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Social enterprise and public procurement/Research Protocol

Introduction This document sets out the Research Programme of Action 2 under the SEEM Development Program (DP) i.e. SEEM 2. The core aim of SEEM 2 is to "increase equal opportunities for employment through encouraging an increase in economic activity of Social Enterprises (SEs)". This is to be achieved by increasing the ability of SEs to access greater levels of business in the public sector. The underlying key assumption is that SEs deliver a wider range of social (and environmental?) benefits than their private sector counterparts, including equal opportunities employment, and that a greater level of social benefits can be delivered by increasing the size of the social economy. The DP intends to help social enterprises and voluntary and community sector organisations to access procurement opportunities made available by the public sector, to help the public sector purchase better labour market outcomes through its mainstream procurement practices and to help social enterprises to provide high quality employment opportunities for people from Black and Minority Ethnic (BME) communities, women, people with disabilities and people aged over 50 years. From DP Application form "The BEST Procurement Development Partnership is focused on improving the prevailing conditions in the labour market in order to achieve long term structural change that increases equality in the labour market. Disadvantage in the labour market is created not only by the relative situation of the "disadvantaged" individuals but also by the value ascribed by the labour market to those individuals and their situation and willingness to include them." The DP is focused on achieving a change in practice within the East Midlands Region that other parts of the country can learn from, that provides evidence of use to national policy makers and ultimately that informs European policy. BEST Procurement operates under Theme D and contributes to achieving the Community Initiative Plan (CIP)'s recommendation that the social economy needs to address sustainable routes to regeneration and employment rather than isolated initiatives. The DP's aim is to increase the conversion rate between public expenditure and labour market equality within the East Midlands Region. To do this it will be necessary to improve value for public money in targeted areas and establish the social economy, particularly social enterprises and voluntary and community sector organisations, as key players in achieving this goal. The main objectives of the DP are to:  Understand and influence the demand for added value in public sector purchasing;  To develop purchasing frameworks and specific contracts that deal with issues of sustainable development;  To undertake supplier development of social enterprises and the VCS; and  To develop an evidence base that addresses key areas.  The SEEM 2 project is split into two distinct, but related programs of interventions as identified in the Action 1 research, and indicated in the design of the Partnership Schematic shown in Figure 1 Figure 1 BEST Procurement Partnership Schematic src="http://upload.wikimedia.org/wikibooks/en/0/05/SEEM_model.jpg" /> In the model above, the supply-side interventions are being delivered under the Social Enterprise Development Interventions component and the demand-side under the Local Procurement Practice/Policy component. SDRC's role is to investigate the interactions between actors within the components and between the components over the two year programme to identify the changes that have occurred and theorise on the changes and the reasons for these changes in order to inform public policy.

Research Methodology [this is supposed to be in boxes...can you see what its trying to say - if not will send sepapertly]

This methodology emerged from the approaches outlined earlier and from the availability of data. Qualitative and quantitative data were used to collect three types of data. Table 3 below notes the data types, analysis and methods used.

Table 3 - Research Methodology

Literature Review

Quantitative data	Quantitative data	Qualitative data Questionnaire online	Ordinal data plus nominal data held elsewhere 	Semi structured interviews – digitally recorded Correlation coefficient	Relationship modelling	Textual analysis Method: SPSS	Method : MS Access	Method: Atlasti

Table 3 shows that the literature is the will focus on which the research rest. These methods will employ grounded theory [refs] and discourse analysis [Barton and Hamilton 2002] as an analytical tool in analysisng findings of the semi structured interviews using Atlasti a Non-numerical data textual analysis, the online quesrionnanire will use a Social Science Programme for Statistics (SPSS) to validate and cross reference numerical data the Ordinal data will provide a structure of community, partnerships and relationship building during the process using a Human Resource modelling concept [Peter??? Luton] using MS Access.

The presentation of this table illustrates the methods employed to gain access to new insights and to develop the research into an intellectually rigorous piece of investigation. The literature review on topics such as: on social enterprise, public procurement, change management [maybe] and the role of government [s] as an enabling device to question: How, and under what conditions, do market development activities geared towards public procurement, such as the East Midlands BEST Procurement programme, contribute to the sustainability of social enterprises. Moreover in attempting a theory or paradigm shift we need to understand what this entails. The idea that an assortment of facts, concepts and constructs can lead to the development of a theory contains as Cohen and Mannion (1991) noted that it

''is itself a potential source of further information and discoveries. It is in this way a source of new hypothesis and hitherto unasked questions: it identifies critical areas for further investigation: it discloses gaps in our knowledge; and enables a researcher to postulate the existence of previously unknown phenomena.'' (Cohen and Mannion 1991:15)

In using the ‘mixed method’ approach one can increase the validity (it has some foundation: based on truth, legally acceptable) and reliability (trusted predictable, dependable) of the research data. The validity of this mixed method lies in the notion that this study needs to extrapolate from data the complexity of the prevailing paradigm within the social enterprise arena. Furthermore the reliability of the data lies in way in which it is collected and tested. Both sets of data will be tested rigorously and monitored through a series of interventions from the funder and colleagues at SDRC and elsewhere using WIKIbooks [over to you Tim] in order to escape the criticism of researcher subjectivity. Moreover this eliminates the problem of using one method alone for as Shipman (1981:147) argued it would produce “a one-dimensional snapshot of a very wide and deep social scene”. A ‘mixed method’ supports Shipman’s (1981) identification of a variety of methods to provide a cohesive rather than complex illustration of a fairly new field of research. What is needed for this particular research is an approach which identifies evidence of the transference of business/management theories into a social economy setting as it moves into the public procurement arena.


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Talk:Social enterprise and public procurement/Research Protocol

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license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
Social enterprise and public procurement/Research Question

2 Research Question The research question for this project is: How, and under what conditions, do market development activities geared towards public procurement, such as the East Midlands BEST Procurement programme, contribute to the sustainability of social enterprises? To elicit the underlying assumptions and implications of this question, the following questions can also be posed: 2.1 Related questions  What is 'social enterprise' and how does it differ from 'mainstream' business, and what are the implications of this difference? How do organisations, like social enterprises, incorporate new knowledge and skills into their operations and how do they capitalise on these changes? How does a social enterprise change to meet new opportunities such as public contracts? What changes occur within public sector organisations in developing more open markets and mature supply chains that include social enterprises as a business model?  How do contract opportunities change to allow social enterprises to fairly distinguish themselves in tender/contract opportunities? What advantages/disadvantages do social enterprises experience in public procurement opportunities, and are they fair?  2.2 Wider considerations  What contribution does social enterprise, as a concept and in practice, have to make to late capitalism?

Can the social enterprise model contribute to the increased social and environmental sustainability of the 'mainstream' private sector

What are the implications for public policy of increased public sector contracting of social enterprises?

What policy implications are there for the East Midlands in developing the social enterprise sector?


