Relevant bibliographies by topics / Projective Lattice

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Projective Lattice'

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Published: 6 September 2023

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Journal articles on the topic "Projective Lattice"

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de Pagter, Ben, and Anthony W. Wickstead. "Free and projective Banach lattices." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 145, no. 1 (January 30, 2015): 105–43. http://dx.doi.org/10.1017/s0308210512001709.

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We define and prove the existence of free Banach lattices in the category of Banach lattices and contractive lattice homomorphisms, and establish some of their fundamental properties. We give much more detailed results about their structure in the case when there are only a finite number of generators, and give several Banach lattice characterizations of the number of generators being, respectively, one, finite or countable. We define a Banach lattice P to be projective if, whenever X is a Banach lattice, J is a closed ideal in X, Q : X → X/J is the quotient map, T : P → X/J is a linear lattice homomorphism and ε > 0, there exists a linear lattice homomorphism : P → X such that T = Q º and ∥∥ ≤ (1 + ε)∥T∥. We establish the connection between projective Banach lattices and free Banach lattices, describe several families of Banach lattices that are projective and prove that some are not.
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Symonds, Peter. "Relative characters for H-projective RG-lattices." Mathematical Proceedings of the Cambridge Philosophical Society 104, no. 2 (September 1988): 207–13. http://dx.doi.org/10.1017/s0305004100065397.

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If G is a group with a subgroup H and R is a Dedekind domain, then an H-projective RG-lattice is an RG-lattice that is a direct summand of an induced lattice for some RH-lattice N: they have been studied extensively in the context of modular representation theory. If H is the trivial group these are the projective lattices. We define a relative character χG/H on H-projective lattices, which in the case H = 1 is equivalent to the Hattori–Stallings trace for projective lattices (see [5, 8]), and in the case H = G is the ordinary character. These characters can be used to show that the R-ranks of certain H-projective lattices must be divisible by some specified number, generalizing some well-known results: cf. Corollary 3·6. If for example we take R = ℤ, then |G/H| divides the ℤ-rank of any H-projective ℤG-lattice.
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Pfeiffer, Thorsten, and Stefan E. Schmidt. "Projective mappings between projective lattice geometries." Journal of Geometry 54, no. 1-2 (November 1995): 105–14. http://dx.doi.org/10.1007/bf01222858.

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RUMP, WOLFGANG. "CHARACTERIZATION OF PROJECTIVE QUANTALES." Journal of the Australian Mathematical Society 100, no. 3 (January 8, 2016): 403–20. http://dx.doi.org/10.1017/s1446788715000506.

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It is proved that a quantale is projective if and only if it is isomorphic to a derived tensor quantale over a completely distributive sup-lattice. Furthermore, an intrinsic characterization of projectivity is given in terms of inertial sup-lattices and derivations of quantales.
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Jakubík, Ján. "On projective intervals in a modular lattice." Mathematica Bohemica 117, no. 3 (1992): 293–98. http://dx.doi.org/10.21136/mb.1992.126283.

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Uchino, K. "Arnold's Projective Plane and -Matrices." Advances in Mathematical Physics 2010 (2010): 1–9. http://dx.doi.org/10.1155/2010/956128.

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We will explain Arnold's 2-dimensional (shortly, 2D) projective geometry (Arnold, 2005) by means of lattice theory. It will be shown that the projection of the set of nontrivial triangular -matrices is the pencil of tangent lines of a quadratic curve on Arnold's projective plane.
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Zhuravlev, V., and I. Tsyganivska. "Projective lattices of tiled orders." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 4 (2018): 16–19. http://dx.doi.org/10.17721/1812-5409.2018/4.2.

