143 resultados para LIE ALGEBRA


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Network Jamming systems provide real-time collaborative media performance experiences for novice or inexperienced users. In this paper we will outline the theoretical and developmental drivers for our Network Jamming software, called jam2jam. jam2jam employs generative algorithmic techniques with particular implications for accessibility and learning. We will describe how theories of engagement have directed the design and development of jam2jam and show how iterative testing cycles in numerous international sites have informed the evolution of the system and its educational potential. Generative media systems present an opportunity for users to leverage computational systems to make sense of complex media forms through interactive and collaborative experiences. Generative music and art are a relatively new phenomenon that use procedural invention as a creative technique to produce music and visual media. These kinds of systems present a range of affordances that can facilitate new kinds of relationships with music and media performance and production. Early systems have demonstrated the potential to provide access to collaborative ensemble experiences to users with little formal musical or artistic expertise.This presentation examines the educational affordances of these systems evidenced by field data drawn from the Network Jamming Project. These generative performance systems enable access to a unique kind of music/media’ ensemble performance with very little musical/ media knowledge or skill and they further offer the possibility of unique interactive relationships with artists and creative knowledge through collaborative performance. Through the process of observing, documenting and analysing young people interacting with the generative media software jam2jam a theory of meaningful engagement has emerged from the need to describe and codify how users experience creative engagement with music/media performance and the locations of meaning. In this research we observed that the musical metaphors and practices of ‘ensemble’ or collaborative performance and improvisation as a creative process for experienced musicians can be made available to novice users. The relational meanings of these musical practices afford access to high level personal, social and cultural experiences. Within the creative process of collaborative improvisation lie a series of modes of creative engagement that move from appreciation through exploration, selection, direction toward embodiment. The expressive sounds and visions made in real-time by improvisers collaborating are immediate and compelling. Generative media systems let novices access these experiences with simple interfaces that allow them to make highly professional and expressive sonic and visual content simply by using gestures and being attentive and perceptive to their collaborators. These kinds of experiences present the potential for highly complex expressive interactions with sound and media as a performance. Evidence that has emerged from this research suggest that collaborative performance with generative media is transformative and meaningful. In this presentation we draw out these ideas around an emerging theory of meaningful engagement that has evolved from the development of network jamming software. Primarily we focus on demonstrating how these experiences might lead to understandings that may be of educational and social benefit.

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The crystal structure of the modified unsymmetrically N, N'-substituted viologen chromophore, N-ethyl- N'-(2-phosphonoethyl)-4, 4'-bipyridinium dichloride 0.75 hydrate. (1) has been determined. Crystals are triclinic, space group P-1 with Z = 2 in a cell with a = 7.2550(1), b = 13.2038(5), c = 18.5752(7) Å, α = 86.495(3), β = 83.527(2), γ = 88.921(2)o. The two independent but pseudo-symmetrically related cations in the asymmetric unit form one-dimensional hydrogen-bonded chains through short homomeric phosphonic acid O-H...O links [2.455(4), 2.464(4)A] while two of the chloride anions are similarly strongly linked to phosphonic acid groups [O-H…Cl, 2.889(4), 2.896(4)Å]. The other two chloride anions together with the two water molecules of solvation (one with partial occupancy) form unusual cyclic hydrogen-bonded bis(Cl...water) dianion units which lie between the layers of bipyridylium rings of the cation chain structures with which they are weakly associated.

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In the structure of the title compound, the salt 2(C12H10N3O4+) (C12H8O6S2)2- . 3H2O, determined at 173 K, the biphenyl-4,4'-disulfonate dianions lie across crystallographic inversion centres with the sulfonate groups interacting head-to-head through centrosymmetric cyclic bis(water)-bridged hydrogen-bonding associations [graph set R4/4(11)], forming chain structures. The 2-(2,4-dinitrobenzyl)pyridinium cations are linked to these chains through N+-H...O(water) hydrogen bonds and a two-dimensional network structure is formed through water bridges between sulfonate and 2-nitro O atoms, while the structure also has weak cation--anion pi-pi aromatic ring interactions [minimum ring centroid separation 3.8441(13)A].

