Academic literature on the topic 'Jacobi equivalence'
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Journal articles on the topic "Jacobi equivalence"
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Kozhan, Rostyslav. "Equivalence classes of block Jacobi matrices." Proceedings of the American Mathematical Society 139, no. 03 (March 1, 2011): 799. http://dx.doi.org/10.1090/s0002-9939-2010-10582-8.
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Ryckman, E. "A spectral equivalence for Jacobi matrices." Journal of Approximation Theory 146, no. 2 (June 2007): 252–66. http://dx.doi.org/10.1016/j.jat.2006.12.005.
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Murre, J. P. "Abel-Jacobi equivalence versus incidence equivalence for algebraic cycles of codimension two." Topology 24, no. 3 (1985): 361–67. http://dx.doi.org/10.1016/0040-9383(85)90008-4.
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Koornwinder, Tom H. "On the equivalence of two fundamental theta identities." Analysis and Applications 12, no. 06 (October 22, 2014): 711–25. http://dx.doi.org/10.1142/s0219530514500559.
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Two fundamental theta identities, a three-term identity due to Weierstrass and a five-term identity due to Jacobi, both with products of four theta functions as terms, are shown to be equivalent. One half of the equivalence was already proved by R. J. Chapman in 1996. The history and usage of the two identities, and some generalizations are also discussed.
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Lekner, John. "Four solutions of a two-cylinder electrostatic problem, and identities resulting from their equivalence." Quarterly Journal of Mechanics and Applied Mathematics 73, no. 3 (August 1, 2020): 251–60. http://dx.doi.org/10.1093/qjmam/hbaa010.
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Summary Four distinct solutions exist for the potential distribution around two equal circular parallel conducting cylinders, charged to the same potential. Their equivalence is demonstrated, and the resulting analytical identities are discussed. The identities relate the Jacobi elliptic function $sn$, the Jacobi theta functions $\theta _1 ,~\theta _2 $ and infinite series over trigonometric and hyperbolic functions.
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Faraggi, Alon E., and Marco Matone. "Equivalence principle, Planck length and quantum Hamilton–Jacobi equation." Physics Letters B 445, no. 1-2 (December 1998): 77–81. http://dx.doi.org/10.1016/s0370-2693(98)01484-1.
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Faraggi, Alon E. "The Equivalence Postulate of Quantum Mechanics, Dark Energy, and the Intrinsic Curvature of Elementary Particles." Advances in High Energy Physics 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/957394.
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The equivalence postulate of quantum mechanics offers an axiomatic approach to quantum field theories and quantum gravity. The equivalence hypothesis can be viewed as adaptation of the classical Hamilton-Jacobi formalism to quantum mechanics. The construction reveals two key identities that underlie the formalism in Euclidean or Minkowski spaces. The first is a cocycle condition, which is invariant underD-dimensional Möbius transformations with Euclidean or Minkowski metrics. The second is a quadratic identity which is a representation of theD-dimensional quantum Hamilton-Jacobi equation. In this approach, the solutions of the associated Schrödinger equation are used to solve the nonlinear quantum Hamilton-Jacobi equation. A basic property of the construction is that the two solutions of the corresponding Schrödinger equation must be retained. The quantum potential, which arises in the formalism, can be interpreted as a curvature term. The author proposes that the quantum potential, which is always nontrivial and is an intrinsic energy term characterising a particle, can be interpreted as dark energy. Numerical estimates of its magnitude show that it is extremely suppressed. In the multiparticle case the quantum potential, as well as the mass, is cumulative.
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Xie, Chuanfu. "The equivalence between two jacobi identities for twisted vertex operators." Communications in Algebra 23, no. 7 (January 1995): 2453–67. http://dx.doi.org/10.1080/00927879508825354.
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Wang, Jianjun, Chan-Yun Yang, and Shukai Duan. "Approximation Order for Multivariate Durrmeyer Operators with Jacobi Weights." Abstract and Applied Analysis 2011 (2011): 1–12. http://dx.doi.org/10.1155/2011/970659.
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Using the equivalence relation betweenK-functional and modulus of smoothness, we establish a strong direct theorem and an inverse theorem of weak type for multivariate Bernstein-Durrmeyer operators with Jacobi weights on a simplex in this paper. We also obtain a characterization for multivariate Bernstein-Durrmeyer operators with Jacobi weights on a simplex. The obtained results not only generalize the corresponding ones for Bernstein-Durrmeyer operators, but also give approximation order of Bernstein-Durrmeyer operators.
