Laplacian Abelian Projection is discussed. This term refers to the use of a new (“Laplacian”) gauge fixing prescription for implementing the Abelian Projection of QCD. The gauge condition is based on the lowest-lying eigenvector of the covariant Laplacian operator in the adjoint representation. This Laplacian gauge fixing procedure is free of the ambiguities which plague lattice simulations whi...

In this paper we give the definition of 1/2-harmonic maps u : D → N , where D is an open set of IR and N is a k dimensional submanifold N of IRm as critical points of the functional ∫ Ω |∆ 1/4u|2dx . We write the Euler-Lagrange equation satisfied in a weak sense by the 1/2-harmonic maps, which is a nonlocal partial differential equation involving the 1/2-Laplacian operator . We prove the local ...

where Δ is the forward difference operator Δxn = xn+1 − xn, Δxn = Δ(Δxn), φp(s) is p-Laplacian operator φp(s) = |s|p−2s (1 < p < ∞), and f : Z×R3 → R is a continuous functional in the second, the third, and fourth variables and satisfies f (t +m,u,v,w) = f (t,u,v,w) for a given positive integerm. We may think of (1.1) as being a discrete analogue of the second-order functional differential equa...

Metrized graphs are finite graphs equipped with a distance function on their edges. For a metrized graph Γ, the tau constant τ(Γ) is an invariant which plays important roles in both harmonic analysis on metrized graphs and arithmetic of curves. T. Chinburg and R. Rumely [CR] introduced a canonical measure μcan of total mass 1 on a metrized graph Γ. The diagonal values of the Arakelov-Green’s fu...

Independent component analysis (ICA) of a mixed signal into a linear combination of its independent components, is one of the main problems in statistics, with wide range of applications. The un-mixing is usually performed by finding a rotation that optimizes a functional closely related to the differential entropy. In this paper we solve the linear ICA problem by analyzing the spectrum and eig...

Following Hartigan [1975], a cluster is defined as a connected component of the t-level set of the underlying density, i.e., the set of points for which the density is greater than t. A clustering algorithm which combines a density estimate with spectral clustering techniques is proposed. Our algorithm is composed of two steps. First, a nonparametric density estimate is used to extract the data...

We investigate the existence ofmultiple positive solutions for three-point boundary value problemof fractional differential equation with p-Laplacian operator −Dt β (φp(Dt α x))(t) = h(t)f(t, x(t)), t ∈ (0, 1), x(0) = 0,Dt γ x(1) = aDt γ x(ξ),Dt α x(0) = 0, where Dt β ,Dt α ,Dt γ are the standard Riemann-Liouville derivatives with 1 < α ≤ 2, 0 < β ≤ 1, 0 < γ ≤ 1, 0 ≤ α − γ − 1, ξ ∈ (0, 1) and t...

We employing a minimization arguments on appropriate Nehari manifolds, we obtain ground state solutionsfor non-local elliptic system driven by the fractional a(.)-Laplacian operator, with Dirichlet boundaryconditions type.

It is shown that analyses based on Symmetric Daubechies Wavelets (SDW) lead to a multiresolution form of the Laplacian operator. This property, which is related to the complex values of the SDWs, gives a way to new methods of image enhancement applications. After a brief recall of the construction and main properties of the SDW, we propose a representation of the sharpening operator at di erent...

In this work, we consider the Cauchy problem for u′ − Au = f with A the Laplacian operator on some Riemannian manifolds or a sublapacian on some Lie groups or some second order elliptic operators on a domain. We show the boundedness of the operator of maximal regularity f 7→ Au and its adjoint on appropriate Hardy spaces which we define and study for this purpose. As a consequence we reobtain t...