An inequality for pseudo-subplanes of sets of orthogonal latin squares

AbstractLet L1, L2,…, Lt be a given set of t mutually orthogonal order-n latin squares defined on a symbol set S, |S| = n. The squares are equivalent to a (t + 2)-netN of order n which has n2 points corresponding to the n2 cells of the squares. A line of the net N defined by the latin square Li comprises the n points of the net which are specified by a set of n cells of Li all of which contain the same symbol x of S. If we pick out a particular r × r block B of cells, a line which contains points corresponding to r of the cells of B will be called an r-cell line. If there exist r(r − 1) such lines among the tn lines of N, we shall say that they form a pseudo-subplane of order r-the “pseudo” means that these lines need not belong to only r − 1 of the latin squares. The purpose of the present note is to prove that the hypothesis that such a pseudo-plane exists in N implies that r3 − (t + 2)r2 + r + nt ⩾∗0

On nonreconstructable tournaments

AbstractPairs of non-isomorphic strong tournaments of orders 5 and 6 are given for which the subtournaments of orders 4 and 5, respectively, are pairwise isomorphic. Herefore, only pairs of orders 3 and 4 were known

Nonexistence of a triple of orthogonal latin squares of order 10 with group of order 25—A search made short

There does not exist a set of four 5-cycles with marks 0, 1, 2, 3, and 4, with and without primes, such that each difference (mod 5) in the four patterns with respect to primes occurs once in adjacent and nonadjacent positions

Deterministically Driven Avalanche Models of Solar Flares

We develop and discuss the properties of a new class of lattice-based avalanche models of solar flares. These models are readily amenable to a relatively unambiguous physical interpretation in terms of slow twisting of a coronal loop. They share similarities with other avalanche models, such as the classical stick--slip self-organized critical model of earthquakes, in that they are driven globally by a fully deterministic energy loading process. The model design leads to a systematic deficit of small scale avalanches. In some portions of model space, mid-size and large avalanching behavior is scale-free, being characterized by event size distributions that have the form of power-laws with index values, which, in some parameter regimes, compare favorably to those inferred from solar EUV and X-ray flare data. For models using conservative or near-conservative redistribution rules, a population of large, quasiperiodic avalanches can also appear. Although without direct counterparts in the observational global statistics of flare energy release, this latter behavior may be relevant to recurrent flaring in individual coronal loops. This class of models could provide a basis for the prediction of large solar flares.Comment: 24 pages, 11 figures, 2 tables, accepted for publication in Solar Physic

Analytic approximation and an improved method for computing the stress-energy of quantized scalar fields in Robertson-Walker spacetimes

An improved method is given for the computation of the stress-energy tensor of a quantized scalar field using adiabatic regularization. The method works for fields with arbitrary mass and curvature coupling in Robertson-Walker spacetimes and is particularly useful for spacetimes with compact spatial sections. For massless fields it yields an analytic approximation for the stress-energy tensor that is similar in nature to those obtained previously for massless fields in static spacetimes.Comment: RevTeX, 8 pages, no figure

Spin dynamics of wave packets evolving with the Dirac Hamiltonian in atoms with high Z

The motion of circular WP for one electron in central Coulomb field with high Z is calculated. The WP is defined in terms of solutions of the Dirac equation in order to take into account all possible relevant effects in particular the spin-orbit potential. A time scale is defined within which spin dynamics must be taken into account mainly in the atoms with high Z. Within this time scale there exists a mechanism of collapses and revivals of the spin already shown by the authors for harmonic oscillator potential and called the 'spin-orbit pendulum'. However this effect has not the exact periodicity of the simpler model, but the WP's spatial motion is nevertheless quite similar.Comment: 17 pages, 9 figures, LaTeX2e, uses IOP style files (included). Title changed, one reference adde