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Social enterprise and public procurement/Theory

Theoretical underpinnings

The overriding approach of this research is to derive theory i.e. lessons and a structure in which progress may be built, from the evidence placed before the research team. Rather than deriving a theory about procurement in the social economy and seeking to prove, or disprove, that theory, the concept is to observe the organisations that will participate in the DP on both the supply and demand side of the market and to develop a theory from what is observed. Given that the research is concerned with values, perceptions and meanings, it is clearly qualitative in nature, particularly as it seeks to develop an in-depth understanding of the experience of people in organisations and to explore why they think and act the way they do (Meloy, 2002).   This research is Inductive in nature because it does not test theory but provides inferences to inform theory (Maxwell,1996). This research is Interpretivist in that the research is based on the understanding and values of the participants and the interviewer's own interpretation of their perceptions (Kincheloe and McLaren, 2001	 This research is Constructivist in that the 'reality' of the supply and demand relationships that are being researched are 'constructed' by individuals in their interaction with each other (Lincoln and Guba, 1985).

In terms of the methodological approach, the intent is to compare two locations, Nottingham City and Northamptonshire, looking at the policy responses of the two councils in their engagement with and procurement from social enterprises in their area. The two local authorities differ in wealth, political background and social structure (details to be developed later) and early bipartite discussions with local authority officials has indicated that their councils have adopted quite different political strategies with respect to their response to social justice, community development, infrastructure and procurement processes. The response and nature of social enterprises engaging with these councils can be expected to be different, especially in the nature of the procurement opportunities.

Methodological theory Situational Analysis: Popper Soft Systems Methodology:Checkland and Scholes Grounded theory: Glasser Wikipedia -Grounded Theory Grounded theory %28Glaser%29

The goal of a GT is to formulate hypotheses based on conceptual ideas that others may try to verify. In these circumstances, the research project is designed to undertake research in the 'real world' which is by necessity messy and contigent, in order to develop hypotheses about the utility of public procurement as a means of improving labour market equality through public procurement processes, with social enterprises. It may be possible to verify some of the hypotheses that will be developed- certainly the quantitative techniques to be employed may contribute to this verifucation.

Validity in its traditional sense is consequently not an issue in GT, which instead should be judged by fit, relevance, workability, and modifiability (Glaser & Strauss 1967, Glaser 1978, Glaser 1998).

Fit has to do with how closely concepts fit with the incidents they are representing, and this is related to how thoroughly the constant comparison of incidents to concepts was done. The imperative in BEST Procurement will be to accurately reflect the 'incidents' i.e the emerging procurement opportunities and the responses of both the local authority and the social enterprises to the situations presented by BEST Procurement. Close engagement on behalf of the research team with the different stakeholders over an extended period will help to put them at their ease and allow the researchers ask searching questions. Recordings of the interviews will be made to ensure that the research team have the opportunity to review the interviews in detail after the fact and allow group evaluations to limit researcher bias

Relevance. A relevant study deals with the real concern of participants, evokes "grab" (captures the attention) and is not only of academic interest.

Workability. The theory works when it explains how the problem is being solved with much variation.

Modifiability. A modifiable theory can be altered when new relevant data is compared to existing data. A GT is never right or wrong, it just has more or less fit, relevance, workability and modifiability, and readers of Paper V are asked to judge its quality according to these principles.


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Social enterprise and public procurement/Supply-side Interventions

Supply-side Interventions Intervention objectives The objectives of the supply side interventions are:   Creating market opportunities for the social economy and develop the capacity of the social economy; and To create a number (between 100 and 200) of new market opportunities within the public sector appropriate to the social economy, focused on labour market integration and the needs of underrepresented groups and matched with the potential capacity of the social economy to deliver within the timeframe.  To provide targeted support to the social economy for it to capitalise on the market opportunities created through winning and sustaining contracts. Develop approaches including consortia, partnerships, incubation of new social enterprises and support for the voluntary and community sector to contract with the public sector.  Research objectives To observe and measure the interventions to establish:  The extent to which social enterprises are procurement ready and capable The extent to which the interventions develop and enhance that capacity The conditions under which the interventions are most effective</li> </ul> Supply-side interventions There were 12 supply-side interventions identified from Action 1. These are summarised in Table 1. Table 1 Supply side interventions in BEST Following the process of applying for partner organisations the number of interventions have been reduced to 8. These are summarised in Table 2 along with the lead partner for each intervention. Table 2 Supply-side intervention partners 1. Enterprising Directions Northants CDA 2. Enterprising Ideas DTA 3. Replication Leicester CAN 4. Incubation 5. Culture Change DTA 6. Enterprising Management 7. Market Reports 8. Sales Broker Northants CDA 9. Contract Finder ISDB 10. Contracting Know-How ISDB 11. Collaborative Frameworks 12. Equality of Employment LCCDA 13. Chair ISDB 14. Advisory Partners Hurt Trust Each of the partners will be developing, testing and implementing an intervention in their area of the DP with a number of social enterprise beneficiaries who will be recruited through the networks of the partners. The intention is that the development requirements of each beneficiary will be measured at the start of their engagement with BEST, by Northants CDA, using their existing (and modified in collaboration with SDRC for the purposes of the BEST programme research) diagnostic tools. These evaluations will set a baseline against which the beneficiaries will be measured and also help to identify which of the interventions are best suited to the needs of the beneficiary


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Talk:Social enterprise and public procurement/Supply-side Interventions

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Latonic/Adjectives

Different kinds of adjectives
Adjectives conjugate similarly to nouns, therefore good knowledge of the nouns ir reccomended. Having read on the nouns at least once is a minimal requirement to understand adjectives. Adjectives are divided first into anteméssa (placed before the noun) and posteméssa (placed after the noun). Anteméssa are generaly conugated like the article, while posteméssa follow the noun itself.

Behind the noun
Just like nouns, adjectives are divided into two conjugations. Adjectives of the first conjugation always ends on -o in their male form. Replacing this -o with -a and -u give you their respective female and neuter forms. Most adjectives are placed behind the noun, a few few before them, and some nouns have a different meaning depending on their place. For example, bello, when placed behind the noun means beautiful, handsome, pretty, while bel before a noun is more generale: nice, good, pretty, ... When placed behind the noun (or with no noun at all), the adjective copies the exits from the nouns of the first conjugation:

Before the noun
Adjectives behind a noun will be found in the dictionary as for example bello, -a, u. Adjectives before the will be found as for example bel, bella* (he asterisk is to remind you to put it before the noun). From this you can derive the root bell- and the short form bel. The short form will be used in the nominative and accusative with male or neuter nouns. All other forms will gets the root with the exit of the article.

