Geometrical optics /

Mode of access: Internet.

Euclid's Elements of geometry, chiefly from the text of Dr. Simson...together with a selection of geometrical exercises from the Senate-house and college examination papers ...

Mode of access: Internet.

Ad quadratum; a study of the geometrical bases of classic & medieval religious architecture, with special reference to their application in the restoration of the cathedral of Nidaros (Throndhjem) Norway,

"Rules of religious architecture were a secret science in the middle ages, just as they were in classic times ... Through this secrecy, the rules became forgotten ... It is this forgotten science which we have discovered, and which we develop in this work."--p. xxii.

Electronic energy-transfer rate constants for geometrical isomers of a bichromophoric macrocyclic complex

The rate of electronic energy transfer (EET) between a naphthalene donor and an anthracene acceptor in [ZnL3]-(ClO4)(2) and [ZnL4](ClO4)(2) was determined by time-resolved fluorescence measurements, where L 3 and L 4 are the geometrical isomers of 6-[(anthracen-9-ylmethyl)amino]-trans-6,13-dimethyl-1,4,8,11-tetraazacyclotetradecane-13-amine (L-2), substituted with either a naphthalen-1-ylmethyl or naphthalen-2-ylmethyl donor, respectively. The energy transfer rate constant, k(EET), was determined to be (0.92 +/- 0.02) x 10(9) s(-1) for the naphthalen-1-ylmethyl-substituted isomer, while that for the naphthalen-2-ylmethyl-substituted isomer is somewhat faster, with k(EET) = (1.31 +/- 0.01) x 10(9) s(-1). The solid-state structure of [(ZnLCl)-Cl-3]ClO4 has been determined, and using molecular modeling calculations, the likely distributions of solution conformations in CH3CN have been evaluated for both complexes. The calculated conformational distributions in the common trans-III N-based isomeric form gave Forster EET rate constants that account for the differences observed and are in excellent agreement with the experimental values. It is shown that the full range of conformers must be considered to accurately reproduce the observed EET kinetics.

Isomeric distribution and catalyzed isomerization of cobalt(III) complexes with pentadentate macrocyclic ligands. Importance of hydrogen bonding

We have investigated the isomeric distribution and rearrangement of complexes of the type [CoXLn](2+,3+) (where X = Cl-, OH-, H2O, and L-n represents a pentadentate 13-, 14-, and 15-membered tetraaza or diaza-dithia (N-4 or N2S2) macrocycle bearing a pendant primary amine). The preparative procedures for chloro complexes produced almost exclusively kinetically preferred cis isomers (where the pendant primary amine is cis to the chloro ligand) that can be separated by careful cation-exchange chromatography. For L-13 and L-14 the so-called cis-V isomer is isolated as the kinetic product, and for L-15 the cis-VI form (an N-based diastereomer) is the preferred, while for the L-14(S) complex both cis-V and trans-I forms are obtained. All these complexes rearrange to form stable trans isomers in which the pendent primary amine is trans to the monodentate aqua or hydroxo ligand, depending on pH and the workup procedure. In total 11 different complexes have been studied. From these, two different trans isomers of [CoCIL14S](2+) have been characterized crystallographically for the first time in addition to a new structure of cis-V-[CoCIL14S](2+); all were isolated as their chloride perchlorate salts. Two additional isomers have been identified and characterized by NMR as reaction intermediates. The remaining seven forms correspond to the complexes already known, produced in preparative procedures. The kinetic, thermal, and baric activation parameters for all the isomerization reactions have been determined and involve large activation enthalpies and positive volumes of activation. Activation entropies indicate a very important degree of hydrogen bonding in the reactivity of the complexes, confirmed by density functional theory studies on the stability of the different isomeric forms. The isomerization processes are not simple and even some unstable intermediates have been detected and characterized as part of the above-mentioned 11 forms of the complexes. A common reaction mechanism for the isomerization reactions has been proposed for all the complexes derived from the observed kinetic and solution behavior.

A Geometrical Interpretation to Define Contradiction Degrees between Two Fuzzy Sets

For inference purposes in both classical and fuzzy logic, neither the information itself should be contradictory, nor should any of the items of available information contradict each other. In order to avoid these troubles in fuzzy logic, a study about contradiction was initiated by Trillas et al. in [5] and [6]. They introduced the concepts of both self-contradictory fuzzy set and contradiction between two fuzzy sets. Moreover, the need to study not only contradiction but also the degree of such contradiction is pointed out in [1] and [2], suggesting some measures for this purpose. Nevertheless, contradiction could have been measured in some other way. This paper focuses on the study of contradiction between two fuzzy sets dealing with the problem from a geometrical point of view that allow us to find out new ways to measure the contradiction degree. To do this, the two fuzzy sets are interpreted as a subset of the unit square, and the so called contradiction region is determined. Specially we tackle the case in which both sets represent a curve in [0,1]2. This new geometrical approach allows us to obtain different functions to measure contradiction throughout distances. Moreover, some properties of these contradiction measure functions are established and, in some particular case, the relations among these different functions are obtained.

