Image fusion is an important visualization technique of integrating coherent spatial and temporal information into a compact form. Laplacian fusion is a process that combines regions of images from different sources into a single fused image based on a salience selection rule for each region. In this paper, we proposed an algorithmic approach using a Laplacian and Gaussian pyramid to better loc...

For a k-uniform hypergraph H, we obtain some trace formulas for the Laplacian tensor of H, which imply that ∑n i=1 d s i (s = 1, . . . , k) is determined by the Laplacian spectrum of H, where d1, . . . , dn is the degree sequence of H. Using trace formulas for the Laplacian tensor, we obtain expressions for some coefficients of the Laplacian polynomial of a regular hypergraph. We give some spec...

The signless Laplacian separator of a graph is defined as the difference between the largest eigenvalue and the second largest eigenvalue of the associated signless Laplacian matrix. In this paper, we determine the maximum signless Laplacian separators of unicyclic, bicyclic and tricyclic graphs with given order.

195Pt and 1H NMR has been used to show that addition of chlorine and bromine to [Pt(CN)4]2_ in presence of perchloric acid in water results in cyanide and water scrambling with formation of eleven complexes of the type [Pt(CN)4-nCl(H2O)n+1](n-1)+ (n=0, 1, 2, 3, 4). Addition of NBu4OH ...

In this work, the effects of preparation methods such as CE oven, microwave irradiation, and ultrasound on the morphology, particle size and crystallinity of MIL-53(Fe) are firstly investigated. Furthermore, the methods are utilized to prepare Pt NPs@MIL-53(Fe). As a result, well-defined Pt NPs@MIL-53(Fe) prepared by microwave irradiation exhibits uniformed morphology, hig...

The method of iterated conformal maps for the study of diffusion limited aggregates (DLA) is generalized to the study of Laplacian growth patterns and related processes. We emphasize the fundamental difference between these processes: DLA is grown serially with constant size particles, while Laplacian patterns are grown by advancing each boundary point in parallel, proportional to the gradient ...

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...

We consider a one-phase free boundary problem involving a fractional Laplacian (−∆), 0 < α < 1, and we prove that “flat free boundaries” are C . We thus extend the known result for the case α = 1/2.

Rjk = R̄jk + ∇̄mD jk − ∇̄jD mk −Dn jkD nm −Dn mkD nj . (To see why this is true, just compute in local normal coordinates for ḡ!) From now on all components are tensorial (as opposed to local coordinate components.) The terms involving second covariant derivatives of the metric are: 1 2 g(−∇̄m∇̄lgjk +∇̄m∇̄kgjl +∇̄m∇̄jglk +∇̄j∇̄lgmk−∇̄j∇̄kgml−∇̄j∇̄mglk). The first term is a kind of Laplacian. The third and six...

Let D be a convex planar domain, symmetric about both the xand y-axes, which is strictly contained in (−a, a) × (−b, b) = Γ. It is proved that, unless D is a certain kind of rectangle, the difference (gap) between the first two eigenvalues of the Dirichlet Laplacian in D is strictly larger than the gap for Γ. We show how to give explicit lower bounds for the difference of the gaps.