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This thesis investigates Theatre for Young People (TYP) as a site of performance innovation. The inquiry is focused on contemporary dramaturgy and its fieldwork aims to identify new dramaturgical principles operating in the creation and presentation of TYP. The research then seeks to assess how these new principles contribute to Postdramatic Theatre theory. This research inquiry springs from an imperative based in practice: Young people under 25 years have a literacy based on online hypertextual experiences which take the reader outside the frames of a dramatic narrative and beyond principles such as linearity, dramatic unity, teleology and resolution. As a dramaturg and educator I wanted to understand the new ways that young people engage in cultural products, to identify and utilize the new principles of dramaturgy that are now in evidence. My research examines how two playwright/directors approach their work and the new principles that can be identified in their dramaturgy. The fieldwork is scoped into two case studies: the first on TJ Eckleberg working in Australian Theatre for Young People and the second on Kristo Šagor working in German Children’s and Young People’s Theatre (KJT). These case studies address both types of production dramaturgy - the dramaturgy emergent through process in devised performance making, and that emergent in a performance based on a written playscript. On Case Study One the researcher, as participant observer, worked as production dramaturg on a large scale, site specific performance, observing the dramaturgy in process of its director and chief devisor. On Case Study Two the researcher, as observer and analyst, undertook a performance analysis of three playscripts and productions by a contemporary German playwright and director. Utilizing participant observation, reflective practice and grounded analysis the case studies have identified two new principles animating the dramaturgy of these TYP practitioners, namely ‘displacement’ and ‘installation.’ Taking practice into theory, the thesis concludes by demonstrating how displacement and installation contribute to Postdramatic Theatre’s “arsenal of expressive gestures which serve as theatre’s response to changed social communication under the conditions of generalized communication technologies” (Lehmann, H.-T., 2006, p.23). This research makes an original contribution to knowledge by evidencing that the principles of Postdramatic Theory lie within the practice of contemporary Theatre for Young People. It also contributes valuable research to a specialized, often overlooked terrain, namely Dramaturgy in Theatre for Young People, presented here with a contemporary, international and intercultural perspective.

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This paper describes an automated procedure for analysing the significance of each of the many terms in the equations of motion for a serial-link robot manipulator. Significance analysis provides insight into the rigid-body dynamic effects that are significant locally or globally in the manipulator's state space. Deleting those terms that do not contribute significantly to the total joint torque can greatly reduce the computational burden for online control, and a Monte-Carlo style simulation is used to investigate the errors thus introduced. The procedures described are a hybrid of symbolic and numeric techniques, and can be readily implemented using standard computer algebra packages.

