Authors:Dongrui Wan; Wei Wang Abstract: Publication date: Available online 12 April 2017 Source:Bulletin des Sciences Mathématiques Author(s): Dongrui Wan, Wei Wang In this paper, we introduce the first-order differential operators d 0 and d 1 acting on the quaternionic version of differential forms on the flat quaternionic space H n . The behavior of d 0 , d 1 and △ = d 0 d 1 is very similar to ∂ , ∂ ‾ and ∂ ∂ ‾ in several complex variables. The quaternionic Monge-Ampère operator can be defined as ( △ u ) n and has a simple explicit expression. We define the notion of a closed positive current in the quaternionic case, and extend several results in complex pluripotential theory to the quaternionic case: define the Lelong number of a closed positive current, obtain the quaternionic version of Lelong-Jensen type formula, and generalize Bedford-Taylor theory, i.e., extend the definition of the quaternionic Monge-Ampère operator to locally bounded quaternionic plurisubharmonic functions and prove the corresponding convergence theorem.

Authors:Nikolaos S. Papageorgiou; Vicenţiu D. Rădulescu Abstract: Publication date: Available online 5 April 2017 Source:Bulletin des Sciences Mathématiques Author(s): Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu We consider a semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded using a suitable version of the symmetric mountain pass theorem, we show that the problem has an infinity of nodal solutions whose energy level diverges to +∞.

Authors:Todd A. Oliynyk Abstract: Publication date: Available online 4 March 2017 Source:Bulletin des Sciences Mathématiques Author(s): Todd A. Oliynyk We demonstrate that a sufficiently smooth solution of the relativistic Euler equations that represents a dynamical compact liquid body, when expressed in Lagrangian coordinates, determines a solution to a system of non-linear wave equations with acoustic boundary conditions. Using this wave formulation, we prove that these solutions satisfy energy estimates without loss of derivatives. Importantly, our wave formulation does not require the liquid to be irrotational, and the energy estimates do not rely on divergence and curl type estimates employed in previous works.

Authors:Vianney Combet; Yvan Martel Abstract: Publication date: Available online 20 January 2017 Source:Bulletin des Sciences Mathématiques Author(s): Vianney Combet, Yvan Martel Let S be a minimal mass blow up solution of the critical generalized KdV equation as constructed in [25]. We prove both time and space sharp asymptotics for S close to the blow up time. Let Q be the unique ground state of (gKdV), satisfying Q ″ + Q 5 = Q . First, we show that there exist universal smooth profiles Q k ∈ S ( R ) (with Q 0 = Q ) and a constant c 0 ∈ R such that, fixing the blow up time at t = 0 and appropriate scaling and translation parameters, S satisfies, for any m ⩾ 0 , ∂ x m S ( t ) − ∑ k = 0 [ m / 2 ] 1 t 1 2 + m − 2 k Q k ( m − k ) ( ⋅ + 1 t t + c 0 ) → 0 in L 2 as t ↓ 0 . Second, we prove that, for 0 < t ≪ 1 , x ⩽ − 1 t − 1 , S ( t , x ) ∼ − 1 2 ‖ Q ‖ L 1 x − 3 / 2 , and related bounds for the derivatives of S ( t ) of any order. We also prove ∫ R S ( t , x ) d x = 0 .

Authors:Annamaria Canino; Luigi Montoro; Berardino Sciunzi; Marco Squassina Abstract: Publication date: Available online 20 January 2017 Source:Bulletin des Sciences Mathématiques Author(s): Annamaria Canino, Luigi Montoro, Berardino Sciunzi, Marco Squassina We investigate existence and uniqueness of solutions for a class of nonlinear nonlocal problems involving the fractional p-Laplacian operator and singular nonlinearities.

