Prime Rational Functions and Integral Polynomials

Let f(x) be a complex rational function. In this work, we study conditions under which f(x) cannot be written as the composition of two rational functions which are not units under the operation of function composition. In this case, we say that f(x) is prime. We give sufficient conditions for complex rational functions to be prime in terms of their degrees and their critical values, and we derive some conditions for the case of complex polynomials. We consider also the divisibility of integral polynomials, and we present a generalization of a theorem of Nieto. We show that if f(x) and g(x) are integral polynomials such that the content of g divides the content of f and g(n) divides f(n) for an integer n whose absolute value is larger than a certain bound, then g(x) divides f(x) in Z[x]. In addition, given an integral polynomial f(x), we provide a method to determine if f is irreducible over Z, and if not, find one of its divisors in Z[x].

An educator's perspective of Dr. Feingold's K-P (Kaiser- Permanents) elimination diet for hyperkinetic children and others

Do evaluation of the literature and a regional observational report support Dr. Feingold's claim that the K-P (Kaiser-Permanente) elimination diet improves the behaviours of hyperkinetic children, and others? Dr. Feingold suggests that some hyperkinetic children, and other children as well, are genetically predisposed to intolerance of food additives, particularly food colours and flavours. He claims that the K-P diet, that eliminates salicylates and artificial food colours and flavours, improves the hyperkinetic child's behaviour, muscle co-ordination, and scholastic performance. Public acceptance of the K-P diet has outstripped acceptance in the medical and scientific communities. Evaluation of available data and additional studies are needed to arrive at a conclusion of acceptance or rejection of the K-P diet for hyperkinetic children and others. My interest in the K-P elimination diet for hyperkinetic children is educational. My experience as an elementary school teacher in special education and in the classroom from K-8 has taught me that attentiveness is crucial to learning. Hyperkinesis appears to impair a child's ability to attend. Learning problems appear, followed by behavioural and social problems. l If we accept the possibility of a relationship between diet and attentiveness, and attentiveness and school behaviours, then the diet-behaviour link could be of lay importance. For instance, if a diet such as the K-P diet could do what is claimed, substantial benefits could accrue to the child. One could, for example, improve a child's behaviours. One could identify attending disturbances early in the child's education, possibly minimizing, or eliminating future difficulties in school. Finally, the greatest benefit may be the fulfillment of the basic goal of our Ontario schools, that the eh~ld-,lIla1p.evelop happily and competently within our educational framework. 2 This thesis reports evidence from the literature and from a regional observational investigation to determine the possibility of a link between the behaviours of children and Dr. Feingold's K-P elimination diet. The literature research examines (1) Dr. Feingold's concept of H-LD, (2) his K-P elimination diet, and (3) the response from three sectors, medicine, science, and the public. The regional investigation examines the observed behaviours of nine children in Regional Niagara during a nine-month period on the K-P diet.

Effects of intracerebroventricular bombesin administration on local cerebral glucose utilization in the restrained and unrestrained rat