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This thesis is about the derivation of the addition law on an arbitrary elliptic curve and efficiently adding points on this elliptic curve using the derived addition law. The outcomes of this research guarantee practical speedups in higher level operations which depend on point additions. In particular, the contributions immediately find applications in cryptology. Mastered by the 19th century mathematicians, the study of the theory of elliptic curves has been active for decades. Elliptic curves over finite fields made their way into public key cryptography in late 1980’s with independent proposals by Miller [Mil86] and Koblitz [Kob87]. Elliptic Curve Cryptography (ECC), following Miller’s and Koblitz’s proposals, employs the group of rational points on an elliptic curve in building discrete logarithm based public key cryptosystems. Starting from late 1990’s, the emergence of the ECC market has boosted the research in computational aspects of elliptic curves. This thesis falls into this same area of research where the main aim is to speed up the additions of rational points on an arbitrary elliptic curve (over a field of large characteristic). The outcomes of this work can be used to speed up applications which are based on elliptic curves, including cryptographic applications in ECC. The aforementioned goals of this thesis are achieved in five main steps. As the first step, this thesis brings together several algebraic tools in order to derive the unique group law of an elliptic curve. This step also includes an investigation of recent computer algebra packages relating to their capabilities. Although the group law is unique, its evaluation can be performed using abundant (in fact infinitely many) formulae. As the second step, this thesis progresses the finding of the best formulae for efficient addition of points. In the third step, the group law is stated explicitly by handling all possible summands. The fourth step presents the algorithms to be used for efficient point additions. In the fifth and final step, optimized software implementations of the proposed algorithms are presented in order to show that theoretical speedups of step four can be practically obtained. In each of the five steps, this thesis focuses on five forms of elliptic curves over finite fields of large characteristic. A list of these forms and their defining equations are given as follows: (a) Short Weierstrass form, y2 = x3 + ax + b, (b) Extended Jacobi quartic form, y2 = dx4 + 2ax2 + 1, (c) Twisted Hessian form, ax3 + y3 + 1 = dxy, (d) Twisted Edwards form, ax2 + y2 = 1 + dx2y2, (e) Twisted Jacobi intersection form, bs2 + c2 = 1, as2 + d2 = 1, These forms are the most promising candidates for efficient computations and thus considered in this work. Nevertheless, the methods employed in this thesis are capable of handling arbitrary elliptic curves. From a high level point of view, the following outcomes are achieved in this thesis. - Related literature results are brought together and further revisited. For most of the cases several missed formulae, algorithms, and efficient point representations are discovered. - Analogies are made among all studied forms. For instance, it is shown that two sets of affine addition formulae are sufficient to cover all possible affine inputs as long as the output is also an affine point in any of these forms. In the literature, many special cases, especially interactions with points at infinity were omitted from discussion. This thesis handles all of the possibilities. - Several new point doubling/addition formulae and algorithms are introduced, which are more efficient than the existing alternatives in the literature. Most notably, the speed of extended Jacobi quartic, twisted Edwards, and Jacobi intersection forms are improved. New unified addition formulae are proposed for short Weierstrass form. New coordinate systems are studied for the first time. - An optimized implementation is developed using a combination of generic x86-64 assembly instructions and the plain C language. The practical advantages of the proposed algorithms are supported by computer experiments. - All formulae, presented in the body of this thesis, are checked for correctness using computer algebra scripts together with details on register allocations.

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This paper presents a simple and intuitive approach to determining the kinematic parameters of a serial-link robot in Denavit– Hartenberg (DH) notation. Once a manipulator’s kinematics is parameterized in this form, a large body of standard algorithms and code implementations for kinematics, dynamics, motion planning, and simulation are available. The proposed method has two parts. The first is the “walk through,” a simple procedure that creates a string of elementary translations and rotations, from the user-defined base coordinate to the end-effector. The second step is an algebraic procedure to manipulate this string into a form that can be factorized as link transforms, which can be represented in standard or modified DH notation. The method allows for an arbitrary base and end-effector coordinate system as well as an arbitrary zero joint angle pose. The algebraic procedure is amenable to computer algebra manipulation and a Java program is available as supplementary downloadable material.

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In a consumerist society obsessed with body image and thinness, obesity levels have reached an all-time high. This multi-faceted book written by a range of experts, explores the social, cultural, clinical and psychological factors that lie behind the Obesity Epidemic . It is required reading for the many healthcare professionals dealing with the effects of obesity and for anyone who wants to know more about the causes of weight gain and the best ways of dealing with it. Fat Matters covers a range of issues from sociology through medicine to technology. This is not a book for the highly specialised expert. Rather it is a book that shows the diversity of approaches to the phenomenon of obesity, tailored to the reader who wants to be up-to-date and well-informed on a subject that is possibly as frequently discussed and as misunderstood as the weather.