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Tiled orders over discrete valuation ring have been studied since the 1970s by many mathematicians, in particular, by Yategaonkar V.A., Tarsy R.B., Roggenkamp K.W, Simson D., Drozd Y.A., Zavadsky A.G. and Kirichenko V.V. Yategaonkar V.A. proved that for every n > 2, there is, up to an isomorphism, a finite number of tiled orders over a discrete valuation ring O of finite global dimension which lie in $M_n(K)$ where K is a field of fractions of a commutatively discrete valuation ring O. The articles by R.B. Tarsy, V.A. Yategaonkar, H. Fujita, W. Rump and others are devoted to the study of the global dimension of tiled orders. H. Fujita described the reduced tiled orders in Mn(D) of finite global dimension for n = 4; 5. V.M. Zhuravlev and D.V. Zhuravlev described reduced tiled orders in Mn(D) of finite global dimension for n = 6: This paper examines the necessary condition for the finiteness of the global dimension of the tile order. Let A be a tiled order. The kernel of the projective resolvent of an irreducible lattice has the form M1f1 +M2f2 + ::: +Msfs, where Mi is irreducible lattice, fi is some vector. If the tile order has a finite global dimension, then there is a projective lattice that is the intersection of projective lattices. This condition is the one explored in the paper.
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Day, Alan. "Doubling Constructions in Lattice Theory." Canadian Journal of Mathematics 44, no. 2 (April 1, 1992): 252–69. http://dx.doi.org/10.4153/cjm-1992-017-7.

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AbstractThis paper examines the simultaneous doubling of multiple intervals of a lattice in great detail. In the case of a finite set of W-failure intervals, it is shown that there in a unique smallest lattice mapping homomorphically onto the original lattice, in which the set of W-failures is removed. A nice description of this new lattice is given. This technique is used to show that every lattice that is a bounded homomorphic image of a free lattice has a projective cover. It is also used to give a sufficient condition for a fintely presented lattice to be weakly atomic and shows that the problem of which finitely presented lattices are finite is closely related to the problem of characterizing those finite lattices with a finite W-cover.
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Hirai, Hiroshi. "Uniform modular lattices and affine buildings." Advances in Geometry 20, no. 3 (July 28, 2020): 375–90. http://dx.doi.org/10.1515/advgeom-2020-0007.

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AbstractA simple lattice-theoretic characterization for affine buildings of type A is obtained. We introduce a class of modular lattices, called uniform modular lattices, and show that uniform modular lattices and affine buildings of type A constitute the same object. This is an affine counterpart of the well-known equivalence between projective geometries (≃ complemented modular lattices) and spherical buildings of type A.
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Osofsky, Barbara L. "Projective dimension is a lattice invariant." Journal of Pure and Applied Algebra 161, no. 1-2 (July 2001): 205–17. http://dx.doi.org/10.1016/s0022-4049(00)00090-6.

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Dissertations / Theses on the topic "Projective Lattice"

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Le, Tran Bach. "On k-normality and regularity of normal projective toric varieties." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/31531.

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We study the relationship between geometric properties of toric varieties and combinatorial properties of the corresponding lattice polytopes. In particular, we give a bound for a very ample lattice polytope to be k-normal. Equivalently, we give a new combinatorial bound for the Castelnuovo-Mumford regularity of normal projective toric varieties. We also give a new combinatorial proof for a special case of Reider's Theorem for smooth toric surfaces.
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Hart, A. "Magnetic monopoles and confinement in lattice gauge theory." Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.337718.

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Hickel, Tilmann. "Theory of many body effects in the Kondo lattice model projection operator method /." [S.l.] : [s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=980739764.

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Yoon, Young-jin. "Characterizations of Some Combinatorial Geometries." Thesis, University of North Texas, 1992. https://digital.library.unt.edu/ark:/67531/metadc277894/.

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We give several characterizations of partition lattices and projective geometries. Most of these characterizations use characteristic polynomials. A geometry is non—splitting if it cannot be expressed as the union of two of its proper flats. A geometry G is upper homogeneous if for all k, k = 1, 2, ... , r(G), and for every pair x, y of flats of rank k, the contraction G/x is isomorphic to the contraction G/y. Given a signed graph, we define a corresponding signed—graphic geometry. We give a characterization of supersolvable signed graphs. Finally, we give the following characterization of non—splitting supersolvable signed-graphic geometries : If a non-splitting supersolvable ternary geometry does not contain the Reid geometry as a subgeometry, then it is signed—graphic.
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Hickel, Tilmann. "Theory of many-body effects in the Kondo-lattice model." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2006. http://dx.doi.org/10.18452/15500.

