319 research outputs found
Applying the proto-theory of design to explain and modify the parameter analysis method of conceptual design
This article reports on the outcomes of applying the notions provided by the reconstructed proto-theory of design, based on Aristotleâs remarks, to the parameter analysis (PA) method of conceptual design. Two research questions are addressed: (1) What further clarification and explanation to the approach of PA is provided by the proto-theory? (2) Which conclusions can be drawn from the study of an empirically derived
design approach through the proto-theory regarding usefulness, validity and range of that theory? An overview of PA and an application example illustrate its present model and unique characteristics. Then, seven features of the proto-theory are explained and demonstrated through geometrical problem solving and analogies are drawn between these features and the corresponding ideas in modern design thinking.
Historical and current uses of the terms analysis and synthesis in design are also outlined and contrasted, showing that caution should be exercised when applying them. Consequences regarding the design moves, process and strategy of PA allow proposing modifications to its model, while demonstrating how the ancient method of analysis can contribute to better understanding of contemporary design-theoretic issues
Stochastic Line-Motion and Stochastic Conservation Laws for Non-Ideal Hydromagnetic Models. I. Incompressible Fluids and Isotropic Transport Coefficients
We prove that smooth solutions of non-ideal (viscous and resistive)
incompressible magnetohydrodynamic equations satisfy a stochastic law of flux
conservation. This property involves an ensemble of surfaces obtained from a
given, fixed surface by advecting it backward in time under the plasma velocity
perturbed with a random white-noise. It is shown that the magnetic flux through
the fixed surface is equal to the average of the magnetic fluxes through the
ensemble of surfaces at earlier times. This result is an analogue of the
well-known Alfven theorem of ideal MHD and is valid for any value of the
magnetic Prandtl number. A second stochastic conservation law is shown to hold
at unit Prandtl number, a random version of the generalized Kelvin theorem
derived by Bekenstein-Oron for ideal MHD. These stochastic conservation laws
are not only shown to be consequences of the non-ideal MHD equations, but are
proved in fact to be equivalent to those equations. We derive similar results
for two more refined hydromagnetic models, Hall magnetohydrodynamics and the
two-fluid plasma model, still assuming incompressible velocities and isotropic
transport coefficients. Finally, we use these results to discuss briefly the
infinite-Reynolds-number limit of hydromagnetic turbulence and to support the
conjecture that flux-conservation remains stochastic in that limit.Comment: 20 pages, no figures, submitted to J. Math. Phys
A nullstellensatz for sequences over F_p
Let p be a prime and let A=(a_1,...,a_l) be a sequence of nonzero elements in
F_p. In this paper, we study the set of all 0-1 solutions to the equation a_1
x_1 + ... + a_l x_l = 0. We prove that whenever l >= p, this set actually
characterizes A up to a nonzero multiplicative constant, which is no longer
true for l < p. The critical case l=p is of particular interest. In this
context, we prove that whenever l=p and A is nonconstant, the above equation
has at least p-1 minimal 0-1 solutions, thus refining a theorem of Olson. The
subcritical case l=p-1 is studied in detail also. Our approach is algebraic in
nature and relies on the Combinatorial Nullstellensatz as well as on a Vosper
type theorem.Comment: 23 page
Stevin numbers and reality
We explore the potential of Simon Stevin's numbers, obscured by shifting
foundational biases and by 19th century developments in the arithmetisation of
analysis.Comment: 22 pages, 4 figures. arXiv admin note: text overlap with
arXiv:1104.0375, arXiv:1108.2885, arXiv:1108.420
A Cauchy-Dirac delta function
The Dirac delta function has solid roots in 19th century work in Fourier
analysis and singular integrals by Cauchy and others, anticipating Dirac's
discovery by over a century, and illuminating the nature of Cauchy's
infinitesimals and his infinitesimal definition of delta.Comment: 24 pages, 2 figures; Foundations of Science, 201
La rĂ©action dâhĂ©magglutination (RĂ©action de Middlebrook-Dubos ) dans la paratuberculose bovine (EntĂ©rite chronique hypertrophiante, maladie de Johne)
Gernez-Rieux Charles, Tacquet Albert, Gaumont R., Verge Jean, Cauchy Laurent. La réaction d'hémagglutination (Réaction de Middlebrook-Dubos) dans la paratuberculose bovine (Entérite chronique hypertrophiante, maladie de Johne). In: Bulletin de l'Académie Vétérinaire de France tome 103 n°9, 1950. pp. 465-468
Ten Misconceptions from the History of Analysis and Their Debunking
The widespread idea that infinitesimals were "eliminated" by the "great
triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an
uninterrupted chain of work on infinitesimal-enriched number systems. The
elimination claim is an oversimplification created by triumvirate followers,
who tend to view the history of analysis as a pre-ordained march toward the
radiant future of Weierstrassian epsilontics. In the present text, we document
distortions of the history of analysis stemming from the triumvirate ideology
of ontological minimalism, which identified the continuum with a single number
system. Such anachronistic distortions characterize the received interpretation
of Stevin, Leibniz, d'Alembert, Cauchy, and others.Comment: 46 pages, 4 figures; Foundations of Science (2012). arXiv admin note:
text overlap with arXiv:1108.2885 and arXiv:1110.545
Minkowski-type and Alexandrov-type theorems for polyhedral herissons
Classical H.Minkowski theorems on existence and uniqueness of convex
polyhedra with prescribed directions and areas of faces as well as the
well-known generalization of H.Minkowski uniqueness theorem due to
A.D.Alexandrov are extended to a class of nonconvex polyhedra which are called
polyhedral herissons and may be described as polyhedra with injective spherical
image.Comment: 19 pages, 8 figures, LaTeX 2.0
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