It is known that there are no local scalar Lie fields in more than two dimensions. Bilocal fields, however, which naturally arise in conformal operator product expansions, do generate infinite Lie algebras. It is demonstrated that these Lie algebras of local observables admit highly reducible unitary positive energy representations in a Fock space. The multiplicity of their irreducible componen...

In this paper, we study stochastic orders of scalar products of random vectors. Based on the study of Ma (2000), we first obtain more general conditions under which linear combinations of random variables can be ordered in the increasing convex order. As an application of this result, we consider the scalar product of two random vectors which separates the severity effect and the frequency effe...

A recursive algebraic method which allows to obtain the Feynman or Schwinger parametric representation of a generic L-loops and (E+1) external lines diagram, in a scalar φ⊕φ theory, is presented. The representation is obtained starting from an Initial Parameters Matrix (IPM ), which relates the scalar products between internal and external momenta, and which appears explicitly when this paramet...

We perform a QCD sum rule analysis for the light scalar meson σ (f0(600)) with a tetraquark current related to the instanton picture for QCD vacuum. We demonstrate that instanton current, including equal weights of scalar and pseudoscalar diquarkantidiquarks, leads to a strong cancelation between the contributions of high dimension operators in the operator product expansion (OPE). Furthermore,...

We perform a systematic investigation of free-scalar realisations of the Zamolodchikov W 3 algebra in which the operator product of two spin-three generators contains a non-zero operator of spin four which has vanishing norm. This generalises earlier work where such an operator was required to be absent. By allowing this spin-four null operator we obtain several realisations of the W 3 algebra ...

In this paper, we propose a new mathematical model for image processing. It is a logarithmical one. We consider the bounded interval (-1, 1) as the set of gray levels. Firstly, we define two operations: addition 〈+〉 and real scalar multiplication 〈×〉. With these operations, the set of gray levels becomes a real vector space. Then, defining the scalar product (.|.) and the norm || . ||, we obtai...

Many combinatorial generating functions can be expressed as combinations of symmetric functions, or extracted as sub-series and specializations from such combinations. Gessel has outlined a large class of symmetric functions for which the resulting generating functions are D-finite. We extend Gessel’s work by providing algorithms that compute differential equations these generating functions sa...

In this paper, we examine the solution of second-order, scalar boundary value problems on nonuniform meshes. We show that certain commonly used difference schemes yield second-order accurate solutions despite the fact that their truncation error is of lower order. This result illuminates a limitation of the standard stability, consistency proof of convergence for difference schemes defined on n...

As a toy model for the implementation of the diffeomorphism constraint, the interpretation of the resulting states, and the treatment of ordering ambiguities in loop quantum gravity, we consider the Hilbert space of spatially diffeomorphism invariant states for a scalar field. We give a very explicit formula for the scalar product on this space, and discuss its structure. Then we turn to the qu...