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Das magnetische Verhalten zahlreicher Materialien lässt sich auf eine indirekte Wechselwirkung lokalisierter magnetischer Momente, vermittelt durch die Elektronen eines Leitungsbandes, zurückführen. Das Kondo-Gitter-Modell hat sich als elegante Möglichkeit bewährt, diesen Prozess quantenmechanisch zu beschreiben. Es reduziert die Physik auf eine intraatomare Wechselwirkung der Spins von lokalisierten und itineranten Elektronen. Die vorliegende Arbeit ist den analytischen Eigenschaften dieses Modells gewidmet. Die besondere Herausforderung des Kondo-Gitter-Modells besteht dabei im Zusammenwirken zweier verschiedener Teilchensorten, beschrieben durch Fermi-Operatoren sowie quantenmechanische Spins. Bisherige Untersuchungen haben sich in der Regel nur auf eine der beiden Teilchensorten konzentriert. Mit der Projektions-Operator-Methode stellen wir eine Möglichkeit vor, beide Teilsysteme in gleicher Qualität zu behandeln. Die Auswertung des Teilsystems der itineranten Elektronen führt auf einen Ausdruck für die Selbstenergie, der lineare und quadratische Effekte in der Wechselwirkung exakt beschreibt. Die resultierenden Zustandsdichten weisen starke Korrelationseffekte auf. Deren Untersuchung dient sowohl der Bestätigung von Ergebnissen weniger systematischer Zugänge als auch dem Aufzeigen neuer Vielteilchen-Phänomene. Die Anwendung der Projektions-Operator-Methode auf das System der lokalisierten Momente führt zu einer Analyse der bereits bekannten RPA (random phase approximation). Zu diesem Zweck werden die Magnonenspektren und die Curie-Temperaturen systematisch untersucht. Dabei treten bisher unbekannte Schwachpunkte der RPA zu Tage, die auch die Kombination mit Theorien für das itinerante Teilsystem verhindern. Verbesserungen und Alternativen zur RPA werden diskutiert.
The magnetic behaviour of various materials is due to an indirect interaction of localized magnetic moments, which is based on itinerant electrons in a conduction band. The Kondo-lattice model is an elegant approach for a quantum-mechanical description of this process. It reduces the relevant physics to an intra-atomic exchange interaction of the localized and the itinerant electrons. The aim of the present work is a detailed investigation of analytic properties of this model. Here, the interplay of two distinct types of particles, described by Fermi operators and quantum-mechanical spin operators respectively, is a major challenge of the considered model. Previous studies have focused on one of these subsystems only. Using the projection-operator method, we suggest an efficient way to describe both subsystems on the same level of approximation. An evaluation of the subsystem of itinerant electrons yields an expression for the self-energy, which describes linear and quadratic interaction effects exactly. The densities of states derived with this theory show strong correlation effects. We were able to assess results obtained with less systematic approaches and to predict new many-particle effects. The application of the projection-operator method to the subsystem of localized magnetic moments results in a detailed analysis of the RPA (random phase approximation). The dependence of magnon spectra and Curie temperatures on model parameters are investigated systematically. Previously unknown drawbacks of the RPA are revealed, which prevent the combination of these results with theories for the itinerant subsystem. Improvements beyond RPA and alternative approximations are discussed.
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Addakiri, Soumia. "Développement de schémas hybrides de tvpe Lattice Boltzmann : volumes Finis pour la modélisation des transferts de chaleur et de masse en projection thermique." Limoges, 2010. https://aurore.unilim.fr/theses/nxfile/default/733f20cb-3ea7-4e5a-bb01-f3d1aad91633/blobholder:0/2010LIMO4071.pdf.

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Dans ce travail de thèse, le transfert de chaleur et de masse est modélisé numériquement par la méthode de Boltzmann sur réseau (Lattice Boltzmann). Dans un premier temps, les fondements de base de cette méthode numérique sont présentés. Une attention particulière est donnée à l'application de cette méthode aux problèmes de diffusion multidimensionnels. Dans un second temps, l'extension de la méthode de Boltzmann sur réseau est traitée: d'une part pour résoudre les phénomènes de transmission à l'interface, d'autre part pour résoudre un problème diphasique solide-liquide par l'élaboration d'un couplage entre la méthode LBM non uniforme et la méthode des volumes finis
In this thesis, we formulate and implement the numerical modeling of the heat and the mass transfer by the Lattice Boltzmann method (LBM). In a first part we present the basic foundations of this numerical method. Particular attention is given to the application of this method to multidimensional diffusion problems. In a second part we treat an extension of the Lattice Boltzmann method: firstly to solve the transmission phenomena at the interface, secondly to solve a two-phase solid-liquid through the development of a coupling between the non-uniform LBM method and finite volume method
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Rammal, Hadia. "Problèmes de Complémentarité aux Valeurs Propres : Théories, Algorithmes et Applications." Limoges, 2013. http://aurore.unilim.fr/theses/nxfile/default/08806eb2-33e6-4642-b821-b7218aaac0f2/blobholder:0/2013LIMO4036.pdf.

