature and other variables on the reheat rate of PET, in: Proceedings of ANTEC''91 Conference, 1991, pp. 1420–1424; G. Venkateswaran, M.R. Cameron, S.A. Jabarin, Effect of temperature profiles trough preform thickness on the properties of reheat-blown PET containers, Adv. Polymer Technol. 17 (3) (1997) 237–249], we have assumed that extinction and absorption coefficients are equal, the corresponding albedo being zero. The radiative transfer equation can thus be rewritten in a reduced form (12). Moreover, for the temperature range prevailing in the processes of PET thermoforming and preforms blowing, temperatures of radiation sources are generally much higher than those used for the forming of these thermoplastic media. Under these conditions, the cold medium hypothesis is used [Y. Le Maoult, F.M. Schmidt, V. Laborde, M. El Hafi, P. Lebaudy, Measurement and calculation of perform infrared heating: a first approach, in: Proceeedings of the Fourth International Workshop on Advanced Infrared, 1997, pp. 321–331], which allows to express transmission of spectral intensity across the material as a function of position and direction (13), and to write the radiative flux divergence in a simplified form as well (14). For one-dimensional radiation, solution of the radiative transfer equation [R. Siegel, J.R. Howel, Thermal Radiation Heat Transfer, Hemisphere Publishing Corporation, Washington, 1992] is given by Eq. (15), which combines with Eq. (14) to yield the spectral flux generated inside the semi-transparent medium, Eq. (16). In case of radiation propagation in the same direction as the normal to the polymeric membrane surface, radiation intensity can then be expressed by the Beer–Lambert law (17). This permits to deduce the expression of spectral flux transmitted across the PET membrane thickness (18). Infrared radiation intercepted by the membrane For determining the infrared radiation intercepted by the membrane surface, the medium between the radiation source and the thermoplastic material is assumed to be completely transparent to radiation. It is also assumed that the surface of the source is diffuse. This allows to infer, from spectral expressions of the energy emitted by the source (Eqs. (19) and (20)) and of the energy received by the semi-transparent membrane (Eq. (21)), a relation for radiation intercepted by the surface at all wavelengths (Eqs. (22) and (23)). For an isotropically radiating source (Lambertian source) when considering an average emissivity of the heating source, Eq. (24), total radiation intercepted by the surface is given by Eq. (25). Infrared radiation absorbed by the membrane For the determination of infrared radiation absorbed by the polymeric membrane, first, based on the principle of energy conservation, spectral relation (27) which links reflectivity, absorptivity and transmissivity is recalled, as well as relation (28) associating spectral absorption and transmission coefficients following the Beer–Lambert law. Consequently, this allows to find the spectral energy absorbed by the semi-transparent medium (29) with the aid of Eq. (25). Concentrating on wavelength bands that constitute the transmission spectrum of the medium, Eq. (29) is then replaced by Eq. (30) where average values of reflectivity (31) and transmissivity (32) are considered. As a result, the volumetric total energy absorbed by the medium, the flux divergence, is then given by Eqs. (33) and (34). Furthermore, considering that reflectivity is low for polymeric materials (generally lower than 5%), the latter is neglected leading to Eq. (35) instead of Eq. (34). Fig. 1 illustrates a typical transmissivity curve for PET [G. Venkateswaran, M.R. Cameron, S.A. Jabarin, Effect of temperature profiles trough preform thickness on the properties of reheat-blown PET containers, Adv. Polymer Technol. 17 (3) (1997) 237–249]. Shape factor In order to take into account arbitrary shapes of sources and preforms, a semi-analytical approach is used for the computation of shape factors [G. Venkateswaran, M.R. Cameron, S.A. Jabarin, Effect of temperature profiles trough preform thickness on the properties of reheat-blown PET containers, Adv. Polymer Technol. 