This paper aims to develop a linearly implicit structure-preserving numerical scheme for the space fractional sine-Gordon equation, which is based on newly developed invariant energy quadratization method. First, we reformulate equation as canonical Hamiltonian system by virtue of variational derivative functional with Laplacian. Then, utilize centered difference formula discrete equivalent der...

1 Introduction The inverse spectral problem on a Riemannian manifold (M, g), possibly with boundary, is to determine as much as possible of the geometry of (M, g) from the spectrum of its Laplacian ∆ g (with some given boundary conditions). The special inverse problem of Kac is to determine a Euclidean domain Ω ⊂ R n up to isometry from the spectrum Spec B (Ω) of its Laplacian ∆ B with Dirichle...

Our aim is to propose a multi-dimensional operator framework that provides a bridge between approximation theory (in particular, the construction of polyharmonic splines and wavelets) and the investigation of self-similar stochastic processes. Our investigation starts with the identification of the linear differential operators that are translation-, scaleand rotation-invariant; these are the f...

The Yamabe invariant of a smooth compact manifold is by definition the supremum of the scalar curvatures of unit-volume Yamabe metrics on the manifold. For an explicit infinite class of 4-manifolds, we show that this invariant is positive but strictly less than that of the 4-sphere. This is done by using spin Dirac operators to control the lowest eigenvalue of a perturbation of the Yamabe Lapla...

Gutman et al. introduced the concepts of energy E (G) and Laplacian energy EL(G) for a simple graph G, and furthermore, they proposed a conjecture that for every graph G, E (G) is not more than EL(G). Unfortunately, the conjecture turns out to be incorrect since Liu et al. and Stevanović et al. constructed counterexamples. However, So et al. verified the conjecture for bipartite graphs. In the ...

In this article, we study and settle several structural questions concerning the exact solvability of the Olshanetsky-Perelomov quantum Hamiltonians corresponding to an arbitrary root system. We show that these operators can be written as linear combinations of certain basic operators admitting infinite flags of invariant subspaces, namely the Laplacian and the logarithmic gradient of invariant...

The Yamabe invariant of a smooth compact manifold is by definition the supremum of the scalar curvatures of unit-volume Yamabe metrics on the manifold. For an explicit infinite class of 4-manifolds, we show that this invariant is positive but strictly less than that of the 4-sphere. This is done by using spinc Dirac operators to control the lowest eigenvalue of a perturbation of the Yamabe Lapl...

The emission of ee pairs from C+C collisions at an incident energy of 1 GeV per nucleon has been investigated. The measured production probabilities, spanning from the π-Dalitz to the ρ/ω invariant-mass region, display a strong excess above the cocktail of standard hadronic sources. The bombarding-energy dependence of this excess is found to scale like pion production, rather than like eta prod...

The emission of ee pairs from C+C collisions at an incident energy of 1 GeV per nucleon has been investigated. The measured production probabilities, spanning from the π-Dalitz to the ρ/ω invariant-mass region, display a strong excess above the cocktail of standard hadronic sources. The bombarding-energy dependence of this excess is found to scale like pion production, rather than like eta prod...