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Cette thèse porte sur le développement des méthodes mathématiques applicables à l’étude théorique et numérique d’une large classe de problèmes unilatéraux. Nous considérons plus particulièrement les problèmes de complémentarité aux valeurs propres PCVP engendrés par le cône de Pareto et le cône de Lorentz. De tels problèmes apparaissent dans de nombreuses disciplines scientifiques comme la physique, la mécanique et l’ingénierie. Dans un premier temps, nous nous intéressons à la résolution de PCVP en utilisant une méthode adéquate, “Lattice Projection Method LPM”, menant à un résultat efficace et performant. L’originalité de cette formulation, en comparaison avec la littérature existante, réside dans le fait qu’elle ne repose pas sur l’approche de complémentarité. Notre contribution se reflète aussi par l’étude des conditions de la non-singularité des matrices Jacobiennes utilisées dans la méthode de Newton semi-lisse SNM pour détecter les solutions de tels problèmes. Ensuite, en nous basant sur les profils de performance, nous comparons LPM avec d’autres solveurs très connus dans la littérature. Les résultats obtenus s’avèrent en accord avec les observations expérimentales et montrent l’efficacité de LPM. Dans un second temps, nous traitons le cas stochastique de PCVP au sens des cônes de Pareto et de Lorentz. Nous reformulons un tel problème pour trouver les zéros d’une fonction semi-lisse. Ensuite, nous étudions les conditions de la non-singularité de la Jacobienne de cette fonction pour résoudre de tels problèmes. Puis, nous transformons le problème sous forme d’un problème de minimisation. Dans un dernier temps, nous abordons le problème inverse de complémentarité aux valeurs propres de Pareto PICVP. Cette tâche s’articule plus précisément sur la résolution de PICVP où nous présentons une nouvelle méthode, “Inverse Lattice Projection Method ILPM”, pour résoudre ces problèmes
This manuscript deals with the development of mathematical methods applicable to the theoretical and numerical study of a wide class of unilateral problems. To put it more precisely, we consider the Pareto and Lorentz cones eigenvalue complementarity problems PCVP. Such problems appear in many scientific disciplines such as physics, mechanics and engineering. Firstly, we are interested to the resolution of PCVP using an adequate method, “Lattice Projection Method LPM”, leading to an efficient and effective result. The originality of this formulation in comparison with the existing literature is that it is not based on the complementarity approach. Then, our contribution is reflected in the study of the non-singularity conditions of the Jacobian matrices used in the semismooth Newton method SNM to detect solutions of such problems. Then, by using the performance profiles, we compare LPM with other solvers known in the literature. The results prove in accordance with the experimental observations and show the efficiency of LPM. Secondly, we treat the stochastic case of PCVP in the sense of Pareto and Lorentz cones. We reformulate such problem to find the zeros of a semismooth function. Furthermore, we study the non-singularity conditions of the Jacobian matrix of this function to solve such problems. Moreover, we transform the problem as a constrained minimization reformulation. Finally, we discuss the inverse Pareto eigenvalue complementarity problem PICVP. This task focuses more precisely on the resolution of PICVP where we present a new method, “Inverse Lattice Projection Method ILPM”, to solve such problems
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Bookjans, Eva M. "Relative number squeezing in a Spin-1 Bose-Einstein condensate." Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/37148.

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The quantum properties of matter waves, in particular quantum correlations and entanglement are an important frontier in atom optics with applications in quantum metrology and quantum information. In this thesis, we report the first observation of sub-Poissonian fluctuations in the magnetization of a spinor 87Rb condensate. The fluctuations in the magnetization are reduced up to 10 dB below the classical shot noise limit. This relative number squeezing is indicative of the predicted pair-correlations in a spinor condensate and lay the foundation for future experiments involving spin-squeezing and entanglement measurements. We have investigated the limits of the imaging techniques used in our lab, absorption and fluorescence imaging, and have developed the capability to measure atoms numbers with an uncertainly < 10 atoms. Condensates as small as ≈ 10 atoms were imaged and the measured fluctuations agree well with the theoretical predictions. Furthermore, we implement a reliable calibration method of our imaging system based on quantum projection noise measurements. We have resolved the individual lattice sites of a standing-wave potential created by a CO2 laser, which has a lattice spacing of 5.3 µm. Using microwaves, we site-selectively address and manipulate the condensate and therefore demonstrate the ability to perturb the lattice condensate of a local level. Interference between condensates in adjacent lattice sites and lattice sites separated by a lattice site are observed.
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Doan, Van Tu. "Modèles réduits pour des analyses paramètriques du flambement de structures : application à la fabrication additive." Thesis, Valenciennes, 2018. http://www.theses.fr/2018VALE0017/document.