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Zanelli, Lorenzo. "Hamilton–Jacobi Homogenization and the Isospectral Problem." Symmetry 13, no. 7 (July 2, 2021): 1196. http://dx.doi.org/10.3390/sym13071196.
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We consider the homogenization theory for Hamilton–Jacobi equations on the one-dimensional flat torus in connection to the isospectrality problem of Schrödinger operators. In particular, we link the equivalence of effective Hamiltonians provided by the weak KAM theory with the class of the corresponding operators exhibiting the same spectrum.
Dissertations / Theses on the topic "Jacobi equivalence"
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Hitchcock, Yvonne Roslyn. "Elliptic curve cryptography for lightweight applications." Thesis, Queensland University of Technology, 2003. https://eprints.qut.edu.au/15838/1/Yvonne_Hitchcock_Thesis.pdf.
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Elliptic curves were first proposed as a basis for public key cryptography in the mid 1980's. They provide public key cryptosystems based on the difficulty of the elliptic curve discrete logarithm problem (ECDLP) , which is so called because of its similarity to the discrete logarithm problem (DLP) over the integers modulo a large prime. One benefit of elliptic curve cryptosystems (ECCs) is that they can use a much shorter key length than other public key cryptosystems to provide an equivalent level of security. For example, 160 bit ECCs are believed to provide about the same level of security as 1024 bit RSA. Also, the level of security provided by an ECC increases faster with key size than for integer based discrete logarithm (dl) or RSA cryptosystems. ECCs can also provide a faster implementation than RSA or dl systems, and use less bandwidth and power. These issues can be crucial in lightweight applications such as smart cards. In the last few years, ECCs have been included or proposed for inclusion in internationally recognized standards. Thus elliptic curve cryptography is set to become an integral part of lightweight applications in the immediate future. This thesis presents an analysis of several important issues for ECCs on lightweight devices. It begins with an introduction to elliptic curves and the algorithms required to implement an ECC. It then gives an analysis of the speed, code size and memory usage of various possible implementation options. Enough details are presented to enable an implementer to choose for implementation those algorithms which give the greatest speed whilst conforming to the code size and ram restrictions of a particular lightweight device. Recommendations are made for new functions to be included on coprocessors for lightweight devices to support ECC implementations Another issue of concern for implementers is the side-channel attacks that have recently been proposed. They obtain information about the cryptosystem by measuring side-channel information such as power consumption and processing time and the information is then used to break implementations that have not incorporated appropriate defences. A new method of defence to protect an implementation from the simple power analysis (spa) method of attack is presented in this thesis. It requires 44% fewer additions and 11% more doublings than the commonly recommended defence of performing a point addition in every loop of the binary scalar multiplication algorithm. The algorithm forms a contribution to the current range of possible spa defences which has a good speed but low memory usage. Another topic of paramount importance to ECCs for lightweight applications is whether the security of fixed curves is equivalent to that of random curves. Because of the inability of lightweight devices to generate secure random curves, fixed curves are used in such devices. These curves provide the additional advantage of requiring less bandwidth, code size and processing time. However, it is intuitively obvious that a large precomputation to aid in the breaking of the elliptic curve discrete logarithm problem (ECDLP) can be made for a fixed curve which would be unavailable for a random curve. Therefore, it would appear that fixed curves are less secure than random curves, but quantifying the loss of security is much more difficult. The thesis performs an examination of fixed curve security taking this observation into account, and includes a definition of equivalent security and an analysis of a variation of Pollard's rho method where computations from solutions of previous ECDLPs can be used to solve subsequent ECDLPs on the same curve. A lower bound on the expected time to solve such ECDLPs using this method is presented, as well as an approximation of the expected time remaining to solve an ECDLP when a given size of precomputation is available. It is concluded that adding a total of 11 bits to the size of a fixed curve provides an equivalent level of security compared to random curves. The final part of the thesis deals with proofs of security of key exchange protocols in the Canetti-Krawczyk proof model. This model has been used since it offers the advantage of a modular proof with reusable components. Firstly a password-based authentication mechanism and its security proof are discussed, followed by an analysis of the use of the authentication mechanism in key exchange protocols. The Canetti-Krawczyk model is then used to examine secure tripartite (three party) key exchange protocols. Tripartite key exchange protocols are particularly suited to ECCs because of the availability of bilinear mappings on elliptic curves, which allow more efficient tripartite key exchange protocols.
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Hitchcock, Yvonne Roslyn. "Elliptic Curve Cryptography for Lightweight Applications." Queensland University of Technology, 2003. http://eprints.qut.edu.au/15838/.
