Related papers: Factorization is not violated
Let $\M(A,\theta)$ be a free partially commutative monoid. We give here a necessary and sufficient condition on a subalphabet $B\subset A$ such that the right factor of a bisection $\M(A,\theta)=\M(B,\theta\_B).T$ be also partially…
In this note, we prove the existence of a set of $n$-fold Pfister forms of cardinality $2^n$ over $\mathbb{C}(x_1,\dots,x_n)$ which do not share a common $(n-1)$-fold factor. This gives a negative answer to a question raised by Becher. The…
QCD analysis of F_2^{\gamma}(x,Q^2) is revisited. It is emphasized that the presence of the inhomogeneous term in the evolution equations for quark distribution functions of the photon implies important difference in the way factorization…
Description of hadronic reactions at high energies is conventionally done on basis of QCD factoriza- tion so that factorization convolutions involve non-perturbative inputs mimicking non-perturbative contributions and perturbative evolution…
We consider an extension of the modal logic of transitive closure K+ with some inifinitary derivations and present a sequent calculus for this extension, which allows non-well-founded proofs. For the given calculus, we obtain the…
We find and prove a factorization formula for certain Macdonald Littlewood-Richardson coefficients $c_{\lambda\mu}^{\nu}(q,t)$. Namely, we consider the case that the Kostka number $K_{\mu, \nu -\lambda}$ is $1$. This settles a particular…
Reported is a factorization theorem for large-s behavior of total cross sections obtained in a straightforward fashion from ordinary perturbation theory. The theorem extends the standard factorization results for the Bjorken and Drell-Yan…
We apply the 't Hooft $\bar{MS}$-based scheme to study the scheme-dependence of the QCD generalization of Crewther relation for the product of the normalised non-singlet perturbative contributions to the $e^+e^-$-annihilation Adler function…
The main goal of the present paper is two-fold. First we extend the theory of toroidal embeddings introduced by Kempf, Knudsen, Mumford and Saint-Donat to the class of toroidal varieties with stratifications (which is the main body of the…
Heavy-to-light transition form factors at large recoil energy of the light meson have been conjectured to obey a factorization formula, where the set of form factors is reduced to a smaller number of universal form factors up to…
Factorizations of monoids are studied. Two necessary and sufficient conditions in terms of so-called descent 1-cocyles for a monoid to be factorized through two submonoids are found. A full classification of those factorizations of a monoid…
We consider the factorisation problem for bialgebras: when a bialgebra $K$ factorises as $K=HL$, where $H$ and $L$ are algebras and coalgebras (but not necessarly bialgebras). Given two maps $R: H\ot L\to L\ot H$ and $W:L\ot H\to H\ot L$,…
Recent works have discussed the violation of factorization and universality in hadronic hard scattering processes aimed at measurements of T-odd distributions. We use simple arguments to show that it is possible to restore an approximate…
We establish a form of the h-principle for the existence of foliations quasi-complementary to a given one; the same methods also provide a proof of the classical Mather-Thurston theorem.
A complication in proving factorization theorems in Feynman gauge is that individual graphs give a super-leading power of the hard scale when all the gluons inducing the hard scattering are longitudinally polarized. With the aid of an…
In a famous paper, R. A. Gordon proved a dozen theorems using tagged partitions and Cousin's theorem. The purpose of this paper is to present several classical results using the key-lemma underlying Cousin's theorem.
Using Newton polygons, a key factorization result for polynomials over discrete valuation domains is proved, which in particular yields new irreducibility criteria including a generalization of the classical irreducibility criterion of…
We present a factorization formula for valence quark distributions in a hadron in x-->1 limit. For the example of pion, we arrive at the form of factorization by analyzing momentum flow in the leading and high-order Feynman diagrams. The…
We have constructed a concrete example of a non-factorable positive operator. As a result, for the well-known problems (Ringrose, Kadison and Singer problems) we replace existence theorems by concrete examples.
This paper introduces a Laws of Form version of the Quaternions. We call this the Q-Calculus, a 16-valued extension of Laws of Form (LoF) which is closely related to the BF Calculus (where we have a single square root of the mark) and the…