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Le développement de la fabrication additive permet d'élaborer des pièces de forme extrêmement complexes, en particulier des structures alvéolaires ou "lattices", où l'allégement est recherché. Toutefois, cette technologie, en très forte croissance dans de nombreux secteurs d'activités, n'est pas encore totalement mature, ce qui ne facilite pas les corrélations entre les mesures expérimentales et les simulations déterministes. Afin de prendre en compte les variations de comportement, les approches multiparamétriques sont, de nos jours, des solutions pour tendre vers des conceptions fiables et robustes. L'objectif de cette thèse est d'intégrer des incertitudes matérielles et géométriques, quantifiées expérimentalement, dans des analyses de flambement. Pour y parvenir, nous avons, dans un premier temps, évalué différentes méthodes de substitution, basées sur des régressions et corrélations, et différentes réductions de modèles afin de réduire les temps de calcul prohibitifs. Les projections utilisent des modes issus soit de la décomposition orthogonale aux valeurs propres, soit de développements homotopiques ou encore des développements de Taylor. Dans un second temps, le modèle mathématique, ainsi créé, est exploité dans des analyses ensemblistes et probabilistes pour estimer les évolutions de la charge critique de flambement de structures lattices
The development of additive manufacturing allows structures with highly complex shapes to be produced. Complex lattice shapes are particularly interesting in the context of lightweight structures. However, although the use of this technology is growing in numerous engineering domains, this one is not enough matured and the correlations between the experimental data and deterministic simulations are not obvious. To take into account observed variations of behavior, multiparametric approaches are nowadays efficient solutions to tend to robust and reliable designs. The aim of this thesis is to integrate material and geometric uncertainty, experimentally quantified, in buckling analyses. To achieve this objective, different surrogate models, based on regression and correlation techniques as well as different reduced order models have been first evaluated to reduce the prohibitive computational time. The selected projections rely on modes calculated either from Proper Orthogonal Decomposition, from homotopy developments or from Taylor series expansion. Second, the proposed mathematical model is integrated in fuzzy and probabilistic analyses to estimate the evolution of the critical buckling load for lattice structures
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Pai, Srikanth B. "Classical Binary Codes And Subspace Codes in a Lattice Framework." Thesis, 2015. http://etd.iisc.ernet.in/handle/2005/2708.

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The classical binary error correcting codes, and subspace codes for error correction in random network coding are two different forms of error control coding. We identify common features between these two forms and study the relations between them using the aid of lattices. Lattices are partial ordered sets where every pair of elements has a least upper bound and a greatest lower bound in the lattice. We shall demonstrate that many questions that connect these forms have a natural motivation from the viewpoint of lattices. We shall show that a lattice framework captures the notion of Singleton bound where the bound is on the size of the code as a function of its parameters. For the most part, we consider a special type of a lattice which has the geometric modular property. We will use a lattice framework to combine the two different forms. And then, in order to demonstrate the utility of this binding view, we shall derive a general version of Singleton bound. We will note that the Singleton bounds behave differently in certain respects because the binary coding framework is associated with a lattice that is distributive. We shall demonstrate that lack of distributive gives rise to a weaker bound. We show that Singleton bound for classical binary codes, subspace codes, rank metric codes and Ferrers diagram rank metric codes can be derived using a common technique. In the literature, Singleton bounds are derived for Ferrers diagram rank metric codes where the rank metric codes are linear. We introduce a generalized version of Ferrers diagram rank metric codes and obtain a Singleton bound for this version. Next, we shall prove a conjecture concerning the constraints of embedding a binary coding framework into a subspace framework. We shall prove a conjecture by Braun, Etzion and Vardy, which states that any such embedding which contains the full space in its range is constrained to have a particular size. Our proof will use a theorem due to Lovasz, a subspace counting theorem for geometric modular lattices, to prove the conjecture. We shall further demonstrate that any code that achieves the conjectured size must be of a particular type. This particular type turns out to be a natural distributive sub-lattice of a given geometric modular lattice.
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Books on the topic "Projective Lattice"

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Schmidt, Stefan E. Projektive Räume mit geordneter Punktmenge. Giessen: Selbstverlag des Mathematischen Instituts, 1987.