Authors:Han Abstract: Publication date: January 2017 Source:Bulletin des Sciences Mathématiques, Volume 141, Issue 1 Author(s): Qi Han In this paper, we study mainly the existence of multiple positive solutions for a quasilinear elliptic equation of the following form on R N , when N ≥ 2 , (0.1) − Δ N u + V ( x ) u N − 2 u = λ u r − 2 u + f ( x , u ) . Here, V ( x ) > 0 : R N → R is a suitable potential function, r ∈ ( 1 , N ) , f ( x , u ) is a continuous function of N-superlinear and subcritical exponential growth without having the Ambrosetti–Rabinowitz condition, while λ > 0 is a constant. A suitable Moser–Trudinger inequality and the compact embedding W V 1 , N ( R N ) ↪ L r ( R N ) are proved to study problem (0.1). Moreover, the compact embedding H V 1 ( R N ) ↪ L K t ( R N ) is also analyzed to investigate the existence of a positive ground state to the following nonlinear Schrödinger equation (0.2) − Δ u + V ( x ) u = K ( x ) g ( u ) with potentials vanishing at infinity in a measure-theoretic sense when N ≥ 3 .

Authors:Giovanni Catino Pages: 901 - 907 Abstract: Publication date: Available online 11 April 2016 Source:Bulletin des Sciences Mathématiques Author(s): Giovanni Catino In this note we characterize compact hypersurfaces of dimension n ≥ 2 with constant mean curvature H immersed in space forms of constant curvature and satisfying an optimal integral pinching condition: they are either totally umbilical or, when n ≥ 3 and H ≠ 0 , they are locally contained in a rotational hypersurface. In dimension two, the integral pinching condition reduces to a topological assumption and we recover the classical Hopf-Chern result.

Authors:Constantin Buşe; Donal O'Regan; Olivia Saierli; Afshan Tabassum Pages: 908 - 934 Abstract: Publication date: Available online 29 March 2016 Source:Bulletin des Sciences Mathématiques Author(s): Constantin Buşe, Donal O'Regan, Olivia Saierli, Afshan Tabassum Denote by Z + the set of all nonnegative integer numbers. Let A n be an m × m invertible q-periodic complex matrix, for all n ∈ Z + and some q ≥ 1 . First we prove that the discrete problem ( A n ) x n + 1 = A n x n , x n ∈ C m . is Hyers-Ulam stable if and only if the monodromy matrix T q associated to the family A = { A n } n ∈ Z + possesses a discrete dichotomy. Let ( a n ) , ( b n ) be complex valued 2-periodic sequences. Consider the non-autonomous recurrence ( a n , b n ) z n + 2 = a n z n + 1 + b n z n , n ∈ Z + , z n ∈ C and the matrix A n = ( 1 1 a n + b n − 1 a n − 1 ) , n ∈ Z + . We prove that the recurrence ( a n , b n ) is Hyers-Ulam stable if and only if the monodromy matrix T 2 : = A 1 A 0 has no eigenvalues on the unit circle.

Authors:S.C. Coutinho Pages: 935 - 952 Abstract: Publication date: November 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 8 Author(s): S.C. Coutinho We construct explicit examples of one dimensional foliations over P n , with no proper invariant subvarieties of positive dimension, that are defined over a pure transcendental extension of Q whose transcendence degree is linear in n and independent of the degree of the foliation.

Authors:Suratno Basu Pages: 953 - 989 Abstract: Publication date: Available online 6 May 2016 Source:Bulletin des Sciences Mathématiques Author(s): Suratno Basu In this paper, we prove a relative version of the classical Mumford-Newstead theorem for a family of smooth curves degenerating to a reducible curve with a simple node. We also prove a Torelli-type theorem by showing that certain moduli spaces of torsion free sheaves on a reducible curve allows us to recover the curve from the moduli space.

Authors:Pabitra Barik; Arijit Dey; B.N. Suhas Pages: 990 - 1002 Abstract: Publication date: November 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 8 Author(s): Pabitra Barik, Arijit Dey, B.N. Suhas We show that each of the irreducible components of moduli of rank 2 torsion-free sheaves with odd Euler characteristic over a reducible nodal curve is rational.

