149 research outputs found
Six Overtures Composed by C. F. Abel. Adapted for the Harpsichord or Piano Forte : being Opera First / By the Author
No full textSIX OVERTURES COMPOSED BY C. F. ABEL. ADAPTED FOR THE HARPSICHORD OR PIANO FORTE : BEING OPERA FIRST / BY THE AUTHOR
Six Overtures Composed by C. F. Abel. Adapted for the Harpsichord or Piano Forte : being Opera First / By the Author (1)
Cover (1)
Titelseite (2)
Overture I. (3)
Overture II. (8)
Overture III. (12)
Overture IV. (16)
Overture V. (20)
Overture VI. (24
Multi-operator brackets acting thrice
No full textJ.Phys.A42:462001,2009 We generalize an identity, first found by Bremner, for the action of three
nested Nambu brackets
Two- to Eight-Month-Old Infants' Perception of Dynamic Auditory-Visual Spatial Colocation
No full textFrom birth, infants detect associations between the locations of static visual objects and sounds they emit, but there is limited evidence regarding their sensitivity to the dynamic equivalent when a sound-emitting object moves. In 4 experiments involving thirty-six 2-month-olds, forty-eight 5-month-olds, and forty-eight 8-month-olds, we investigated infants' ability to process this form of spatial colocation. Whereas there was no evidence of spontaneous sensitivity, all age groups detected a dynamic colocation during habituation and looked longer at test trials in which sound and sight were dislocated. Only 2-month-olds showed clear sensitivity to the dislocation relation, although 8-month-olds did so following additional habituation. These results are discussed relative to the intersensory redundancy hypothesis and work suggesting increasing specificity in processing with age
The contribution of visual and vestibular information to spatial orientation by 6- to 14-month-old infants and adults
No full textAlthough there is much research on infants' ability to orient in space, little is known regarding the information they use to do so. This research uses a rotating room to evaluate the relative contribution of visual and vestibular information to location of a target following bodily rotation. Adults responded precisely on the basis of visual flow information. Seven-month-olds responded mostly on the basis of visual flow, whereas 9-month-olds responded mostly on the basis of vestibular information, and 12-month-olds responded mostly on the basis of visual information. Unlike adults, infants of all ages showed partial influence by both modalities. Additionally, 7-month-olds were capable of using vestibular information when there was no visual information for movement or stability, and 9-month-olds still relied on vestibular information when visual information was enhanced. These results are discussed in the context of neuroscientific evidence regarding visual-vestibular interaction, and in relation to possible changes in reliance on visual and vestibular information following acquisition of locomotion
Training to Enhance Psychiatrist Communication with patients with Psychosis (TEMPO): A Cluster Randomized Controlled Trial
No full textThis is the author accepted manuscript. The final version is available from the Royal College of Psychiatrists via the DOI in this record.Background: A better therapeutic relationship predicts better outcomes. However, there is no trial based evidence on how to improve therapeutic relationships in psychosis.
Aims: To test the effectiveness of communication training for psychiatrists on improving shared understanding and the therapeutic relationship.
Methods: In a cluster randomized controlled trial in the U.K., 21 psychiatrists were randomized. 97 (51% of those approached) outpatients with schizophrenia/schizoaffective disorder were recruited. 64 (66% of the sample recruited at baseline) were followed up after 5 months. The intervention group received four group and one individualized session. The primary outcome, rated blind, was psychiatrist effort in establishing shared understanding, self-repair. Secondary outcome was the therapeutic relationship.
Results: Psychiatrists receiving the intervention used 44% more self-repair than the control group (6.4, 95% CI 1.46 to 11.33, p<.011, a large effect) adjusting for baseline self-repair. Psychiatrists rated the therapeutic relationship more positively (0.20, 95%CI 0.03 to 0.37, p=.022, a large effect), as did patients (0.21, 95% CI 0.01 to 0.41, p=.043, a medium effect).
Conclusions: Shared understanding can be successfully targeted in training and improves relationships in treating psychosis.
