Sphérique et sphéropée en Grèce ancienne

In ancient Greece, astronomy and geography were closely connected. Geography was based on the teachings of astronomy, but it determined them as well: for example the needs of scientific geography forced astronomers to use geocentric hypotheses. To study the relationship between a motionless earth situated in the central part of the cosmos and a sky moving in a circle round the axis of the world, two methods were available, either the geometrical method, used more particularly in the selection called Small Astronomy (Autolycos, Euclid, Theodose of Bithynia) or the experimental approach, dealing with reduced representations of the world, more or less precise (celestial globes or armillary spheres). The first method was supported by Spheric, or Geometry of the sphere; the second resorted to Spheropoeia, a branch of Mechanics. There was mutual interaction between these two methods.     

Hierarchical Production-planning Systems: Extensions and Modifications

This paper extends earlier hierarchical production-planning approaches initiated by Hax and Meal. The proposed model incorporates both functional and hierarchical interfaces simultaneously as encountered in practice, and assures feasibility and consistency among the decisions made at the different hierarchical levels of the firm. The problem of infeasibility which arises in disaggregating the aggregate production plan into detailed schedules is solved using goal programming at the product-family disaggregation level, and using branch and bound at the item-disaggregation level. The proposed approach minimizes backlogging regardless of the underlying cost structure of the problem at hand.     

Le rapport di isou (Euclide V, définition 17): Définition, utilisation, transmission

Dans le livre V des Eléments d'Euclide, la définition 17, du di isou logos, se compose de deux énoncés juxtaposés, qui ne sont pas équivalents. Le premier étant une simple réfection du théorème V,22, il convient de regarder le second seul comme authentique, comme le suggérent aussi bien l'emploi de l'expression di isou en géométrie grecque, que l'analyse précise de la tradition indirecte. En conséquence, la définition 17 doit être débarrassée de sa première partie; la définition 18.1, celle de la proportion réglée, doit être restituée comme authentique; la définition 18.2, de la proportion déréglée, doit être réduite à son libellé original, analogue à celui de 18.1.In Euclid's Elements V, Definition 17 (di isou logos) consists of two statements, which are not equivalent. The first one being a remake of theorem V,22, the second is the only one to be taken as genuine. This can be proved by the use of the expression di isou in Greek geometry, and also by a close scrutiny of the various witnesses of this part of the text. Consequently, Definition 17 should be cleared of its first part; Definition 18.1, of the ordered proportion, should be restored as genuine; Definition 18.2, of the perturbed proportion, should be reduced to its original core, and made similar to 18.1.     

Physical properties of the solvent mixtures triethylphosphate+hexamethylphosphoric triamide at 25°C

Densities and viscosities have been determined, from 25 to 45°C, as well as the refractive indices and dielectric constants at 25°C, for mixtures of triethylphosphate (TEP) and hexamethylphosphoric triamide (HMPT), in the complete mole fraction interval. As far as steric considerations are concerned, comparison has been made with the properties of the two intermediate organophosphorus compounds, ethoxytetramethylphosphorodiamide (EtO)(Me₂N)₂PO and diethoxydimethylphosphoramide (EtO)₂(Me₂N)PO.     

Enthalpies de complexation de quelques phosphoramides avec le chlorure d'antimoine(V). Influence de la structure sur le nombre donneur selon Gutmann

Complexation enthalpies for various compounds with SbCl₅ have been calorimetrically determined in dilute dichloro-1,2 ethane solution at 25°C. In the case of 22 organo-phosphorylated compounds OPX_x,Y_3-x, (X, Y = NMe₂, Net₂, NHEt,

, OEt; x = 0, 1, 2, 3), our calorimetric results allow a characterization of Lewis basicity variations (as Gutmann's donor number DN) against the nature of substituents at the phosphorus atom. Within this scale, many compounds are more basic than HMPA OP(Nme₂)₃ whose DN is, according to our results, greater than currently admitted; if no systematic effects are noted, the influence of conformation may, however, explain the DN variations in each series (for X and Y given, x varying from 0 to 3). Moreover, thanks to conductometric measurements, an instantaneous reaction of triethylamine with the solvent is evidenced.     

Moments dipolaires et conformations de l'hexaméthyl-phosphotriamide (HMPT) et des dérivés aziridinylés correspondants

Some physical properties (density, refractive index, dielectric constant, dipole moment) have been determined for the phosphoramides

Variations of dielectric constant and dipole moment as a function of the structure show a minimum for n = 2. In order to explain this minimum, the dipole moments are evaluated for various conformations, using both a rigid dipoles summation and quantum calculations (CNDO/2). The values adopted for the bond angles and for the interatomic distances are discussed. The conformation in which the three nitrogen lone pairs are essentially parallel to the PO axis (one in the same direction, two in the opposite direction) seems to be applicable to all the phosphoramides studied. In the case of HMPT (n = 0), however, the arrangement in which the nitrogen lone pair is parallel to the PO axis in the opposite direction, and the two others in a plane perpendicular to PO, seems to be more reasonable. These structures are compared with those for some related compounds. Relationships between the basicity (deduced from proton NMR chemical shifts of hcci₃) and the orientation of dipole moment are discussed.     