Intracerebroventricular (ICV) administration of bombesin (BN) induces a syndrome characterized by stereotypic locomotion and grooming, hyperactivity and sleep elimination, hyperglycemia and hypothermia, hyperhemodynamics, feeding inhibition, and gastrointestinal function changes. Mammalian BN-like peptides (MBNs), e.g. gastrin-releasing peptide (GRP), Neuromedin C (NMC), and Neuromedin B (NMB), have been detected in the central nervous system. Radio-labeled BN binds to specific sites in discrete cerebral regions. Two specific BN receptor subtypes (GRP receptor and NMB receptor) have been identified in numerous brain regions. The quantitative 2-[14C]deoxyglucose ([14C]20G) autoradiographic method was used to map local cerebral glucose utilization (LCGU) in the rat brain following ICV injection of BN (vehicle, BN O.1Jlg, O.5Jlg). At each dose, experiments were conducted in freely moving or restrained conditions to determine whether alterations in cerebral function were the result of BN central administration, or were the result of BN-induced motor stereotypy. The anteroventral thalamic nucleus (AV) (p=O.029), especially its ventrolateral portion (AVVL) (pand the suprachiasmatic nucleus (SCh) (p=O.003) exhibited BN treatment effects. BN effects on LCGU were also observed in the median eminence (ME) (p=O.011). Restraint, however, decreased LCGU in the lateral dorsal thalamic nucleus, ventrolateral and dorsomedial parts (LOVL and LOOM) (p=O.044, p=O.009), and the lateral geniculate (LG) (p=O.027). In sum, BN induced a marked and highly localized alteration in cerebral metabolism within parts of the anterior thalamus, which is the principle relay in the limbic circuitry. BN effects were also observed in IGr, Mi, SCh, and ME. Effects of restraint were found in LOVL, LOOM, and LG. It is suggested that increased LCGU in AV and AVVL may be the result of functional change in the limbic circuitry and the hypothalamus caused by BN receptor functional modification. In IGr, increased LCGU following BN administration is considered to be mainly the result the activation of NMB receptor, a subtype of BN receptors. In SCh, increased LCGU is believed to be caused both by BN effects on the thalamic, the hypothalamic, and the limbic functions and by activation of GRP receptor, another BN receptors subtype found in SCh. In ME, increased LCGU is suggested to be caused by BN effects on the hypothalamic functions, especially those related to the neuroendocrine functions. None of the alterations seen in these regions reflects the emission of stereotyped motor behaviors. Rather, they reflect a direct influence of BN central administration upon functioning of the cerebral regions influenced by BN administration. The restraint effects seen in LO, including LOOM and LOVL, are suggested to be the result of altered behavioral expression. The restraint effects seen in LG is suggested to be the result of reduced locomotion.

On the equation of state and atomic mean square displacement of crystals

We have presented a Green's function method for the calculation of the atomic mean square displacement (MSD) for an anharmonic Hamil toni an . This method effectively sums a whole class of anharmonic contributions to MSD in the perturbation expansion in the high temperature limit. Using this formalism we have calculated the MSD for a nearest neighbour fcc Lennard Jones solid. The results show an improvement over the lowest order perturbation theory results, the difference with Monte Carlo calculations at temperatures close to melting is reduced from 11% to 3%. We also calculated the MSD for the Alkali metals Nat K/ Cs where a sixth neighbour interaction potential derived from the pseudopotential theory was employed in the calculations. The MSD by this method increases by 2.5% to 3.5% over the respective perturbation theory results. The MSD was calculated for Aluminum where different pseudopotential functions and a phenomenological Morse potential were used. The results show that the pseudopotentials provide better agreement with experimental data than the Morse potential. An excellent agreement with experiment over the whole temperature range is achieved with the Harrison modified point-ion pseudopotential with Hubbard-Sham screening function. We have calculated the thermodynamic properties of solid Kr by minimizing the total energy consisting of static and vibrational components, employing different schemes: The quasiharmonic theory (QH), ).2 and).4 perturbation theory, all terms up to 0 ().4) of the improved self consistent phonon theory (ISC), the ring diagrams up to o ().4) (RING), the iteration scheme (ITER) derived from the Greens's function method and a scheme consisting of ITER plus the remaining contributions of 0 ().4) which are not included in ITER which we call E(FULL). We have calculated the lattice constant, the volume expansion, the isothermal and adiabatic bulk modulus, the specific heat at constant volume and at constant pressure, and the Gruneisen parameter from two different potential functions: Lennard-Jones and Aziz. The Aziz potential gives generally a better agreement with experimental data than the LJ potential for the QH, ).2, ).4 and E(FULL) schemes. When only a partial sum of the).4 diagrams is used in the calculations (e.g. RING and ISC) the LJ results are in better agreement with experiment. The iteration scheme brings a definitive improvement over the).2 PT for both potentials.

