Displaying similar documents to “Asymptotic stability of a semigroup generated by randomly connected Poisson driven differential equations”

Sums of Three Prime Squares

Hiroshi Mikawa, Temenoujka Peneva (2007)

Bollettino dell'Unione Matematica Italiana

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Let A , ϵ > 0 be arbitrary. Suppose that x is a sufficiently large positive number. We prove that the number of integers n ( x , x + x θ ] , satisfying some natural congruence conditions, which cannot be written as the sum of three squares of primes is x θ ( log x ) - A , provided that 7 16 + ϵ θ 1 .

On geodesics of phyllotaxis

Roland Bacher (2014)

Confluentes Mathematici

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Seeds of sunflowers are often modelled by n ϕ θ ( n ) = n e 2 i π n θ leading to a roughly uniform repartition with seeds indexed by consecutive integers at angular distance 2 π θ for θ the golden ratio. We associate to such a map ϕ θ a geodesic path γ θ : > 0 PSL 2 ( ) of the modular curve and use it for local descriptions of the image ϕ θ ( ) of the phyllotactic map ϕ θ .

Some remarks on the interpolation spaces A θ , A θ

Mohammad Daher (2016)

Commentationes Mathematicae Universitatis Carolinae

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Let ( A 0 , A 1 ) be a regular interpolation couple. Under several different assumptions on a fixed A β , we show that A θ = A θ for every θ ( 0 , 1 ) . We also deal with assumptions on A ¯ β , the closure of A β in the dual of ( A 0 * , A 1 * ) β .

Comments on the fractional parts of Pisot numbers

Toufik Zaïmi, Mounia Selatnia, Hanifa Zekraoui (2015)

Archivum Mathematicum

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Let L ( θ , λ ) be the set of limit points of the fractional parts { λ θ n } , n = 0 , 1 , 2 , , where θ is a Pisot number and λ ( θ ) . Using a description of L ( θ , λ ) , due to Dubickas, we show that there is a sequence ( λ n ) n 0 of elements of ( θ ) such that Card ( L ( θ , λ n ) ) < Card ( L ( θ , λ n + 1 ) ) , n 0 . Also, we prove that the fractional parts of Pisot numbers, with a fixed degree greater than 1, are dense in the unit interval.

The Martingale Problem in Hilbert Spaces

Giuseppe Da Prato, Luciano Tubaro (2008)

Bollettino dell'Unione Matematica Italiana

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We consider an SPDE in a Hilbert space H of the form d X ( t ) = ( A X ( t ) + b ( X ( t ) ) ) d t + σ ( X ( t ) ) d W ( t ) , X ( 0 ) = x H and the corresponding transition semigroup P t f ( x ) = 𝔼 [ f ( X ( t , x ) ) ] . We define the infinitesimal generator L ¯ of P t through the Laplace transform of P t as in [1]. Then we consider the differential operator L φ = 1 2 Tr [ σ ( x ) σ * ( x ) D 2 φ ] + b ( x ) , D φ defined on a suitable set V of regular functions. Our main result is that if V is a core for L ¯ , then there exists a unique solution of the martingale problem defined in terms of L . Application to the Ornstein-Uhlenbeck equation and to some regular...

Linearly-invariant families and generalized Meixner–Pollaczek polynomials

Iwona Naraniecka, Jan Szynal, Anna Tatarczak (2013)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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The extremal functions  f 0 ( z )   realizing the maxima of some functionals (e.g. max | a 3 | , and  max a r g f ' ( z ) ) within the so-called universal linearly invariant family U α (in the sense of Pommerenke [10]) have such a form that f 0 ' ( z )   looks similar to generating function for Meixner-Pollaczek (MP) polynomials [2], [8]. This fact gives motivation for the definition and study of the generalized Meixner-Pollaczek (GMP) polynomials P n λ ( x ; θ , ψ ) of a real variable x as coefficients of G λ ( x ; θ , ψ ; z ) = 1 ( 1 - z e i θ ) λ - i x ( 1 - z e i ψ ) λ + i x = n = 0 P n λ ( x ; θ , ψ ) z n , | z | < 1 , where the parameters λ , θ , ψ satisfy the conditions:...

Singularities of 2 Θ -divisors in the jacobian

Christian Pauly, Emma Previato (2001)

Bulletin de la Société Mathématique de France

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We consider the linear system | 2 Θ 0 | of second order theta functions over the Jacobian J C of a non-hyperelliptic curve C . A result by J.Fay says that a divisor D | 2 Θ 0 | contains the origin 𝒪 J C with multiplicity 4 if and only if D contains the surface C - C = { 𝒪 ( p - q ) p , q C } J C . In this paper we generalize Fay’s result and some previous work by R.C.Gunning. More precisely, we describe the relationship between divisors containing 𝒪 with multiplicity 6 , divisors containing the fourfold C 2 - C 2 = { 𝒪 ( p + q - r - s ) p , q , r , s C } , and divisors singular along C - C , using...

