Accounting Opinion About Cash Discounts and Trade Discounts free essay sample

Year end: Mr. Williams 4 weeks Accounting v IFRS v US GAAP AASB IFRS for SME / Differential Reporting Standards Auditing Ethics Other (specify): 30 April, 2012 30 June, 2012 Prepared for (name of supervisor): Time spent on this opinion: What type of opinion (select options)? Accounting Standards applied: Query or issue: Whether the debit-balance account â€Å"Cash Discounts† in the Statement of Comprehensive Income should be treated the same way as the â€Å"Trade Discounts† account. Background and pertinent facts: Trade discount is allowed by the supplier of the goods to the purchaser when he buys from the supplier in bulk quantities. The purchaser is accountable for the invoice price which is the list price less the trade discount. Whereas, cash discount (also known as sales discount) is a decrease granted by supplier from the invoice price of the goods in order to encourage prompt payment. Authoritative Guidance and Research: AASB 101 Presentation of Financial Statements IAS 18 Revenue (IAS 18. We will write a custom essay sample on Accounting Opinion About Cash Discounts and Trade Discounts or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page 0) http://www. e-conomic. co. uk/accountingsystem/glossary/cash-discount http://www. letslearnfinance. com/difference-between-cash-and-trade-discount. html http://accountingexplained. com/financial/receivables/cash-discount-on-sales http://basiccollegeaccounting. com/2008/08/summary-of-difference-between-cash-discount-and-tr ade-discount/ Discussion and Analysis: Trade discount is given before the exchange happens; therefore, the amount recorded as sales revenue is the invoice price. Hence, there is no entry in the books of the account. Sales should be recorded after the deduction of such trade discounts. Unlike trade discount, cash discount is allowed on the payment of money after the invoice is made by the supplier; therefore, the cash discount is not shown on the invoice. In order to indicate the difference of amount between the sales revenue and the cash received, a cash discount account should be opened on the ledger. There are two methods of accounting for sales that offer cash discounts: the gross method and the net method. Once one method is chosen, it would be used to record all sales according to this method. The gross method records sales and Accounts Receivable at their gross amount and the discounts are recorded only when they are taken. The following journal entries should be recorded for the sale and for the full invoice amount payment: Dr. Accounts Receivable Cr. Sales Dr. Cash Dr. Sales Discounts Cr. Accounts Receivable IAS 18 Revenue requires cash discounts to be treated as reductions in revenue; thus, this special Sales Discounts account should be subtracted from Sales to calculate net sale. The net method puts forward a special revenue account Sales Discounts Forfeited. At the time of sale, sales and receivables are recorded net of possible discounts: Net Price = Gross Price ? Potential Cash Discount Thus, the journal entry at the time of sale is like: Dr. Accounts Receivable (Net Price) Cr. Sales (Net Price) If the payment is received within the time that was entitled on the invoice and the discounts are taken by the purchaser, it should be recorded as: Dr. Cash (Net Price) Cr. Accounts Receivable (Net Price) If the discounts are not taken, the amount is debited to Account Receivable and credited to Sales Discounts Forfeited which is calculated into an â€Å"other revenue† account that appears on the Income Statement. The journal entry should be recorded as: Dr. Cash (Gross Price)

Qualities of a Great President essays

Qualities of a Great President essays What are the qualities of presidential leadership? What makes a president a great leader? The presidents were great leaders because they knew how to guide and to inspire the American People. The great presidents had leadership qualities such as possessing persistence like Lincoln, having resilience through education like Truman, demanding excellence like Kennedy, having sympathy or compassion like Lincoln, communicating and informing people like Reagan, being decisive like Grant the general, developing esteem like Franklin Roosevelt, having nerve or courage like Washington, practicing team leadership like Eisenhower, and finally sharing a vision like Thomas Jefferson. All these great presidents had these qualities as leaders that have transformed vision into reality. A quality most commonly associated with the president is leadership. A president must be able to lead the country. The president who comes to mind is Abraham Lincoln. Abraham Lincoln was a great man. He was honest, humble, and most of all: a great leader. He led in his early political days as well as leading the United States through the toughest time in our nations history. Lincoln issued the Emancipation Proclamation, which was extremely controversial; however, Lincoln held his ground, as all great leaders must. He stood up for what he believed in. He believed in the Constitution, the Bible, and the idea that all men are created equal. For a president to be successful, he needs to be ambitious. Also, the most successful presidents tend to be hard working and persistent. Presidents who succeed set ambitious goals for themselves and move heaven and earth to meet them. Lyndon B. Johnson was a very hard-working and ambitious president. Congress passed his proposals for increased federal aid to education, a cut in excise taxes, stronger safety measures for automobiles, and the establishment of two new executive departments-the Department of Housing and Urban D...

