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1. A Note on Twisted Moments of Dirichlet $L$-functions

Author

Andrade, J. C. and MacMillan, J.

Subjects
Mathematics - Number Theory, 11M38, 11M06, 11T06, 11T55
Abstract

In this paper, we establish an asymptotic formula for the twisted second moments of Dirichlet $L$-functions with one and two twists when averaged over all primitive Dirichlet characters of modulus $R$, where $R$ is a monic polynomial in $\mathbb{F}_q[T]$. The main result in this paper generalizes the work of Djankovi\'c [`The reciprocity law for the twisted second moment of Dirichlet $L$-functions over rational function fields', Bull. Aust. Math. Soc. 98 (2018), no. 3, 382--388]., Comment: 12 pages. Comments welcome

Published
2023

2. Conjectures for the Integral Moments and Ratios of L-functions in Even characteristic

Author

MacMillan, J.

Subjects
Mathematics - Number Theory, 11M38, 11M06, 11G20
Abstract

In this paper, we extend to the function field setting the heuristics developed by Conrey, Farmer, Keating, Rubinstein and Snaith for the integral moments of L-functions. Also, we adapt to function field setting the heuristics first developed by Conrey, Farmer and Zirnbauer to the study of mean values of ratios of L-functions. Specifically, we obtain an asymptotic formula for the integral moments and ratios of the quadratic Dirichlet L-functions $L(s,\chi_u)$ over the rational function field $\mathbb{F}_q(T)$, when $q$ is a power of 2 and over a given family. As an application, we calculate the one-level density for the zeros of these L-functions., Comment: 37 pages, Comments are welcome. arXiv admin note: text overlap with arXiv:1407.3099 by other authors

Published
2021

3. Rudnick and Soundarajan's Theorem over Prime Polynomials for the Rational Function Field

Author

MacMillan, J.

Subjects
Mathematics - Number Theory, 11M38, 11G20, 11M06 13F30, 11R58, 14G10
Abstract

In this paper, we use the methods of Andrade, Rudnick and Soundarajan to prove a Theorem about Lower bounds of moments of quadratic Dirichlet L-functions associated to monic irreducible polynomials over function fields., Comment: 9 pages, Comments are welcome

Published
2020

4. Remark on a Simple Proof of the Mean Value of $K_2(\mathcal{O})$ in Function Fields

Author

MacMillan, J.

Subjects
Mathematics - Number Theory, 11M38, 11G20, 11M06, 13F30, 11R58, 14G10
Abstract

Let $\mathbb{F}_q$ denote a finite field of odd cardinality $q$, $\mathbb{A}=\mathbb{F}_q[T]$ the polynomial ring over $\mathbb{F}_q$ and $k=\mathbb{F}_q(T)$ the rational function field over $\mathbb{F}_q$. In this paper, we compute the average value of the size of the group $K_2(\mathcal{O}_{\gamma D})$, where $\mathcal{O}_{\gamma D}$ denotes the integral closure of $\mathbb{A}$ in $k(\sqrt{\gamma D})$, $D$ is a monic, square-free polynomial of even degree and $\gamma$ is a fixed generator of $\mathbb{F}_q^*$., Comment: 6 pages; Comments are welcome

Published
2019

5. The First Moment of $L(\frac{1}{2},\chi)$ for Real Quadratic Function Fields

Author

Andrade, J. C. and MacMillan, J.

Subjects
Mathematics - Number Theory, 11M38, 11M06, 11G20
Abstract

In this paper we use techniques first introduced by Florea to improve the asymptotic formula for the first moment of the quadratic Dirichlet L-functions over the rational function field, running over all monic, square-free polynomials of even degree at the central point. With some extra technical difficulties that doesn't appear in Florea's paper, we prove that there are extra main terms of size $(2g+2)q^{\frac{2g+2}{3}}, q^{\frac{g}{6}+\left[\frac{g}{2}\right]}$ and $q^{\frac{g}{6}+\left[\frac{g-1}{2}\right]}$, whilst bounding the error term by $q^{\frac{g}{2}(1+\epsilon)}$., Comment: 33 pages

Published
2019

7. The Charcot-Marie-Tooth Syndrome : a population genetic study in South Wales

Author

MacMillan, J. C.

