267 research outputs found
Triangle areas in line arrangements
A widely investigated subject in combinatorial geometry, originated from
Erd\H{o}s, is the following. Given a point set of cardinality in the
plane, how can we describe the distribution of the determined distances? This
has been generalized in many directions. In this paper we propose the following
variants. Consider planar arrangements of lines. Determine the maximum
number of triangles of unit area, maximum area or minimum area, determined by
these lines. Determine the minimum size of a subset of these lines so that
all triples determine distinct area triangles.
We prove that the order of magnitude for the maximum occurrence of unit areas
lies between and . This result is strongly connected
to both additive combinatorial results and Szemer\'edi--Trotter type incidence
theorems. Next we show a tight bound for the maximum number of minimum area
triangles. Finally we present lower and upper bounds for the maximum area and
distinct area problems by combining algebraic, geometric and combinatorial
techniques.Comment: Title is shortened. Some typos and small errors were correcte
STUDY OF THE EFFECTIVENESS OF DIFFERENT GROUNDCOVER MATTER ON MACRONUTRIENT CONTENT OF LEAF IN APPLE ORCHARD IN EAST HUNGARY
This study investigated the effects of different groundcover materials on soil and plant nutrition. Trees of apple cv. ‘Idared’/MM.106 (Malus domestica Borkh.) were planted into lowland chernozem soil in the spring of 1999. Applied treatments can be divided into two groups: different livestock manures and mulches. Soil strips of 150 cm width were covered either with straw, different livestock manure, black plastic foil, pine bark mulch or were without cover i.e. clean
cultivation as a check. Leaf and soil samples were collected for chemical analysis. It was found that all groundcover treatments induced an increase in leaf nitrogen, sulphur and calcium. Leaf magnesium was not affected so obviously by different groundcover treatments. Leaf potassium was not affected by applying different livestock manures, except horse manure but lower in mulch treatments compared to the control. Leaf phosphorous was decreased by treatments except using horse manure. Examination of ratios of nutrients showed that there were disharmonies in the available nutrients supply of soil. The best results were obtained by applying horse manure
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
Multi-jet cross sections in deep inelastic scattering at next-to-leading order
We present the perturbative prediction for three-jet production cross section
in DIS at the NLO accuracy. We study the dependence on the renormalization and
factorization scales of exclusive three-jet cross section. The perturbative
prediction for the three-jet differential distribution as a function of the
momentum transfer is compared to the corresponding data obtained by the H1
collaboration at HERA.Comment: 5 pages, 3 figure
Next-to-Leading Order Calculation of Four-Jet Shape Variables
We present the next-to-leading order calculation of two four-jet event shape
variables, the D parameter and acoplanarity differential distributions. We find
large, more than 100% radiative corrections. The theoretical prediction for the
D parameter is compared to L3 data obtained at the Z peak and corrected to
hadron level.Comment: 11 pages, latex with aps, epsf, rotate styles 3 tables, 3 figures
typo in eq. 10 corrected, note and reference added, introduction revise
Three-jet cross sections in hadron-hadron collisions at next-to-leading order
We present a new QCD event generator for hadron collider which can calculate
one-, two- and three-jet cross sections at next-to-leading order accuracy. In
this letter we study the transverse energy spectrum of three-jet hadronic
events using the kT algorithm. We show that the next-to-leading order
correction significantly reduces the renormalization and factorization scale
dependence of the three-jet cross section.Comment: 4 pages, 4 figures, REVTEX
General subtraction method for numerical calculation of one-loop QCD matrix elements
We present a subtraction scheme for eliminating the ultraviolet, soft, and
collinear divergences in the numerical calculation of an arbitrary one-loop QCD
amplitude with an arbitrary number of external legs. The subtractions consist
of local counter terms in the space of the four-dimensional loop momentum. The
ultraviolet subtraction terms reproduce MSbar renormalization. The key point in
the method for the soft and collinear subtractions is that, although the
subtraction terms are defined graph-by-graph and the matrix element is also
calculated graph-by-graph, the sum over graphs of the integral of each the
subtraction term can be evaluated analytically and provides the well known
simple pole structure that arises from subtractions from real emission graphs,
but with the opposite sign.Comment: 38 pages, 10 figures, axodraw styl
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