Behind the noun
Nouns of the second conjugation are slightly harder because their gender is hard to define. In the dative and genitive singular, and in all the plural forms, they follow the noun or the article depending on it's position. In the accusative and nominative singular, they take a differnent form. In most cases, male and neuter adjectives have root + -e here, while female ones have root + -i. However: As an example, we'll take grande, -di, -de, which means big when place behind a noun. Before a noun it becomes gran, grandi which means great as in "very good".
 * Some adjectives have -er, -(e)ri, -(e)re: aguer, agri, agre
 * Some adjectives (mainly active participles have -ns, -nti, -nte: carmínans, carmínanti, carmínante

Before the noun
Adjectives before a noun work just the way they do when they follow the first conjugation, except for the accusative and nominative singular. Also keep in mind that the exit -o is always replaced with -e!

Demonstrative Pronouns
Demonstrative pronouns are words like this and that have the same function as the defintite article but are stronger and more specific. English has two "places": here and there (and archaic yonder) Latonic has three: cuí (here), lí (within eye range) and ví (far away). Therefore, it also has three demonstrative pronouns: In modern spoken language, illu and istu may be used less specifically, having the same function but istu being stronger, while illu always refers to something earlier mentioned. The demonstrative pronouns are placed before the noun and conjugated like the adjectives before a noun. They may also be used on their own, in which case they are conjugated like the adjective behind a noun. An overview of genders:
 * Istu is usually associated with quí.
 * Illu is usually associated with lí.
 * Víe is usually associated with ví.
 * Sol. isto, ista, istu, Adj. iste, ista (1st/1st Cg.)
 * Sol. illo, illa, illu, Adj. ille, illa (1st/1st Cg.)
 * Sol. víe, víi, víe, Adj. ví, vía (2nd/1st Cg.)

title: Latonic/Adjectives


text: File:Egm6321 f10 team6 HW5 problem2.png

title: File:Egm6321 f10 team6 HW5 problem2.png


text:
User:Egm6321.f10.team3.cook/HW5

=Problem 7: Find $$ {u}_{1},  {u}_{2} $$ using trial solution and variation of parameters=

Given
Give the reverse engineered equation on [|Mtg 31-1] of the lecture notes

 * {| style="width:100%" border="0"

$$ \left(x+1 \right) {y}^{''} - \left(2x+3 \right) {y}^{'} + 2y=0 $$ $$
 * style="width:95%" |
 * style="width:95%" |
 * $$\displaystyle (Eq. 7.1)
 * }

Find
Find $$ {u}_{1},  {u}_{2} $$ 2 Homogeneous solutions of $$\displaystyle (Eq 7.1) $$ using the trial solution:

 * {| style="width:100%" border="0"

y= {e}^{rx} $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 7.2)
 * style= |
 * }

Solution
To solve we first find the roots to the characteristic equation by plugging $$\displaystyle (Eq 7.2) $$ into $$\displaystyle (Eq 7.1) $$ to obtain

 * {| style="width:100%" border="0"

\left(x+1 \right) {r}^{2} - \left(2x+3 \right) r + 2=0 $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 7.3)
 * style= |
 * }

Find the roots by using the quadratic formula
 * {| style="width:100%" border="0"

r= \frac{\left(2x+3 \right) \pm \sqrt{{\left(2x+3 \right)}^{2}-8\left(x+1 \right)}} {2 \left( x+1\right)}= \frac{\left(2x+3 \right) \pm \left(2x+1 \right) } {2 \left( x+1\right)} $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 7.4)
 * style= |
 * }

Solving we get the two roots to the characteristic equation:

 * {| style="width:25%; padding:1px; border:2px solid #0000FF"

{r}_{1} = 2 ; {r}_{2}=  \frac{1}{ \left( x+1\right)} $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 7.5)
 * style= |
 * }

Now we use the trial solution $$\displaystyle y= {e}^{rx} $$ and the constant root to obtain:

 * {| style="width:25%; padding:1px; border:2px solid #0000FF"

{u}_{1} = exp(2x) $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 7.6)
 * style= |
 * }

To find $$\displaystyle {u}_{2}(x) $$ we will use the variation of parameters method.

 * {| style="width:100%" border="0"

y(x)=U(x) {u}_{1}(x) $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 7.7)
 * style= |
 * }

Plugging $$\displaystyle (Eq. 7.7)$$ into $$\displaystyle (Eq. 7.7)$$ gives us

 * {| style="width:100%" border="0"

{U}^{'}(x) \left[ -\left(2x+3 \right) {u}_{1}(x)+ \left( x+1\right) {u}^{'}_{1}(x) \right] + \left( x+1\right) {u}_{1}(x) {U}^{''}(x)=0 $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 7.8)
 * style= |
 * }

Now use the reduction of order method 0 to find the expression for $$\displaystyle {u}_{2}$$. Using equation 1 from [|Mtg 31-1] we can now solve for $$\displaystyle {u}_{2}(x)$$

 * {| style="width:100%" border="0"

{u}_{2}(x)= {u}_{1}(x) \int \frac{1}{ {u}^{2}_{1}}exp \left[ - \int {a}_{1}dx\right]dx $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 7.9)
 * style= |
 * }

where $$\displaystyle {a}_{1}:= \frac{2x+3}{x+1} $$. Solving the integral for $$\displaystyle {a}_{1}$$ first we have
 * {| style="width:100%" border="0"

\int {a}_{1}dx= \int \frac{2x+3}{x+1} dx = \left[2x+ log(x+1)\right] $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 7.10)
 * style= |
 * }

Now plug $$\displaystyle (Eq. 7.10)$$ into $$\displaystyle (Eq. 7.9) $$ to obtain

 * {| style="width:100%" border="0"

{u}_{2}(x)= {u}_{1}(x) \int \frac{x+1}{ {u}^{2}_{1}}exp \left[ -2x\right]dx $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 7.11)
 * style= |
 * }

Substituting in our expression for $$\displaystyle {u}_{1}(x)=exp\left(2x\right)$$ we have

 * {| style="width:100%" border="0"

{u}_{2}(x)= exp \left(2x \right) \int \left(x+1\right) {exp \left(-2x \right)}^{2}exp \left[ -2x\right]dx= exp \left(2x \right) \int \left(x+1\right) exp \left[ -6x\right]dx $$ $$ Solving the above equation by parts yields the solution for $$\displaystyle {u}_{2}(x)$$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 7.11)
 * style= |
 * }

 * {| style="width:100%" border="0"

{u}_{2}(x)= exp \left(2x \right) \left[ - \frac{1}{6}x exp \left(-6x \right)- \frac{1}{36}exp \left(-6x \right)-\frac{1}{6}exp \left(-6x \right)\right]= - \frac{1}{36} \left( 6x+7\right)exp \left( -4x\right) $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 7.12)
 * style= |
 * }

The two homogeneous solutions are:

 * {| style="width:25%; padding:1px; border:2px solid #0000FF"

{u}_{1} = exp(2x); {u}_{2}(x)= - \frac{1}{36} \left( 6x+7\right)exp \left( -4x\right) $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle
 * style= |
 * }

title: User:Egm6321.f10.team3.cook/HW5


text:
Java Programming/Inheritance

Syntax
In Java, the syntax for deriving a child class from a parent class is:

Example
Here is a program that uses a class Video to represent movies available at a video rental store. The Video class has basic information in it, and would be OK for documentaries and instructional tapes. But movies need more information. An additional class, Movie, is created that is similar to Video, but has the name of the director and a rating.

