3,219 research outputs found
Syzygies and the Rees algebra
Get PDFAbstractLet a,b,c be linearly independent homogeneous polynomials in the standard Z-graded ring R≔k[s,t] with the same degree d and no common divisors. This defines a morphism P1→P2. The Rees algebra Rees(I)=R⊕I⊕I2⊕⋯ of the ideal I=〈a,b,c〉 is the graded R-algebra which can be described as the image of an R-algebra homomorphism h: R[x,y,z]→Rees(I). This paper discusses one result concerning the structure of the kernel of the map h and its relation to the problem of finding the implicit equation of the image of the map given by a, b, c. In particular, we prove a conjecture of Hong, Simis and Vasconcelos. We also relate our results to the theory of adjoint curves and prove a special case of a conjecture of Cox
Liturgy, imagination and poetic language : a study of David Jones's The Anathemata.
Get PDFThe thesis seeks to attempt an examination of David Jones's long poem The Anathemata primarily from a theologically informed standpoint. It sets out to understand, from the literary-critical point of view, the forces and influences that have come together in order to make the poem. At the same time, it is aware of and tries to explore the theological, liturgical and mythological material which provides Jones with both the background to and the content of his poem. It is argued that the form of poem, its linguistic content and the experience of reading it, are best understood in terms of pilgrimage and that such a metaphor is best suited to encompass both its huge scale and its attention to detail.
From an overall examination of the available secondary literature, the thesis proceeds examine something of the experience of reading the poem, whether or not the poem can be conveniently understood as an epic and what Jones himself thought he was doing, at the same time his own theoretical stance is illuminated by reference to other contemporary thinkers.
An extensive examination of the terms 'myth' and 'anamnesis' and the backgrounds and links between the two both in general and within the context of the poem precede chapters which explore the language of the poem both in terms of stylistic features and also in terms of the literary sources on which Jones draws and which make up the intertexual space within which the poem exists. These matters are further examined in a discussion of the most significant themes with which the poet works in the course of The Anathemata. Finally, some account is given of the formal shape of the poem before a 'commentary' or 'paraphrase' of the poem draws out, in context, the significant features
Joint angle affects volitional and magnetically-evoked neuromuscular performance differentially
Get PDFThis study examined the volitional and magnetically-evoked neuromuscular performance of the quadriceps femoris at functional knee joint angles adjacent to full extension. Indices of volitional and magnetically-evoked neuromuscular performance (N= 15 healthy males; 23.5 ± 2.9 years; 71.5 ± 5.4 kg; 176.5 ± 5.5 cm) were obtained at 25°; 35° and 45° of knee flexion. Results showed that volitional and magnetically-evoked peak force (PFV; PTFE, respectively) and electromechanical delay (EMDV; EMDE, respectively) were enhanced by increased knee flexion. However, greater relative improvements in volitional compared to evoked indices of neuromuscular performance were observed with increasing flexion from 25° to 45° (e.g. EMDV; EMDE: 36% vs. 11% improvement, respectively; F[2,14] = 6.8; p < 0.05). There were no significant correlations between EMDV and EMDE or PFV and PTFE, respectively at analogous joint positions. These findings suggest that the extent of the relative differential between volitional and evoked neuromuscular performance capabilities is joint angle-specific and not correlated with performance capabilities at adjacent angles, but tends to be smaller with increased flexion. As such, effective prediction of volitional from evoked performance capabilities at both analogous and adjacent knee joint positions would lack robustness
Ideals and finiteness conditions for subsemigroups
No full textIn this paper we consider a number of finiteness conditions for semigroups related to their ideal structure, and ask whether such conditions are preserved by sub- or supersemigroups with finite Rees or Green index. Specific properties under consideration include stability, D=J and minimal conditions on ideals.Peer reviewe
Hilbert schemes and Rees algebras [Elektronisk resurs]
No full textThe topic of this thesis is algebraic geometry, which is the mathematical subject that connects polynomial equations with geometric objects. Modern algebraic geometry has extended this framework by replacing polynomials with elements from a general commutative ring, and studies the geometry of abstract algebra. The thesis consists of six papers relating to some different topics of this field.The first three papers concern the Rees algebra. Given an ideal of a commutative ring, the corresponding Rees algebra is the coordinate ring of a blow-up in the subscheme defined by the ideal. We study a generalization of this concept where we replace the ideal with a module. In Paper A we give an intrinsic definition of the Rees algebra of a module in terms of divided powers. In Paper B we show that features of the Rees algebra can be explained by the theory of coherent functors. In Paper C we consider the geometry of the Rees algebra of a module, and characterize it by a universal property.The other three papers concern various moduli spaces. In Paper D we prove a partial generalization of Gotzmann’s persistence theorem to modules, and give explicit equations for the embedding of a Quot scheme inside a Grassmannian. In Paper E we expand on a result of Paper D, concerning the structure of certain Fitting ideals, to describe projective embeddings of open affine subschemes of a Hilbert scheme. Finally, in Paper F we introduce the good Hilbert functor parametrizing closed substacks with proper good moduli spaces of an algebraic stack, and we show that this functor is algebraic under certain conditions on the stack. </p