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Sardella, Edson. Elastic properties of the Abrikosov flux line lattice for anisotropic superconductors and some applications of the projection operator method to phenomenological and exact Hamiltonian systems. Manchester: University of Manchester, 1993.

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Petrich, M. Categories of Algebraic Systems: Vector and Projective Spaces, Semigroups, Rings and Lattices. Springer London, Limited, 2006.

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Hrushovski, Ehud, and François Loeser. A closer look at the stable completion. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161686.003.0005.

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This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is extended to the projective setting. The linear topology is then related to the one induced by the finite level morphism L(Hsubscript d). The chapter also considers the condition that if a definable set in L(Hsubscript d) is an intersection of relatively compact sets, then it is itself relatively compact.
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Succi, Sauro. The Hermite–Gauss Route to LBE. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0015.

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This chapter describes the side-up approach to Lattice Boltzmann, namely the formal derivation from the continuum Boltzmann-(BGK) equation via Hermite projection and subsequent evaluation of the kinetic moments via Gauss–Hermite quadrature. From a slightly different angle, one may also interpret the Gauss–Hermite quadrature as an optimal sampling of velocity space, or, better still, an exact sampling of the bulk of the distribution function, the one contributing most to the lowest order kinetic moments (frequent events). Capturing higher–order moments, beyond hydrodynamics (rare events), requires an increasing number of nodes and weights.
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Book chapters on the topic "Projective Lattice"

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Faure, Claude-Alain, and Alfred Frölicher. "Fundamental Notions of Lattice Theory." In Modern Projective Geometry, 1–24. Dordrecht: Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-015-9590-2_1.

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Wang, Zilong, Honggang Hu, Mengce Zheng, and Jiehui Nan. "Symmetric Lattice-Based PAKE from Approximate Smooth Projective Hash Function and Reconciliation Mechanism." In Communications in Computer and Information Science, 95–106. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-15-0818-9_7.

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Faure, Claude-Alain, and Alfred Frölicher. "Lattices of Closed Subspaces." In Modern Projective Geometry, 301–22. Dordrecht: Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-015-9590-2_13.

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Faure, Claude-Alain, and Alfred Frölicher. "Projective Geometries and Projective Lattices." In Modern Projective Geometry, 25–53. Dordrecht: Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-015-9590-2_2.

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Freese, Ralph, Jaroslav Jezek, and J. Nation. "Sublattices of free lattices and projective lattices." In Mathematical Surveys and Monographs, 95–134. Providence, Rhode Island: American Mathematical Society, 1995. http://dx.doi.org/10.1090/surv/042/05.

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Bost, Jean-Benoît. "Infinite-Dimensional Vector Bundles over Smooth Projective Curves." In Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves, 219–36. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-44329-0_9.

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Katz, Jonathan, and Vinod Vaikuntanathan. "Smooth Projective Hashing and Password-Based Authenticated Key Exchange from Lattices." In Advances in Cryptology – ASIACRYPT 2009, 636–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-10366-7_37.

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Bost, Jean-Benoît. "Countably Generated Projective Modules and Linearly Compact Tate Spaces over Dedekind Rings." In Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves, 77–106. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-44329-0_4.

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Bost, Jean-Benoît. "Summable Projective Systems of Hermitian Vector Bundles and Finiteness of θ-Invariants." In Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves, 155–75. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-44329-0_7.

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Haymaker, Richard W., and Andrei Alexandru. "Connections Between Thin, Thick and Projection Vortices in SU(2) Lattice Gauge Theory." In Confinement, Topology, and Other Non-Perturbative Aspects of QCD, 197–204. Dordrecht: Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-010-0502-9_21.

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Conference papers on the topic "Projective Lattice"

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Solus, Liam. "Local h*-polynomials of some weighted projective spaces." In Summer Workshop on Lattice Polytopes. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789811200489_0024.