Subjects
616.7
Abstract

The Charcot-Marie-Tooth (CMT) syndrome comprises a heterogeneous group of disorders affecting the peripheral nerves and anterior horn cells of the spinal cord. They constitute a significant proportion of the burden of disability due to the single gene neurological disorders, with a prevalence of 18.1 per 100000 of the South Wales population. The clinical manifestations of these disorders have been documented and their severity assessed using a standard protocol. The commonest disorder in the group is type I hereditary motor and sensory neuropathy (type I HMSN) (prevalence 11.0 per 100000 population) which has been mapped using genetic linkage analysis to chromosome 17, band p11.2 (the CMT1a locus). There was no evidence of genetic heterogeneity (ie any locus other than that at 17p11.2) within the type I HMSN group in the study population. Families with type V HMSN and the spinal form of the Charcot-Marie-Tooth syndrome have been shown not to be linked to this locus in this study. A number of families gave inconclusive results due either to small family size or to lack of informativeness for the polymorphisms studied. It has been possible to document in 91% of affected individuals with type I HMSN, heterozygous for the Msp1 polymorphisms of locus D17S122, trisomy (using the cDNA probe pVAW409R3a) within band 17p11.2. This was not seen in any normal individuals nor in any case of the spinal form of the Charcot-Marie-Tooth syndrome nor in HMSN types II or V. The demonstration of this trisomy in individual cases and families not suitable for conventional linkage analysis provides a rapid means of determining affection status for the CMT1a mutation. Presymptomatic and prenatal testing for this disorder is now feasible for individuals who request it.

Published
1991

10. Education in Area Economic Development. Center for Settlement Studies, Series 2: Research Report No. 10.

Author

Manitoba Univ., Winnipeg. Center for Settlement Studies., Molgat, Paul, and MacMillan, J. A.

Abstract

The study determined the: (1) relationship between dropout rates and the quality of education, teachers' qualifications, diversity of curriculum and extra-curricular activities, average town income, percentage of the high school population of American Indian or Metis descent, and school size; (2) effects of educational expenditures on business sales, jobs, and incomes in the Interlake Area of Manitoba; and (3) human capital value. The study's objective was to develop a viable framework for determining the role of education in the area's economic development. Data, obtained from the Department of Education and the 13 high schools in the Interlake Area, were analyzed by multiple regression analysis, an input-output table, and present value equations. Among the findings were: (1) the schools provided employment for a large number of teachers and support staff who spent money in the community and supported local businesses; (2) construction of schools provided jobs in the community and supported the level of local business sales; (3) the higher the town average income, the lower the dropout rate; (4) human capital value increased when the dropout rate was lowered; and (5) towns with low average income levels had teachers with low salaries and low qualifications which led to low quality of education. (NQ)

Published
1972

12. Farmer Responses to Brexit: Attitudes towards Risk in Scottish Farming – Briefing Note

Author

Barnes, A,P., MacMillan, J., Thomson, S.G, Spencer, M., Hopkins, J., Sutherland, L-A, and Mathews, K