Authors:A. Trescases Pages: 796 - 829 Abstract: Publication date: October 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 7 Author(s): A. Trescases We present new results of existence of global solutions for a class of reaction cross-diffusion systems of two equations presenting a cross-diffusion term in the first equation, and possibly presenting a self-diffusion term in any (or both) of the two equations. This class of systems arises in Population dynamics, and notably includes the triangular SKT system. In particular, we recover and extend existing results for the triangular SKT system. Our proof relies on entropy and duality methods.

Authors:Alexander Brudnyi Pages: 830 - 863 Abstract: Publication date: October 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 7 Author(s): Alexander Brudnyi In this paper we describe the Hopf algebra approach to the center problem for the differential equation d v d x = ∑ i = 1 ∞ a i ( x ) v i + 1 , x ∈ [ 0 , T ] , and study some combinatorial properties of the first return map of this equation. The paper summarizes and extends previously developed approaches to the center problem due to Devlin and the author.

Authors:Gordon Blower; Caroline Brett; Ian Doust Pages: 864 - 899 Abstract: Publication date: October 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 7 Author(s): Gordon Blower, Caroline Brett, Ian Doust This paper analyses the periodic spectrum of Schrödinger's equation − f ″ + q f = λ f when the potential is real, periodic, random and subject to the invariant measure ν N β of the periodic KdV equation. This ν N β is the modified canonical ensemble, as given by Bourgain (1994) [7], and ν N β satisfies a logarithmic Sobolev inequality. Associated concentration inequalities control the fluctuations of the periodic eigenvalues ( λ n ) . For β , N > 0 small, there exists a set of positive ν N β measure such that ( ± 2 ( λ 2 n + λ 2 n − 1 ) ) n = 0 ∞ gives a sampling sequence for Paley–Wiener space PW ( π ) and the reproducing kernels give a Riesz basis. Let ( μ j ) j = 1 ∞ be the tied spectrum; then ( 2 μ j − j ) belongs to a Hilbert cube in ℓ 2 and is distributed according to a measure that satisfies Gaussian concentration for Lipschitz functions. The sampling sequence ( μ j ) j = 1 ∞ arises from a divisor on the spectral curve, which is hyperelliptic of infinite genus. The linear statistics ∑ j g ( λ 2 j ) with test function g ∈ PW ( π ) satisfy Gaussian concentration inequalities.

Authors:Hichem Chtioui; Wael Abdelhedi Pages: 617 - 628 Abstract: Publication date: September 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 6 Author(s): Hichem Chtioui, Wael Abdelhedi In this paper, we consider a fractional Nirenberg type problem involving σ-exponent of the Laplacian on the standard n-dimensional spheres S n . We prove existence and multiplicity result under β-flatness condition, n − 2 σ < β < n . In particular, we give a new existence criterium which generalizes the previous results of [22] and [23] for σ ∈ ( 0 , 1 ) and recovers the already known result for the classical case σ = 1 .

Authors:Marco Sabatini Pages: 629 - 637 Abstract: Publication date: September 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 6 Author(s): Marco Sabatini We extend a result proved in [7] for mirror symmetries of planar systems to measure-preserving non-linear reversibilities of n-dimensional systems, dropping the analyticity and nondegeneracy conditions.

Authors:P.G. Grinevich; R.G. Novikov Pages: 638 - 656 Abstract: Publication date: September 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 6 Author(s): P.G. Grinevich, R.G. Novikov We show that local studies of generalized analytic functions with the simplest contour poles are reduced to the regular case via simple Moutard-type transforms. This work continues studies of [13,14].

Authors:Ewa Cygan; Maciej P. Denkowski Pages: 657 - 674 Abstract: Publication date: September 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 6 Author(s): Ewa Cygan, Maciej P. Denkowski In this paper we are interested in two kinds of singular points of weakly holomorphic functions. Points where a weakly holomorphic function is not holomorphic and points at which it just is not continuous. The latter are closely connected to points of irreducibility of the given analytic set. We investigate the structure of such points proving they form analytically constructible sets and we study the analytic cycle obtained from this result. We prove also that non-holomorphicity points of a given weakly or c-holomorphic function form an analytic subset of the singularities and give a new criterion for a weakly holomorphic function to be holomorphic.