The class Movie is a derived class (subclass) of Video. An object of type Movie has the following members in it:

Both classes are defined: the Video class can be used to construct objects of that type, and now the Movie class can be used to construct objects of the Movie type.

The class definition for Video has a constructor that initializes the member data of Video objects. The class Movie has a constructor that initializes the data of Movie objects. The constructor for class Movie looks like this:

The statement super(title, len) invokes the base class' constructor to initialize some of the data. Then the next two statements (on one line) initialize the members that only Movie has. When super is used in this way, it must be the first statement in the subclass' constructor.

4. It is not necessary to use super; the following would also work as a constructor for Movie:

In this constructor, each variable of the newly created Movie object is set to an initial value.

title: Java Programming/Inheritance


text:
Motivation and emotion/Textbook/Emotion/Mood

Introduction
Mood and emotion are experienced everyday by every individual. This field is commonly studied in psychology. An understanding of the causes and effects of mood and emotion is important in interpreting how an individual will behave and react.

This chapter will be explored through focus questions. The first looks at the difference between emotion and mood. Followed by whether positive and negative moods are polar opposites. After this different sections of the brain, the anterior cingulate cortex, the amygdala and the hippocampus, will be explored through mood and emotion. This section will also look at the effects of mood and the brain in Alzheimer's disease and schizophrenia. The section on the brain will be followed by what mood and emotion effects. Depressive and manic mood disorders, risk-taking behaviour and prosocial behaviour will also be examined in this section. Then substances that effect mood and emotion, such as alcohol, nicotine, cannabis and MDMA (ecstacy), will be discussed. This chapter will conclude with a look at the PANAS, a measurement of mood.

What is the difference between emotion and mood?
Reeve, 2009, notes three main difference between mood and emotion; cause, action specificity and time. Emotions are caused by significiant life events whereas moods emerge from ill defined, often unknown, causes. Emotions influence behaviours while mood influences cognitions. Finally, emotions are short lived events that last seconds or minutes. On the other hand, moods are mental events that can last hours or days. In short, emotions are less enduring than moods. Moods are also different from personality traits and temperament, as these last even longer than moods.

There are also more classes of emotion than mood. Moods tend to be noted as either positive or negative (Reeve, 2009) whereas Ekman and Davidson's (1994: cited in Reeve, 2009) noted six basic emotions; fear, anger, disgust, sadness, joy or happiness and interest. These six basic emotions can also be noted as either positive or negative. Fear, anger, disgust and sadness are negative emotions and joy/happiness and interest are positve emotions.

Mood also differs from affect. Mood is an overall state of being, normally refered to as either positive or negative. Whereas affect is the experience of emotions. Affect is more commonly seen than moods, normally through facial or vocal expressions or body gestures (Watson, Clark & Tellegan, 1988). Affect is generally seperated into two groups; normal affect, for example positive and negative emotions, and pathological affect (see table below; Watson, Clark & Tellegan, 1988).

Are Positive and Negative Moods Polar Opposites?
The emotional equivalent of a positive mood is most commonly stated as happiness and sadness for a negative mood (Reeve, 2009). This may lead individuals to believe that they are polar opposites. However, these are correlated together and have different psychological correlates (Cook, Spring, McChargue & Hedeker, 2004). For these two mood states to be polar opposites their effects on behaviours would also have to be opposite. It is generally thought that individuals are more creative when in a positive mood, but many famous masterpieces have been created while the artist was in a self-reported negative mood, such as most of Vincint Van Gogh's work (Montgomery, Hodges & Kaufman, 2004). Also, individuals tend to report tasks easier when in a positive mood than a negative mood. For example, smokers find it easier to quit when in a positive mood than a negative mood (Cook, et al, 2004). This is not to say that individuals in a negative mood cannot quit smoking. Examples of how positive and negative moods effect behaviour and how behaviour effects moods will be explored throughtout this chapter.

What Does Mood and Emotion Do in the Brain?
A lot of the research on mood and emotion in psychology is based around what areas of the brain correlate to mood and/or emotion. The two main areas of the brain that have been correlated with mood and emotion are the anterior cingulate cortex, the amygdala and the hippocampus.

How are the Anterior Cingulate Cortex and Mood and Emotion Linked?
One part of the brain that has been linked to mood and emotion is the anterior cingulate cortex. The anterior cingulate cortex (ACC) is located around the corpus callosum and is the frontal area of the cingulate cortex (see right; Alexopoulous, Gunning-Dixon, Latoussakis, Kanellopoulos & Murphy, 2008; Barrett, Pike & Paus, 2004). The ACC is connected to the limbic structures of the brain (Alexopoulous, et al, 2008) and regulates emotional responses, as well as autonomic and visceral responses (Alexopoulous, et al, 2008; Barrett, Pike & Paus, 2004). This area of the brain has also been linked to response error and, in turn, response error has been linked to mood and cognitive changes in depression (Alexopoulous, et al, 2008). Response error refers to how an individual responds to error. Dysfunction of coginitive division in the ACC can be seen when an individual has an abnormal response to error (Alexpoulous, et al, 2008). Abnormal response to error is found more in individuals with negative affect before the response than those with positive affect before the response (Alexopoulous, et al, 2008). This abnormal response could be a drastic increase in negative affect, including crying or signs of depression (Alexopoulous, et al, 2008). Research has also found the ACC to be involved in normal affect, such as sadness, as well as pathological affect, such as major depression (Barrett, Pike & Paus, 2004). Depression and induced negative affect increase activity in the ACC (Barrett, Pike & Paus, 2004). Therefore, mood and emotion have been linked to activation of the anterior cingulate cortex.

How are the Amygdala and Mood and Emotion Linked?
Another part of the brain that effects mood and emotion is the amygdala. The amygalae are found in the temperal lobes of the brain. Each lobe has one amygdala; a group of nuclei shaped like an almond (Derntl, et al, 2009; Hamann, Ely, Hoffman & Kilts, 2002; Tranel, Gullickson, Koch & Adolphs, 2006). Strong evidence has linked the amygdala to negative or aversive emotions, such as fear (Derntl, et al, 2009; Hamann, Ely, Hoffman & Kilts, 2002; Tranel, Gullickson, Koch & Adolphs, 2006). However, little research has looked into, or found evidence of, a link between positive emotions and the amygdala (Hamann, Ely, Hoffman & Kilts, 2002). Hamann, Ely, Hoffman and Kilts (2002) showed participants positive and negative photographs while said participants underwent a Positron emission tomography (PET) scan. This study looked at how neural correlates of positive and negative emotions affect the amygdala. The results of this study found negative emotions create bilateral amygdala activation and positive emotions to create left amygdala and prefrontal cortex activation. However, Derntl and colleages found bilateral activation in both positive and negative emotional states. Damage to the amygdala interfers with processing emotional signals, such as facial expression and negative emotions like fear, anger and sadness (Derntl, et al, 2009; Tranel, Gullickson, Koch & Adolphs, 2006). Therefore, mood and emotion have been linked to the amygdala.