Analyse conformationnelle théorique du diméthylsulfoxyde (CH3)2SO

Résumé La méthode SCF-LCAO-MO dans l'approximation CNDO/2 est utilisée pour l'étude de l'analyse conformationnelle du diméthylsulfoxyde (CH₃)₂SO. On montre ainsi que, parmi les déterminations géométriques de la littérature, celle (r _OIV) obtenue par Dreizler et Coll. en 1969 au moyen de la spectroscopie de microondes semble devoir être retenue. La carte de potentiel, décrivant la rotation simultanée des deux groupements méthyle autour des liaisons (S-C), est tracée: elle montre que la molécule (CH₃)₂SO appartient bien au groupe de symétrie C _s, non seulement au niveau des atomes lourds (C, S, O) mais aussi à celui des hydrogènes. On note toutefois que les deux hydrogènes qui, dans la conformation (60, 60), auraient été dans le plan CSC, sont alors décalés tous deux de quelque 3,64° hors de ce plan et du côté de l'atome d'oxygène. La barrière à la rotation d'un CH₃ est trouvée égale à 3,5 kcal/mole (expérimentalement: 2,8 kcal/mole [7]). Un découpage bicentrique de l'énergie totale montre enfin que 60% des variations de cette grandeur sont dûs à la seule somme, E (S...H) des interactions dans l'espace entre l'atome de soufre et les six atomes d'hydrogène.

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Theoretical conformational analysis of dimethylsulfoxide (CH₃)₂SO

The conformational analysis of (CH₃)₂SO is investigated within the framework of the CNDO/2 approximation. The preferred conformation of heavy atoms (C, S, O) is found to be the one (r _OIV) which was proposed by Dreizler et al. in 1969 on the basis of microwave measurements. The map of isoenergy curves was drawn, describing the variation of energy as a result of mutual rotation of the two methyl groups. This showed that the equilibrium symmetry for the complete molecule, including the hydrogens, was C _sHowever, it may be noticed that the two hydrogens which, for the (60, 60) conformation, would have been located into the CSC plane, are actually staggered of 3.64° out of this plane and nearer to the oxygen atom than to the sulphur lone pair. The rotational barrier for one CH₃ group is 3.5 kcal/mole, in agreement with the experimental value (2.8 kcal/mole [7]). A bicentric energy partitioning shows that about 60% of the variation in total energy is reflected by the single sum, E(S...H), of the spatial interaction terms between sulphur and the six hydrogens.

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Zusammenfassung Die Konformation von (CH₃)₂SO wird im Rahmen des CNDO/2-Verfahrens analysiert, wobei sich für C-, S- und O-Atome das gleiche Ergebnis wie bei Mikrowellenmessungen (Dreizler, 1969) ergibt. Ferner wird die Energiehyperfläche für Methyl-Rotationen angegeben, mit der Symmetrie C _sam tiefsten Punkt. Allerdings sind die zwei H-Atome, die bei der (60, 60)-Konformation in der CSC-Ebene liegen sollten, um 3,64° aus dieser Ebene herausgedreht und näher an den einsamen Elektronen des Sauerstoffs als an denen des Schwefels. Die Rotationsbarriere einer CH₃-Gruppe beträgt 3,5 kcal/ Mol (experimentell 2,8 kcal/Mol [7]). Eine Energieaufspaltung auf Zentrenpaare zeigt, daß etwa 60% der Änderung der Gesamtenergie in der Einfachsumme E(S...H) der räumlichen Wechselwirkungs-systeme zwischen den S- und den sechs H-Atomen enthalten ist.

     

Anomalous transport and diffusion phenomena induced by biharmonic forces in deformable potential systems

We study transport properties of an inertial Brownian motor which moves in a deformable Remoissenet-Peyrad periodic potential and is subjected to both a static bias force and time periodic driving biharmonic force. By modifying the shape of the potential, the anomalous transport is identified for a particular set of the system parameters. For a particular potential shape, the mean velocity of a particle is modified by going from negative to positive values according to the external bias force. These features also depend on both the biharmonic parameter and the phase-lag of two signals. A remarkable transition of the negative velocity depending on the shape of the potential is observed. We also focus on the efficiency of the motor and discuss velocity fluctuation. In addition, within selected system parameters, different types of diffusion particle such as subdiffusion, superdiffusion, normal diffusion, ballistic diffusion, hyperdiffusion and dispersionless transport phenomena are generated in the system.