PDF superior Gerbes and prequantization of dirac structures

Gerbes and prequantization of dirac structures

Gerbes and prequantization of dirac structures

The classical description of the dynamics of a physical system can be archived geomet- rically associating to the system a Poisson algebra of observables, in terms of which the evolution of the system is written down trough simple differential equations involving the Poisson bracket. The process of quantization, which assigns to each classical ob- servable an operator in some Hilbert space, has been studied for many decades and it is still not well understood (mathematically and philosophically). Geometric quantization is a mathematical proposal to attack this problem using the geometrical structure of Hamilton’s formalism: the phase space has a natural structure of symplectic manifold [22]. The first part of the geometric quantization programme, known as prequanti- zation, is devoted to build up the geometric object from which a Hilbert space can be associated to the symplectic manifold: a line bundle with connection. With this line bundle at hand and, finally, a representation of the classical Poisson algebra as an algebra of self-adjoint operators acting on the Hilbert space of sections is given. As we will see, this representation uses explicitly the connection of the line bundle.
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Physical principles of memory and logic devices based on nanostructured Dirac materials

Physical principles of memory and logic devices based on nanostructured Dirac materials

Opposite to the top-down techniques, bottom-up approaches are expected to produce GNRs with well-defined structures and controlled electronic properties. The process described by Cai and colleagues in [134] allows the formation of defect-free AGNRs on Au(111) and Ag(111) surfaces. The process consists in using a precursor monomer molecule (10,10’-dibromo-9,9’-bianthryl) to form a linear polymer after dehalogena- tion and C-C coupling; then, a cyclodehydrogenation process is used to obtain the AGNR. Atomically precise GNRs with different topologies and defined width and edge periphery can be obtained depending on the structure of the precursor. For instance, the authors obtained a 7-AGNR with a bandgap of 1.6 eV. Similarly, Bronner and colleagues obtain a non-aromatic polymer with bandgap of 5.25 eV, starting with the same precursor molecule. After a cyclodehydrogenation process, the authors obtain a GNR with a bandgap of 2.6 eV [139, 140]. Moreover, structurally perfect GNRs (sol- uble in organic solvers, such as toluene, tetrahydrofuran, and dichloromethane) can be obtained using polyphenylene precursors and an oxidative cyclodehydrogenation process [55]. Therefore, it is possible to fabricate defect-free GNRs on Au/Ag surfaces and organic solvents, but one of the main issues is to obtain the adequate precursor. Bennett and co-workers use a similar process to fabricate GNR arrays and include a layer transfer process to build and measure FETs [141]. The authors report difficulties in obtaining GNRs with controlled orientation, width and length, which make it dif- ficult to guarantee that the ribbons are in contact with the source and drain, leading to very low on-currents.
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125 Lee mas

The cylindrical delta potential and the Dirac equation

The cylindrical delta potential and the Dirac equation

Singular δ-type potentials have been considered in quantum mechanics from the beginning. In general, singular δ -type potentials can be considered as toy models which allow us to obtain a physical insight, being, at the same time, more easy to deal with in comparison with more realistic extended potentials. An example is the well-known Dirac- comb or Kronig–Penney model [5] in non-relativistic quantum mechanics, which provided us with an understanding and intuition about the emergence of band structures in solid-state

11 Lee mas

Triangular structures of Hopf algebras and
tensor Morita equivalences

Triangular structures of Hopf algebras and tensor Morita equivalences

Given a Hopf algebra A, it is fundamental to know whether A has a (quasi-)tri- angular structure, and to determine all the (quasi-)triangular structures of A. As a trivial example of Hopf algebras having a triangular structure, one may take the group Hopf algebra k [G] of a finite group G over a field k . If G is not com- mutative, then the dual Hopf algebra ( k [G]) ∗ has no quasitriangular structure. A non-trivial family of Hopf algebras which are not (quasi-)triangular and not co(quasi-)triangular is found by Masuoka [14, Proposition 2.5], [15, Corollary 2]. Another examples are given by Suzuki [22]. He introduced a family of cosemisim- ple Hopf algebras A νλ
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Full PDF