17 (3) (1997) 237–249]. The definition of shape factor is recalled in Eq. (36) and Fig. 2. An equivalent form based on the contour principle [R. Rammohan, Efficient evaluation of diffuse view factors for radiation, Int. J. Heat Mass Transfer. 39 (1996) 1281–1286] is given by Eq. (37), while the semi-analytical formula [F. Erchiqui, N.G. Dituba, Analyse comparative des méthodes de calcul des facteurs de formes pour des surfaces à contours rectilignes, Internat. J. Thermal Sci. 46 (2007) 284–293] is expressed by Eq. (39). Validation of this semi-analytical approach is obtained by comparison with the analytical solution [H.C. Hottel, Radiant heat transmission between surfaces separated by non-absorbing media, Trans. ASME 53 (1931) 265–273, FSP-53-196; A. Feingold, Radiant-interchange configuration factors between various selected plane surfaces, Proc. Roy. Soc. London Ser. A 292 (1996) 51–60; J.R. Ehlert, T.F. Smith, View factors for perpendicular and parallel rectangular plates, J. Thermophys. Heat Trans. 7 (1993) 173–174] as well as with results yielded by three different techniques, i.e. the area-integration method, the Gauss quadratic technique and the contour method. Table 1 summarizes the numerical results obtained in each case and gives the relative error. Analytical validation of the reheating Regarding the numerical validation, we have considered a PET semi infinite medium subjected to a uniform incident radiative flux density. The boundaries of the semi transparent medium are taken as adiabatic. Thermophysical properties and geometrics are given in Table 2. The one-dimensional Laplace equation which governs the radiation heat transfer is solved analytically with the aid of Laplace transforms. The temperature evolution within the depth of the semi transparent medium is obtained by analytical solution [A.B. De Vriendt, in: G. Morin, (Ed.), La transmission de la chaleur, vol. 1, Chicoutimi, Québec, 1984], Eq. (40). Fig. 3 shows a comparison between the numerical solution obtained by the 3D finite elements method and the analytical one. It is seen that, for the three cases, the relative error between numerical and analytical results stays lower than 0.1%. Numerical modeling of infrared heating An amorphous PET sheet is considered. The face of the membrane is a square of side 20 cm with a thickness of 1.5 mm. The lateral walls are assumed adiabatic. For modeling with the 3D finite elements method, the sheet is meshed with identical hexahedra comprising eight nodes. The thermophysical properties used for this study are given in [S. Monteix, F. Schmidt, Y. Le Maoult, R Ben Yedder, R.W. Diraddo, D. Laroche, Experimental study and numerical simulation of perform or sheet exposed to infrared radiative heating, Journal of Materials Processing Technology 119 (2001) 90–97] and the reheating time is 35 seconds. The heat transfer coefficient h on front and rear faces is 10 W m−2 K−1. Heat flux received by the polymer during heating To estimate the incident heat flux distribution on the surface of the polymer, we first calculate the shape factors between each pair of emitting/receiving surfaces. Then the flux distribution is obtained with Eq. (25). Fig. 4 illustrates this distribution. Validation against experimental results Figs. 5 and 6 compare the numerical results obtained by the simulation (via MEF 3D) with those obtained experimentally. Fig. 5 displays the temperature distribution on the front and rear surfaces. Results Figs. 7–10 illustrate the numerical results obtained for the temporal temperature evolution, during the first five seconds of heating, of the upper receiving face (surface directly exposed to the infrared source), the central plane and the lower face of the PET membrane, respectively. Figs. 11 and 12 give the temperature evolution at four positions on upper and lower faces of the membrane: 0 cm (edge), 2.5 cm, 5 cm and 10 cm (middle). It is observed that the trend is nearly linear during the period of infrared heating. On Figs. 13 and 14 is displayed the temperature evolution in the center of the membrane along its thickness during periods 0–4 and 5–35 seconds. [Copyright &y& Elsevier]