Authors:M. Corrêa; Luis G. Maza Pages: 675 - 686 Abstract: Publication date: September 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 6 Author(s): M. Corrêa, Luis G. Maza We prove a singular version of the Engel theorem. We prove a normal form theorem for germs of holomorphic singular Engel systems with good conditions on its singular set. As an application, we prove that there exists an integral analytic curve passing through the singular points of the system. Also, we prove that a globally decomposable Engel system on a four dimensional projective space has singular set with atypical codimension.

Authors:Troels Roussau Johansen Pages: 687 - 717 Abstract: Publication date: September 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 6 Author(s): Troels Roussau Johansen We establish several uncertainty principles for the Heckman–Opdam ‘hypergeometric’ Fourier transform associated with a root system of arbitrary rank, including analogues of the Donoho–Stark and Benedicks–Amrein–Berthier principles, and the Hirschman entropic uncertainty inequality. For rank one root systems, these results hold more generally for the Cherednik–Opdam transform.

Authors:Guangying Lv; Jinqiao Duan; Hongjun Gao; Jiang-Lun Wu Pages: 718 - 746 Abstract: Publication date: September 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 6 Author(s): Guangying Lv, Jinqiao Duan, Hongjun Gao, Jiang-Lun Wu In this paper, we are interested in the Dirichlet boundary value problem for a multi-dimensional nonlocal conservation law with a multiplicative stochastic perturbation in a bounded domain. Using the concept of measure-valued solutions and Kruzhkov's semi-entropy formulations, a result of existence and uniqueness of entropy solution is proved.

Authors:Hiroki Saito; Hitoshi Tanaka; Toshikazu Watanabe Pages: 757 - 773 Abstract: Publication date: September 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 6 Author(s): Hiroki Saito, Hitoshi Tanaka, Toshikazu Watanabe Let μ be a locally finite Borel measure and D a family of measurable sets equipped with a certain dyadic structure. For E ⊂ R n and 0 < α ≤ n , by α-dimensional Hausdorff content we mean H μ α ( E ) = inf ∑ j μ ( Q j ) α / n , where the infimum is taken over all coverings of E by countable families of the abstract dyadic cubes { Q j } ⊂ D . In this paper we study the boundedness of the Hardy–Littlewood maximal operator M D μ adapted to D and μ, that is, we prove the strong type ( p , p ) inequality ∫ ( M D μ f ) p d H μ α ≤ 2 2 p + 2 min ( 1 , p ) − ( α / n ) ∫ f p d H μ α for α / n < p < ∞ , and the weak type ( α / n , α / n ) inequality H μ α ( { x ∈ R n : M D μ f ( x ) > t } ) ≤ 4 ( n / α ) α / n t − α / n ∫ f α / n d H μ α , t > 0 , where the integrals are taken in the Choquet sense.

Authors:Arijit Dey; Mainak Poddar Pages: 471 - 487 Abstract: Publication date: June 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 5 Author(s): Arijit Dey, Mainak Poddar We give a classification of the holomorphic (resp. algebraic) torus equivariant principal G-bundles on a nonsingular toric variety X when G is an Abelian, closed, holomorphic (resp. algebraic) subgroup of the complex general linear group. We prove that any such bundle splits, that is, admits a reduction of structure group to a torus. We give an explicit parametrization of the isomorphism classes of such bundles for a large family of G when X is complete.