Globalization revisited Essay Example | Topics and Well Written Essays - 250 words

Globalization revisited - Essay Example This is valuable as concepts for democracy and equality are espoused influencing leaders of other countries who incorporate them into their own governments. The more educated people spread their elevated ideas to others, the more the society becomes as a whole. Over time, this has and will continue to create a more globalized world. The somewhat less beneficial effects are initiated by big business. They hope to reach as many markets as possible to increase their profits. While the youth may enjoy these modern developments there is a great deal to be said about preserving a countries rich national culture. These elements also lead to a more globalized world but at what cost. Coca Cola sold in parts of Africa and China, Disneyland and such other American things may not necessarily contribute to the culture but rather direct every nation to be as the United States is. Is this really beneficial? Perhaps the US would benefit more by learning from other cultures, rich in tradition and values rather than being so profit driven. This leads to man’s lust for power. Imperialism started 500 years ago with ancient empires conquering other lands. Their desire to have as much power possible led to great expansion and the conquering of other lands. The Ottoman Empire, British Empire and Roman Empire all led to domination over the conquered peoples and forced influences on their own cultures (Hussain 2011). Today as the empires are broken up into individual nation states we see the lust for power rise to the surface in other ways. The United States, seen as the greatest defender of democracy, also hopes to impose it on other countries. Such is evidenced today by our militaristic intervention in Iraq and Afghanistan. While we don’t wish to maintain any level of control in these countries as some do by hoping to include Canada and Mexico as part

Stop and frisk Research Proposal Example | Topics and Well Written Essays - 500 words

Stop and frisk - Research Proposal Example causal relationship exist between two variables when a cause exist and some consequences follow the cause and policy enforcement is the cause with change in gun violence rate as the effect. Existence of a correlation relationship that other factors cannot explain is another requirement for a causal relations and research control can ensure this (Aparasu 72). Implementation of the policy is the independent variable while incidence of gun violence is the dependent variable. Implementation of the stop and frisk policy and effects of the implementation are the concepts for measure. Implementation defines effective enforcement of the policy within the perception of citizens while effects of implementation define associated change in gun violence behavior among the public because of the policy implementation. In addition to peer group questionnaire that background study identified, I plan to use existing data on the subject and opinions among psychology and criminology experts in collecting data on the concepts. Individuals who have been accused of gun violence and those who have close relation to the already accused individuals ate the study’s target population. One of the major characteristics of the population is arrest or issuance of arrest warrant against an individual. These characteristics forms the characteristics of the remaining population segments, associated of the accused. Criminal records from attorney’s office will help in identification of individuals who have been arrested or against whom arrest warrants have been issued for gun violence crimes. Background study on the identified individuals will facilitate identification of their associates. A survey design will be used will be used for data collection because of its potential to collect data of human traits (Aparasu 161). Cross sectional approach will be implemented to collect data relating to periods before the policy and after the policy. This will also incorporate data on application and

Theology Marriage in the 20th Century Essay Example | Topics and Well Written Essays - 750 words