Abstract: The fundamental example of Gerstenhaber algebra is the space of polyvector fields on , equipped with the wedge product and the Schouten bracket. In this paper, we explicitely describe what is the enveloping algebra of a Gerstenhaber algebra . This structure gives us a definition of the Chevalley–Harrison cohomology operator for . We finally show the nontriviality of a Chevalley–Harrison cohomology group for a natural Gerstenhaber subalgebra in . [Copyright &y& Elsevier]

Abstract: In the first part of the paper, we prove the existence of a unique global solution to the axisymmetric Navier–Stokes system with initial data and external force with . This improves the result obtained by S. Leonardi, J. Málek, J. Necǎs and M. Pokorný [S. Leonardi, J. Málek, J. Necǎs, M. Pokorný, On axially symmetric flows in , Zeitschrift für analysis und ihre anwendungen, J. Anal. Appl. 18 (3) (1999) 639–649], where regularity was required. In the second part, we state global existence and uniqueness for the axisymmetric Navier–Stokes system with initial data in and external force in with . This also improves [S. Leonardi, J. Málek, J. Necǎs, M. Pokorný, On axially symmetric flows in , Zeitschrift für analysis und ihre anwendungen, J. Anal. Appl. 18 (3) (1999) 639–649] because less integrability is required on and on f. [Copyright &y& Elsevier]

Abstract: This paper generalizes the first author''s preceding works concerning admissible functions on certain Fano manifolds [A. Ben Abdesselem, Lower bound of admissible functions on sphere, Bull. Sci. Math. 126 (2002) 675–680 ; A. Ben Abdesselem, Enveloppes inférieures de fonctions admissibles sur l''espace projectif complexe. Cas symétrique, Bull. Sci. Math. 130 (2006) 341–353 ]. Here, we study a larger class of functions which can be less symmetric than the ones studied before. When the sup of these functions is null, we prove that they admit a lower bound, giving precisely Tian invariant [G. Tian, On Kähler–Einstein metrics on certain Kähler manifolds with , Invent. Math. 89 (1987) 225–246 ] (see also [T. Aubin, Réduction du cas positif de l''équation de Monge–Ampère sur les variétés Kählériennes à la démonstration d''une inégalité, J. Funct. Anal. 57 (1984) 143–153 ]) on these manifolds. [Copyright &y& Elsevier]

Abstract: In this paper we study the centered and non-centered Hardy–Littlewood maximal functions, M and , for a wide class of non-doubling measure μ defined on cusped manifolds. In particular, we give a class of manifolds with exponential volume growth on which M is of weak type and is bounded on for all . [Copyright &y& Elsevier]

Abstract: Results of H. Cartan about holomorphic automorphisms on bounded domains are generalized to the case of hyperbolic manifolds in the sense of Kobayashi. In this setting, we give an identity theorem together with its topological version. We show also that a sequence of automorphisms which converges uniformly on some nonempty open set, has a limit on the whole space which is an automorphism. At the end of the paper, conditions are given for the sequence of iterates of a self holomorphic map in order to be an automorphism. [Copyright &y& Elsevier]

Abstract: In this paper we consider a class of non-negative, 2π-periodic, even functions. For such a function f we obtain an asymptotic of the eigenvalues of the Toeplitz matrice such goes to a positive real when N goes to the infinity. for all real , we infer from this result the asymptotic of the same eigenvalues of the Toeplitz matrice , where , and a regular function. With these hypotheses we give also the order of the little nad of the greatest eigenvalue of the matrix. [Copyright &y& Elsevier]

Abstract: In this paper we prove that every entire curve in a smooth hypersurface of degree in must satisfy an algebraic differential equation of order 3. The logarithmic version of this result is given proving that every entire curve in the complement of a smooth surface of degree in must satisfy an algebraic differential equation of order 3. [Copyright &y& Elsevier]

Abstract: In this paper we will study some questions concerning solutions of Yamabe''s equation on an annulus of with different data on the boundary. The important problem: “what about the radial solution u satisfying () and ” is solved. [Copyright &y& Elsevier]

Abstract: The results of study concerning energy transformation within the variable geometry nozzle of a turbocharger are presented in this paper. A detailed analysis is carried out in order to study the effect of losses on the permeability characteristics of the vaned channel, and to observe the flow-turbine structure interaction resulting at the rotor. Particular attention is paid to the local jet structure at outlet from the variable geometry channel when sonic conditions are likely to be reached at the diffuser throat. A supersonic flow layer can be observed in the mixing zone at the rotor inlet, this phenomenon generates high losses in this region. [Copyright &y& Elsevier]