Authors:Arghya Mondal; Parameswaran Sankaran Pages: 488 - 505 Abstract: Publication date: June 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 5 Author(s): Arghya Mondal, Parameswaran Sankaran Let X be a locally symmetric space Γ \ G / K where G is a connected non-compact semisimple real Lie group with trivial centre, K is a maximal compact subgroup of G, and Γ ⊂ G is a torsion-free irreducible lattice in G. Let Y = Λ \ H / L be another such space having the same dimension as X. Suppose that real rank of G is at least 2. We show that any f : X → Y is either null-homotopic or it is homotopic to a covering projection of degree an integer that depends only on Γ and Λ. As a corollary we obtain that the set [ X , Y ] of homotopy classes of maps from X to Y is finite. We obtain results on the (non-)existence of orientation reversing diffeomorphisms on X as well as the fixed point property for X.

Authors:Li-Juan Cheng Pages: 541 - 561 Abstract: Publication date: June 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 5 Author(s): Li-Juan Cheng Let L t : = Δ t + Z t for a C 1 , 1 -vector field Z on a differential manifold M possibly with a boundary ∂M, where Δ t is the Laplacian operator induced by a time dependent metric g t differentiable in t ∈ [ 0 , T c ) . In this article, by constructing suitable coupling, transportation-cost inequalities on the path space of the (reflecting if ∂ M ≠ ∅ ) diffusion process generated by L t are proved to be equivalent to a new curvature lower bound condition and the convexity of the geometric flow (i.e., the boundary keeps convex). Some of them are further extended to non-convex flows by using conformal changes of the flows. As an application, these results are applied to the Ricci flow with the umbilic boundary.

Authors:Khalifa Dabbek; Noureddine Ghiloufi; Jawhar Hbil Pages: 562 - 574 Abstract: Publication date: June 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 5 Author(s): Khalifa Dabbek, Noureddine Ghiloufi, Jawhar Hbil In this paper, we study the existence of the tangent cone to a positive plurisubharmonic or plurisuperharmonic current with a suitable condition. Some estimates of the growth of the Lelong functions associated with the current and to its d d c are given to ensure the existence of the strict transform of this current. A second proof for the existence of the tangent cone is derived from these estimates.

Authors:Kazuo Yamazaki Pages: 575 - 614 Abstract: Publication date: June 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 5 Author(s): Kazuo Yamazaki We study the criterion for the velocity and magnetic vector fields that solve the three-dimensional magnetohydrodynamics system, given any initial data sufficiently smooth, to experience a finite-time blowup. Following the work of Chemin and Zhang [12] and making use of the structure of the system, we obtain a criterion that is imposed on the magnetic vector field and only one of the three components of the velocity vector field, both in scaling-invariant spaces.

Authors:Hassan Azad; Indranil Biswas; C.S. Rajan; Shehryar Sikander Pages: 1 - 10 Abstract: Publication date: May 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 4 Author(s): Hassan Azad, Indranil Biswas, C.S. Rajan, Shehryar Sikander Let K \ G be an irreducible Hermitian symmetric space of noncompact type and Γ ⊂ G a closed torsionfree discrete subgroup. Let X be a compact Kähler manifold and ρ : π 1 ( X , x 0 ) ⟶ Γ a homomorphism such that the adjoint action of ρ ( π 1 ( X , x 0 ) ) on the Lie algebra Lie ( G ) is completely reducible. A theorem of Corlette associates to ρ a harmonic map H : X ⟶ K \ G / Γ . We give a criterion for this harmonic map H to be holomorphic. We also give a criterion for it to be anti-holomorphic.

Authors:Indranil Biswas; Alfonso Zamora Pages: 58 - 69 Abstract: Publication date: May 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 4 Author(s): Indranil Biswas, Alfonso Zamora We give an example of an orthogonal bundle where the Harder–Narasimhan filtration, with respect to Gieseker semistability, of its underlying vector bundle does not correspond to any parabolic reduction of the orthogonal bundle. A similar example is given for the symplectic case.