Full PDF

Significant differences were observed in the number of secondary and antral follicles between the oestrous phases in collared pec- caries. The means numbers were higher in the follicular phase, when the follicle is recruited, selected and becomes dominant. The mean number of primordial follicles was close to that of primary follicles, in contrast to what is generally observed in mammals. This result can be due to the follicle classification used in this work, which included in primary follicles cat- egory those with granulosa pavimentous cells or cuboidal shape, thus increasing the mean values in this category.
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O-asymptotic classes of finite structures, pseudofinite dimension and forking

O-asymptotic classes of finite structures, pseudofinite dimension and forking

My sincere thanks also goes to the Logic Group at University of California - Berkeley, especially to Alex Kruckman, Will Johnson, Michael Wan and James Fre- itag - for their kindness and hospitality during my internships. Additionally, I would like to thank all professors and students that participated in the semester Model Theory, Number Theory and Geometry at the MSRI for all the talks and conversa- tions that allowed me to grow as a mathematician and as a person. Among them, I would like to mention professors Charles Steinhorn, Dugald Macpherson, Ward Henson, Carol Wood, Sergei Starchenko, Maryanthe Malliaris, Cameron Hill, Vin- cent Guingona, as well as the students Santiago Camacho, Caroline Terry, Gabriel Conant, Silvain Rideau and Samaria Montenegro.
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131 Lee mas

The Future of the Technologies of Shell and spatial Structures. Bridges

The Future of the Technologies of Shell and spatial Structures. Bridges

This fact represents mainly a technical problem, that means that for a given state of available materials, known structural types, methods of analysis and constructi[r]

16 Lee mas

Formulación simpléctica de teorías topológicas en términos de nuevas variables: la segunda clase de Chern y la clase de Euler

Formulación simpléctica de teorías topológicas en términos de nuevas variables: la segunda clase de Chern y la clase de Euler

Por otra parte, es importante señalar que el Formalismo de FJ es más práctico debido a que no fue necesario clasicar las restricciones, lo cual nos sirve como método alternativo para poder obtener de manera más rápida la estructura simpléctica de la teoría, y así más adelante ser promovidos como operadores en la cuantización. Desde luego que el trabajo hecho en esta tesis no es un ejercicio de consistencia. La cuantización canónica en teorías de norma con covarianza general es un problema difícil de abordar. Desde el punto de vista de Dirac, si se tienen restricciones de primera y segunda clase, pri- mero se construyen los paréntesis de Dirac, posteriormente, se usa la correspondencia clásica-cuántica en las variables canónicas y se pide que se escriban las restricciones de primera clase como operadores. Una vez que se tienen las restricciones en forma de operadores, uno busca estados que las resuelvan puesto que los estados cuánticos deben ser invariantes de norma. Posteriormente, con los estados que se encuentran uno debe denir un producto interno de tal manera que se pueda construir el espacio de Hilbert con funciones cuadráticamente integrables, digamos L 2 (A/g) , donde A/g es el conjunto
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First principles calculations of electronic structures and metal mobility of NaxSi46 and NaxSi34 clathrates

First principles calculations of electronic structures and metal mobility of NaxSi46 and NaxSi34 clathrates