Subjects
Risk Perception, Brexit, Farmer Intentions Survey
Abstract

The UKs withdrawal from the European Union presents multiple uncertainties for farm management planning. Encouraging growth within the agricultural economy requires some acceptance of risk within farming decision making. This briefing note outlines the results of a survey of 2,494 farmers, crofters and smallholders, run during the summer of 2018, on their approaches towards farming and how this may affect business planning post-Brexit. We find three categories of farmers based on their risk perceptions. Risk averse farmers (39%), risk taking farmers (17%), and risk cautious farmers (44%). Risk taking farmers appear to be more likely to have increased their intensity of production and their level of diversification. In addition they are more likely to have invested in new technologies and new capital. On more environmental led approaches, the differences are less extreme, especially in aspects around woodland expansion which may indicate different motivates towards public good activities. There is a fairly even spread of risk perceptions across farming types, with risk takers more likely to emerge from very large farms, and risk averse farmers from very small farms. Older farmers are more risk averse, and a higher proportion of risk cautious and risk takers are under 45. Only a slightly higher proportion of new entrants are risk takers compared to established farmers. Understanding risk perception is crucial as support systems may change. Risk taking activity can lead to higher levels of investment and therefore increasing on farm efficiencies. On more greener activities there is less evidence. However, whilst risk taking may lead to more sustainable growth, the high level of debt within Scottish farming may support more risk cautious approaches to investment. Nevertheless, supporting farmers away from risk averse behaviours (which compose 39% of the sample) should be encouraged.

Published
2021
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16. Guidelines for the Use of Fishes in Research

Author

Jenkins, J. A., primary, Bart, H. L., additional, Bowker, J. D., additional, Bowser, P. R., additional, MacMillan, J. R., additional, Nickum, J. G., additional, Rose, J. D., additional, Sorensen, P. W., additional, Whitledge, G. W., additional, Rachlin, J. W., additional, and Warkentine, B. E., additional

Published
2014
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22. Letter to J.M. Synge from J. MacMill[?an]

Author

MacMillan, J.

Subjects
Synge, J. M. (John Millington), 1871-1909--Correspondence, MacMillan, J.--Correspondence, Ireland--History--19th century, Ireland--History--20th century
Abstract

17 ?June. J. MacMill[?an], Gresham Hotel, Dublin to [J.M.S].

Published
2020
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31. Royal Academy of Medicine in Ireland Section of Biomedical Sciences

