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 Aristotle’s 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

Etude théorique d’hélicènes fonctionalisés par un TTF

Date du colloque : 06/2011National audienc

Tetrathiafulvalene-Triazine-Dipyridylamines as Multifunctional Ligands for Electroactive Complexes: Synthesis, Structures, and Theoretical Study

The electroactive ligands (2,4-bis-tetrathiafulvalene[6-(dipyridin-2-ylamino)]-1,3,5-triazine) TTF2-tz-dpa (1) and (2-tetrathiafulvalene[4,6-bis-(dipyridin-2-ylamino)]-1,3,5-triazine) TTF-tz-dpa(2) (2) have been synthesized by palladium cross-coupling catalysis, and the single crystal X-ray structure for 1 was determined. In the solid state the TTF and triazine units are practically coplanar and short intermolecular S center dot center dot center dot S contacts are established. Two neutral and one tetracationic Zn(II) complexes, formulated as (TTF2-tz-dpa)ZnCl2 (3), [ZnCl2(TTF-tz-dpa(2))Zn(H2O)Cl-2] (4), and ([(H2O)(2)Zn(TTF-tz-dpa(2))](ClO4)(2)}(2) (5) have been crystallized and analyzed by single crystal X-ray analysis. A peculiar feature is the evidence for anion-pi interactions, as shown by the short Cl center dot center dot center dot triazine and O(perchlorate)center dot center dot center dot triazine distances of 3.52 and 3.00 angstrom, respectively. A complex set of intermolecular pi center dot center dot center dot pi, S center dot center dot center dot S and hydrogen bonding interactions sustain the supramolecular organizations of the complexes in the solid state. Electronic absorption spectra provide evidence for the intramolecular charge transfer from TTF to triazine, also supported by time-dependent density functional theory (TD DFT) calculations

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

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

Discrete structures in continuum descriptions of defective crystals

I discuss various mathematical constructions that combine together to provide a natural setting for discrete and continuum geometric models of defective crystals. In particular I provide a quite general list of `plastic strain variables', which quantifies inelastic behaviour, and exhibit rigorous connections between discrete and continuous mathematical structures associated with crystalline materials that have a correspond-ingly general constitutive specification