Trial Registration: Current Controlled Trials ISRCTN94846422National Institute for Health Research (NIHR
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Topics in Elementary Particle Physics
No full textThe author of this thesis discusses two topics in elementary particle physics: n-ary algebras and their applications to M-theory (Part I), and functional evolution and Renormalization Group flows (Part II). In part I, Lie algebra is extended to four different n-ary algebraic structure: generalized Lie algebra, Filippov algebra, Nambu algebra and Nambu-Poisson tensor; though there are still many other n-ary algebras. A natural property of Generalized Lie algebras — the Bremner identity, is studied, and proved with a totally different method from its original version. We extend Bremner identity to n-bracket cases, where n is an arbitrary odd integer. Filippov algebras do not focus on associativity, and are defined by the Fundamental identity. We add associativity to Filippov algebras, and give examples of how to construct Filippov algebras from su(2) , bosonic oscillator, Virasoro algebra. We try to include fermionic charges into the ternary Virasoro-Witt algebra, but the attempt fails because fermionic charges keep generating new charges that make the algebra not closed. We also study the Bremner identity restriction on Nambu algebras and Nambu-Poisson tensors. So far, the only example 3-algebra being used in physics is the BLG model with 3-algebra A4, describing two M2-branes interactions. Its extension with Nambu algebra, BLG-NB model, is believed to describe infinite M2-branes condensation. Also, there is another propose for M2-brane interactions, the ABJM model, which is constructed by ordinary Lie algebra. We compare the symmetry properties between them, and discuss the possible approaches to include these three models into a grand unification theory. In Part II, we give an approximate solution for Schroeder’s equations, based on series and conjugation methods. We use the logistic map as an example, and demonstrate that this approximate solution converges to known analytical solutions around the fixed point, around which the approximate solution is constructed. Although the closed-form solutions for Schroeder’s equations can not always be approached analytically, by fitting the approximation solutions, one can still obtain closed-form solutions sometimes. Based on Schroeder’s theory, approximate solutions for trajectories, velocities and potentials can also be constructed. The approximate solution is significantly useful to calculate the beta function in renormalization group trajectory. By “wrapping” the series solutions with the conjugations from different inverse functions, we generate different branches of the trajectory, and construct a counterexample for a folk theorem about limited cycles.</p
The art of playing the guitar or cittra : containing several compositions with a bass for the violoncello or harpsichord /
No full textPublisher's no.: Performers' Editions 99216.Reproduced from a copy in the Library of Congress.Originally published: Edinburgh : Printed for the author by R. Bremner, 1760."These compositions are contrived so as to make very proper solos for the violin ..."--Original t.p.Mode of access: Internet
On symmetric square values of quadratic polynomials
No full textIn this note we are dealing with the following problem. Given a degree two polynomial f(x) = ax2 +bx+c ∈ Z[x] which is not a square of a degree one polynomial, how many consecutive integer values f(i) can be squares in Z? This problem has been considered by D. Allison in [1] and [2], who found infinitely many examples with eight consecutive values, and by A. Bremner in [3], who found more examples with seven consecutive values. The examples found by Allison are all by polynomials which are symmetric with an axis of symmetry midway between two integers. This means that, after some easy translation, all the examples are of the form f(x) = a(x 2 +x) +c and the values are f(i) for i = −3, −2, −1, 0, 1, 2, 3 and 4. This result was obtained by translating the problem to computing rational points on some elliptic curve which has rank one. On the other hand, Bremner [3] shows that there does not exist any example which is symmetric about an integral value and with seven values, by showing that these examples would be described by rational points on some rank zero elliptic curve, which has 12 points, all corresponding to the polynomial f(x) being the square of a polynomial. In the same paper, Bremner asks if there are examples as the ones found by Allison, but with ten consecutive squares. The problem translates to finding all the rational points of a genus 5 curve, a fact already noticed by Allison and by Bremner. He conjectures that there is no such example. In this note we prove this conjecture, and so, together with the results of Bremner and Allison, we get the following theoremWe thank J. Brzezinski for pointing out to us the relation between quadratic polynomials taking consecutive square values and sequences of squares whose second differences are constant. The first author was supported in part by grants MTM 2009-07291 (Ministerio de Ciencia e Innovación, Spain) and CCG08-UAM/ESP-3906 (Universidad Autónoma de Madrid, Comunidad de Madrid, Spain). The second author was partially supported by the grant MTM 2009-10359 (Ministerio de Ciencia e Innovación, Spain
The Home Front in the Fiction of Henry Green
No full textFull text is available to authenticated members of The University of Auckland only.Between 1926 and 1952, the English author Henry Green published nine novels. Highly esteemed in their day, these works have since fallen into disregard and obscurity: besides the efforts of a devoted few, Green has been persistently under-read and under-studied. This thesis aims to remedy something of this neglect by examining the novels which he set within wartime Britain – Party Going (1939), Caught (1943), and Back (1946). It pays close attention to the experiences of the Home Front which are represented within each
Some Diophantine Problems
No full textabstract: Diophantine arithmetic is one of the oldest branches of mathematics, the search
for integer or rational solutions of algebraic equations. Pythagorean triangles are
an early instance. Diophantus of Alexandria wrote the first related treatise in the
fourth century; it was an area extensively studied by the great mathematicians of the seventeenth century, including Euler and Fermat.
The modern approach is to treat the equations as defining geometric objects, curves, surfaces, etc. The theory of elliptic curves (or curves of genus 1, which are much used in modern cryptography) was developed extensively in the twentieth century, and has had great application to Diophantine equations. This theory is used in application to the problems studied in this thesis. This thesis studies some curves of high genus, and possible solutions in both rationals and in algebraic number fields, generalizes some old results and gives answers to some open problems in the literature. The methods involve known techniques together with some ingenious tricks. For example, the equations , , the two previously unsolved cases for , are solved using algebraic number theory and the ‘elliptic Chabauty’ method. The thesis also studies the genus three quartic curves where F is a homogeneous quadratic form, and extend old results of Cassels, and Bremner. It is a very delicate matter to find such curves that have no rational points, yet which do have points in odd-degree extension fields of the rationals.
The principal results of the thesis are related to surfaces where the theory is much less well known. In particular, the thesis studies some specific families of surfaces, and give a negative answer to a question in the literature regarding representation of integers n in the form Further, an example, the first such known, of a quartic surface is given with remarkable properties: it is everywhere locally solvable, yet has no non-zero rational point, despite having a point in (non-trivial) odd-degree extension fields of the rationals. The ideas here involve manipulation of the Hilbert symbol, together with the theory of elliptic curves.Dissertation/ThesisDoctoral Dissertation Mathematics 201
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