Full textAbstract:
Elliptic curves were first proposed as a basis for public key cryptography in the mid 1980's. They provide public key cryptosystems based on the difficulty of the elliptic curve discrete logarithm problem (ECDLP) , which is so called because of its similarity to the discrete logarithm problem (DLP) over the integers modulo a large prime. One benefit of elliptic curve cryptosystems (ECCs) is that they can use a much shorter key length than other public key cryptosystems to provide an equivalent level of security. For example, 160 bit ECCs are believed to provide about the same level of security as 1024 bit RSA. Also, the level of security provided by an ECC increases faster with key size than for integer based discrete logarithm (dl) or RSA cryptosystems. ECCs can also provide a faster implementation than RSA or dl systems, and use less bandwidth and power. These issues can be crucial in lightweight applications such as smart cards. In the last few years, ECCs have been included or proposed for inclusion in internationally recognized standards. Thus elliptic curve cryptography is set to become an integral part of lightweight applications in the immediate future. This thesis presents an analysis of several important issues for ECCs on lightweight devices. It begins with an introduction to elliptic curves and the algorithms required to implement an ECC. It then gives an analysis of the speed, code size and memory usage of various possible implementation options. Enough details are presented to enable an implementer to choose for implementation those algorithms which give the greatest speed whilst conforming to the code size and ram restrictions of a particular lightweight device. Recommendations are made for new functions to be included on coprocessors for lightweight devices to support ECC implementations Another issue of concern for implementers is the side-channel attacks that have recently been proposed. They obtain information about the cryptosystem by measuring side-channel information such as power consumption and processing time and the information is then used to break implementations that have not incorporated appropriate defences. A new method of defence to protect an implementation from the simple power analysis (spa) method of attack is presented in this thesis. It requires 44% fewer additions and 11% more doublings than the commonly recommended defence of performing a point addition in every loop of the binary scalar multiplication algorithm. The algorithm forms a contribution to the current range of possible spa defences which has a good speed but low memory usage. Another topic of paramount importance to ECCs for lightweight applications is whether the security of fixed curves is equivalent to that of random curves. Because of the inability of lightweight devices to generate secure random curves, fixed curves are used in such devices. These curves provide the additional advantage of requiring less bandwidth, code size and processing time. However, it is intuitively obvious that a large precomputation to aid in the breaking of the elliptic curve discrete logarithm problem (ECDLP) can be made for a fixed curve which would be unavailable for a random curve. Therefore, it would appear that fixed curves are less secure than random curves, but quantifying the loss of security is much more difficult. The thesis performs an examination of fixed curve security taking this observation into account, and includes a definition of equivalent security and an analysis of a variation of Pollard's rho method where computations from solutions of previous ECDLPs can be used to solve subsequent ECDLPs on the same curve. A lower bound on the expected time to solve such ECDLPs using this method is presented, as well as an approximation of the expected time remaining to solve an ECDLP when a given size of precomputation is available. It is concluded that adding a total of 11 bits to the size of a fixed curve provides an equivalent level of security compared to random curves. The final part of the thesis deals with proofs of security of key exchange protocols in the Canetti-Krawczyk proof model. This model has been used since it offers the advantage of a modular proof with reusable components. Firstly a password-based authentication mechanism and its security proof are discussed, followed by an analysis of the use of the authentication mechanism in key exchange protocols. The Canetti-Krawczyk model is then used to examine secure tripartite (three party) key exchange protocols. Tripartite key exchange protocols are particularly suited to ECCs because of the availability of bilinear mappings on elliptic curves, which allow more efficient tripartite key exchange protocols.
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TORTORELLA, ALFONSO GIUSEPPE. "Deformations of coisotropic submanifolds in Jacobi manifolds." Doctoral thesis, 2017. http://hdl.handle.net/2158/1077777.
Full textAbstract:
In this thesis, we investigate deformation theory and moduli theory of coisotropic submanifolds in Jacobi manifolds. Originally introduced by Kirillov as local Lie algebras with one dimensional fibers, Jacobi manifolds encompass, unifying and generalizing, locally conformal symplectic manifolds, locally conformal Poisson manifolds, and non-necessarily coorientable contact manifolds.
