In this article, we propose the Mapping-based Pseudo Binary Differential Evolution (MPBDE) algorithm for solving discrete optimization problems. Based on the framework of the standard DE, a new boundary constraint-handling operator ensures that the results of the mutation operator meet the boundary conditions. Then the real values of the genotypes mapped into the discrete ones in the phenotypes...

Yang–Mills theory in four dimensions is studied by using the Coulomb gauge. The Coulomb gauge Hamiltonian involves integration of matrix elements of an operator P built from the Laplacian and from a first-order differential operator. The operator P is studied from the point of view of spectral theory of pseudo-differential operators on compact Riemannian manifolds, both when self-adjointness ho...

A new method is proposed for deriving embedding formulae in 2-D diffraction problems. In contrast to the approach developed in [7], which is based on a differential operator, here a pseudo-differential, i.e., a non-local operator is applied to the wave field. Using this non-local operator a new embedding formula is derived for scattering by a single wedge. The formula has uniform structure for ...

We complete the classification of second order, bundle valued differential operator invariants of Riemannian and pseudo-Riemannian conformal structure, by classifying such operators which pass between bundles associated to different representations of the rotation or spin group.

The stochastic Euler-Poincaré equations with pseudo-differential/multiplicative noise are considered in this work. We first establish two new cancellation properties on pseudo-differential operators, which considerably extend the previous results for transport type only involving gradient operator. Then, we obtain local solution, blow-up criterion, and global existence. interplay between stabil...

A description of the number N(K) of eigenvalues less than K for a pseudo-differential operator with positive symbol is given in terms of the number of unit cubes canonically imbedded in the subset of phase space where the symbol is less than CK. This gives back in particular the order of magnitude of N(K) for elliptic symbols.

In [ l ] Hörmander defines the generalized symbol of a pseudodifferential operator P as a sequence of partially defined maps between function spaces. Our purpose here is to comment on the existence of characteristic polynomial type symbols <r(P) and to obtain their composition by introducing a product structure on suitable jet bundles. In particular, this gives the lower order symbol for differ...

The aim of the present paper is to obtain a Sjölin-type maximal estimate for pseudo-differential operators with homogeneous symbols. The crux of the proof is to obtain a phase decomposition formula which does not involve the time traslation. The proof is somehow parallel to the paper by Pramanik and Terwilleger (P. Malabika and E. Terwilleger, A weak L2 estimate for a maximal dyadic sum operato...

A Carleman estimate for a differential operator P is a weighted energy estimate with a weight of exponential form exp(τφ) that involves a large parameter, τ > 0. The function φ and the operator P need to fulfill some sub-ellipticity properties that can be achieved for instance by choosing φ = exp(αψ), involving a second large parameter, α > 0, with ψ satisfying some geometrical conditions. The ...

In this paper, we study the boundedness of pseudo-differential operators with symbols in Sm ρ,δ on the modulation spaces M p,q. We discuss the order m for the boundedness Op(Sm ρ,δ) ⊂ L(M p,q(Rn)) to be true. We also prove the existence of a Calderón-Zygmund operator which is not bounded on the modulation space Mp,q with q 6= 2. This unboundedness is still true even if we assume a generalized T...