An algebraic treatment of shape-invariant potentials in supersymmetric quantum mechanics is discussed. By introducing an operator which reparametrizes wave functions, the shape-invariance condition can be related to a oscillator-like algebra. It makes possible to define a coherent state associated with the shape-invariant potentials. For a large class of such potentials, it is shown that the in...

This paper studies the stability of the trajectories of self-propelled bodies immersed in a fluid at low Reynolds number, with respect to their dynamic shape deformation. We consider both adherence and perfect slip boundary conditions on the moving body. Using shape derivative arguments in association with recent higher order regularity results for the Bogovskĭı operator, we bring the shape sta...

in this paper we study properties of symbols such that these belong to class of symbols sitting insidesm ρ,φ that we shall introduce as the following. so for because hypoelliptic pseudodifferential operatorsplays a key role in quantum mechanics we will investigate some properties of m−hypoelliptic pseudodifferential operators for which define base on this class of symbols. also we consider maxi...

We derive expressions for the shape Hessian operator of the data misfit functional corresponding to the inverse problem of inferring the shape of a scatterer from reflected acoustic waves, using a Banach space setting and the Lagrangian approach. The shape Hessian is then analyzed in both Hölder and Sobolev spaces. Using an integral equation approach and compact embeddings in Hölder and Sobolev...

We derive expressions for the shape Hessian operator of the data misfit functional corresponding to the inverse problem of inferring the shape of a scatterer from reflected acoustic waves, using a Banach space setting and the Lagrangian approach. The shape Hessian is then analyzed in both Hölder and Sobolev spaces. Using an integral equation approach and compact embeddings in Hölder and Sobolev...

We consider the eigenvalues of the biharmonic operator subject to several homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov). We show that simple eigenvalues and elementary symmetric functions of multiple eigenvalues are real analytic, and provide Hadamard-type formulas for the corresponding shape derivatives. After recalling the known results in shape optimization, we prove ...

The limit q-Bernstein operator B q emerges naturally as a modification of the Szász-Mirakyan operator related to the Euler distribution, which is used in the q-boson theory to describe the energy distribution in a q-analogue of the coherent state. At the same time, this operator bears a significant role in the approximation theory as an exemplarymodel for the study of the convergence of the q-o...

Here, we introduce a joint topology and harmonic analysis formulation for the extraction of global shape descriptors which are invariant under a given group of geometrical transformations. The topology approach allows the rigorous definition of the notions of shape, shape space, the invariant features space, and a metric between shapes. Therefore a new definition of completeness is given. A sta...