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 $g\geq1$ has at most $13g-4$ vertices. The best previous bound was $171g-72$.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 $\Sigma$ and an integer $n$, what is the maximum number of cliques in an $n$-vertex graph embeddable in $\Sigma$? We characterise the extremal graphs for this question, and prove that the answer is between $8(n-\omega)+2^{\omega}$ and $8n+{3/2} 2^{\omega}+o(2^{\omega})$, where $\omega$ is the maximum integer such that the complete graph $K_\omega$ embeds in $\Sigma$. For the surfaces $\mathbb{S}_0$, $\mathbb{S}_1$, $\mathbb{S}_2$, $\mathbb{N}_1$, $\mathbb{N}_2$, $\mathbb{N}_3$ and $\mathbb{N}_4$ 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 $S\to X$ such that any spin structure $S^h\to X$ associated with a tetrad field $h$ is a subbundle of the bundle $S\to X$. In this model, gravitational fields correspond to different tetrad (or metric) fields. (ii) A background tetrad field $h$ and the associated spin structure $S^h$ 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 $h$. One can think of \wt h as being effective tetrad fields. We show that there exist gauge transformations which keep the background tetrad field $h$ 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

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