Division, adjoints, and dualities of bilinear maps

The distributive property can be studied through bilinear maps and various morphisms between these maps. The adjoint-morphisms between bilinear maps establish a complete abelian category with projectives and admits a duality. Thus the adjoint category is not a module category but nevertheless it is suitably familiar. The universal properties have geometric perspectives. For example, products are orthogonal sums. The bilinear division maps are the simple bimaps with respect to nondegenerate adjoint-morphisms. That formalizes the understanding that the atoms of linear geometries are algebraic objects with no zero-divisors. Adjoint-isomorphism coincides with principal isotopism; hence, nonassociative division rings can be studied within this framework. This also corrects an error in an earlier pre-print; see Remark 2.11

Indecomposable knots and concordance

R. C. Kirby and W. B. R. Lickorish have proved (cf. (4)) that any classical knot is concordant to an indecomposable knot. In the present note we show that this statement is also true for higher dimensional knots: more precisely, for any higher-dimensional knot K there exist infinitely many non-isotopic indecomposable simple knots which are concordant to K. This, together with the result of Kirby and Lickorish, gives a complete solution of problem 13 of (1

Forms in odd degree extensions and selfdual normal bases

Introduction. Let K be a field. Springer has proved that an ani-sotropic quadratic form over K is also anisotropic over any odd degree extension of K (see [31], [14]). If the characteristic of K is not 2, this implies that two nonsingular quadratic forms that become isomorphic over an extension of odd degree of K are already isomorphic over

Relativistic Proton Production During the 14 July 2000 Solar Event: The Case for Multiple Source Mechanisms

Protons accelerated to relativistic energies by transient solar and interplanetary phenomena caused a ground-level cosmic ray enhancement on 14 July 2000, Bastille Day. Near-Earth spacecraft measured the proton flux directly and ground-based observatories measured the secondary responses to higher energy protons. We have modelled the arrival of these relativistic protons at Earth using a technique which deduces the spectrum, arrival direction and anisotropy of the high-energy protons that produce increased responses in neutron monitors. To investigate the acceleration processes involved we have employed theoretical shock and stochastic acceleration spectral forms in our fits to spacecraft and neutron monitor data. During the rising phase of the event (10:45 UT and 10:50 UT) we find that the spectrum between 140 MeV and 4 GeV is best fitted by a shock acceleration spectrum. In contrast, the spectrum at the peak (10:55 UT and 11:00 UT) and in the declining phase (11:40 UT) is best fitted with a stochastic acceleration spectrum. We propose that at least two acceleration processes were responsible for the production of relativistic protons during the Bastille Day solar event: (1) protons were accelerated to relativistic energies by a shock, presumably a coronal mass ejection (CME). (2) protons were also accelerated to relativistic energies by stochastic processes initiated by magnetohydrodynamic (MHD) turbulence.Comment: 38 pages, 9 figures, accepted for publication in the Astrophysical Journal, January, 200

Propagation of Ultra-High Energy Cosmic Rays above 101910^{19} eV in a Structured Extragalactic Magnetic Field and Galactic Magnetic Field

We present numerical simulations on propagation of Ultra-High Energy Cosmic Rays (UHECRs) above $10^{19}$ eV in a structured extragalactic magnetic field (EGMF) and simulate their arrival distributions at the earth. We use the IRAS PSCz catalogue in order to construct a model of the EGMF and source models of UHECRs, both of which reproduce the local structures observed around the Milky Way. We also consider modifications of UHECR arrival directions by the galactic magnetic field. We follow an inverse process of their propagation from the earth and record the trajectories. This enables us to calculate only trajectories of UHECRs arriving at the earth, which saves the CPU time. From these trajectories and our source models, we construct arrival distributions of UHECRs and calculate the harmonic amplitudes and the two point correlation functions of them. We estimate number density of sources which reproduces the Akeno Ground Air Shower Array (AGASA) observation best. As a result, we find that the most appropriate number density of the sources is $\sim 5 \times 10^{-6}$ Mpc$^{-3}$. This constrains the source candidates of UHECRs. We also demonstrate skymaps of their arrival distribution with the event number expected by future experiments and examine how the EGMF affects their arrival distribution. A main result is diffusion of clustering events which are obtained from calculations in the absence of the EGMF. This tendency allows us to reproduce the observed two point correlation function better.Comment: 13 pages, 14 figures. Revised version, accepted for publication in the Astrophysical Journal. Higher resolution image of fig.5 will be in the published versio

Assessing the Role of Computer Simulation in Chemistry Learning

Simulation and Computation make a versatile teaching strategy, and may be an important way to motivate students and lecturers to achieve meaningful learning. Indeed, this work refers to a study whose main objective is to set the influence that a teaching approach based on the use of computer simulation would have on students’ learning, compared to the one in use today. This work involved the participation of two classes of 11th grade at a Secondary School in Lisbon, Portugal, where the main goal is to teach a specific topic to an untried student’s group. With regard to the simulation environment, it will be grounded on a Proof Theoretical approach to Knowledge Representation and Reasoning, which caters for the handling of incomplete, unknown or even self-contradictory information or knowledge

Ultra high energy cosmic rays and the large scale structure of the galactic magnetic field

We study the deflection of ultra high energy cosmic ray protons in different models of the regular galactic magnetic field. Such particles have gyroradii well in excess of 1 kpc and their propagation in the galaxy reflects only the large scale structure of the galactic magnetic field. A future large experimental statistics of cosmic rays of energy above 10$^{19}$ eV could be used for a study of the large scale structure of the galactic magnetic field if such cosmic rays are indeed charged nuclei accelerated at powerful astrophysical objects and if the distribution of their sources is not fully isotropic.Comment: 9 pages LaTeX file (AASTeX), 4 eps figures, submitted to The Astrophysical Journa

Secure Data Transfer Guidance for Industrial Control and SCADA Systems

This document was developed to provide guidance for the implementation of secure data transfer in a complex computational infrastructure representative of the electric power and oil and natural gas enterprises and the control systems they implement. For the past 20 years the cyber security community has focused on preventative measures intended to keep systems secure by providing a hard outer shell that is difficult to penetrate. Over time, the hard exterior, soft interior focus changed to focus on defense-in-depth adding multiple layers of protection, introducing intrusion detection systems, more effective incident response and cleanup, and many other security measures. Despite much larger expenditures and more layers of defense, successful attacks have only increased in number and severity. Consequently, it is time to re-focus the conventional approach to cyber security. While it is still important to implement measures to keep intruders out, a new protection paradigm is warranted that is aimed at discovering attempted or real compromises as early as possible. Put simply, organizations should take as fact that they have been, are now, or will be compromised. These compromises may be intended to steal information for financial gain as in the theft of intellectual property or credentials that lead to the theft of financial resources, or to lie silent until instructed to cause physical or electronic damage and/or denial of services. This change in outlook has been recently confirmed by the National Security Agency [19]. The discovery of attempted and actual compromises requires an increased focus on monitoring events by manual and/or automated log monitoring, detecting unauthorized changes to a system's hardware and/or software, detecting intrusions, and/or discovering the exfiltration of sensitive information and/or attempts to send inappropriate commands to ICS/SCADA (Industrial Control System/Supervisory Control And Data Acquisition) systems

Open Problems on Central Simple Algebras

We provide a survey of past research and a list of open problems regarding central simple algebras and the Brauer group over a field, intended both for experts and for beginners.Comment: v2 has some small revisions to the text. Some items are re-numbered, compared to v