Abstract: Let T be a closed positive current of dimension p in and H an analytic subvariety of of dimension . We denote by the slice of T in H if it exists. We consider the functions on defined by and . The aim of this paper is to establish relationship between the growth of these functions. We prove results generalizing those of L. Gruman in [Séminaire Lelong–Skoda 1981–1983, Lecture Notes in Math., vol. 1028, Springer-Verlag, Berlin, 1983, pp. 125–162] and B. Molzan, B. Shiffman and N. Sibony in [Math. Ann. 257 (1981) 43]. [Copyright &y& Elsevier]

Abstract: Let f be a function with a regular strictly positive function and a real number α in . In a previous paper for such a number α we have obtained the asymptotic behaviour of the entries of the inverse of the Toeplitz matrix when N goes to infinity. These results allow us to give trace formulas, which extend a classical expression of Szegö''s limits theorems. [Copyright &y& Elsevier]

Let Lω2(R) be a weighted space with weight ω. In this paper we show that for every bounded operator T on Lω2(R) which commutes with translations, and for every a∈Iω, there exists a function νa∈L∞(R) such that Here (g)a denotes the function x↠g(x)eax for g∈Lω2(R) and Iω=[lnRω-,lnRω+], where Rω+ is the spectral radius of the bilateral shift S :f(x)↠f(x-1) on Lω2(R), while 1/Rω- is the spectral radius of S-1. Moreover there exists a constant Cω depending on ω such that ǁνaǁ∞⩽CωǁTǁ for every a∈Iω. If Rω-, there exists a bounded holomorphic function ν on Åω:={z∈C∣Imz∈&Iring;ω}, such that Tf=ν&fcirc;, ∀f∈D(R) and ǁνǁ∞⩽CωǁTǁ, where Tf(a+ix)=(Tf)a(x) for a∈&Iring;ω. [Copyright &y& Elsevier]

In this paper we study the equation of an anisotropic rotating fluid evolving in a three-dimensional torus. The anisotropy of the fluid concerns the vertical viscosity which can be considered to be null. We prove that the equation is well posed on arbitrarily long time intervals, if the Rossby number is small enough. We also prove that the “filtered” solutions converge to the solution of the limit system. Those results hold for all tori (without imposing the non-resonant condition on the domain), in a functional frame very close to the critical regularity level. When the initial data is of null horizontal average, in the case of non-resonant tori as well as for certain resonant tori, we obtain the global existence and uniqueness of the solution. [Copyright &y& Elsevier]

Let Ω⊂RN be an open set. We consider on Ω the competitors (U,K) for the reduced Mumford–Shah functional, that is to say the Mumford–Shah functional in which the L2-norm of U term is removed, where K is a closed subset of Ω and U is a function on Ω&z.drule;K with gradient in L2. The main result of this paper is the following: there exists a constant c for which, whenever (U,K) is a quasi-minimizer for the reduced Mumford–Shah functional and B(x,r) is a ball centered on K and contained in Ω with bounded radius, the HN−1-measure of K∩B(x,r) is bounded above by crN−1 and bounded below by c−1rN−1. [Copyright &y& Elsevier]

In this paper, we present and solve some very general new Pade´ approximant problems, whose solutions can be expressed with hypergeometric series. These series appear in the proofs of the irrationality of ζ(3), of infinitely many ζ(2n+1), and in essentially all results of this kind in the literature. We also prove two new Diophantine results with this method. [Copyright &y& Elsevier]

In this paper, we consider the Lp boundedness of the Riesz transforms on the cone C(N)=R+×N, where N is a complete noncompact Riemannian manifold whose Ricci curvature is bounded from below. [Copyright &y& Elsevier]

In this paper, we propose a model concerning the thermal transfers inside an emulsion of aqueous saline binary solution during the crystallization of the dispersed undercooled droplets. This model takes into account the erratic character owed to the probability of water crystallization, and to the probability of salt apparition. It also takes into account the phenomenon of the progressive crystallization owed to the thermodynamic balance in every drop. The model is based on the resolution of the energy equation with a heat source depending on the probability of crystallization of every drop. It has been applied to the scanning calorimetry in the case of an aqueous solution of sodium chloride dispersed within an industrial oil. The studied samples have a cylindrical shape of a few mm3 in volume. The good agreement between the numerical results and the experimental results permitted to validate the model, and therefore to better describe the thermal transfers in these dispersions. We determined the space–time distribution of the temperature and transformed part of every drop. An evaluation of the different exchange coefficients of involved in the model has also been brought. [Copyright &y& Elsevier]