How are the Hippocampus and Mood and Emotion Linked?
The final part of the brain that effects mood and emotion to be discussed is the hippocampus. As the picture on right depicts, the hippocampus is located near the amygdala in the limbic system (Richardson, Strange & Dolan, 2004). Many studies have found a link between fear and hippocampus activation (see Richardson, Strange & Dolan, 2004), as well as links to other psychopathological disorders. Individuals with Alzheimers disease tend to have disruptions in the hippocampus (Richardson, Strange & Dolan, 2004). Also, individuals who suffer from schizophrenia tend to have smaller hippocampi than individuals who do not suffer from this disorder (Richardson, Strange & Dolan, 2004). Alzheimers disease and schizophrenia influence sufferers' mood and emotions as well (Richardson, Strange & Dolan, 2004).

How are Alzheimer's Disease and Mood and Emotion Linked?
Alzheimers disease is a disorder that is noted in the Diagnostic and statistical manual of mental disorders IV (DSM-IV) as dementia of the Alzheimer's type (p154) and is a cognitive disorder (American Psychiatric Association [APA], 2008). This disease has been associated with social withdrawal and depression that are thought to be due to sufferers frustration in diminishing memory and cognitive abilities (Lancioni, et al, 2009). Although there tends to be a decline in general mood as individuals enter retirement age and older, sufferers of Alzheimer's disease have higher rates and longer periods of negative moods than others their age (Lancioni, 2009). Currently there is no cure for this disease. However, there are pharmacological treatments, such as antioxidants, acetylcholinesterase inhibitors and the N-menthyl-D-aspartate receptor-antagonist and memantine, which can also effect an individual's mood (Lancioni, 2009).

How are Schizophrenia and Mood and Emotion Linked?
The typical onset of Schizophrenia is between the late teens and mid-30s (APA, 2008). Studies have found that gray matter in the brains frontal, temporal and limbic lobes decreases in sufferers of schizophrenia over time (Smieskova, et al, 2009). Like Alzheimer's disease, schizophrenia has high comorbidity with major depression (Martin, Allan, Fleming & Atkinson, 2008). There is also a high comorbidity between schizophrenia and nicotine dependence, which also effects mood (see below; Martin, Allan, Fleming & Atkinson, 2008). Nearly all sufferers of schizophrenia experience mood disturbance (Martin, Allan, Fleming & Atkinson, 2008). Mood disturbance can include abnormal reactions to stimuli as well as rapid mood swings or unprevoked mood swings (Martin, Allan, Fleming & Atkinson, 2008).

What does Mood and Emotion effect?
It might not come as a surprise that individuals in a positive mood smile more than individuals in a negative mood (Vrugt & Vet, 2009). However, there are many other things that mood and emotion effect. Although there are five common mood disorders (see above), only three will be discussed in this chapter. Depression is a significantly depressed or irritable mood whereas bipolar I and II are disorders that alternate between depressed and manic moods. Both depression and bipolar I and II have effects on mood and emotion. Risk taking behaviours also increase with an increase in positive moods. The final effect on mood and emotion to be discussed is prosocial behaviour, such as helping behaviour and altruism.

How does Mood and Emotion effect Mood Disorders?
There are numerous mood disorders that effect mood and emotion, such as major depressive disoder, and bipolar I and  bipolar II disorders. Firstly, depression can lead to psychomotor retardation such as changes in speech and motor activity, which can cause an individual frustration and a negative mood state (Barrett, Pike & Paus, 2004). The age of onset for major depressive disorder is lowering, and so it is hard to say what is the mean age of onset (Durand & Barlow, 2010). Depression normally follows a significant life stressor, such as the loss of a loved one (Patten, 2009). Individuals with depression normally experience negative moods and more negative emotions, such as anger and sadness, than positive emotions (Wadsworth, Moss, Simpson & Smith, 2005). Depression can also effect eating and sleeping patterns as well as self-esteem (APA, 2008). The most commonly prescribed antidepressant medication is selective serotonin reuptake inhibitors (SSRIs; Wadsworth, Moss, Simpson & Smith, 2005). Although depression has a significant effect on mood, individuals taking SSRIs have reported their belief that on SSRIs they can no longer experiences moods, either positive or negative (Wadsworth, Moss, Simpson & Smith, 2005).

Bipolar I and II both consisted of depressive and manic episodes. The difference between these two disorders is that sufferers of bipolar I experience full depressive and manic episode whereas bipolar II sufferers alternate between depressive and hypomanic episodes. Hypomanic episodes are less severe than manic episodes (Durand & Barlow, 2010). Individuals during manic episodes have elevated positive moods and emotions (APA, 2008). These individuals are also easily distracted and more likely to partake in risk taking behaviours than individuals not suffering from bipolar (APA, 2008). These two disturbances can lead to harm of the sufferer (Durand & Barlow, 2010).

How does Mood and Emotion effect Risk Taking Behaviour?
Unlike individuals experiencing a manic episode, the majority of individuals are more likely to partake in risk taking behaviours when in a negative mood than a positive mood (Chuang & Chang, 2007). A lot of literature has looked into large risk taking behaviours, such as gambling and risky business ventures (Chuang & Chang, 2007). However, Chuang and Chang (2007) looked into everyday risk taking behaviours and mood. The experiment consisted of 82 students, 38 men and 44 women ranged in age from 21 to 53, enrolled in a executive master of business administration course. The experimenters enduced a positive mood in half of the participants and a negative mood in the remaining half and then given 13 scenarios with differing risk taking behaviours. One scenario looked at buying a new pair of shoes. Chuang and Chang (2007) noted that this involves social and economic danger; social due to the influence of friends and society and econimic due to the price of the shoes. This experiment found that individuals with a negative mood take more risk in everyday life than those in a positive mood.

How does Mood and Emotion effect Prosocial Behaviour?
The final thing that mood and emotion effect to be discussed is prosocial behaviour. Experiments on the effect of mood on prosocial behaviour have been conducted for years (see Latane & Darley, 1968). Prosocial behaviour has two main forms; helping behaviour and altruism. Helping behaviour is when an individual deliberately and voluntarily behaves in a way that will benefit other individuals. This behaviour may also benefit the individual who performed the behaviour (Crisp & Turner, 2010). As helping behaviour must be deliberate, this definition excludes accidental help; such as dropping money that another individual later finds (Crisp & Turner, 2010, p283-4). This definition also excludes behaviours that might seem to be helping others but are mostly selfish, such as companies giving money to charities, as this would also help their public image (Crisp & Turner, 2010, p284). Altruism, on the other hand, is a behaviour that is not expected to help the individual who is being altruistic (Crisp & Turner, 2010).