A Geometrical Construction for the Polynomial Invariants of some Reflection Groups

2000 Mathematics Subject Classification: Primary 20F55, 13F20; Secondary 14L30.

A geometrical model for surface roughness prediction when face milling Al 7075-T7351 with square insert tools

Surface quality is important in engineering and a vital aspect of it is surface roughness, since it plays an important role in wear resistance, ductility, tensile, and fatigue strength for machined parts. This paper reports on a research study on the development of a geometrical model for surface roughness prediction when face milling with square inserts. The model is based on a geometrical analysis of the recreation of the tool trail left on the machined surface. The model has been validated with experimental data obtained for high speed milling of aluminum alloy (Al 7075-T7351) when using a wide range of cutting speed, feed per tooth, axial depth of cut and different values of tool nose radius (0.8. mm and 2.5. mm), using the Taguchi method as the design of experiments. The experimental roughness was obtained by measuring the surface roughness of the milled surfaces with a non-contact profilometer. The developed model can be used for any combination of material workpiece and tool, when tool flank wear is not considered and is suitable for using any tool diameter with any number of teeth and tool nose radius. The results show that the developed model achieved an excellent performance with almost 98% accuracy in terms of predicting the surface roughness when compared to the experimental data. © 2014 The Society of Manufacturing Engineers.

Support enhanced α-pinene isomerization over HPW/SBA-15

A family of mesoporous SBA-15 supported H3PW12O40 (HPW) catalysts were synthesized by wet-impregnation and compared with fumed silica analogues for the solventless isomerization of α-pinene under mild conditions. Structural and acidic properties of supported HPW materials were characterized by powder XRD, HRTEM, XPS, TGA, N2 porosimetry, DRIFTS, and ammonia and propylamine chemisorption and TPD. The high area, mesoporous SBA-15 architecture facilitates the formation of highly dispersed (isolated or low dimensional) HPW clusters and concomitant high acid site densities (up to 0.54 mmol g−1) relative to fumed silica wherein large HPW crystallites are formed even at low HPW loadings. α-Pinene exhibits a volcano dependence on HPW loading over the SBA-15 support due to competition between the number and accessibility of acid sites to the non-polar reactant, with the superior acid site accessibility for HPW/SBA-15 conferring a 10-fold rate enhancement with respect to HPW/fumed silica and pure HPW. Monocyclic limonene and terpinolene products are favoured over polycyclic camphene and β-pinene by weaker polyoxometallate analogues over SBA-15.

Geometrical optimization of a fast pyrolysis bubbling fluidized bed reactor using comutational fluid dynamics

This paper analyzes the physical phenomena that take place inside an 1 kg/h bubbling fluidized bed reactor located at Aston University and presents a geometrically modified version of it, in order to improve certain hydrodynamic and gas flow characteristics. The bed uses, in its current operation, 40 L/min of N2 at 520 °C fed through a distributor plate and 15 L/min purge gas stream, i.e., N2 at 20 °C, via the feeding tube. The Eulerian model of FLUENT 6.3 is used for the simulation of the bed hydrodynamics, while the k - ε model accounts for the effect of the turbulence field of one phase on the other. The three-dimensional simulation of the current operation of the reactor showed that a stationary bubble was formed next to the feeding tube. The size of the permanent bubble reaches up to the splash zone of the reactor, without any fluidizaton taking place underneath the feeder. The gas flow dynamics in the freeboard of the reactor is also analyzed. A modified version of the reactor is presented, simulated, and analyzed, together with a discussion on the impact of the flow dynamics on the fast pyrolysis of biomass. © 2010 American Chemical Society.

Perforated tunnel exit regions and micro-pressure waves : geometrical influence

ACKNOWLEDGEMENTS The authors are grateful to the following bodies that provided financial support for the project: (i) China Scholarship Council, (ii) National Natural Science Foundation of China (Grant No. U1334201 and (iii) UK Engineering and Physical Sciences Research Council (Grant No. EP/G069441/1).

Identification and classification of geometrical parameeters related to foot pathologies

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.