We attach an L-infinity-algebra to any coisotropic submanifold in a Jacobi manifold. Our construction generalizes and unifies analogous constructions by Oh-Park (symplectic case), Cattaneo-Felder (Poisson case), and Le-Oh (locally conformal symplectic case). As a completely new case we also associate an L-infinity-algebra with any coisotropic submanifold in a contact manifold. The L-infinity-algebra of a coisotropic submanifold S controls the formal coisotropic deformation problem of S, even under Hamiltonian equivalence, and provides criteria both for the obstructedness and for the unobstructedness at the formal level. Additionally we prove that if a certain condition ("fiberwise entireness") is satisfied then the L-infinity-algebra controls the non-formal coisotropic deformation problem, even under Hamiltonian equivalence.
We associate a BFV-complex with any coisotropic submanifold in a Jacobi manifold. Our construction extends an analogous construction by Schatz in the Poisson setting, and in particular it also applies in the locally conformal symplectic/Poisson setting and the contact setting. Unlike the L-infinity-algebra, we prove that, with no need of any restrictive hypothesis, the BFV-complex of a coisotropic submanifold S controls the non-formal coisotropic deformation problem of S, even under both Hamiltonian equivalence and Jacobi equivalence.
Notwithstanding the differences there is a close relation between the approaches to the coisotropic deformation problem via L-infinity-algebra and via BFV-complex. Indeed both the L-infinity-algebra and the BFV-complex of a coisotropic submanifold S provide a cohomological reduction of S. Moreover they are L-infinity quasi-isomorphic and so they encode equally well the moduli space of formal coisotropic deformations of S under Hamiltonian equivalence.
In addition we exhibit two examples of coisotropic submanifolds in the contact setting whose coisotropic deformation problem is obstructed at the formal level. Further we provide a conceptual explanation of this phenomenon both in terms of the L-infinity-algebra and in terms of the BFV-complex.
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Cochran, Caroline. "THE EQUIVALENCE PROBLEM FOR ORTHOGONALLY SEPARABLE WEBS ON SPACES OF CONSTANT CURVATURE." 2011. http://hdl.handle.net/10222/14191.
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This thesis is devoted to creating a systematic way of determining all inequivalent
orthogonal coordinate systems which separate the Hamilton-Jacobi equation for a
given natural Hamiltonian defined on three-dimensional spaces of constant, non-zero
curvature. To achieve this, we represent the problem with Killing tensors and employ
the recently developed invariant theory of Killing tensors.
Killing tensors on the model spaces of spherical and hyperbolic space enjoy a
remarkably simple form; even more striking is the fact that their parameter tensors
admit the same symmetries as the Riemann curvature tensor, and thus can be
considered algebraic curvature tensors. Using this property to obtain invariants and
covariants of Killing tensors, together with the web symmetries of the associated orthogonal
coordinate webs, we establish an equivalence criterion for each space. In
the case of three-dimensional spherical space, we demonstrate the surprising result
that these webs can be distinguished purely by the symmetries of the web. In the
case of three-dimensional hyperbolic space, we use a combination of web symmetries,
invariants and covariants to achieve an equivalence criterion. To completely solve the
equivalence problem in each case, we develop a method for determining the moving
frame map for an arbitrary Killing tensor of the space. This is achieved by defining
an algebraic Ricci tensor.
Solutions to equivalence problems of Killing tensors are particularly useful in the
areas of multiseparability and superintegrability. This is evidenced by our analysis
of symmetric potentials defined on three-dimensional spherical and hyperbolic space.
Using the most general Killing tensor of a symmetry subspace, we derive the most
general potential “compatible” with this Killing tensor. As a further example, we
introduce the notion of a joint invariant in the vector space of Killing tensors and use
them to characterize a well-known superintegrable potential in the plane.
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Books on the topic "Jacobi equivalence"
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Murre, Jacob. Lectures on Algebraic Cycles and Chow Groups. Edited by Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, and Lê Dũng Tráng. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161341.003.0009.
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This chapter showcases five lectures on algebraic cycles and Chow groups. The first two lectures are over an arbitrary field, where they examine algebraic cycles, Chow groups, and equivalence relations. The second lecture also offers a short survey on the results for divisors. The next two lectures are over the complex numbers. The first of these features discussions on the cycle map, the intermediate Jacobian, Abel–Jacobi map, and the Deligne cohomology. The following lecture focuses on algebraic versus homological equivalence, as well as the Griffiths group. The final lecture, which returns to the arbitrary field, discusses the Albanese kernel and provides the results of Mumford, Bloch, and Bloch–Srinivas.
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Mercati, Flavio. Best Matching: Technical Details. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198789475.003.0005.