D. Mobility of sodium inside the structure cavities The geometry optimizations performed in order to obtain the relaxed structures used in the above analyses were car- ried out initially keeping the maximal symmetry allowed by the topology of the structure, with any Na atoms present located at the centers of the cavities following the results of the diffraction studies published in the literature. 29,30 Tests with decreased 共 or completely destroyed 兲 symmetry were also made in which the Na atoms were initially more or less displaced from the centers of the cavities, particularly for the larger ones. The energies found with the atoms located at the cavity centers were always the lowest; however, in some cases it was found that only very small energy changes were obtained by subjecting the Na atoms to quite significant dis- placements. This was most remarkable in the case of the MTN structure, when displacing Na from the center of its larger cavities; as an example, Fig. 7 shows the energy changes obtained for this structure, with both large cavities in the primitive cell occupied, when moving the two Na at- oms along one 共 common 兲 ternary axis of the respective cavi- ties, while keeping a trigonal symmetry 共 rombohedral space group R–3m, Nr. 166 兲 , so that these atoms approach sym- metrically the six-member ring connecting both cavities 关 the situation depicted in Fig. 8 共 a 兲兴 . A very similar behavior is found when the movement does not imply an approach be- tween neighboring Na atoms 关 as in the situation given in Fig. 8 共 b 兲兴 . Significant movements of Na away from the cavity center would therefore be allowed; for example, a 0.65 Å displacement, reducing the shortest Na–Si distances to val- ues around 3.35 Å, would be possible within an energy in- crease per Na atom lower than the ambient thermal energies (kT ⫽ 0.026 eV at T ⫽ 300 K). It thus seems that the Na at- oms can move rather freely within a large space in these large cavities, which act as an oversized container.
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Horizontal transport and mixing and their connection with dynamical and biological processes in the ocean

Horizontal transport and mixing and their connection with dynamical and biological processes in the ocean

Filaments affect different processes of the ocean dynamics. Horizontally, the elongation of water masses in thin structures intensifies local gradients, greatly enhancing the dispersion and mixing (Lapeyre and Klein, 2006; Pasquero et al., 2001). Other can act as dynamical barriers or can reinforce the coherence of mesoscale eddies (Joseph and Legras, 2002; Koh and Legras, 2002). Through lateral stirring, filaments disperse tracers like pollutants, nutrient, phytoplank- ton or zooplankton, affecting the plankton pattern formation (Abraham, 1998; Abraham et al., 2000; López et al., 2001; Martin, 2003; Hernández-García et al., 2003; Lehan et al., 2007), as well as the fate of contaminants (Lekien et al., 2005). They affect the low frequency variability of the ocean dynamics by redistributing heat and salinity anomalies. When they transport density anomalies, filaments are able to create intense cells of very strong vertical velocities (several tens of meters per day), exchanging material between different layers (Legal et al., 2007). For all these reasons, filament dynamics is of great importance for understand- ing the ocean dynamics. Nevertheless, owing to the relative scarcity of high resolution observational data and the very high cost of submesoscale-resolving circulation models, the filamental dynamics remains still unclear. For instance, to survey only one filament in situ it is needed to sample during one month a region of 100 km at a ∼1 km and ∼1 day of resolution. Which is obviously impossible to achieve for global or even regional information about filaments. On the other hand, high resolution SST and ocean color images are not reliable since they are highly affected by clouds. Altimetry is not affected by clouds, but its spatial resolution is not enough.
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210 Lee mas

TítuloN+N Structures in Present Day English Word Formation

TítuloN+N Structures in Present Day English Word Formation

N+N structures are sequences of two nouns, such as drug addiction or heart attack; often, structures of this type appear to be formations to which speakers and writers resort on the spur of the moment in order to fill a semantic gap, and which will never be used again. However, reasons such as their relevance or their easiness to be understood help them to remain through time as structures which enter the everyday vocabulary of a given language. The present paper is an approach to the consideration that N+N structures are a productive word formation type in Present-Day English. For this reason, I will try to establish which the motivations for their use are and I will make reference to the process of lexicalisation they may undergo. Likewise, I will make use of a corpus of English written texts to illustrate the lexical richness that these formations may provide to the vocabulary of English. The data taken from the corpora show that there is an active progress in the development of new compositional nominal groups.
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10 Lee mas

An electron localization function and catastrophe theory analysis on the molecular mechanism of gas phase identity SN2 reactions