Compatibility of the theta correspondence with the Whittaker functors

Vincent Lafforgue, Sergey Lysenko (2011)

Bulletin de la Société Mathématique de France

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We prove that the global geometric theta-lifting functor for the dual pair ( H , G ) is compatible with the Whittaker functors, where ( H , G ) is one of the pairs ( S 𝕆 2 n , 𝕊 p 2 n ) , ( 𝕊 p 2 n , S 𝕆 2 n + 2 ) or ( 𝔾 L n , 𝔾 L n + 1 ) . That is, the composition of the theta-lifting functor from H to G with the Whittaker functor for G is isomorphic to the Whittaker functor for H .

Singularities of theta divisors and the geometry of 𝒜 5

Gavril Farkas, Samuele Grushevsky, Salvati R. Manni, Alessandro Verra (2014)

Journal of the European Mathematical Society

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We study the codimension two locus H in 𝒜 g consisting of principally polarized abelian varieties whose theta divisor has a singularity that is not an ordinary double point. We compute the class [ H ] C H 2 ( 𝒜 g ) for every g . For g = 4 , this turns out to be the locus of Jacobians with a vanishing theta-null. For g = 5 , via the Prym map we show that H 𝒜 5 has two components, both unirational, which we describe completely. We then determine the slope of the effective cone of 𝒜 5 ¯ and show that the component N 0 ' ¯ of the Andreotti-Mayer...

Asymptotics for Eigenvalues of a Non-Linear Integral System

D.E. Edmunds, J. Lang (2008)

Bollettino dell'Unione Matematica Italiana

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Let I = [ a , b ] , let 1 < q , p < , let u and v be positive functions with u L p ( I ) e v L q ( I ) and let T : L p ( I ) L q ( I ) be the Hardy-type operator given by ( T f ) ( x ) = v ( x ) a x f ( t ) u ( t ) d t , x I . We show that the asymptotic behavior of the eigenvalues λ of the non-linear integral system g ( x ) = ( T F ) ( x ) ( f ( x ) ) ( p ) = λ ( T * g ( p ) ) ) ( x ) (where, for example, t ( p ) = | t | p - 1 sgn ( t ) is given by lim n n λ ^ n ( T ) = c p , q I ( u v ) r ) 1 / r d t 1 / r , for 1 < p < q < lim n n λ ˇ n ( T ) = c p , q I ( u v ) r d t 1 / r for 1 < q < p < Here r = 1 p + 1 p , c p , q is an explicit constant depending only on p and q , λ ^ ( T ) = max ( s p n ( T , p , q ) ) , λ ˇ n ( T ) = min ( s p n ( T , p , q ) ) where s p n ( T , p , q ) stands for the set of all eigenvalues λ corresponding to eigenfunctions g with n zeros.

Limits of minimum problems for general integral functionals with unilateral obstacles

Gianni Dal Maso (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Se il problema di minimo ( 𝒫 ) è il limite, in senso variazionale, di una successione di problemi di minimo con ostacoli del tipo min u ψ h A [ f h ( x , u , D u ) + b ( x , u ) ] 𝑑 x , allora ( 𝒫 ) può essere scritto nella forma min u { A [ f ( x , u , D u ) + b ( x , u ) ] 𝑑 x + A g ( x , u ~ ( x ) ) 𝑑 λ ( x ) } dove u ~ è un conveniente rappresentante di u e λ è una misura non negativa.

Convergence to Equilibrium of the Solution of Kac's Kinetic Equation. A Probabilistic View

Eugenio Regazzini (2009)

Bollettino dell'Unione Matematica Italiana

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Let f ( , t ) be the probability density function representing the solution of Kac's Boltzmann-like equation at time t , with initial data f 0 , and let g σ be the Gaussian density with zero mean and variance σ 2 , σ 2 being the value of the second moment of f 0 . Henry McKean Jr. put forward the conjecture that the total variation distance between f ( , t ) and g σ goes to zero, as t + , with an exponential rate equal to - 1 / 4 . This lecture aims at explaining the main efforts made to a view to validating this conjecture,...

The CR Yamabe conjecture the case n = 1

Najoua Gamara (2001)

Journal of the European Mathematical Society

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Let ( M , θ ) be a compact CR manifold of dimension 2 n + 1 with a contact form θ , and L = ( 2 + 2 / n ) Δ b + R its associated CR conformal laplacien. The CR Yamabe conjecture states that there is a contact form θ ˜ on M conformal to θ which has a constant Webster curvature. This problem is equivalent to the existence of a function u such that L u = u 1 + 2 / n , u > 0 on M . D. Jerison and J. M. Lee solved the CR Yamabe problem in the case where n 2 and ( M , θ ) is not locally CR equivalent to the sphere S 2 n + 1 of 𝐂 n . In a join work with R. Yacoub, the CR Yamabe...