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The best matching procedure described in Chapter 4 is equivalent to the introduction of a principal fibre bundle in configuration space. Essentially one introduces a one-dimensional gauge connection on the time axis, which is a representation of the Euclidean group of rotations and translations (or, possibly, the similarity group which includes dilatations). To accommodate temporal relationalism, the variational principle needs to be invariant under reparametrizations. The simplest way to realize this in point–particle mechanics is to use Jacobi’s reformulation of Mapertuis’ principle. The chapter concludes with the relational reformulation of the Newtonian N-body problem (and its scale-invariant variant).
Book chapters on the topic "Jacobi equivalence"
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van den Essen, Arno, Shigeru Kuroda, and Anthony J. Crachiola. "The Jacobian Conjecture: New Equivalences." In Frontiers in Mathematics, 91–111. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-60535-3_4.
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Tang, Limin, and Bo Wu. "IGN Method and Matrices Equivalence of Regularization Jacobian Matrix in Solving NLS Survey Adjustment Problems." In Lecture Notes in Civil Engineering, 1023–34. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-2349-6_70.
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Adam, John A. "Introduction to the Mathematics of Rays." In Rays, Waves, and Scattering. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691148373.003.0003.
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This chapter provides an overview of the mathematics of rays. It begins with a discussion of the theory of geometrical optics and how it can be formulated by means of the ray equations or the Hamilton-Jacobi equation. The two equations are of seemingly different types, but they are in fact equivalent. The ray equations are the characteristic equations of the Hamilton-Jacobi equation. This remark leads to the geometrical interpretation: the family of rays of geometrical optics is perpendicular to the wavefronts S = constant, if S denotes the appropriate solution of the Hamilton-Jacobi equation. The chapter considers the Hamilton-Jacobi theory in more detail, along with Hamilton's principle, ray differential geometry and the eikonal equation, and dispersion relations. It also presents the general solution of the linear wave equation before concluding with an analysis of the behavior of rays and waves in a slowly varying environment.
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Björk, Tomas. "Stochastic Optimal Control." In Arbitrage Theory in Continuous Time, 333–50. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198851615.003.0025.
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We study a general stochastic optimal control problem within the framework of a controlled SDE. This problem is studied using dynamic programming and we derive the Hamilton–Jacobi–Bellman PDE. By stating and proving a verification theorem we show that solving this PDE is equivalent to solving the control problem. As an example the theory is then applied to the linear quadratic regulator.
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Stundžia, Bonifacas. "Compound Calques in an Eighteenth-Century German-Lithuanian Dictionary." In The Interaction of Borrowing and Word Formation, 67–85. Edinburgh University Press, 2020. http://dx.doi.org/10.3366/edinburgh/9781474448208.003.0005.
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This chapter presents research on the Lithuanian determinative, possessive, and verbal governing compound calques that were patterned on the German compounds encountered in the manuscript of the 18th c. German-Lithuanian dictionary by Jacob Brodowski from East Prussia (Lithuania Minor). The author distinguishes between absolute compound calques (i.e. item-by-item copies of donor language compounds, including both the pattern of a compound and the semantics of its members) and non-absolute (or creative) compound calques that have differences in the semantics of one member, in the pattern of the compound, or in both. The analysis also encompasses the overall characteristics of the Lithuanian compounds and their German equivalents as well as the integration of compound calques into the word formation system of Lithuanian.
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Sime, Stuart. "Inherent Jurisdiction and the Limits of Civil Procedure." In Principles, Procedure, and Justice, 269–90. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198850410.003.0014.
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This chapter considers the modern scope and limitations on the use of the court’s inherent jurisdiction in common law jurisdictions. It considers the underlying juridical basis for the jurisdiction, and the underlying theories, namely that residuary powers were vested in the High Court in England and Wales by the Judicature Acts, and that all courts have inherent powers to prevent abuse of process. It considers the ramifications of the distinction between inherent jurisdiction and inherent powers. Changes in the legal landscape since the seminal articles by Master Jacob and Professor Dockray, including the codification of civil procedure in many common law jurisdictions, and modern understanding of the rule of law and the separation of powers, are considered. It is argued that while existing applications of the inherent jurisdiction should be retained, it is no longer acceptable for the English High Court, and equivalent courts in other jurisdictions, to generate new procedural law by resorting to the inherent jurisdiction.
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Cummings, Brian. "The Book After the French Revolution." In Bibliophobia, 333–49. Oxford University Press, 2022. http://dx.doi.org/10.1093/oso/9780192847317.003.0021.