An electron localization function and catastrophe theory analysis on the molecular mechanism of gas phase identity SN2 reactions

chemical research should also be to interpret the results in terms of quantitative concepts derived from first principle calculations. A promising theory to reach this goal, is Rich- ard Bader’s "Atoms in Molecules" (AIM) [1] in which all the chemical information is provided by the charge density distribution, an observable quantity. Moreover, the concept of bond path [2] should play a central role in the descrip- tion of the evolution of the electronic structure along a reac- tion path. Bader and his co-workers [3] have made some important achievements in this direction, particularly from a methodological point of view introducing Thom’s Catastro- phe Theory [4] (CT) for the first time in quantum chemistry. However, the applicability of AIM to the study of reaction mechanisms rapidly appeared to be mostly limited to intra- molecular processes because there is no topological change in the charge density gradient field when a diatom dissociates. Bader’s methodology has been further revisited by Krokidis et al. [5] who used the electron localization function (ELF) of Becke and Edgecombe [6] instead of the charge density. This approach, the bonding evolution theory (BET) accord- ing to its authors has proven its efficiency in a wide range of reactions such as proton transfers [7], two state reaction between a transition metal cation and a small molecule [8– 10], sigmatropic rearrangements [11], cyclizations [12–14], and ring opening reactions [15,16]. Nevertheless, as far as one is concerned by electronic reaction mechanisms (in other words electron density transfer along the reaction path), it is very important to recover a more traditional description of the bonding in terms of Lewis structures.
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9 Lee mas

Structures and stabilities of Aln+, Aln, and Aln− (n=13–34) clusters

Structures and stabilities of Aln+, Aln, and Aln− (n=13–34) clusters

As in our previous works, 55–57 the search for global minima was planned as a multistage task. In a first stage, we generated a sufficiently diverse set of initial structures for each cluster size. These structures are either taken directly from existing databases, 63 explicitly built by considering typical icosahedral, decahedral, and octahedral atomic pack- ing, or obtained by quenching from finite temperature simu- lations performed with the same SIESTA code. These trial structures include, in particular, the global minima of differ- ent potential models not necessarily mimicking aluminum clusters. In this sense, we employ the system comparison approach advocated by Paz-Borbón et al., 64 so that we do not rely on the accuracy of any potential model specifically de- signed for aluminum. This is especially important for Al clusters because, as previously mentioned, 55 present inter- atomic potentials do not describe well the structures of Al clusters. We also include explicitly in this first step the struc- tures previously obtained by other authors. In a second stage, all those structures are fully optimized with the SIESTA code. Some of the isomers can be excluded from further consider- ation at the end of this stage due to their very high energy. In a last and most computationally expensive stage, we take the five to ten more stable structures for each size and consider them as seeds for further refinement. From each cluster of size n, we build n + m and n − m clusters 共 with m = 1 – 5 兲 by adding or removing atoms from its surface in many different ways. Each time we identify a better minimum for a given cluster size, it is considered the seed for a new refinement cycle, which is stopped only when we repeatedly reobtain the same structures. The procedure is possibly as systematic as it can be without the explicit employment of unbiased algorithms, and the number of different isomers tried for each size is at least 100 共except for the smallest sizes n = 13– 15兲. The success of this “manual” search strategy has been demonstrated for larger clusters by the good agreement between the experimental and theoretical cohesive energies. 55,56 We expect it to be even more reliable for the smaller cluster sizes considered here, as the number of local minima on the PES is correspondingly reduced. In fact, a direct demonstration of the reliability of our search method is the fact that we find better global minima than previously reported for n = 19, 22, 24, 25, 26, 29, 30, 32, 33, 34.
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9 Lee mas

Análisis de sistemas dinámicos describiendo relatividad general en tres dimensiones

Análisis de sistemas dinámicos describiendo relatividad general en tres dimensiones