Reality status evaluations in mediated experiences /

This paper explores the cognitive functions of the Reality Status Evaluation (RSE) system in our experiences of narrative mediated messages (NMM) (fictional, narrative, audio-visual one-way input and moving picture messages), such as fictional TV programs and films. We regard reality in mediated experiences as a special mental and emotional construction and a multi-dimensional concept. We argue that viewers' reality sense in NMM is influenced by many factors with "real - on" as the default value. Some of these factors function as primary mental processes, including the content realism factors of those messages such as Factuality (F), Social Realism (SR), Life Relevance (LR), and Perceptual Realism - involvement (PR), which would have direct impacts on reality evaluations. Other factors, such as Narrative Meaning (NM), Emotional Responses, and personality trait Absorption (AB), will influence the reality evaluations directly or through the mediations of these main dimensions. I designed a questionnaire to study this theoretical construction. I developed items to form scales and sub-scales measuring viewers' subjective experiences of reality evaluations and these factors. Pertinent statistical techniques, such as internal consistency and factorial analysis, were employed to make revisions and improve the quality of the questionnaire. In the formal experiment, after viewing two short films, which were selected as high or low narrative structure messages from previous experiments, participants were required to answer the questionnaire, Absorption questionnaire, and SAM (Self-Assessment Manikin, measuring immediate emotional responses). Results were analyzed using the EQS, structural equation modeling (SEM), and discussed in terms oflatent relations among these subjective factors in mediated experience. The present results supported most of my theoretical hypotheses. In NMM, three main jactors, or dimensions, could be extracted in viewers' subjective reality evaluations: Social Realism (combining with Factuality), Life Relevance and Perceptual Realism. I designed two ways to assess viewers' understanding of na"ative meanings in mediated messages, questionnaire (NM-Q) and rating (NM-R) measurement, and its significant influences on reality evaluations was supported in the final EQS models. Particularly in high story stnlcture messages, the effect of Narrative Meaning (NM) can rarely be explained by only these dimensions of reality evaluations. Also, Empathy seems to playa more important role in RSE of low story structure messages. Also, I focused on two other factors that were pertinent to RSE in NMM, the personality trait Absorption, and Emotional Responses (including two dimensions: Valence and Intensity). Final model results partly supported my theoretical hypotheses about the relationships among Absorption (AB), Social Realism (SR) and Life Relevance (LR); and the immediate impact of Emotional Responses on Perceptual Realism cPR).

The Gentleman's Magazine and Historical Chronicle - 1815 January to June Index and Selected Pages

The Gentleman's Magazine and Historical Chronicle was a monthly periodical published in England during the years of 1736-1833. The volumes of interest from 1812-1815 were written and compiled by Sylvanus Urban, Gentleman. These volumes were Printed in London by Nichols, Son and Bentley at Cicero's Head, Red Lion Passage and Fleet Street. Click on the pdf links to the right to view the monthly issue. This bound volume has been divided by months. The page divisions are as listed. *In this volume only the Index and selected relevant pages have been digitized, for the full Periodical please contact the Brock University Special Collections and Archives. Listed are the pages that have been digitized. Index pages 653-680 Supplement page 577 January pages 1-96 February page 97 March pages 193,260-272 April pages 289,353-357 May pages 385,463,576 June page 481

Electrocortical indices of cognitive control in working memory : exploring the effects of proactive interference, cognitive load, and aging