Authors:Lei Qiao; Guoshuang Pan Pages: 70 - 85 Abstract: Publication date: May 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 4 Author(s): Lei Qiao, Guoshuang Pan This paper is concerned with a class of harmonic functions in a cone. Exploiting some ideas of Levin, we derive lower-bound estimates for them. Using these estimates, we investigate Masaev's Type inequalities.

Authors:Amiran Gogatishvili; Tengiz Kopaliani Pages: 86 - 97 Abstract: Publication date: May 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 4 Author(s): Amiran Gogatishvili, Tengiz Kopaliani In this paper we study some estimates of norms in variable exponent Lebesgue spaces for maximal multiplier operators. We will consider the case when multiplier is the Fourier transform of a compactly supported Borel measure.

Authors:Vladimir Petrov Kostov Pages: 98 - 111 Abstract: Publication date: May 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 4 Author(s): Vladimir Petrov Kostov The series θ ( q , x ) : = ∑ j = 0 ∞ q j ( j + 1 ) / 2 x j converges for q ∈ [ 0 , 1 ) , x ∈ R , and defines a partial theta function. For any fixed q ∈ ( 0 , 1 ) it has infinitely many negative zeros. For q taking one of the spectral values q ˜ 1 , q ˜ 2 , … (where 0.3092493386 … = q ˜ 1 < q ˜ 2 < ⋯ < 1 , lim j → ∞ q ˜ j = 1 ) the function θ ( q , . ) has a double zero y j which is the rightmost of its real zeros (the rest of them being simple). For q ≠ q ˜ j the partial theta function has no multiple real zeros. We prove that q ˜ j = 1 − π / 2 j + ( log j ) / 8 j 2 + O ( 1 / j 2 ) and y j = − e π e − ( log j ) / 4 j + O ( 1 / j ) .

Authors:Claire Levaillant Abstract: Publication date: Available online 5 December 2016 Source:Bulletin des Sciences Mathématiques Author(s): Claire Levaillant We provide a protocol to physically generate a 2-qutrit entangling gate in the Kauffman-Jones version of S U ( 2 ) Chern-Simons theory at level 4. The protocol uses elementary operations on anyons consisting of braids, interferometric measurements, fusions and unfusions and ancilla pair creations.

Authors:Daniel Gonçalves; Danilo Royer Abstract: Publication date: Available online 2 December 2016 Source:Bulletin des Sciences Mathématiques Author(s): Daniel Gonçalves, Danilo Royer In this paper we further develop the theory of one-sided shift spaces over infinite alphabets, characterizing one-step shifts as edge shifts of ultragraphs and partially answering a conjecture regarding shifts of finite type (we show that there exists shifts of finite type that are not conjugate, via a conjugacy that is eventually finite periodic, to an edge shift of a graph ). We also show that there exists edge shifts of ultragraphs that are shifts of finite type, but are not conjugate to a full shift, a result that is not true for edge shifts of graphs. One of the key results needed in the proofs of our conclusions is the realization of a class of ultragraph C*-algebras as partial crossed products, a result of interest on its own.

Authors:David Kalaj Abstract: Publication date: Available online 17 November 2016 Source:Bulletin des Sciences Mathématiques Author(s): David Kalaj In this paper we extend Radó-Kneser-Choquet theorem for the mappings with weak homeomorphic Lipschitz boundary function and Dini's smooth boundary but without restriction on the convexity of the image domain, provided that the Jacobian satisfies a certain boundary condition. The proof is based on a recent extension of Radó-Kneser-Choquet theorem by Alessandrini and Nesi [1] and is used the approximation principle.

Authors:Pralay Chatterjee; Chandan Maity Abstract: Publication date: Available online 4 October 2016 Source:Bulletin des Sciences Mathématiques Author(s): Pralay Chatterjee, Chandan Maity In [1], the second de Rham cohomology groups of nilpotent orbits in all the complex simple Lie algebras are described. In this paper we consider non-compact non-complex exceptional Lie algebras, and compute the dimensions of the second cohomology groups for most of the nilpotent orbits. For the rest of cases of nilpotent orbits, which are not covered in the above computations, we obtain upper bounds for the dimensions of the second cohomology groups.