Let M be a CR manifold. The main results of this paper are the following:(A)When M is real analytic, a semi-global Hartogs extension phenomenon occurs for real analytic CR functions if and only if M is nowhere strictly pseudoconvex and dimRM⩾3.(B)When M is a standard manifold, the Hartogs–Bochner extension phenomenon occurs for non-CR-confined domains if and only if M is nowhere strictly pseudoconvex and dimCRM⩾2.(C)If M is a smooth submanifold of Cn foliated by complex curves, a semi-global Hartogs–Bochner extension phenomenon occurs for smooth non-CR-confined domains if and only if dimCRM⩾2.(D)If M is a real analytic nowhere strictly pseudoconvex manifold and if Ω is a sufficiently small domain in M, a hyperfunction which is real analytic in a neighborhood of bΩ and CR in a neighborhood of Ω is in fact real analytic on Ω. [Copyright &y& Elsevier]

Trigeneration is defined as the production of three useful forms of energy—heat, cold and power—from a primary source of energy such as natural gas or oil. For instance, trigeneration systems typically produce electrical power via a reciprocating engine or gas turbine and recover a large percentage of the heat energy retained in the lubricating oil, exhaust gas and coolant water systems to maximize the utilization of the primary fuel. The heat produced can be totally or partially used to fuel absorption refrigerators. Therefore, trigeneration systems enjoy an inherently high efficiency and have the potential to significantly reduce the energy-related operation costs of facilities. In this paper, we describe a model of characterization of trigeneration systems trough the condition of primary energy saving and the quality index, compared to the separate production of heat, cold and power. The study highlights the importance of the choice of the separate production reference system on the level of primary energy saving and emissions reduction. [Copyright &y& Elsevier]

Numerical simulation methods permit the control of most parameters in surface heat treatment by Laser and constitute tools for treatment conditions prediction and optimisation. This paper deals with a transient numerical model which enables the simulation of all thermal history for three-dimensional space with any boundary conditions till the return to the thermal equilibrium at cooling. The problem formulation integrates a standard FEM code to solve the heat equation in non-linear transient behaviour. The numerical scheme proposed authorises the resolution with moving boundary condition in consideration of suitable space and time meshing. This model takes into account the non-linearities in relation with the variation of thermophysics properties with temperature and the loss by radiation and convection. The heat of solid phase changing is introduced as conditional source into the thermal affected zone. Compared with several contributions in this subject, this model should give a more subtle approach which gets free from classical simplifying assumptions. [Copyright &y& Elsevier]

In this paper, we study the monodromy of the ramified Cauchy problem for operators with multiple characteristics of constant multiplicity. More precisely, we give an estimation of the eigenvalues of the solution''s monodromy, first with the assumptions of the theorem of Hamada–Leray–Wagschal, then with the assumptions of the theorem of Leichtnam. [Copyright &y& Elsevier]

This paper concerns a numerical and analytical investigation of the self-similarity of the turbulent plumes evolving in a stratified medium. The analytical investigation allows us to bring out the self-similarity conditions of the flow. The laws obtained are as valid for the case of a plume of warm air as for light gas and are verified experimentally in the case of a helium plume. The axial evolution of the mean velocity and concentration does not follow the classical laws, but follows new self-similarity laws that depend on the stratification of the medium. The self-similarity is even observed for the turbulent field, especially for the vertical velocity component while it is reached more slowly by the radial component. A simple numerical model is proposed for the prediction of the mean fields. The influence of the different coefficients of the model on the progressing of the flow is investigated. The results we obtain are compared to the experimental data and good agreement between theory and experiments is observed. [Copyright &y& Elsevier]

The paper describes the modelling of coriander essential oil extraction by steam distillation. Two models are applied: the first one takes only diffusion into account, in the second the solution of the transferred species is additionally modelled. The model is formulated as the system of partial differential equations. It is space discretized and than solved using Runge–Kutta method. The comparison of the simulation results with experimental data shows that the more complex model gives good agreement with experimental data. [Copyright &y& Elsevier]