A Dutch experiment by Vrugt and Vet (2009) looked into prosocial behaviour. A convience sample of 240 male and 240 female passers-by were approached by a male or female experimenter who was either smiling or had a neutral expression and asked to help by participating in an investigation. This experiment found smiling experimenters were more likely to receive a smile from participants and women smiled more often than men. The results also showed a positive correlation between participants who smiled and those who accepted to participate in the investigation. Also, that a smiling male experimenter elicited more helping behaviour from female participants than any other combination of experimenter/ participant genders. Vrugt and Vet (2009) state that participants who were in a positive mood, defined as smiling, were more likely to participate in the investigation.

How does Alcohol Effect Mood and Emotion?
In Australia alcohol tends to be used as a legal, typically reliable way to alter mood (Lindsay, 2009). Alcohol is a depressant, which decreases central nervous system activity (Durand & Barlow, 2010). Relaxation and a reduction in physiological arousal are the typical effects of depressants (Durand & Barlow, 2010). At first the effects of alcohol tend to be seen as a stimulant, with people experiencing a lowering of inhibition. However, alcohol has been linked to negative mood and emotions (Durand & Barlow, 2010). High rates of alcohol intake have been linked to aggression, property damage, sexual assaults and attempted suicides (Jennison, 2004). Excessive drinking has also been associated with risky sexual behaviour and unplanned pregnancy (Jones & Gregory, 2009).

How does Nicotine Effect Mood and Emotion?
Nicotine withdrawal has been linked to negative mood and emotions, such as anger, as well as depression (Durand & Barlow, 2010). This may suggest that nicotine increases mood. However, ther is a strong positive relationship between nicotine dependence and major depressive episodes (Durand & Barlow, 2010). Cook and colleagues' (2004) study deprived 35 smokers, aged between 18 and 65 years (M = 17.5) who smoked at least ten cigarrettes a day for the past year, of nicotine for a 48 hour period (Cook, et al). Each participant's mood was tested six times in the 48 hour period using the Profile of Mood States questionnaire. This questionnaire consisted of 65 questions rated on five point Likert scales (0= not at all; 4 = extremely) (Cook, et al). Postive moods were noted as activation, elation, enthusiasm, happiness, jubilation and peppiness. Negative moods were noted as distress, hositility, nervousness, scorn, gloominess, tension, depression and anger. Cook and colleagues found that cigarette craving is due to a decrease in positive mood rather than an increase in negative mood. This study also found that smokers who partake in pleasurable activities during the nicotine deprevation have lower rates of cigarette cravings than those who do not.

How does Cannabis Effect Mood and Emotion?
Cannabis, commonly known as marijuana, is currently the most frequently used hallucinogen (Durand & Barlow, 2010). Hallucinogens effect the way an individual perceives the world by distorting sight, sound, taste, smell and feelings (Durand & Barlow, 2010). Cannabis has different effects on different people (Durand & Barlow, 2010). Individuals under the influence of cannabis tend to experience mood swings and typically normal experiences are thought to be extremely funny (Durand & Barlow, 2010). Most users report increased positive mood and emotions. However, this can change to paranoia if taken in larger doses (Durand & Barlow, 2010).

How does MDMA (Ecstasy) Effect Mood and Emotion?
Methylenedioxymethamphetamine (MDMA) otherwise known as ecstasy, was fist synthesised in Germany in 1912. Recreational use rose sharply in the 1980s (Durand & Barlow, 2010). MDMA is an amphetamine, which is a stimulant drug (Durand & Barlow, 2010). Caffeine and nicotine are also stimulants (Durand & Barlow, 2010). Amphetamine use induces a positive mood and feelings of elation and vigor as well as reducing fatigue. However, amphetamine withdrawal induces feelings of depression and tiredness (Durand & Barlow, 2010). In fact, both amphetamine use and withdrawal have been linked to sleep and eating behaviour disturbances (Roiser & Sahakian, 2004).

What is the PANAS?
The Positive Affect Negative Affect Schedule (PANAS) is a 20-item self report measure of mood states on a 5-point Likert scale (1= very slightly or not at all, 5= extremely) (Watson, Clark & Tellegan, 1988). Items are divided into positive or negative, with ten items in each category. A score between 10 and 50 is possible in both categories. The mean score for positive affect is 35.7 (SD = 6.2) and for negative affect is 19.5 (SD 6.0) (Watson & Clark, 1994). This measure is used with one of seven different time instuctions; at the moment, today, in the past few days, in the past week, in the past few weeks, in the past year, or in general (Watson, Clark & Tellegen, 1988). A longer version, the PANAS-X, contains not only positive and negative affect but also fear, hostility, guilt, sadness, joviality, self-assurance, attentiveness, shyness, fatigue, serenity and surprise (Watson & Clark. 1994). The PANAS-X is a 74-item self report measure on the same 5-point Likert scale as the original (Watson & Clark, 1994). Both measures were constructed so each item held high factor loading on the selected scale, such as positive affect, and near-zero factor loadings on all other scales (Watson, Clark & Tellegan, 1988). An example of the PANAS can be found here (see the bottom of the fourth page).

Conclusion
Mood and emotion are related and have similar cause and effects. Emotions are short-lived reactions to life events that influence behaviours, whereas moods are mental events from ill defined causes that influence cognition and can last for hours or days. Moods are generally defined as either positive or negative. Positive moods have been found to have a positive influence on creativity in people, yet this does not mean that individuals in negative moods cannot be creative. Positive and negative moods are not polar opposites dispite them commonly being identified as such. Instead these two moods are correlated and have different psychological correlates. A person can be experiencing both positive and negative moods simultaneously.

The brain plays an important role in mood and emotion. The anterior cingulate cortex shows cognitive changes when an individual is depressed. A relationship has also been found between this area of the brain and normal affect and pathological affect. Futhermore, bilateral amygdala activation is seen during positive and negative moods. The amygdala and the hippocampus have also been linked to negative emotions, such as fear. Changes in the hippocampus can be seen in sufferers of both Alzheimer's disease and schizophrenia. There is a comorbidity between Alzheimer's disease and depression, as well as schizophrenia and depression. The medications perscribed to lessen the effects of Alzheimer's disease and schizophrenia can also effect mood and emotion.

In this chapter, four main areas were discussed in relation to what mood and emotion have an effect on. The first two were depression and mania. Depression decreases positive moods and increases negative moods and emotions. Whereas mania elevates positive moods and decreases negative moods. Mania has been linked to risk taking behaviour. However, individuals who do not suffer from mania have higher rates of risk taking behaviour when in a negative mood than a positive. Prosocial behaviour was the final discussion point in this section. Positive mood states increase prosocial behaviour such as helping behaviour and altruism.