Author

Ruddock, W., Burns, D. M., Brown, J. C. W., Allen, J. M., Hirst, D. G., Love, G. P., Keenan, A. K., Lally, C., Bird, A., Ryan, M. P., O’Connor, N., O’Boyle, K. M., McGeown, J. G., McCarron, J. G., Drummond, R. M., Fay, F. S., Connor, T. J., Kelly, J. P., Leonard, B. E., Gilmartin, L., O’Cuinn, G., MacDonncha, C., Watson, A. W. S., McGrath, S., Brady, K. J., McKillen, H-C., Taylor, C. W., Smith, S. K., Thornton, S., Martin, A. D., Bailie, J. R., McKeown, S. R., Higgins, C. A., Hatton, W. J., McKerr, G., Harvey, D., Carson, J., Hannigan, B. M., Morrow, D. M. P., McGlynn, H., Thompson, C. M. G., Higgins, C., Galligan, E. S., Murray, M. M., Leckey, J. L., Nevin, G. B., Soppitt, D. S., Esfandiary, M. H., Gilmore, W. S., Robson, T., Dineen, T., Greer, A., Houghton, J. A., O’Halloran, K. D., Bradford, A., McGuire, M., MacDermott, M., Coogan, A., O’Connor, J. J., Regan, C. S., Redmond, A. M., Harkin, A., Lowe, A. S., Baxter, G. D., Kennovin, G. D., Leek, M., Friery, O. P., Hejmadi, M. V., Patterson, L. H., Robinson, J., Hill, I., Kilbride, J., Cotton, K. D., Hollywood, M. A., McHale, N. G., Thornbury, K. D., Halligan, C. P., O’Connell, D. P., Harvey, B. J., Fanning, P., O’Farrell, A., Cantillon, D., Cryan, J. F., O’Leary, D., O’Malley, D. T., Nolan, A., Moran, A. P., Fitzgerald, K. A., O’Neill, L. A. J., McElligott, A., Baker, A. H., Joyce, K. M., Ruane, T., Hall, W. J., Markos, F., Carey, M. F., Galvin, C., Perl, E. R., Curran, A. K., Connolly, C., Abdullah, K., Docherty, J. R., Gavin, K. T., Browne, M., Frazer, C-A., Walsh, D. M., Atkinson, S., Brown, D., O’Connor, J. M., Wasson, G. R., Bonham, M. P., McKelvey-Martin, V. J., Strain, J. J., Downes, C. S., Dineen, T. M., Powell, R., Van Hemelrijk, B., Abujaffom, T. Mubarak, Caulfield, B., Garrett, M., Brennan, L., Griffin, M. J., McShane, A. J., Convery, P. N., Milligan, K. R., Quinn, P., Scott, K., Fee, J. P. H., Cashman, M., Dunne, A., Healy, E., Walsh, J., Watson, A. J., Walsh, D. M., Noble, G., Baxter, G. D., Allen, J. M., Campion, D. P., Leek, B. F., Ryan, J. P., Quinn, T., Dumbleton, M., Smith, K. M., McGrath, J. C., Macmillan, J. B., Doherty, L., Lynch, F., Sweeney, M., O’Regan, R. G., McLoughlin, P., Padua, R. A., Dudeney, S., O’Byrne, J., Moran, R., O’Kelly, K. U., McCormack, B. A. O., Lyons, C. G., Brady, C. L., Simms, C., Maher, S., Schreiber, B., Taylor, D., Carr, A. J., Higgins, B., Dempsey, G. J., Imam, S. Z., Harbinson, M., Adgey, A. A. J., Anderson, J., Aodha, S. Ní, Wilcox, D., Rice, J., Jenkinson, A., O’Rourke, K., O’Brien, T., Devitt, A., McCormack, D., Ikadi, Y., Quinlan, W., Noelke, L., McMahon, G. T., Mulville, J. P., Lee, T. C., Rizvi, A., Fitzpatrick, D., McCarthy, M. A., McGloughlin, T., Monaghan, J., Shine, J., Arendt, E., Lew, B., Lewis, J., Kelly, P. A., Lennon, A. B., Hill, R. G., Dunne, N. J., Thompson, C., Orr, J. F., Beverland, D. E., Prenderville, T., Prendergast, P. J., Huiskes, R., Søballe, K., Mukunda, M. C., Kelly, C. J., Cregg, N., Leahy, A., Dwyer, R., Watson, R. G. K., Bouchier-Hayes, D. J., O’Boyle, C. J., Murchan, P., Mitchell, C. J., Macfie, J., Delicata, R. J., Davies, E. V., Lloyds, D., Petitt, E. J., Carey, P. D., Buckley, D. J., Riordain, M. G. O., Barry, T., Gorey, T. F., Fitzpatrick, J. M., Rothwell, J., Flaherty, J., Wilson, G., Walsh, T. N., Hennessy, T. P. J., O’Donoghue, J., Panchal, J., Mehdi, S., O’Sullivan, S. T., O’Shaughnessy, M., O’Connor, T. P. F., Cox, M. A., Dingle, J. T., Flavin, B. M., Regan, M. C., and O’Connell, P. R.

Published
1997
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39. After interventionism: a typology of U.S. strategies

Author

Macmillan, J

Abstract

Intervention has been a vital instrument of statecraft for the United States yet following Iraq and Afghanistan the projection of ‘troops on the ground’ has become a toxic political issue. Accordingly, what strategies does the United States pursue when this form of intervention is no longer perceived as politically viable or desirable but the problems or issues for which it was formerly undertaken remain? Drawing upon the conceptual work of Peter Hall, this article develops a typology of strategies according to the magnitude of change embraced. These range from adjustment in the levels or settings of interventionism (persistence); the substitution of alternative instruments of foreign policy, typically diplomacy (ameliorism); through to the principled rejection of interventionism in conjunction with a more systematic critique of the assumptions upon which foreign policy is based (transformationalism). These ideal-types are then applied to the three crises of interventionism faced by the United States since becoming a world power, occurring in the 1920s-30s, 1960s-mid ‘80s, and in the present age. The fate of these three strategies, when considered across the three periods, is shown to be beset with certain path-dependent tensions and contradictions arising from the domestic institutional and cultural context of foreign policy. Understanding these does not in and of itself resolve them, but can enable a fuller appreciation of the nature of the challenges – and the opportunities – each presents.