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The modern book appears to be denuded of its associations with either holiness or embodiment. A book is a book, equivalent to a mundane sense of contents. Letter appears to give way to spirit alone. This chapter considers the French Revolution as a threshold of modernity in attitudes towards writing and the press, including concepts of copyright and the free press. These ideas are examined both in relation to the production of books, and in the representation of writing in visual art, such as David’s Death of Marat. Rather than a process of desacralization, this is revealed as a crisis in the idea of ‘spirit’. The concept is analysed philosophically in relation to Hegel’s Phenomenology of Spirit, and then historically in the revolutionary quarrels between Robespierre and other Jacobins, and the use of the guillotine as a literal metaphor of justice. As reason triumphs, the repressed body returns.
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Constantinesco, Thomas. "Willing Pain in Harriet Jacobs’s Incidents in the Life of a Slave Girl." In Writing Pain in the Nineteenth-Century United States, 59–86. Oxford University Press, 2022. http://dx.doi.org/10.1093/oso/9780192855596.003.0003.
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This chapter explores how Harriet Jacobs’s Incidents in the Life of a Slave Girl (1861) exposes the problematic function of pain in the disciplinary apparatus of slavery and in the constitution of Black subjectivity. It considers how Jacobs illuminates the contradiction of slavery’s biopolitical power, which treated enslaved men and women as both possessing and not possessing a will. As property, the chapter shows, enslaved people had no will, only a body that did not belong to them; as legal persons, they were granted a negative will of criminal intent, which returned them to their commodified body, experienced through the pain of forced labor and corporeal punishment. The chapter demonstrates however that, rather than seeking to escape from body to will, Jacobs’s journey from enslavement to emancipation takes the form of a looping structure, whereby she comes to will her own pain of body and mind through her escape in the “loophole of retreat” she finds in her grandmother’s garret. It further argues that the narrativization of her pain complicates the equivalence between literacy and liberation that underwrites slave narratives, as much as it challenges the conventions of sentimentalism that Incidents nevertheless deploys. It eventually makes the claim that, by willing pain as a paradoxical source of agency, Jacobs’s narrative reveals how pain is integral both to the reappropriation of embodied selfhood and to the familial and social bonds she strives to recover after her flight from enslavement.
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Carr, David M. "The Non-P Primeval History." In The Formation of Genesis 1-11, 223–49. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780190062545.003.0009.
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This chapter surveys two main levels in the non-Priestly primeval history. The first is an originally independent primeval history that likely started with the Garden of Eden story and concluded with the account of Shem’s fathering of “all of the sons of Eber”—the closest primeval equivalent the non-P author could have for later Israelites who possessed traditions of the origins of their people from post-Primeval ancestors (e.g., Abraham, Jacob) and/or out of an exodus from Egypt. This originally independent primeval history contained various materials, but it centered in particular on three stories exploring the three major types of pairs of relationships in a patriarchal primary family: (hu)man-wife (Genesis 2–3), brother-brother (Gen 4:1–16), and father-son (Gen 9:20–27). Since this history treats what it takes to be age-old truths and only features semimythic loci such as Eden (Gen 2:8) and the “land of Nod” (Gen 4:16), it provides few indicators with which to date it. Nevertheless, it seems to precede the previously discussed revision of this history through the addition of a flood narrative, a Babel account, Nimrod materials, and also some version of the non-P ancestral story that follows. These latter materials show various signs of likely authorship in the Neo-Assyrian period, drawing deeply and specifically on Mesopotamian traditions (e.g., flood narratives) and mentioning Mesopotamian topoi already prominent in the Neo-Assyrian period (e.g., Babylon, Nineveh).
Conference papers on the topic "Jacobi equivalence"
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Luk, Franklin T., and Haesun Park. "On The Equivalence And Convergence Of Parallel Jacobi SVD Algorithms." In 31st Annual Technical Symposium, edited by Franklin T. Luk. SPIE, 1988. http://dx.doi.org/10.1117/12.942028.
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Mattson, Keith G., and Gordon R. Pennock. "A Geometric Inspection of Two 3-R Robots Manipulating a Four-Bar Linkage Payload: The Velocity Problems." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0099.