After the effects of mood and behaviour, the effects on mood and behaviour were explored. Alcohol is a depressant that increases rates of anger and aggression. Nicotine use and withdrawal have also been linked to anger. Cannabis is a hallucinogen that distorts users' experiences of feelings as well as causes mood swings. The final drug discussed was MDMA or ecstacy. MDMA creates positive moods while in an individual's system. However, withdrawal from the drug can cause intense negative mood states.

The final topic explored in this chapter was the measure of mood, the positive and negative affect schedule (PANAS). This version is a 20 item self report questionnaire that measures mood in one of seven time periods. A longer version of this measurement, the PANAS-X, using 74 items across 13 categories is also available. Emotions and moods are experienced on a daily basis and have a marked effect on an individual's experience of the world. {{Hide in print|


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Talk:Motivation and emotion/Textbook/Motivation/Gambling

Feedback
Wow, I've only had a quick look but this is really shaping up fast - nice work. One very (very) minor tip: -- Jtneill - Talk - c 23:59, 1 November 2010 (UTC)
 * 1) APA style - 461 - 465 -> 461-465 (for pages numbers, there is no space before and after -).

Here's some more feedback, based on a closer review of your current draft: -- Jtneill - Talk - c 11:43, 2 November 2010 (UTC)
 * 1) Overall, currently, I'd say 75% done, probably CR-level - with potential for higher with some redrafting. Well done on getting a solid first draft up. Take or leave any of these suggestions - mostly they are about a bit of restructuring to improve overall flow and logic, with some APA style suggestions.
 * 2) Include a brief definition of gambling in the Introduction (I realise an expanded definition is also in the glossary).
 * 3) Gambling definition - the adopted definition seems to closely match the philosophical definition (I'm not sure of the distinction being made).
 * 4) Good to see the Australian focus, but I'm curious as to how the connection between motivation and gambling differs cross-culturally - is there anything particularly unique about gambling in Australia? (It looks like the rest of the content is not specific to Australia; perhaps the Gambling in Australia section then could be put into a separate side-box/highlight box since it's not really part of the main narrative). Perhaps to give a greater focus on gambling research in Australia, focus on citing from key government and federal grant research findings in the area e.g., Uni of Western Sydney has been doing work in this area e.g., http://pubapps.uws.edu.au/news/index.phtml?act=view&story_id=1091, also see http://www.aph.gov.au/library/INTGUIDE/sp/gambling_ebrief.htm, http://www.olgr.nsw.gov.au/gaming_research_year.asp, http://www.pc.gov.au/projects/inquiry/gambling-2009, http://www.pc.gov.au/projects/inquiry/gambling-2009/report etc.
 * 5) Motivation definition - maybe tailor this to a gambling context?
 * 6) Emotion definition - this is a somewhat complex conceptualisation (the claim that it is the most holistic is a bit (overly?) bold?) - perhaps it could be simplified - the key point seems to be a conceptual difference between positive and negative emotions, both of which are triggered by gambling experiences.
 * 7) APA style
 * 8) Use ampersands inside brackets for citations e.g., (Griffiths and Delfabbro, 2002) --> (Griffiths & Delfabbro, 2002) and if there is a subsequent citation of the same source within a paragraph, do not repeat the year, i.e., (Griffiths & Delfabbro).
 * 9) Citations in brackets should be in alphabetical order e.g., fix (Reeve, 2009; Chantral, Vallerand and Vallieres, 1995)
 * 10) et al -> et al.
 * 11) Cite all authors on first citation e.g., check Lee et al.
 * 12) Check that subsequent citations of references with three or more authors use first name and et al e.g., Chantral, Vallerand and Vallieres (1995) -> Chantral et al. (1995) after first citation of it with all authors.
 * 13) Avoid one-sentence paragraphs (usually a paragraph would be 3 to 5 sentences long)
 * 14) Explain South Oaks Gambling Screen
 * 15) What is problem gambling (perhaps explain in Introduction, Definitions - or it could be a Focus Question)?
 * 16) Lee et al - what were the other three factors?
 * 17) Maybe introduce the Focus Questions as part of the Introduction - and explain why these are important issues. Whet the reader's appetite - and then provide the more detailed answers.
 * 18) The rest of the focus questions are reasonably well addressed. Other topics perhaps to consider include the relationship between personality and gambling (are some vulnerable?) and the psychology of risk-taking. You may also be interested to consider "gambling addiction" as distinct from or related to problem gambling. Some definitions of such distinctions could be useful.
 * 19) Consider incorporating the "Extras" sections into the main body (they seem a bit disconnected/disjointed added here at the end).
 * 20) Learning Aids - maybe rename as Review Questions - I like these; well done.

-- Jtneill - Talk - c 13:52, 13 December 2010 (UTC)


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User:Theresa Thomas

Hello, I'm Theresa Thomas from Kerala,India.

title: User:Theresa Thomas


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History of Quebec and Canada/Study Guide/Topic 1: mother country colony relations

What was the relationship between the Mother country (France) and the Colony (New France)?

The relationship was one of dependence on France for its:

Population: The settlers came from France.

Economic development: Capital, imports and exports were controlled by France.

Army: Soldiers came from France and all military decisions with regards to peace and war were made in France.

Government: Major political decisions were made in France.


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User:Egm6321.f10.team1.allen/HW5

Solution
First, solve r to satisfy this set of equations.

substitute 7.2-7.4 into 7.1 cancel out exponentials

factor in terms of x

for non-trivial solution satisfy two equations

Put 7.1 in the proper form

such that

Then use the trial solution method to find another solution.

Specifically,

The first integral is carried through to yield: which simplifies to: further simplifying yields The second integral is carried through to yield: which simplifies to:

Author Egm6321.f10.team1.allison 00:33, 1 November 2010 (UTC) 173.24.228.78 05:47, 1 November 2010 (UTC)EGM6321,F10.TEAM1.WILKS 01:57, 2 November 2010 (UTC) Egm6321.f10.team1.allen 02:03, 2 November 2010 (UTC)

title: User:Egm6321.f10.team1.allen/HW5


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History of Quebec and Canada/Study Guide/Topic 2: Royal Government

Why was Royal Government adopted in 1663 and what were its key characteristics ?

King Louis XIV wanted to make France the most powerful country in Europe and to make New France a strong colony. Consequently, the charter of the Company of 100 Associates (1627-1663) was cancelled, since it had defaulted on its promise to transport thousands of settlers to New France, and the colony now came under the king's direct control. Jean-Baptiste Colbert was Louis XIV's most important minister and he was to run the colony through the Ministry of the Marine. To execute their plan, Royal Government was thus established in New France in 1663. Royal Government Intendant: Responsible for the daily economic

affairs of the colony, trade, justice, finance, settlement and seigneurialism.

The Bishop: Was in charge of the church which was responsible

for the spiritual needs of the colony, its schools, charities, hospitals and for the conversion of the Natives.