Como se ha comentado en la introducción, Holst introdujo una acción la cual depende de un parámetro, el parámetro de Barbero-Immirzi [17] , el cual lo llamaraemos de ahora en adelante el parámetro γ . En efecto, dependiendo de los valores que dicho parámetro tome, uno puede obtener los diferentes escenarios que se encuentran en gravedad canónica. Respecto a este punto, para el caso 3D existe una acción la cual es equivalente a la acción de Holst. Dicha acción es conocida como la acción de Bonzom-Livine. La acción de BL está formada por la acción de Palatini más la acción exótica acompañada del parámetro γ, de esta manera, la acción de BL da un conjunto de acciones que reproducen las mismas ecuaciones de movimiento que la acción exótica y la acción de Palatini. Cabe mencionar que en [39] se ha realizado un análisis canónico de la acción de BL, sin embargo, dicho análisis se ha hecho usando el formalismo de Dirac reducido. De esta manera, en esta sección vamos a desarrollar un análisis detallado de la acción de BL mediante el formalismo de Dirac estricto. En general, estamos interesados en conocer la estructura completa de las restricciones y conocer como es la estructura simpléctica de los corchetes de Dirac, así, con este análisis podremos ver cuales son las diferencias entre las acciones de Palatini, exótica y la de BL, dado que las tres acciones conducen a las mismas ecuaciones de movimiento.
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171 Lee mas

La construcción del territorio del Monasterio de San Lorenzo de El Escorial  Agua, territorio y paisaje

La construcción del territorio del Monasterio de San Lorenzo de El Escorial Agua, territorio y paisaje

Eduardo Torroja y la International Association for Shell and Spatial Structures (IASS) Eduardo Torroja and the International Association for Shell and Spatial Structures (IASS) R. Astudi[r]

20 Lee mas

Lilliam Sívoli, Elevina Pérez, Mary Lares y Edgardo Leal
ESTUDIOS DE LOS CAMBIOS CONFORMACIONALES, ESTRUCTURA GRANULAR Y CRISTALINA, Y DIGESTIBILIDAD IN VITRO DE ALMIDONES DE MAÍZ ENTRECRUZADOS Y METILADOS (en inglés)

Lilliam Sívoli, Elevina Pérez, Mary Lares y Edgardo Leal ESTUDIOS DE LOS CAMBIOS CONFORMACIONALES, ESTRUCTURA GRANULAR Y CRISTALINA, Y DIGESTIBILIDAD IN VITRO DE ALMIDONES DE MAÍZ ENTRECRUZADOS Y METILADOS (en inglés)

Van der Burgt et al. (1999) reported that the crystalline linear side-chains of the amy- lopectin in methylated starch- es, which play an important role in the retrogradation of gelatinized starches, contain fewer substituents, than the amorphous branched parts and that they are almost randomly distributed. The same authors (Van der Burgt et al., 2000b) also demonstrated that the methylation process does not have any preference for substi- tution at either branched or lin- early linked glucose residues, taking into account the inher- ently lower amount of substi- tuted sites at branched residues. In order to learn about the relationship between structure and function, it is important to determine the changes in the starch molecules after modi- fication by the derivatization processes and to measure their
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5 Lee mas

Service life design and modelling of concrete structures – background, developments, and implementation

Service life design and modelling of concrete structures – background, developments, and implementation

Service life modelling for reinforced concrete structures involves quantitative calculations or estimates to predict the time to unacceptable damage (e.g. cracking, corrosion, loss of section, etc.) for a given environment. Service life models are often semi-empirical in nature, based on laboratory and site data that are necessary for calibration. Alternatively, SLMs can be constructed from ‘first principles’, using ionic or reactive transport models and principles of flow in porous media (Van der Lee, et al., 2008); these models elaborate the ‘transport-interaction’ aspects of fluid or ionic flow in the concrete, with approaches based on thermodynamic and geochemical principles (Guillon et al, 2013). However, such models are not necessarily more accurate or reliable in their predictions, and the added complexity does not always justify the results obtained. In any event, these models must also be calibrated from laboratory and site data, and herein lies the rub: in almost all cases, concretes of a range of mix constituents and proportions need to be tested in appropriate environments to collect data which can be used to calibrate or construct the model, and subsequently to predict the ingress of harmful substances. SLMs are also useful in ‘back-analysis’ of existing structures when the penetration of contaminants such as chlorides is known for a particular concrete and environment at a particular time; it is then possible to use the model to determine the time to corrosion and possibly damage as well if there is a linked damage model. For a full probabilistic approach, variability also needs to be considered (Muigai, et al, 2009).
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22 Lee mas