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Abstract This paper presents solutions to the forward and inverse velocity problems of two planar three-degree-of-freedom robots, with all revolute joints, manipulating a planar four-bar linkage payload. These kinematic problems are formulated in terms of two Jacobian matrices: one associated with the independent inputs to the robots, and the other associated with the payload outputs. The paper emphasizes how both Jacobian matrices can be obtained from a geometric inspection of the system. This provides kinematic insight into the system and is believed to be important in the design and control of cooperating robot workcells. The paper also shows that the inverse of the Jacobian matrix associated with the independent inputs can be obtained directly from inspection. The inverse of the Jacobian matrix associated with the outputs is obtained from geometric inspection by considering a four-input mechanism equivalent to the passive part of the system. Choosing one input at a time, the instantaneous centers of zero velocity provide relationships between the outputs of the mechanism and each input. The matrix is then formulated from these relationships using the principle of superposition of the outputs. The paper also presents the singular and stationary configurations associated with the system and emphasizes the geometric interpretation of these configurations. For illustrative purposes, a numerical example is included which shows how singular and stationary configurations effect the solutions to the velocity problems.
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Huang, K. J., C. C. Liang, and J. Y. Chen. "Time Varying Approaches to Dynamic Analysis of a Planetary Gear System Using a Discrete and a Continuous Models." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34100.
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Two time varying approaches are executed in analyzing dynamics for an involute planetary gear system, which respectively use a conventional discrete model of the equivalent mass-damping-spring elements and a continuous geometry model by the finite element method. In the discrete approach, the tooth number, position, and phasing difference of the meshing tooth pairs are described by time varying and nonlinear meshing stiffnesses. Natural frequencies, deformations, meshing forces, fillet stresses, and dynamic factors can be calculated by using the Jacobi transformation and the Runge-Kutta integration. In the continuum approach, dynamics of the planetary gear system is analyzed using the software, LS-DYNA. The approach of the continuous geometry model can incorporate the time varying properties intrinsically. In this continuum study, not CAD models, high quality mesh elements of the planetary gear system are automatically generated directly using the derived tooth profile equations. After assigning initial and boundary conditions, dynamic responses for the planetary gear system are solved. Natural frequencies and fillet stresses of the both approaches are verified by each other comparison. Potentially, the continuum approach can extensively and sophistically analyze dynamics problems of the planetary gear systems.
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Lu, Yi, and Zhen Huang. "Resolution of Singular Configuration Space of 3/6-SPS Parallel Manipulator Using an Equivalent SC Simulation Mechanism." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84112.
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The determination of the 6-dimensional singular configurations (SC) space of 3/6-SPS Stewart parallel manipulator is a very important and quite complicated problem. For a long time, its developments, however, have been very limited, especially the general-linear complex-SC (GSC). Currently, the Jacobian matrix and the Grassmann line geometry have been used to solve the SC space of the Stewart parallel robot. However, these two approaches are not straightforward. In this paper, a novel computer aided geometric approach is proposed for solving the 6-dimensional SC space of the 3/6-SPS Stewart parallel manipulator. First, a simulation mechanism of the 3/6-SPS parallel manipulator is created. Second, its equivalent SC simulation mechanism is created. Third, from the equivalent SC simulation mechanism, some analytical geometry formulas for solving 6-dimension SC space are derived. Finally, some SC space characteristics are analyzed, and some important developments are achieved.
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Ting, Kwun-Lon, and Yufeng Long. "Performance Quality, Sensitivity, and Tolerance Specification of Mechanisms." In ASME 1994 Design Technical Conferences collocated with the ASME 1994 International Computers in Engineering Conference and Exhibition and the ASME 1994 8th Annual Database Symposium. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/detc1994-0217.
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Abstract By employing Taguchi’s concept to mechanism synthesis, this paper presents the theory and technique to identify a robust design, which is the least sensitive to the tolerances, for mechanisms and to determine the tolerance specification for the best performance and manufacturability. The method is demonstrated in finite and infinitesimal position synthesis. The sensitivity Jacobian is first introduced to relate the performance tolerances and the dimensional tolerances. The Rayleigh quotient of the sensitivity Jacobian, which is equivalent to Taguchi’s signal to noise ratio, is then used to define the performance quality and a sensitivity index is introduced to measure the sensitivity of the performance quality to the dimensional tolerances for the whole system. The ideal tolerance specification is obtained in closed form. It shows how the tolerance specification affects the performance quality and that the performance quality can be significantly improved by tightening a key tolerance while loosening the others. The theory is general and the technique is readily adaptable to almost any form and type of mechanical system, including multiple-loop linkages and mechanical assemblies or even structures.
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Chablat, Damien, Erika Ottaviano, and Guillaume Moroz. "A Comparative Study of 4-Cable Planar Manipulators Based on Cylindrical Algebraic Decomposition." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47726.
