I present a full leading–order calculation of F2(x,Q ) and FL(x,Q ), including contributions not only from leading order in αs, but also from the leading power of αs for each order in ln(1/x). The calculation is ordered according to the inputs and evolution of the structure functions, and the perturbative form of the inputs is determined. I compare the results of fits to data to those using con...

The notion of absorbent ordered filters in implicative semigroupsis introduced, and its fuzzification is considered. Relations among (fuzzy) orderedfilters, (fuzzy) absorbent ordered filters, and (fuzzy) positive implicativeordered filters are stated. The extensionproperty for (fuzzy) absorbent orderedfilters is established. Conditions for (fuzzy) ordered filters to be (fuzzy)absorbent ordered ...

We prove the following theorem: For a partially ordered set Q such that every countable subset of Q has a strict upper bound, there is a forcing notion satisfying the countable chain condition such that, in the forcing extension, there is a basis of the null ideal of the real line which is order-isomorphic to Q with respect to set-inclusion. This is a variation of Hechler’s classical result in ...

Abstract We construct a family of partially ordered sets (posets) that are q-analogs of the set partition lattice. They are different from the q-analogs proposed by Dowling [5]. One of the important features of these posets is that their Whitney numbers of the first and second kind are just the q-Stirling numbers of the first and second kind, respectively. One member of this family [4] can be c...

Sum rules for twist-3 distributions are reexamined. Integral relations between twist-3 and twist-2 parton distributions suggest the possibility for a δ-function at x = 0. We confirm and clarify this result by constructing hL and h 3 L (quark-gluon interaction dependent part of hL) explicitly from their moments for a one-loop dressed massive quark. The physics of these results is illustrated by ...

We prove the following theorem: For a partially ordered set Q such that every countable subset of Q has a strict upper bound, there is a forcing notion satisfying the countable chain condition such that, in the forcing extension, there is a basis of the null ideal of the real line which is order-isomorphic to Q with respect to set-inclusion. This is a variation of Hechler’s classical result in ...

Since the extensible markup language XML emerged as a new standard for information representation and exchange on the Internet, the problem of storing, indexing, and querying XML documents has been among the major issues of database research. In this paper, we study the twig pattern matching and discuss a new algorithm for processing ordered twig pattern queries. The time complexity of the algo...

Employing a deep convolutional neural network (deep CNN) trained on spin configurations of the 2D Ising model and temperatures, we examine whether CNN can detect phase transition $q$-state Potts model. To this end, generate binarized images ($q\ge 3$) by replacing variables $\{0,1,\dots,\lfloor q/2\rfloor-1\}$ $\{\lfloor q/2\rfloor,\dots,q-1\}$ with $\{0\}$ $\{1\}$, respectively. Then, input th...

We calculate the large-q expansion of the second moment correlation length at the first order phase transition point of the q-state Potts model in two dimensions both in the ordered and disordered phases to order 21 in 1/ √ q. They coincide with each other to the third term of the series but differ a little in higher orders. Numerically the ratio of the second moment correlation length in the t...

In this paper we study the partially ordered set Q of cells in Rietsch’s [20] cell decomposition of the totally nonnegative part of an arbitrary flag variety P ≥0 . Our goal is to understand the geometry of P ≥0 : Lusztig [13] has proved that this space is contractible, but it is unknown whether the closure of each cell is contractible, and whether P ≥0 is homeomorphic to a ball. The order comp...