We discuss the relationship of the forward matrix element of the operator ψ̄ψ, related to the so-called sigma term, to the quark number. We show that in the naive quark model in the canonical formalism these quantities coincide in the limit of small average quark momenta. In the QCD parton model defined through light-front quantization this result is preserved at leading perturbative order but i...

Abstract. In this paper we recall a non-standard construction of the Borel sigma-algebraB in [0, 1] and construct a family of measures (in particular, Lebesgue measure) in B by a completely non-topological method. This approach, that goes back to Steinhaus, in 1923, is now used to introduce natural generalizations of the concept of normal numbers and explore their intrinsic probabilistic proper...

We give an overview of how a huge class of multisum identities can be proven and discovered with the summation package Sigma implemented in the computer algebra system Mathematica. General principles of symbolic summation are discussed. We illustrate the usage of Sigma by showing how one can find and prove a multisum identity that arose in the enumeration of rhombus tilings of a symmetric hexag...

In a short review of recent work, we discuss the general problem of constructing the actions of new conformal field theories from old conformal field theories. Such a construction follows when the old conformal field theory admits new conformal stress tensors in its chiral algebra, and it turns out that the new conformal field theory is generically a new spin-two gauge theory. As an example we ...

In this paper we investigate the non-linear sigma model arising in the reduction of D = 5 supergravity to D = 3, and present the application of this sigma model to supersymmetric black ring solutions in five-dimensional minimal supergravity. With the ansatz of stationary solutions with R×U(1)×U(1) isometry, we obtain a two-dimensional Lagrangian corresponding to geodesic motion of a string-like...

The performance tradeoffs of a smallsat synthetic aperture radar (SAR) system for maritime surveillance in the coastal waters New Zealand are investigated. lower costs platforms allow constellation SAR satellites that can be launched from using an existing local launch service provider. minimum image quality necessary to achieve desired detection is determined X-band satellite data. specified t...

We prove that every strictly positive endofunctor on the category of sets generated by Martin-LL of's extensional type theory has an initial algebra. This representation of inductively deened sets uses essentially the wellorderings introduced by Martin-LL of in \Constructive Mathematics and Computer Programming". 1 Background Martin-LL of 10] introduced a general set former for wellorderings in...

We study the stability of certain spectra under some algebraic conditions weaker than commutativity and we generalize many known commutative perturbation results. In particular, in a complex unital Banach algebra $$\mathcal {A},$$ prove that if $$x \in \hbox {comm}_{w}(a)$$ is nilpotent, then $$\sigma (x)=\sigma (x+a).$$ Among other things, {comm}(xy)\cup {comm}(yx)$$ or $$y\in for all $$x,y \m...