Application of research findings in earthquake disaster : Preparedness planning and management    International Research and Training Seminar on Regional Development Planning for Disaster Prevention  (1987 Oct 13 23:Tokyo)

Application of research findings in earthquake disaster : Preparedness planning and management International Research and Training Seminar on Regional Development Planning for Disaster Prevention (1987 Oct 13 23:Tokyo)

Opportunity should be utilized to learn lessons from the event for the future benefits by damage survey in a scientific manner, collecting instrumental and other field data from the effects of the earthquake like after-shock records, effects on well and spring water, changes of levels and distances, rockfalls and slips, fault ruptures, etc. It is useful to mention that much of present scienti­ fic learning about earthquakes owes 1t to the keen observations made by profes­ sionals as well as the public on what happened during the damaging earthquakes. There has always been something new to learn from each such happening. As a result of such observations through the ages, human ingenuity deveioped, based on locally available materials, such construct1on techniques which made the buildings adequately earthquake resistant. Examples can be cited of braced and brick-nogged wood frames in Jam TlU and Kashmir, Dhajji wall construction in Himachal Pradesh and Assam type Ikra construction in north-eastern regwn of India. Even sun-dried brick, adobe and rarnmed earth constructions had been so well strengthened by use of buttresses and wood elements m H1machal Pra­ desh in India and regions m Yemen Arab Republ1c that they have !asted for centuries under s eism1c environment. These techniques with further improve­ ments brought about by modern research efforts(l) can effectively be used
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26 Lee mas

Mathematical and Numerical Modeling in Maritime Geomechanics

Mathematical and Numerical Modeling in Maritime Geomechanics

Sea bed is usually modeled as a saturated poroelastoplastic media, composed by at least two constituents or phases, soil skeleton and pore fluid, each of them with an independent state of motion, leading to an interaction between them, i.e. a coupled system. In some cases sea bed pores might bear some occluded gas bubbles, raising the compressibility of the pore fluid. Among the different choices to describe this interaction behavior a macroscopic description of the phenomena is usually considered in geotechnical engineering modeling. This description rests over the volume fraction concept, i.e. porosity (Figure 1) where all geometric and physical quantities such as motion, deformation, and stress, are defined in the total control space, so they can be interpreted as the statistical average values of the real quantities. Therefore, the coupled domains are superimposed.
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21 Lee mas

Active patterns for self-optimization . Schemes for the design of intelligent mechatronic systems

Active patterns for self-optimization . Schemes for the design of intelligent mechatronic systems

Abstract. Self-optimizing mechatronic systems react autonomously and flexibly to changing conditions. They are capable of learning and optimize their behavior throughout their life cycle. The paradigm of self-optimization is originally inspired by the behavior of biological systems. The key to the successful development of self-optimizing systems is a conceptual design process that precisely describes the desired system behavior. In the area of mechanical engineering, active principles based on physical effects such as friction or lever are widely used to concretize the construction structure and the behavior. The same approach can be found in the domain of software- engineering with software patterns such as the broker-pattern or the strategy pattern. However there is no appropriate design schema for the development of intelligent mechatronic systems covering the needs to fulfill the paradigm of self-optimization. This article proposes such a schema called Active Patterns for Self-Optimization. It is shown how a catalogue of active patterns can be derived from a set of four basic active patterns. This design approach is validated for a networked mechatronic system in a multiagent setting where the behavior is implemented according to a biologically inspired technique – the neuro-fuzzy learning method.
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