Related papers: An operator expansion for the elastic limit
The behavior under conformal change of the renormalized volume coefficients associated to a pseudo-Riemannian metric is investigated. It is shown that they define second order fully nonlinear operators in the conformal factor whose…
For arbitrary spacetime dimension a systematic procedure is carried on to uniquely decompose nonlocal light-cone operators into harmonic operators of well defined twist. Thereby, harmonic tensor polynomials up to rank 2 are introduced.…
We study the effective potential for composite operators. Introducing a source coupled to the composite operator, we define the effective potential by a Legendre transformation. We find that in three or fewer dimensions, one can use the…
The Roper--Suffridge extension operator and its modifications are powerful tools to construct biholomorphic mappings with special geometric properties. The first purpose of this paper is to analyze common properties of different extension…
The strain-energy formulation of nonlinear elasticity can be extended to the case of significant compression by modulating suitable strain energy terms by a function of relative volume. For isotropic materials this can be accomplished by…
The discovery of configurational forces acting on elastic structures and its initial applications are reviewed. Configurational forces are related to the possibility that an elastic structure can change its configuration, thus inducing a…
We study extension theorems for Lipschitz-type operators acting on metric spaces and with values on spaces of integrable functions. Pointwise domination is not a natural feature of such spaces, and so almost everywhere inequalities and…
We discuss the role of nucleon and its excited state poles in the twist expansion of the nucleon structure function moments. We find that the nucleon pole contribution was overestimated in previous analyses by a factor of two. Inclusion of…
The concept of scattering coefficients has played a pivotal role in a broad range of inverse scattering and imaging problems in acoustic, and electromagnetic media. In view of their promising applications in inverse problems related to…
We study the asymptotic behaviour of a properly normalized time-changed multidimensional Wiener process; the time change is given by an additive functional of the Wiener process itself. At the level of generators, the time change means that…
The logarithmic Laplacian on the (whole) N-dimensional Euclidean space is defined as the first variation of the fractional Laplacian of order 2s at s=0 or, alternatively, as a singular Fourier integral operator with logarithmic symbol.…
Higher twist corrections to the structure function F_2 at small x are studied for the case of a flat initial condition for the twist-two QCD evolution in the next-to-leading order approximation. We present an analytical parameterization of…
We consider various systematic ways of defining unbounded operator valued integrals of complex functions with respect to (mostly) positive operator measures and positive sesquilinear form measures, and investigate their relationships to…
Infrared renormalons and $1/Q^2$ power corrections in deep-inelastic sum rules are studied. The renormalization of operators with power divergence are discussed. The higher-twist terms in the operator product expansion are shown to account…
The paper introduces Laplace-type operators for functions defined on the tangent space of a Finsler Lie algebroid, using a volume form on the prolongation of the algebroid. It also presents the construction of a horizontal Laplace operator…
In this paper, we investigate Li-Yorke composition operators and some of their variations on Lorentz spaces. Further, we also study expansive composition operators on these spaces. The work of the paper is essentially based on the work in…
Lifting operators play an important role in starting a lattice Boltzmann model from a given initial density. The density, a macroscopic variable, needs to be mapped to the distribution functions, mesoscopic variables, of the lattice…
Fixed-point equations with Lipschitz operators have been studied for more than a century, and are central to problems in mathematical optimization, game theory, economics, and dynamical systems, among others. When the Lipschitz constant of…
We consider the short-distance behaviour of the product of the Noether O(N) currents in the lattice nonlinear sigma-model. We compare the numerical results with the predictions of the operator product expansion, using one-loop perturbative…
In this work, we investigate the effects of logarithms on the asymptotic behavior of power expansion/OPE in supper-renormalizable QFTs. We performed a careful investigation of the large $p^2$ expansion of a scalar-scalar two-point function…