11,053 research outputs found
Ordering variable for parton showers
The parton splittings in a parton shower are ordered according to an ordering
variable, for example the transverse momentum of the daughter partons relative
to the direction of the mother, the virtuality of the splitting, or the angle
between the daughter partons. We analyze the choice of the ordering variable
and conclude that one particular choice has the advantage of factoring softer
splittings from harder splittings graph by graph in a physical gauge.Comment: 28 pages, 5 figure
3-Nets realizing a group in a projective plane
In a projective plane PG(2,K) defined over an algebraically closed field
K of characteristic 0, we give a complete classification of 3-nets realizing a finite
group. An infinite family, due to Yuzvinsky (Compos. Math. 140:1614–1624, 2004),
arises from plane cubics and comprises 3-nets realizing cyclic and direct products of
two cyclic groups. Another known infinite family, due to Pereira and Yuzvinsky (Adv.
Math. 219:672–688, 2008), comprises 3-nets realizing dihedral groups.We prove that
there is no further infinite family. Urzúa’s 3-nets (Adv. Geom. 10:287–310, 2010)
realizing the quaternion group of order 8 are the unique sporadic examples.
If p is larger than the order of the group, the above classification holds in characteristic
p >0 apart from three possible exceptions Alt4, Sym4, and Alt5.
Motivation for the study of finite 3-nets in the complex plane comes from the study
of complex line arrangements and from resonance theory; see (Falk and Yuzvinsky
in Compos. Math. 143:1069–1088, 2007; Miguel and Buzunáriz in Graphs Comb.
25:469–488, 2009; Pereira and Yuzvinsky in Adv. Math. 219:672–688, 2008; Yuzvinsky in Compos. Math. 140:1614–1624, 2004; Yuzvinsky in Proc. Am. Math. Soc.
137:1641–1648, 2009
Classification of k-nets
A finite k-net of order n is an incidence structure consisting of k >= 3 pairwise disjoint classes of lines, each of size n, such that every point incident with two lines from distinct classes is incident with exactly one line from each of the k classes. Deleting a line class from a k-net, with k >= 4, gives a derived (k 1)-net of the same order. Finite k-nets embedded in a projective plane PG(2, K) coordinatized by a field K of characteristic 0 only exist for k = 3, 4, see Korchmaros et al. (2014). In this paper, we investigate 3-nets embedded in PG(2, K) whose line classes are in perspective position with an axis r, that is, every point on the line r incident with a line of the net is incident with exactly one line from each class. The problem of determining all such 3-nets remains open whereas we obtain a complete classification for those coordinatizable by a group. As a corollary, the (unique) 4-net of order 3 embedded in PG(2, K) turns out to be the only 4-net embedded in PG(2, K) with a derived 3-net which can be coordinatized by a group. Our results hold true in positive characteristic under the hypothesis that the order of the k-net considered is smaller than the characteristic of K. (C) 2015 Elsevier Ltd. All rights reserved
Operator algebra quantum homogeneous spaces of universal gauge groups
In this paper, we quantize universal gauge groups such as SU(\infty), as well
as their homogeneous spaces, in the sigma-C*-algebra setting. More precisely,
we propose concise definitions of sigma-C*-quantum groups and sigma-C*-quantum
homogeneous spaces and explain these concepts here. At the same time, we put
these definitions in the mathematical context of countably compactly generated
spaces as well as C*-compact quantum groups and homogeneous spaces. We also
study the representable K-theory of these spaces and compute it for the quantum
homogeneous spaces associated to the universal gauge group SU(\infty).Comment: 14 pages. Merged with [arXiv:1011.1073
Smoking as a permissive factor of periodontal disease in psoriasis
published_or_final_versio
H-CMRH: a novel inner product free hybrid Krylov method for large-scale inverse problems
This study investigates the iterative regularization properties of two Krylov
methods for solving large-scale ill-posed problems: the changing minimal
residual Hessenberg method (CMRH) and a novel hybrid variant called the hybrid
changing minimal residual Hessenberg method (H-CMRH). Both methods share the
advantages of avoiding inner products, making them efficient and highly
parallelizable, and particularly suited for implementations that exploit
randomization and mixed precision arithmetic. Theoretical results and extensive
numerical experiments suggest that H-CMRH exhibits comparable performance to
the established hybrid GMRES method in terms of stabilizing semiconvergence,
but H-CMRH has does not require any inner products, and requires less work and
storage per iteration
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