Displaying 781 – 800 of 2163

Showing per page

Inégalités pour l’opérateur intégral fractionnaire sur différents espaces métriques mesurés

David Mascré (2011)

Annales mathématiques Blaise Pascal

Le but de cet article est d’étendre les résultats classiques (inégalité de Hardy-Littlewood-Sobolev, inégalité de Hedberg) sur l’intégrale fractionnaire à deux types différents d’espaces métriques mesurés : les espaces métriques mesurés à mesure doublante d’une part, les espaces métriques mesurés à croissance polynomiale du volume d’autre part. Les deux résultats principaux que nous obtenons sont les suivants :Etant donné ( X , ρ , μ ) un espace métrique mesuré de type homogène, étant donnés p , q , α R tels que 1 p < 1 / α , 1 / q = 1 / p - α ,...

Inequivalence of Wavelet Systems in L ( d ) and B V ( d )

Paweł Bechler (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

Theorems stating sufficient conditions for the inequivalence of the d-variate Haar wavelet system and another wavelet system in the spaces L ( d ) and B V ( d ) are proved. These results are used to show that the Strömberg wavelet system and the system of continuous Daubechies wavelets with minimal supports are not equivalent to the Haar system in these spaces. A theorem stating that some systems of smooth Daubechies wavelets are not equivalent to the Haar system in L ( d ) is also shown.

Infinitely many solutions for boundary value problems arising from the fractional advection dispersion equation

Jing Chen, Xian Hua Tang (2015)

Applications of Mathematics

We consider the existence of infinitely many solutions to the boundary value problem d d t 1 2 0 D t - β ( u ' ( t ) ) + 1 2 t D T - β ( u ' ( t ) ) + F ( t , u ( t ) ) = 0 a.e. t [ 0 , T ] , u ( 0 ) = u ( T ) = 0 . Under more general assumptions on the nonlinearity, we obtain new criteria to guarantee that this boundary value problem has infinitely many solutions in the superquadratic, subquadratic and asymptotically quadratic cases by using the critical point theory.

Inhomogeneous Fractional Diffusion Equations

Baeumer, Boris, Kurita, Satoko, Meerschaert, Mark (2005)

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: Primary 26A33; Secondary 35S10, 86A05Fractional diffusion equations are abstract partial differential equations that involve fractional derivatives in space and time. They are useful to model anomalous diffusion, where a plume of particles spreads in a different manner than the classical diffusion equation predicts. An initial value problem involving a space-fractional diffusion equation is an abstract Cauchy problem, whose analytic solution can be written...

Inhomogeneous self-similar sets and box dimensions

Jonathan M. Fraser (2012)

Studia Mathematica

We investigate the box dimensions of inhomogeneous self-similar sets. Firstly, we extend some results of Olsen and Snigireva by computing the upper box dimensions assuming some mild separation conditions. Secondly, we investigate the more difficult problem of computing the lower box dimension. We give some non-trivial bounds and provide examples to show that lower box dimension behaves much more strangely than upper box dimension, Hausdorff dimension and packing dimension.

Insertion of a Contra-Baire- 1 (Baire- . 5 ) Function

Majid Mirmiran (2019)

Communications in Mathematics

Necessary and sufficient conditions in terms of lower cut sets are given for the insertion of a Baire- . 5 function between two comparable real-valued functions on the topological spaces that F σ -kernel of sets are F σ -sets.

Instability of the eikonal equation and shape from shading

Ian Barnes, Kewei Zhang (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In the shape from shading problem of computer vision one attempts to recover the three-dimensional shape of an object or landscape from the shading on a single image. Under the assumptions that the surface is dusty, distant, and illuminated only from above, the problem reduces to that of solving the eikonal equation |Du|=f on a domain in 2 . Despite various existence and uniqueness theorems for smooth solutions, we show that this problem is unstable, which is catastrophic for general numerical algorithms. ...

Currently displaying 781 – 800 of 2163