Prediction of pathological stage in patients with prostate cancer: a neuro-fuzzy model
No full textThe prediction of cancer staging in prostate cancer is a process for estimating the likelihood that the cancer has spread before treatment is given to the patient. Although important for determining the most suitable treatment and optimal management strategy for patients, staging continues to present significant challenges to clinicians. Clinical test results such as the pre-treatment Prostate-Specific Antigen (PSA) level, the biopsy most common tumor pattern (Primary Gleason pattern) and the second most common tumor pattern (Secondary Gleason pattern) in tissue biopsies, and the clinical T stage can be used by clinicians to predict the pathological stage of cancer. However, not every patient will return abnormal results in all tests. This significantly influences the capacity to effectively predict the stage of prostate cancer. Herein we have developed a neuro-fuzzy computational intelligence model for classifying and predicting the likelihood of a patient having Organ-Confined Disease (OCD) or Extra-Prostatic Disease (ED) using a prostate cancer patient dataset obtained from The Cancer Genome Atlas (TCGA) Research Network. The system input consisted of the following variables: Primary and Secondary Gleason biopsy patterns, PSA levels, age at diagnosis, and clinical T stage. The performance of the neuro-fuzzy system was compared to other computational intelligence based approaches, namely the Artificial Neural Network, Fuzzy C-Means, Support Vector Machine, the Naive Bayes classifiers, and also the AJCC pTNM Staging Nomogram which is commonly used by clinicians. A comparison of the optimal Receiver Operating Characteristic (ROC) points that were identified using these approaches, revealed that the neuro-fuzzy system, at its optimal point, returns the largest Area Under the ROC Curve (AUC), with a low number of false positives (FPR = 0.274, TPR = 0.789, AUC = 0.812). The proposed approach is also an improvement over the AJCC pTNM Staging Nomogram (FPR = 0.032, TPR = 0.197, AUC = 0.582)
Factors influencing the distribution of the yellow-bellied glider (Petaurus australis australis) in Victoria, Australia
No full textn this study we examine broad-scale factors affecting the distribution of the yellow-bellied glider (Petaurus australis australis) in the southern Australian state of Victoria. Using the bioclimatic analysis and prediction system, BIOCLIM, and vegetation-suitability mapping, we assessed the potential distribution of the species at the time of European settlement and compared it to the current distribution. BIOCLIM revealed that P. a. australis is most likely to occur in areas with mean annual rainfall >600 mm and mean annual temperature between 6°C and 14.5°C. Much of its current distribution is skewed to the eastern half of the State, and our results emphasise a disjunction between western and eastern Victorian populations that is attributed to unsuitable climate and vegetation for the species. This indicates that P. australis in the west was most likely separated from eastern Victorian P. australis long before European settlement. Our results also indicate that isolated P. australis populations in south-western Victoria represent fragments of what was probably a much more widely distributed population when European settlement took place. Owing to the highly restricted distribution of suitable remnant native vegetation, these westernmost P. australis populations should be a high priority for future research and conservation work.Michael Rees, David J. Paull, and Susan M. Carthe
The history of Pembrokeshire,
No full text"The author had projected a history that would have dealt with the county to the close of the nineteenth century. His outline included three chapters ... Georgian Pembrokeshire, The landing of the French, and Modern days, which he did not live to write." The incomplete manuscript was pub. after his death under the general superintendence of T. C. Rees. cf. Foreword (by J. and M. Phillips)Mode of access: Internet
Nitrogen fixation in the western English Channel (NE Atlantic Ocean)
Get PDFIn temperate Atlantic waters (18.8 to 20.1°C), biological nitrogen fixation has beendemonstrated by 2 independent measurements: 15N-N2 incorporation and nifH identification in theDNA and expressed messenger RNA (mRNA). At 2 stations in the western English Channel, bulkwaters were incubated with 15N-N2. At the high levels of particulate nitrogen (?11.5 ?mol N l–1),absolute fixation rates of 18.9 ± 0.01 and 20.0 nmol N l–1d–1 were determined. While a caveat mustaccompany the magnitude of the rates presented due to the limited number of data, the presence andactivity of diazotrophic organisms in these waters is of ecological significance and may affect currentattitudes to nitrogen and carbon budgets. In particular, our estimate of the rate of N fixation(0.35 mmol N m–2 d–1) is comparable to that of denitrification rates in UK shelf seas. Molecular analysisidentified a diversity of expressed nifH genes, and 21 different prokaryotic nifH transcripts wereidentified
Rees algebras of modules and Quot schemes of points [Elektronisk resurs]
No full textThis thesis consists of three articles. The first two concern a generalization of Rees algebras of ideals to modules. Paper A shows that the definition of the Rees algebra due to Eisenbud, Huneke and Ulrich has an equivalent, intrinsic, definition in terms of divided powers. In Paper B, we use coherent functors to describe properties of the Rees algebra. In particular, we show that the Rees algebra is induced by a canonical map of coherent functors.In Paper C, we prove a generalization of Gotzmann's persistence theorem to finite modules. As a consequence, we show that the embedding of the Quot scheme of points into a Grassmannian is given by a single Fitting ideal.</p
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