Review of finite fields: Applications to discrete Fourier, transforms and Reed-Solomon coding

An attempt is made to provide a step-by-step approach to the subject of finite fields. Rigorous proofs and highly theoretical materials are avoided. The simple concepts of groups, rings, and fields are discussed and developed more or less heuristically. Examples are used liberally to illustrate the meaning of definitions and theories. Applications include discrete Fourier transforms and Reed-Solomon coding

Many-body Systems Interacting via a Two-body Random Ensemble (I): Angular Momentum distribution in the ground states

In this paper, we discuss the angular momentum distribution in the ground states of many-body systems interacting via a two-body random ensemble. Beginning with a few simple examples, a simple approach to predict P(I)'s, angular momenta I ground state (g.s.) probabilities, of a few solvable cases, such as fermions in a small single-j shell and d boson systems, is given. This method is generalized to predict P(I)'s of more complicated cases, such as even or odd number of fermions in a large single-j shell or a many-j shell, d-boson, sd-boson or sdg-boson systems, etc. By this method we are able to tell which interactions are essential to produce a sizable P(I) in a many-body system. The g.s. probability of maximum angular momentum $I_{max}$ is discussed. An argument on the microscopic foundation of our approach, and certain matrix elements which are useful to understand the observed regularities, are also given or addressed in detail. The low seniority chain of 0 g.s. by using the same set of two-body interactions is confirmed but it is noted that contribution to the total 0 g.s. probability beyond this chain may be more important for even fermions in a single-j shell. Preliminary results by taking a displaced two-body random ensemble are presented for the I g.s. probabilities.Comment: 39 pages and 8 figure

Spectral fluctuation properties of spherical nuclei

The spectral fluctuation properties of spherical nuclei are considered by use of NNSD statistic. With employing a generalized Brody distribution included Poisson, GOE and GUE limits and also MLE technique, the chaoticity parameters are estimated for sequences prepared by all the available empirical data. The ML-based estimated values and also KLD measures propose a non regular dynamic. Also, spherical odd-mass nuclei in the mass region, exhibit a slight deviation to the GUE spectral statistics rather than the GOE.Comment: 10 pages, 2 figure

Generic Rotation in a Collective SD Nucleon-Pair Subspace

Low-lying collective states involving many nucleons interacting by a random ensemble of two-body interactions (TBRE) are investigated in a collective SD-pair subspace, with the collective pairs defined dynamically from the two-nucleon system. It is found that in this truncated pair subspace collective vibrations arise naturally for a general TBRE hamiltonian whereas collective rotations do not. A hamiltonian restricted to include only a few randomly generated separable terms is able to produce collective rotational behavior, as long as it includes a reasonably strong quadrupole-quadrupole component. Similar results arise in the full shell model space. These results suggest that the structure of the hamiltonian is key to producing generic collective rotation.Comment: 11 pages, 5 figure

"Engaging with birth stories in pregnancy: a hermeneutic phenomenological study of women's experiences across two generations"

BACKGROUND: The birth story has been widely understood as a crucial source of knowledge about childbirth. What has not been reported is the effect that birth stories may have on primigravid women's understandings of birth. Findings are presented from a qualitative study exploring how two generations of women came to understand birth in the milieu of other's stories. The prior assumption was that birth stories must surely have a positive or negative influence on listeners, steering them towards either medical or midwifery-led models of care. METHODS: A Heideggerian hermeneutic phenomenological approach was used. Twenty UK participants were purposively selected and interviewed. Findings from the initial sample of 10 women who were pregnant in 2012 indicated that virtual media was a primary source of birth stories. This led to recruitment of a second sample of 10 women who gave birth in the 1970s-1980s, to determine whether they were more able to translate information into knowledge via stories told through personal contact and not through virtual technologies RESULTS: Findings revealed the experience of 'being-in-the-world' of birth and of stories in that world. From a Heideggerian perspective, the birth story was constructed through 'idle talk' (the taken for granted assumptions of things, which come into being through language). Both oral stories and those told through technology were described as the 'modern birth story'. The first theme 'Stories are difficult like that', examines the birth story as problematic and considers how stories shape meaning. The second 'It's a generational thing', considers how women from two generations came to understand what their experience might be. The third 'Birth in the twilight of certainty,' examines women's experience of Being in a system of birth as constructed, portrayed and sustained in the stories being shared. CONCLUSIONS: The women pregnant in 2012 framed their expectations in the language of choice, whilst the women who birthed in the 1970s-1980s framed their experience in the language of safety. For both, however, the world of birth was the same; saturated with, and only legitimised by the birth of a healthy baby. Rather than creating meaningful understanding, the 'idle talk' of birth made both cohorts fearful of leaving the relative comfort of the 'system', and of claiming an alternative birth

The Mariner 6 and 7 flight paths and their determination from tracking data

Determination of orbit estimates for Mariner 6 and 7 space probe flight

Analysis of radiation-induced cell death in head and neck squamous cell carcinoma and rat liver maintained in microfluidic devices

Objective The aim of this study was to investigate how head and neck squamous cell carcinoma (HNSCC) tissue biopsies maintained in a pseudo in vivo environment within a bespoke microfluidic device respond to radiation treatment. Study Design Feasibility study. Setting Tertiary referral center. Subjects and Methods Thirty-five patients with HNSCC were recruited, and liver tissue from 5 Wistar rats was obtained. A microfluidic device was used to maintain the tissue biopsy samples in a viable state. Rat liver was used to optimize the methodology. HNSCC was obtained from patients with T1-T3 laryngeal or oropharyngeal SCC; N1-N2 metastatic cervical lymph nodes were also obtained. Irradiation consisted of single doses of between 2 Gy and 40 Gy and a fractionated course of 5×2 Gy. Cell death was assessed in the tissue effluent using the soluble markers lactate dehydrogenase (LDH) and cytochrome c and in the tissue by immunohistochemical detection of cleaved cytokeratin18 (M30 antibody). Results A significant surge in LDH release was demonstrated in the rat liver after a single dose of 20 Gy; in HNSCC, it was seen after 40 Gy compared with the control. There was no significant difference in cytochrome c release after 5 Gy or 10 Gy. M30 demonstrated a dose-dependent increase in apoptotic index for a given increase in single-dose radiotherapy. There was a significant increase in apoptotic index between 1×2 Gy and 5×2 Gy. Conclusion M30 is a superior method compared with soluble markers in detecting low-dose radiation-induced cell death. This microfluidic technique can be used to assess radiation-induced cell death in HNSCC and therefore has the potential to be used to predict radiation response