Authors:Agrebaoui Abdelkader; Ben Hassine Mohamed Ali Maalaoui Abstract: Publication date: October 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 7 Author(s): Boujemaâ Agrebaoui, Abdelkader Ben Hassine, Mohamed Ali Maalaoui In the present paper, we define the diamond cone for the Lie superalgebra spo ( 2 m , 1 ) , considering the (covariant) tensor representation of spo ( 2 m , 1 ) . The diamond cone is no more indecomposable. Nevertheless, we give a basis for each indecomposable component, using quasistandard Young tableaux for spo ( 2 m , 1 ) . We realize a bijection between the set of semistandard tableaux with shape λ and the set of quasistandard tableaux with shape μ ≤ λ . This gives the compatibility of the diamond cone with the natural stratification of the reduced shape algebra.

Authors:Eric Amar Abstract: Publication date: September 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 6 Author(s): Eric Amar We use duality in the manner of Serre to generalize a theorem of Hedenmalm on solution of the ∂ ¯ equation with inverse of the weight in Hörmander L 2 estimates.

Authors:Pak Tung Abstract: Publication date: June 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 5 Author(s): Pak Tung Ho In this paper, we prove an existence result of prescribing Webster scalar curvature on the CR sphere in cases where the prescribed function exhibits reflection or rotation symmetry.

Authors:C.A. Buzzi; R.D. A.C. Mereu Abstract: Publication date: June 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 5 Author(s): C.A. Buzzi, R.D. Euzébio, A.C. Mereu Detect the birth of limit cycles in non-smooth vector fields is a very important matter into the recent theory of dynamical systems and applied sciences. The goal of this paper is to study the bifurcation of limit cycles from a continuum of periodic orbits filling up a two-dimensional isochronous cylinder of a vector field in R 3 . The approach involves the regularization process of non-smooth vector fields and a method based in the Malkin bifurcation function for C 0 perturbations. The results provide sufficient conditions in order to obtain limit cycles emerging from the cylinder through smooth and non-smooth perturbations of it. To the best of our knowledge they also illustrate the implementation by the first time of a new method based in the Malkin bifurcation function. In addition, some points concerning the number of limit cycles bifurcating from non-smooth perturbations compared with smooth ones are studied. In summary the results yield a better knowledge about limit cycles in non-smooth vector fields in R 3 and explicit a manner to obtain them by performing non-smooth perturbations in codimension one Euclidean manifolds.

Abstract: Publication date: May 2016 Source:Bulletin des Sciences Mathématiques, Volume 140, Issue 4 Author(s): Noël Lohoué We prove L p and weighted L p estimates for the solutions α of the Poisson equation Δ α = β on differential forms with data β in L p or in weighted L p , in a symmetric space M. We study carefully the range of p for which the de Rham–Hodge projection, a priori defined on L 2 , is bounded on L p .

Authors:Sergio Albeverio; Iryna Garko; Muslem Ibragim; Grygoriy Torbin Abstract: Publication date: Available online 5 April 2016 Source:Bulletin des Sciences Mathématiques Author(s): Sergio Albeverio, Iryna Garko, Muslem Ibragim, Grygoriy Torbin In the present paper we study the dependence of fractal and metric properties of numbers which are non-normal resp. essentialy non-normal w.r.t. a chosen system of numeration. In particular, we solve open problems mentioned in [1] and prove that there exist expansions (the Q ⁎ -expansions or Q ⁎ -representations) for real numbers such that the corresponding sets of essentially non-normal numbers and even the whole set of non-normal numbers are of zero Hausdorff dimension. On the other hand, we show that in the same model of Q ⁎ -expansions it is possible to choose the matrix Q ⁎ in such a way that the corresponding set of essentially non-normal numbers is of full Lebesgue measure. Sufficient conditions for full dimensionality resp. zero dimensionality of the set of essentially non-normal numbers are also presented.