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Tran, Bach Le. "A Reider-type result for smooth projective toric surfaces." In Summer Workshop on Lattice Polytopes. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789811200489_0027.

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Portakal, Irem. "A note on deformations and mutations of fake weighted projective planes." In Summer Workshop on Lattice Polytopes. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789811200489_0022.

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Sharpe, Conner, Carolyn Conner Seepersad, Seth Watts, and Dan Tortorelli. "Design of Mechanical Metamaterials via Constrained Bayesian Optimization." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-85270.

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Advances in additive manufacturing processes have made it possible to build mechanical metamaterials with bulk properties that exceed those of naturally occurring materials. One class of these metamaterials is structural lattices that can achieve high stiffness to weight ratios. Recent work on geometric projection approaches has introduced the possibility of optimizing these architected lattice designs in a drastically reduced parameter space. The reduced number of design variables enables application of a new class of methods for exploring the design space. This work investigates the use of Bayesian optimization, a technique for global optimization of expensive non-convex objective functions through surrogate modeling. We utilize formulations for implementing probabilistic constraints in Bayesian optimization to aid convergence in this highly constrained engineering problem, and demonstrate results with a variety of stiff lightweight lattice designs.
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Kazemi, Hesaneh, Ashkan Vaziri, and Julián Norato. "Topology Optimization of Multi-Material Lattices for Maximal Bulk Modulus." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-97370.

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Abstract In this paper, we present a method for multi-material topology optimization of lattice structures for maximum bulk modulus. Unlike ground structure approaches that employ 1-d finite elements such as bars and beams to design periodic lattices, we employ a 3-d representation where each lattice bar is described as a cylinder. To accommodate the 3-d bars, we employ the geometry projection method, whereby a high-level parametric description of the bars is smoothly mapped onto a density field over a fixed analysis grid. In addition to the geometric parameters, we assign a size variable per material to each bar. By imposing suitable constraints in the optimization, we ensure that each bar is either made exclusively of one of a set of a multiple available materials or completely removed from the design. These optimization constraints, together with the material interpolation used in our formulation, make it easy to consider any number of available materials. Another advantage of our method over ground structure approaches with 1-d elements is that the bars in our method need not be connected at all times (i.e., they can ‘float’ within the design region), which makes it easier to find good designs with relatively few design variables. We illustrate the effectiveness of our method with numerical examples of bulk modulus maximization for two-material lattices with orthotropic symmetry, and for two- and three-material lattices with cubic symmetry.
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von Smekal, Lorenz, Dhagash B. Mehta, and Andre Sternbeck. "Lattice Landau Gauge via Stereographic Projection." In VIIIth Conference Quark Confinement and the Hadron Spectrum. Trieste, Italy: Sissa Medialab, 2012. http://dx.doi.org/10.22323/1.077.0048.

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Cusatis, Gianluca, Daniele Pelessone, Andrea Mencarelli, and James T. Baylot. "Simulation of Reinforced Concrete Structures Under Blast and Penetration Through Lattice Discrete Particle Modeling." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-43744.

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In this study, the Lattice Discrete Particle Model (LDPM), a recently developed three-dimensional meso-level model for concrete, is used to simulate the behavior of reinforced concrete under severe loading conditions. LDPM simulates concrete through an assemblage of particles (coarse aggregate pieces) connected through a lattice mesh. In order to simulate steel reinforcement, a mesh of plastic beams is embedded in the lattice system. Nonlinear concrete-reinforcement bond is also included in the formulation. The effectiveness of the approach is demonstrated through the simulation of projectile penetration into reinforced concrete slabs and blast spallation of dividing walls.
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Bahabad, Alon, Noa Voloch, and Ady Arie. "New Quasi Phase Matching Options by Lattice Projection." In Laser Science. Washington, D.C.: OSA, 2006. http://dx.doi.org/10.1364/ls.2006.pdp_fb5.

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Xu, Jun, and Shuning Wang. "Lattice piecewise affine representations on convex projection regions." In 2019 IEEE 58th Conference on Decision and Control (CDC). IEEE, 2019. http://dx.doi.org/10.1109/cdc40024.2019.9030119.

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Bahabad, Alon, Noa Voloch, and Ady Arie. "New Quasi Phase Matching Options by Lattice Projection." In Frontiers in Optics. Washington, D.C.: OSA, 2006. http://dx.doi.org/10.1364/fio.2006.pdp_fb5.

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