Cognitive control involves the ability to flexibly adjust cognitive processing in order to resist interference and promote goal-directed behaviour. Although frontal cortex is considered to be broadly involved in cognitive control, the mechanisms by which frontal brain areas implement control functions are unclear. Furthermore, aging is associated with reductions in the ability to implement control functions and questions remain as to whether unique cortical responses serve a compensatory role in maintaining maximal performance in later years. Described here are three studies in which electrophysiological data were recorded while participants performed modified versions of the standard Sternberg task. The goal was to determine how top-down control is implemented in younger adults and altered in aging. In study I, the effects of frequent stimulus repetition on the interference-related N450 were investigated in a Sternberg task with a small stimulus set (requiring extensive stimulus resampling) and a task with a large stimulus set (requiring no stimulus resampling).The data indicated that constant stimulus res amp ling required by employing small stimulus sets can undercut the effect of proactive interference on the N450. In study 2, younger and older adults were tested in a standard version of the Sternberg task to determine whether the unique frontal positivity, previously shown to predict memory impairment in older adults during a proactive interference task, would be associated with the improved performance when memory recognition could be aided by unambiguous stimulus familiarity. Here, results indicated that the frontal positivity was associated with poorer memory performance, replicating the effect observed in a more cognitively demanding task, and showing that stimulus familiarity does not mediate compensatory cortical activations in older adults. Although the frontal positivity could be interpreted to reflect maladaptive cortical activation, it may also reflect attempts at compensation that fail to fully ameliorate agerelated decline. Furthermore, the frontal positivity may be the result of older adults' reliance on late occurring, controlled processing in contrast to younger adults' ability to identify stimuli at very early stages of processing. In the final study, working memory load was manipulated in the proactive interference Sternberg task in order to investigate whether the N450 reflects simple interference detection, with little need for cognitive resources, or an active conflict resolution mechanism that requires executive resources to implement. Independent component analysis was used to isolate the effect of interference revealing that the canonical N450 was based on two dissociable cognitive control mechanisms: a left frontal negativity that reflects active interference resolution, , but requires executive resources to implement, and a right frontal negativity that reflects global response inhibition that can be relied on when executive resources are minimal but at the cost of a slowed response. Collectively, these studies advance understanding of the factors that influence younger and older adults' ability to satisfy goal-directed behavioural requirements in the face of interference and the effects of age-related cognitive decline.

An Ontario-Developed Online Special Education Teacher Course Model for China

This study investigated the effectiveness of an Ontario-developed online Special Education teacher training course as a model for in-service teacher professional development in China. The study employed a mixed method approach encompassing both a quantitative survey and a qualitative research component to gather perceptions of Chinese and Canadian teachers, educational administrators, and teacher-educators who have intensive experience with online education, Special Education, and teacher preparation programs both in China and Canada. The study revealed insufficient understanding of Special Education among the general Chinese population, underdevelopment of Special Education teacher preparation in China, and potential benefits of using a Canadian online teacher training course as a model for Special Education in China. Based on the literature review and the results of this study, it is concluded that online Canadian Special Education teacher in-service courses can set an example for Chinese Special Education teacher training. A caveat is that such courses would require localized modifications, support of educational authorities, and pilot testing.

Armory and Lineages of Canada 1914

A book called "Armory and Lineages Of Canada 1914" with the copyright year 1913. The book is signed by H.K. Woodruff and it is also signed by Margaret Woodruff Band. Within the back pages is a list of dates of births, weddings and deaths. The full text is available in the Brock University Special Collections and Archives. There are other full text copies of later editions available in the Internet Archive: https://archive.org/search.php?query=title%3A%28armory%20and%20lineages%20of%20canada%29

The New Testament of Our Lord and Saviour Jesus Christ

This book was presented by the Canadian Bible Society (British & Foreign Bible Society) to the Canadian Soldiers in the war of 1914. There is an inscription which reads "Niagara-on-the-Lake, August 15th 1915 Presented to the 35th overseas Battalion Draft. P.C. Band to his father before his departure for the front". The word "confirmed" is written below this but the rest of the page is torn out. There is also a book plate that reads "Presented by the Canadian Bible Society (British & Foreign Bible Society) to the Canadian Soldiers in the War of 1914. 'Be strong and of a Good Courage'". See the full text in the Brock University Special Collections and Archives.

Ontario Game and Fishery Laws 1916

A paperback booklet of the Ontario Game and Fishery Laws 1916. The booklet is 91 pages in length and includes an index. See the full text in the Brock University Special Collections and Archives.