Governor: represented the king in the colony; responsible for the defence

of New France and for relations with the English and the Indians

The Sovereign Council:

intendant and bishop.
 * It consisted of a dozen officials including the governor,
 * It acted as a legislative, administrative and judicial body.

 * It was the sole governing authority in the colony responsible to the king.

Captains of militia

They reported to the intendant the concerns of the habitants and informed the habitants of the intendant's plans.

Try the following questions on Royal Government.


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History of Quebec and Canada/Study Guide/Topic 1: Causes for the French Defeat

The main reason why the French lost to the 13 colonies started from the beginning of New France back in 1608. Due to Mercantilism, the French colony was only over in America to trade with the Native population. Meanwhile, the English had full support from their mother, Britain. Here are the following reasons why the French lost to the English in the year 1760:

Population: The French suffered from a small population (around 3000) in the early stages of New France (1608-1663). While New Britain continued to receive immigration coming from the Mother country. Only around 1665 (95 years before the war) did Jean Talon, Intendant, start to put an increase in New Frances population. Therefore, the English population was a lot bigger than the French population. Defenses: How do you win a war? With soldiers of course. Again, not until 1663 did France start sending over soldiers to help protect their land. The soldier count looked like this for each colonyː English = 10 000 soldiers French = 3000 soldiers.

Territoryː Due to the fur trade with the Amerindians, the French kept on venturing more towards the South, as well as the west to follow their traders. The Amerindians obviously follow their food source, Deer, Elk, Moose, etc. So the French followed them to wherever they were going to go in order to continue on supporting the fur trade. Therefore, the French's population became very big, and hard to defend. Unlike the English, who remained East of the Appalachians, kept to their small and well guarded 13 colonies, which received help from Britain, with immigration of women, soldiers and workers.

This war was dominated by the English due to a higher population, and a well planned attack against the French.


text: History of Quebec and Canada/Study Guide/Royal Proclamation


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User:Egm6321.f10.team6.Kim.MK/hw5

= Problem 1 - Find $$\begin{align}y_{xxxxx}\end{align}$$ =

Statement
Find $$\begin{align}y_{xxxxx}\end{align}$$ in terms of derivative of y with respect to t, where $$\begin{align}y(x(t))\end{align}$$ and $$\begin{align} x=\textbf{e}^{t}\end{align}$$.

Solution
Applying the chain rule to $$\begin{align}y(x(t))\end{align}$$

Then solving for $$\begin{align}y_x\end{align}$$

Taking the derivative with respect to $$\begin{align}x\end{align}$$

Then solving for $$\begin{align}y_{xx}\end{align}$$

Taking another derivative with respect to $$\begin{align}x\end{align}$$

And again solving for higher order derivative with respect to $$\begin{align}x\end{align}$$

Repeating the process again for the fourth derivative

And again solving for higher order derivative with respect to $$\begin{align}x\end{align}$$

Repeating the process one final time for the fifth derivative

And solving for fifth order derivative with respect to $$\begin{align}x\end{align}$$

Note that the coefficients of the equation for the derivative with respect to $$\begin{align}x\end{align}$$ of each order form a Diophantine equation which sums to zero. This is expected as if $$\begin{align}y\end{align}$$ is constant with respect to $$\begin{align}t\end{align}$$ it should also be constant with respect to $$\begin{align}x\end{align}$$

General Solution Method
There is a 'general' recursive algorithm for finding the coefficients of the partial derivatives with respect to $$\begin{align}t\end{align}$$. Expressing the nth partial with respect to $$\begin{align}x\end{align}$$ as a sum of partials with respect to $$\begin{align}t\end{align}$$.

The first coefficient is always one

The second term initiates the recursion and is

Then the next coefficient is found by multiplying each term by the terms to the right, dropping the terms where there are no terms to the right. To demonstrate $$\begin{align}y_{xxxxxx}\end{align}$$ ($$\begin{align}y_{n=6}\end{align}$$) will be found without using $$\begin{align}y_{xxxxx}\end{align}$$.

Then each term times the polynomial to its right

Again applying the recursive rule

Applying again for the fourth term

And once again for the last term

Thus $$y_{xxxxxx}$$ is

The solution is checked by noting the sum of coefficients is zero, i.e. $$\begin{align}1-15+85-225+274-120=0\end{align}$$.

Problem Statement
A general spring-mass-damper system has spring constant k, mass m, and damping coefficient c. The equation of motion is given as :

Which may be rewritten as follows :

Where the homogenouse ODE is given as:

Part 1
1. Solve homogeneous ODE given in equation 5.3 by assuming $$y={{e}^{rt}}$$ to calculate homogeneous equation and obtain roots.

2. If only one root is obtained use variation of parameters to obtain both homogenous solutions.

3. Find the particular solution for equation 5.2.

Part 2
1. For equation 5.4 find the values of  $${_{1}}$$ and $${{{\bar{a}}}_{0}}$$ in terms of  $${{a}_{2}}$$, $${{a}_{1}}$$, and $${{a}_{0}}$$.

2. Find quadratic equation for $$\alpha $$.

3. Reduce order of equation.

4. Apply integrating factor method to part 2.3

5. Show that:

Where $$\alpha $$ and $$\beta $$ are roots of the equation for $$\alpha $$ in part 2.2

6. Deduce and expression for the particular solution for a general excitation  $${{f}_{\left( t \right)}}$$

7. Verify the table presented in fall 2009.

8. Solve $${{f}_{\left( t \right)}}={{e}^{\left( -{{t}^{2}} \right)}}$$ such that:

8.1 The roots for equation 5.1 are obtained from $$\left( r+1 \right)\left( r-2 \right)=0$$.

8.2 The roots for equation 5.1 are obtained from $${{\left( r-4 \right)}^{2}}=0$$. .

Part 1.1
We begin by solving the homogeneous equation given in equation 5.3. First we assume a solution to the equation fits the form:

This yields:

We can divide by a common factor of $${{e}^{rt}}$$ to obtain the auxiliary equation:

In order to calculate the roots of equation 5.9 we must apply the quadratic formula in equation 5.10.

This yields:

Which after some simplification results in the following equation for the roots to equation 5.3:

Part 1.2
The number of roots that are obtained from the auxiliary equation for equation 5.3 depend on the value of $$\varsigma $$.

$$\begin{align} & if: \\ & \varsigma =1\text{ }\to \text{ one real root equal to }{{\omega }_{o}} \\ & \varsigma >1\to \text{ two real roots} \\ & \varsigma <1\to \text{ two complex roots} \\ \end{align}$$

Therefore, if $$\varsigma $$ is unknown it is not possible to know the number of roots.

Given
and

Find
To show that the expressions for $$\begin{align}y_{p}(x)\end{align}$$ is equivalent

Solution
Write (6.3) in follows,

According to (6.1),

Differentiation rules shows that

Along with (6.4) we can get

Therefore (6.5) becomes,

Integration by parts for (6.2)

Comparing (6.9) and (6.10) We can see they are equivalent.

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