229 research outputs found
Irreducible Triangulations are Small
A triangulation of a surface is \emph{irreducible} if there is no edge whose
contraction produces another triangulation of the surface. We prove that every
irreducible triangulation of a surface with Euler genus has at most
vertices. The best previous bound was .Comment: v2: Referees' comments incorporate
Introducing TAXI: a Transportable Array for eXtremely large area Instrumentation studies
A common challenge in many experiments in high-energy astroparticle physics
is the need for sparse instrumentation in areas of 100 km2 and above, often in
remote and harsh environments. All these arrays have similar requirements for
read-out and communication, power generation and distribution, and
synchronization. Within the TAXI project we are developing a transportable,
modular four-station test-array that allows us to study different approaches to
solve the aforementioned problems in the laboratory and in the field.
Well-defined interfaces will provide easy interchange of the components to be
tested and easy transport and setup will allow in-situ testing at different
sites. Every station consists of three well-understood 1 m2 scintillation
detectors with nanosecond time resolution, which provide an air shower trigger.
An additional sensor, currently a radio antenna for air shower detection in the
100 MHz band, is connected for testing and calibration purposes. We introduce
the TAXI project and report the status and performance of the first TAXI
station deployed at the Zeuthen site of DESY.Comment: 4 pages, 3 figures, presented at ARENA 2014, Annapolis, MD, June 201
Conformal Parametrisation of Loxodromes by Triples of Circles
We provide a parametrisation of a loxodrome by three specially arranged
cycles. The parametrisation is covariant under fractional linear
transformations of the complex plane and naturally encodes conformal properties
of loxodromes. Selected geometrical examples illustrate the usage of
parametrisation. Our work extends the set of objects in Lie sphere
geometry---circle, lines and points---to the natural maximal
conformally-invariant family, which also includes loxodromes.Comment: 14 pages. 9 PDF in four figures, AMS-LaTe
The integrability of Lie-invariant geometric objects generated by ideals in the Grassmann algebra
We investigate closed ideals in the Grassmann algebra serving as bases of
Lie-invariant geometric objects studied before by E. Cartan. Especially, the E.
Cartan theory is enlarged for Lax integrable nonlinear dynamical systems to be
treated in the frame work of the Wahlquist Estabrook prolongation structures on
jet-manifolds and Cartan-Ehresmann connection theory on fibered spaces. General
structure of integrable one-forms augmenting the two-forms associated with a
closed ideal in the Grassmann algebra is studied in great detail. An effective
Maurer-Cartan one-forms construction is suggested that is very useful for
applications. As an example of application the developed Lie-invariant
geometric object theory for the Burgers nonlinear dynamical system is
considered having given rise to finding an explicit form of the associated Lax
type representation
The maximum number of cliques in a graph embedded in a surface
This paper studies the following question: Given a surface and an
integer , what is the maximum number of cliques in an -vertex graph
embeddable in ? We characterise the extremal graphs for this question,
and prove that the answer is between and , where is the maximum integer such that the
complete graph embeds in . For the surfaces ,
, , , ,
and we establish an exact answer
Progress and status of APEmille
We report on the progress and status of the APEmille project: a SIMD parallel
computer with a peak performance in the TeraFlops range which is now in an
advanced development phase. We discuss the hardware and software architecture,
and present some performance estimates for Lattice Gauge Theory (LGT)
applications.Comment: Talk presented at LATTICE97, 3 pages, Late
Background Geometry in Gauge Gravitation Theory
Dirac fermion fields are responsible for spontaneous symmetry breaking in
gauge gravitation theory because the spin structure associated with a tetrad
field is not preserved under general covariant transformations. Two solutions
of this problem can be suggested. (i) There exists the universal spin structure
such that any spin structure associated with a tetrad field
is a subbundle of the bundle . In this model, gravitational fields
correspond to different tetrad (or metric) fields. (ii) A background tetrad
field and the associated spin structure are fixed, while
gravitational fields are identified with additional tensor fields q^\la{}_\m
describing deviations \wt h^\la_a=q^\la{}_\m h^\m_a of . One can think of
\wt h as being effective tetrad fields. We show that there exist gauge
transformations which keep the background tetrad field and act on the
effective fields by the general covariant transformation law. We come to
Logunov's Relativistic Theory of Gravity generalized to dynamic connections and
fermion fields.Comment: 12 pages, LaTeX, no figure
Irreducible triangulations of surfaces with boundary
A triangulation of a surface is irreducible if no edge can be contracted to
produce a triangulation of the same surface. In this paper, we investigate
irreducible triangulations of surfaces with boundary. We prove that the number
of vertices of an irreducible triangulation of a (possibly non-orientable)
surface of genus g>=0 with b>=0 boundaries is O(g+b). So far, the result was
known only for surfaces without boundary (b=0). While our technique yields a
worse constant in the O(.) notation, the present proof is elementary, and
simpler than the previous ones in the case of surfaces without boundary
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The production of J//psi/ and associated particles in the collision of 530 GeV/c protons and pions with nuclear targets
We have studied the production of the J//psi/ and associated particles using the E672/E706 spectrometer at Fermilab. Preliminary results are presented from the first run in 1987--1988 with 530 GeV/c p//pi//sup +/ and /pi//sup /minus// beams on a variety of nuclear targets. The A-dependance of J//psi/ production with /pi//sup /minus// beam was found to agree with an A/sup /alpha// parametrization with /alpha/ = 0.85 /plus minus/ 0.06 for X/sub F/ > 0.1. We have found that (41 /plus minus/ 22)% of the J//psi/'s produced in the p//pi//sup +/ beam are consistent with the radiative decay /chi/ /yields/J//psi/+/gamma/. The future analysis goals of the experiment are also discussed. 10 refs., 9 figs
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