Quasiharmonic Fields: a Higher Integrability Result

Patrizia Di Gironimo (2007)

Bollettino dell'Unione Matematica Italiana

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In this paper we study the degree of integrability of quasiharmonic fields. These fields are connected with the study of the equation div ( A ( x ) u ( x ) ) = 0 , where the symmetric matrix A ( x ) satisfies the condition | ξ | 2 + | A ( x ) ξ | 2 K ( x ) A ( x ) ξ , ξ .The nonnegative function K ( x ) belongs to the exponential class, i.e. exp ( β K ( x ) ) is integrable for some β > 0 . We prove that the gradient of a local solution of the equation belongs to the Zygmund spaces L loc 2 log α - 1 L , 0 < α = α ( β ) . Moreover we show exactly how the degree of improved regularity depends on β .

Adding or removing an element from a pseudo-symmetric numerical semigroup

J. C. Rosales (2006)

Bollettino dell'Unione Matematica Italiana

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If S is a pseudo-symmetric numerical semigroup, g is its Frobenius number and S is a minimal generator of S , then S { g } , S { g } S and S { 1 2 g , g } are also numerical semigroups. In this paper we study these constructions.

Some Remarks on Prym-Tyurin Varieties

Giuliano Parigi (2007)

Bollettino dell'Unione Matematica Italiana

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The aims of the present paper can be described as follows: a) In [2] Beauville showed that if some endomorphism u a Jacobian J ( C ) has connected kernel, the principal polarization on J ( C ) induces a multiple of the principal polarization on the image of u . We reformulate and complete this theorem proving "constructively" the following: Theorem. Let Z J ( C ) be an abelian subvariety and Y its complementary variety. Z is a Prym-Tyurin variety with respect to J ( C ) if and only if the following sequence...

On the projective genus of surfaces

Pietro Sabatino (2006)

Bollettino dell'Unione Matematica Italiana

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Let X N be a smooth irreducible non degenerate surface over the complex numbers, N 4 . We define the projective genus of X , denoted by P G ( X ) , as the geometric genus of the singular curve of the projection of X from a general linear subspace of codimension four. Denote by g ( X ) the sectional genus of X . In this paper we conjecture that the only surfaces for which P G ( X ) = g ( X ) - 1 are the del Pezzo surface in 4 , in 5 and a conic bundle of degree 5 in 4 . We prove that for N 5 if P G ( X ) = g ( X ) - 1 + λ , λ a non negative integer, then g ( X ) λ + 1 + α where...

The Schreier Property and Gauss' Lemma

Daniel D. Anderson, Muhammad Zafrullah (2007)

Bollettino dell'Unione Matematica Italiana

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Let D be an integral domain with quotient field D . Recall that D is Schreier if D is integrally closed and for all x , y , z D { 0 } , x | y z implies that x = r s where r | y e s | z . A GCD domain is Schreier. We show that an integral domain D is a GCD domain if and only if (i) for each pair a , b D { 0 } , there is a finitely generated ideal B such that a D b D = B v and (ii) every quadratic in D [ X ] that is a product of two linear polynomials in K [ X ] is a product of two linear polynomials in D [ X ] . We also show that D is Schreier if and only if every...

Geometric theta-lifting for the dual pair 𝕊𝕆 2 m , 𝕊 p 2 n

Sergey Lysenko (2011)

Annales scientifiques de l'École Normale Supérieure

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Let X be a smooth projective curve over an algebraically closed field of characteristic  &gt; 2 . Consider the dual pair H = SO 2 m , G = Sp 2 n over X with H split. Write Bun G and Bun H for the stacks of G -torsors and H -torsors on X . The theta-kernel Aut G , H on Bun G × Bun H yields theta-lifting functors F G : D ( Bun H ) D ( Bun G ) and F H : D ( Bun G ) D ( Bun H ) between the corresponding derived categories. We describe the relation of these functors with Hecke operators. In two particular cases these functors realize the geometric Langlands functoriality for the above pair (in the non...

Eisenstein ideal and reducible λ -adic Representations Unramified Outside a Finite Number of Primes.

Miriam Ciavarella (2006)

Bollettino dell'Unione Matematica Italiana

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The object of this note is to study certain 2-dimensional λ -adic representations of Gal ( Q ¯ / Q ) ; fixed p 1 , , p n distinct primes, we will consider representations ρ : G G L 2 ( A ) , given by the matrix ρ = ( a b c d ) which are unramified outside p 1 , , p n , and the residue characteristic of λ , which are a product of m representations over finite extensions of the ring of Witt vectors of the residue field and which are reducible modulo λ . In analogy with the theory of the modular representations, we will introduce the analogue of Mazur's Hecke...