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Fourier transfonn (FT) Raman, Raman microspectroscopy and Fourier transform infrared (FTIR) spectroscopy have been used for the structural analysis and characterisation of untreated and chemically treated wool fibres. For FT -Raman spectroscopy novel methods of sample presentation have been developed and optimised for the analysis of wool. No significant fluorescence was observed and the spectra could be obtained routinely. The stability of wool keratin to the laser source was investigated and the visual and spectroscopic signs of sample damage were established. Wool keratin was found to be extremely robust with no signs of sample degradation observed for laser powers of up to 600 m W and for exposure times of up to seven and half hours. Due to improvements in band resolution and signal-to-noise ratio, several previously unobserved spectral features have become apparent. The assignment of the Raman active vibrational modes of wool have been reviewed and updated to include these features. The infrared spectroscopic techniques of attenuated total reflectance (ATR) and photoacoustic (P A) have been used to examine shrinkproofed and mothproofed wool samples. Shrinkproofing is an oxidative chemical treatment used to selectively modifY the surface of a wool fibre. Mothproofing is a chemical treatment applied to wool for the prevention of insect attack. The ability of PAS and A TR to vary the penetration depth by varying certain instrumental parameters was used to obtain spectra of the near surface regions of these chemically treated samples. These spectra were compared with those taken with a greater penetration depth, which therefore represent more of the bulk wool sample. The PA and ATR spectra demonstrated that oxidation was restricted to the near-surface layer of wool. Extensive curve fitting of ATR spectra of untreated wool indicated that cuticle was composed of a mixed protein conformation, but was predominately that of an a.-helix. The cortex was proposed to be a mixture of both a.helical and ~-pleated sheet protein conformations. These findings were supported by PAS depth profiling results. Raman microspectroscopy was used in an extensive investigation of the molecular structure of the wool fibre. This included determining the orientation of certain functional groups within the wool fibre and the symmetry of particular vibrations. The orientation ofbonds within the wool fibre was investigated by orientating the wool fibre axis parallel and then perpendicular to the plane of polarisation of the electric vector of the incident radiation. It was experimentally determined that the majority of C=O and N-H bonds of the peptide bond of wool lie parallel to the fibre axis. Additionally, a number of the important vibrations associated with the a-helix were also found to lie parallel to the fibre axis. Further investigation into the molecular structure of wool involved determining what effect stretching the wool fibre had on bond orientation. Raman spectra of stretched and unstretched wool fibres indicated that extension altered the orientation ofthe aromatic rings, the CH2 and CH3 groups of the amino acids. Curve fitting results revealed that extension resulted in significant destruction of the a-helix structure a substantial increase in the P-pleated sheet structure. Finally, depolarisation ratios were calculated for Raman spectra. The vibrations associated with the aromatic rings of amino acids had very low ratios which indicated that the vibrations were highly symmetrical.

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In the structure of the title compound, C6H13N2O+ C8H7O2- . 0.5H2O, the asymmetric unit comprises two isonipecotamide cations, two phenylacetate anions and a water molecule of solvation. The hydrogen-bonding environments for both sets of ion pairs are essentially identical with the piperidinium and amide 'ends' of each cation involved in lateral heteromolecular hydrogen-bonded cyclic N---H...O associations [graph set R2/2(11)] which incorporate a single carboxyl O-atom acceptor. These cyclic motifs enclose larger R5/5(21) cyclic systems forming sheet substructures which lie parallel to (101) and are linked across b by the single water molecule via water O---H...O(carboxyl) associations to give a two-dimensional duplex-sheet structure

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Over the last three years, in our Early Algebra Thinking Project, we have been studying Years 3 to 5 students’ ability to generalise in a variety of situations, namely, compensation principles in computation, the balance principle in equivalence and equations, change and inverse change rules with function machines, and pattern rules with growing patterns. In these studies, we have attempted to involve a variety of models and representations and to build students’ abilities to switch between them (in line with the theories of Dreyfus, 1991, and Duval, 1999). The results have shown the negative effect of closure on generalisation in symbolic representations, the predominance of single variance generalisation over covariant generalisation in tabular representations, and the reduced ability to readily identify commonalities and relationships in enactive and iconic representations. This chapter uses the results to explore the interrelation between generalisation and verbal and visual comprehension of context. The studies evidence the importance of understanding and communicating aspects of representational forms which allowed commonalities to be seen across or between representations. Finally the chapter explores the implications of the studies for a theory that describes a growth in integration of models and representations that leads to generalisation.