Simulations of galactic dynamos

We review our current understanding of galactic dynamo theory, paying particular attention to numerical simulations both of the mean-field equations and the original three-dimensional equations relevant to describing the magnetic field evolution for a turbulent flow. We emphasize the theoretical difficulties in explaining non-axisymmetric magnetic fields in galaxies and discuss the observational basis for such results in terms of rotation measure analysis. Next, we discuss nonlinear theory, the role of magnetic helicity conservation and magnetic helicity fluxes. This leads to the possibility that galactic magnetic fields may be bi-helical, with opposite signs of helicity and large and small length scales. We discuss their observational signatures and close by discussing the possibilities of explaining the origin of primordial magnetic fields.Comment: 28 pages, 15 figure, to appear in Lecture Notes in Physics "Magnetic fields in diffuse media", Eds. E. de Gouveia Dal Pino and A. Lazaria

Ownership of co-creation assets: driving B2B value propositions in the service economy

The benefits of specialization have been driving the rise of the service economy and pushing capability frontiers and economic growth. In service economies, almost any activity, asset, and skill can be bought on competitive markets, making it harder to build competitive advantage on any of those inputs. Against that background, the question emerges what constitutes sustainable value propositions of service providers. Drawing on an emerging stream of research on the non-ownership value of services, we argue that service providers create value by taking on ownership of service assets and thereby transform uncertainty of value creation into economic opportunities. In our view, service providers offer the essential value proposition of transforming their clients’ uncertainty downsides into opportunities related to assets such as vehicles, real estate, equipment and computing platforms. Clients benefit by delegating ownership of assets to the domain of a service provider. In turn, clients can focus their investment on their most promising assets. Service providers create sustainable competitive advantage by assuming ownership and excelling at the management of (a) unique physical assets, (b) unique intangible assets and (c) maintaining an appropriate architecture of social capital through customer relationships and business ecosystems

Unruh--DeWitt detectors in spherically symmetric dynamical space-times

In the present paper, Unruh--DeWitt detectors are used in order to investigate the issue of temperature associated with a spherically symmetric dynamical space-times. Firstly, we review the semi-classical tunneling method, then we introduce the Unruh--DeWitt detector approach. We show that for the generic static black hole case and the FRW de Sitter case, making use of peculiar Kodama trajectories, semiclassical and quantum field theoretic techniques give the same standard and well known thermal interpretation, with an associated temperature, corrected by appropriate Tolman factors. For a FRW space-time interpolating de Sitter space with the Einstein--de Sitter universe (that is a more realistic situation in the frame of $\Lambda$CDM cosmologies), we show that the detector response splits into a de Sitter contribution plus a fluctuating term containing no trace of Boltzmann-like factors, but rather describing the way thermal equilibrium is reached in the late time limit. As a consequence, and unlike the case of black holes, the identification of the dynamical surface gravity of a cosmological trapping horizon as an effective temperature parameter seems lost, at least for our co-moving simplified detectors. The possibility remains that a detector performing a proper motion along a Kodama trajectory may register something more, in which case the horizon surface gravity would be associated more likely to vacuum correlations than to particle creation.Comment: 19 pages, to appear on IJTP. arXiv admin note: substantial text overlap with arXiv:1101.525

Correlation Entropy of an Interacting Quantum Field and H-theorem for the O(N) Model

Following the paradigm of Boltzmann-BBGKY we propose a correlation entropy (of the nth order) for an interacting quantum field, obtained by `slaving' (truncation with causal factorization) of the higher (n+1 th) order correlation functions in the Schwinger-Dyson system of equations. This renders an otherwise closed system effectively open where dissipation arises. The concept of correlation entropy is useful for addressing issues related to thermalization. As a small yet important step in that direction we prove an H-theorem for the correlation entropy of a quantum mechanical O(N) model with a Closed Time Path Two Particle Irreducible Effective Action at the level of Next-to-Leading-Order large N approximation. This model may be regarded as a field theory in $0$ space dimensions.Comment: 22 page