Threefolds with Kodaira Dimension 0 or 3

Ezio Stagnaro (2007)

Bollettino dell'Unione Matematica Italiana

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Using the theory of adjoints and pluricanonical adjoints, we construct three nonsingular threefolds, as desingularizations of degree six hypersurfaces in 4 , having the irregularities q 1 = q 2 = 0 and the following periodical sequences of plurigenera respectively ( p g , P 2 , P 3 , , P m , ) = ( 0 , 0 , 1 , 0 , 0 , 1 , ) , ( 0 , 0 , 0 , 1 , 0 , 0 , 0 , 1 , ) , ( 0 , 0 , 0 , 0 , 1 , 0 , 0 , 0 , 0 , 1 , ) . In the Appendix, starting from the second above-mentioned example, we construct a threefold of general type with q q 1 = q 2 = 0 , p g = 1 , P 2 = 2 whose m-canonical transformation is birational if and only if m 11 .

Isomorphisms of Royden Type Algebras Over 𝕊 1

Teresa Radice, Eero Saksman, Gabriella Zecca (2009)

Bollettino dell'Unione Matematica Italiana

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Let 𝕊 1 and 𝔻 be the unit circle and the unit disc in the plane and let us denote by 𝒜 ( 𝕊 1 ) the algebra of the complex-valued continuous functions on 𝕊 1 which are traces of functions in the Sobolev class W 1 , 2 ( 𝔻 ) . On 𝒜 ( 𝕊 1 ) we define the following norm u = u L ( 𝕊 1 ) + ( 𝔻 | u ~ | 2 ) 1 / 2 where is the harmonic extension of u to 𝔻 . We prove that every isomorphism of the functional algebra 𝒜 ( 𝕊 1 ) is a quasitsymmetric change of variables on 𝕊 1 .

Groups Generated by (near) Mutually Engel Periodic Pairs

Piotr Słanina, Witold Tomaszewski (2007)

Bollettino dell'Unione Matematica Italiana

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We use notations: [ x , y ] = [ x , 1 y ] and [ x , k + 1 y ] e [ [ x , k y ] , y ] . We consider groups generated by x , y satisfying relations x = [ x , n y ] , y = [ y , n x ] or [ x , y ] = [ x , n y ] , [ y , x ] = [ y , n x ] . We call groups of the first type mep-groups and of the second type nmep-groups. We show many properties and examples of mep- and nmep-groups. We prove that if p is a prime then the group S l 2 ( p ) is a nmep-group. We give the necessary and sufficient conditions for metacyclic group to be a nmep-group and we show that nmep-groups with presentation x , y [ x , y ] = [ x , 2 y ] , [ y , x ] = [ y , 2 x ] , x n , y m are finite.

Some Separation Axioms Via Ideals

D. Sivaraj, V. Renuka Devi (2007)

Bollettino dell'Unione Matematica Italiana

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We introduce a new class of spaces, called Hausdorff modulo or T 2 mod spaces with respect to an ideal which contains the class of all Hausdorff spaces. Characterizations of these spaces are given and their properties are investigated. The concept of compactness modulo an ideal was introduced by Newcomb in 1967 and studied by Hamlett and Jankovic in 1990. We study the properties of -compact subsets in Hausdorff modulo spaces and generalize some results of Hamlett and Jankovic....

On the lower semicontinuity of certain integral functionals

Ennio De Giorgi, Giuseppe Buttazzo, Gianni Dal Maso (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Si dimostra che il funzionale Ω f ( u , D u ) 𝑑 x è semicontinuo inferiormente su W l o c 1 , 1 ( Ω ) , rispetto alla topologia indotta da L l o c 1 ( Ω ) , qualora l’integrando f ( s , p ) sia una funzione non-negativa, misurabile in s , convessa in p , limitata nell’intorno dei punti del tipo ( s , 0 ) , e tale che la funzione s f ( s , 0 ) sia semicontinua inferiormente su 𝐑 .

Integrals with respect to a Radon measure added to area type functionals: semi-continuity and relaxation

Michele Carriero, Antonio Leaci, Eduardo Pascali (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Diamo condizioni sulle funzioni f , g e sulla misura μ affinché il funzionale F ( u ) = Ω f ( x , u , D u ) 𝑑 x + Ω ¯ g ( x , u ) 𝑑 μ sia L 1 ( Ω ) -semicontinuo inferiormente su W 1 , 1 ( Ω ) C 0 ( Ω ¯ ) . Affrontiamo successivamente il problema del rilassamento.