Published
2018

43. Workplace wellness: industry associations are well placed and some are ready to take a more active role in workplace health

Author

Marsh, G, Lewis, V, Macmillan, J, Gruszin, S, Marsh, G, Lewis, V, Macmillan, J, and Gruszin, S

Abstract

BACKGROUND: Investments in settings-based health interventions can include workplaces, however, engaging with businesses and convincing them to take a role can be difficult. Our research investigated the potential for trade or industry associations (IAs) to have a role in promoting workplace health initiatives to their members. METHODS: Seventeen semi-structured interviews were undertaken with senior executives from IAs representing industries in the mining, transport, agriculture, manufacturing, farming, hospitality, and construction sectors. Analysis of interviews identified themes around attitudes to workplace health promotion programs and the perceived, actual and potential role/s of IAs in promoting workplace wellness. RESULTS: IA representatives believed workplaces had potential to be promoting the health and wellbeing of workers through their member organisations; however for some the extent of their role was unclear and for others there was confusion between government-mandated safety initiatives and non-mandated health and wellbeing initiatives. All reported that their IA could have a role in promoting worker health and wellbeing initiatives to member organisations. IAs with larger companies as members were more likely to recognise the importance of workplaces promoting workers' health; however, the degree of involvement considered appropriate varied. Most IAs had not discussed the topic with their member organisations although they identified resources and support that could assist them in encouraging members to undertake workplace health programs. Resources included industry-relevant business cases outlining the benefits of workplace health, and industry-appropriate worker health information. CONCLUSIONS: Our research suggests that across many industry sectors, larger IAs in particular are ready to take a more active role in workplace health initiatives and are well placed to promote these to member organisations.

Published
2018

46. Further investigation of the predictors of outcome following first schizophrenic episodes

Author

Johnstone, Eve C., MacMillan, J. Fiona, Frith, Christopher D., Benn, Desmond K., and Crow, Timothy J.

Subjects
Schizophrenia -- Complications, Schizophrenia -- Social aspects, Schizophrenia -- Prognosis, Antipsychotic drugs -- Health aspects, Health
Abstract

Two hundred fifty-two adult patients hospitalized for a first schizophrenic episode were followed-up for two years so that their outcome, in terms of employment and amount of time spent in the hospital, could be evaluated. Upon discharge from the hospital, some of the patients were placed on placebo maintenance, while the remainder received maintenance doses of neuroleptic (anti-psychotic) drugs for the two-year follow-up period. For patients who had been ill for more than one year before treatment began, there was no difference between placebo and neuroleptic-drug groups in outcome, but for those who began treatment within one year, the placebo group had a significantly better outcome. No significant relationships were found between employment outcome and age, sex or ethnic origin. Factors which had a significant positive effect on employment outcome included: no relapse; fewer in-hospital days; and being treated with a placebo rather than a neuroleptic drug. Psychiatric illness in fathers of patients was associated with poor employment outcome for females, but did not seem to affect male employment outcome. Poor employment outcome was significantly related to social withdrawal, lack of close relationships, and poor social adjustment. Factors found to be significant predictors of more days spent in-hospital were social withdrawal, a tendency to speak incoherently or oddly, blunted emotions and several neurological soft signs, including abnormal hand grip, disorder of the lips and tongue, and poor performance on picture vocabulary tests. Since there was no control or comparison group in this study, relationships found between study factors and outcome cannot conclusively be attributed to schizophrenia. (Consumer Summary produced by Reliance Medical Information, Inc.)

Published
1990

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