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The aim of this paper is to present a systematic method for verifying the force-closure condition for general 3-DOF fully-constrained cable manipulators with four cables as based on the CAD (Cylindrical Algebraic Decomposition). A fundamental requirement for a cable manipulator to be fully controllable is that all its cables must be in tension at any working configurations. In other words, all the cable forces must be positive (assuming a positive cable force representing a tension and a negative cable force being a compression). Such a force feasibility problem is indeed referred to a force-closure problem (also called vector-closure problem assuming that the vectors of interest are the row vectors of the Jacobian matrix of the manipulator). The boundaries of the workspace can be obtained by the study of the Jacobian matrix of the manipulator. Therefore, this is equivalent to study the singularity conditions of four 3-RPR parallel robots. By using algebraic tools, it is possible to determine the singularity surfaces and their intersections yielding the workspace. Thus, it will be shown that the use of the CAD allows to get an implicit representation of the workspace as a set of cells. A comparative workspace analysis of three designs of mobile platforms, a line, a square and a triangle will be presented and discussed in this paper for a planar 4-cable fully-constrained robot.
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Safak, Koray K. "Dynamics and Stability of Locomotion for Actively Powered Simplest Walkers." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-59255.
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In this paper we explore methods to achieve actively powered walking on level ground using a simple 2D walker model. The walker is activated either by applying equal joint torques at hip and ankle, or by an impulse applied at toe-off immediately before heel-strike, or by the combination of both. We show that activating the walker by equal joint torques at hip and ankle on level ground is equivalent to the dynamics of the passive walker on a downhill slope. We calculate the stability of the gait cycle by an analytical approximation to the Jacobian of the walking map. Results indicate that short-period gait cycle always has an unstable eigenvalue, whereas stability of the long-period gait cycle depends on the selection of initial stance angle.
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Yang, Fan, Xilun Ding, and Gregory S. Chirikjian. "Kinematic Analysis of Hexapod Manipulation." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-59619.
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This paper provides a method for modeling the center of mass (COM) of hexapod manipulation systems, which is based on the Statically Equivalent Serial Chain (SESC) model. First, the product of exponentials (POE) formula is used to construct the SESC model for the simple tree-like chain. Then, in order to apply this method to real scenarios, the situation when the robot stands on uneven terrain is studied. In addition, the static grasp constraints for the manipulation and the Jacobian matrix for the COM of the system are analyzed. Moreover, we present a modified tumble stability margin, which considers all of the possible ways that the robot can tumble. Finally, based on these kinematic analyses, a motion control scheme for statically stable manipulation is proposed. The results are validated with simulations.
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Müller, Andreas. "A Proposal for a Unified Concept of Kinematic Singularities for Holonomic and Non-Holonomic Mechanisms." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70649.
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The study of mechanism singularities has traditionally focused on holonomic systems. On the other hand many robotic systems are characterized by non-holonomic constraints, such as mobile platforms and manipulators driven by non-holonomic joints, and a general concept of singularities seems in order. In this paper a possible generalization of the singularity concept is proposed that equally accounts for holonomic and non-holonomic kinematic systems. The central object is the associated kinematic control problem. Singularities are identified as those configurations where the iteration depth of Lie brackets required to compute the accessibility Lie algebra changes. This notion of singularities is applied to serial manipulator and to non-holonomic mobile platforms. It is shown for holonomic manipulators that this is equivalent to the usual Jacobian rank condition. As example the condition is discussed for a Scara manipulator, a 6R manipulator, and for a kinematic car with one or two trailers.
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Southwell, W. H. "Rugate Index Profile Which Suppresses all Harmonic Stopbands." In Optical Interference Coatings. Washington, D.C.: Optica Publishing Group, 1988. http://dx.doi.org/10.1364/oic.1988.tuf7.
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In the literature, several multilayer coating configurations have been proposed which have a reflectance stop band at the tuned wavelength and for which various orders of harmonic stopbands have been suppressed. Baumeister 1,2 has outlined a procedure for designing a symmetric multilayer in which any number of higher order harmonic stopbands are suppressed. He makes the statement that, "As more and more contiguous stopbands are suppressed, the stepped-index profile approximates a sinusoid." However, the algebraic complexities of his approach make it difficult to determine the index profile as it approaches the continuous limit. Prior to this, Thelen3 published plots of the equivalent index for an inhomogeneous system where the index varies with the Jacobian elliptic function4 dn. Recently, Carniglia5 showed that stepped-index designs in which the natural log of the index follows a sinusoid will have good harmonic suppression out to a certain order. (This log index sinusoid dependence we call an exponential sinusoid in this paper, since that is how the index itself varies.)