Theology Marriage in the 20th Century - Essay Example Duncan thinks that perhaps knowing how to fight will help his son survive as a man in a man's world, just as he thinks this skill helped himself and his brothers cope with life: "Over time, physical combat begot intellectual combat, and our competitiveness and discipline allowed us to be fairly successful in the world" (Duncan 2009, 1). Mr. Duncan wants to be a just parent, as he worries about "failing [his] children" (Duncan 2009, 1). What he means to be the implications of failing his children, one is not exactly sure. Would his children become effeminate if they didn't learn how to fight Would they not have material success in the world if they didn't learn how to fight Duncan says the conflict between pacifism and fighting "creates a kind of parental dissonance, a discomfort that [he feels] slightly embarrassed to talk about in polite company" (Duncan 2009, 1). Duncan wonders if he is being a good father by not teaching his son to fight-just as his own father seemed to have been an effective father by teaching his sons how to fight, and also carry on the legacy of his grandfather. Duncan seems to be indebted to his father but conflicted by the social message of the Catholic teaching he grew up with: "My father would tell me that my son should learn to fight. My church tells me he should learn to love. Am I a bad father for teaching him one, and not the other I hope not" (Duncan 2009, 1). In some ways, Duncan feels a call to lead a "countercultural" sort of lifestyle. He says he is "a Catholic who takes the call to be a peacemaker much more seriously than [his] own parents did. Though [he] is not a pacifist[he has] great admiration and respect for the kind fo courage pacifism entails[my own] paradox" (Duncan 2009, 1). Some advice for Mr. Duncan is in order. First of all, Mr. Duncan must realize that there are certain unwritten codes which we all follow according to the gender roles which society dictates. In a study of ads, "Goffman's models seem to follow one body of tacit social rules about gender, not two or three, or some mix[a sort of] code" (Hochschild 2003, 46). Mr. Duncan's child is young. It is normal for a child to question at that age who he is. "So, at this point [in a boy's life], [he's] asking [himself], Who and what am I Is this my identity" (Cahill 2006, 146) A good relationship with his father is guaranteed to help his son have success in life, not learning how to fight necessarily. Gathered from the "clinical experience of many psychiatrists and therapists doesstemfrom problematic relationships with parents. The basic idea is that each individual in some sense has to 'achieve' his gender identity by going through a developmental process" (Cahill 2006, 153). This solves the issue of gender roles. Now, Duncan is worried if he is being a just parent. "[W]here the ordinary relationships with parents are disrupted [in this process of achieving gender identity]this process is short-circuited" (Cahill 2006, 153). Clearly Duncan does not have problems here. He may perceive he is being a bad parent if he does not clearly define gender roles-ultra-masculinity being demonstrated by the fact that his son would know how to fight. "Ultra-femininity, like ultra-masculinity, may mask the underlying

Communication Diversity and the Human Services Worker

Communication Diversity and the Human Services Worker Communication Diversity and the Human Services Worker Introduction Effective communication is more than just passing information from one person to another, we communicate both verbally and non-verbally (Howard 1991) in addition, we all hunger for contact that is meaningful. A communicator enters into relationships with other people (Gamble Gamble 2008). Healthy communication is essential, we all like to be valued and heard, and it is fundamental to all people from all facets of life and in all sectors of society (Bolton 1987, p. 4). Daily, human services workers encounter a diverse range of people, from colleagues to clients, professionals, and the public. Therefore, responding appropriately is necessary for effective communication to occur. Communication is never neutral (Tyler, Kossen Ryan 2005, p. 26) furthermore, we construct our world view from our own point of view as well as the point of view of the culture or society that we inhabit (Tyler, Kossen Ryan). Hence, there can be barriers to effective communication when class and low socio-economic circumstances are present. There is a tendency for Australians to look down on low-income earners and those receiving government benefits. To some, a low-income earner has less value because the belief is that they are non-contributors to the wealth and growth of Australian society. While this occurs less in the human services industry than in general, none the less it still occurs. Terms used within the community such as dole bludger have a negative connotation, and present difficulties that impact in an unconstructive manner on low income earners who may already be feeling guilty about their inability to find employment. Careless terms, labels, and negative attitudes build resentment, which has consequences that can flow on from clients to their families, whether from ill health, crime, family breakdowns, or drug and alcohol problems. Ineffective communication causes an interpersonal gap that is experienced in all facets of life and in all sectors of societyeven death results when communication breaks down (Bolton 1987, p.4). Covey (1989, p. 239) states, Unless you are influenced by my uniqueness, Im not going to be influenced by your advice therefore, building effective emotional bank accounts (Covey, p. 239) is crucial for successful communication to occur. This essay will address issues that confront human services workers and the challenges they face when working with unemployed people from low socio-economic backgrounds. Situation Australia is supposed to be an egalitarian society but increasingly it is becoming a nation of haves and have nots. The divide between rich and poor continues to expand (Barrett, Crossley Worswick 1999; The Age 1999, cited in Healey 2001). Stratification based on economic and social position is becoming a part of the Australian identity (Hartley 2002). The success of some at the expense of others has also seen growing resentment by those on welfare who see themselves as victims (The Weekend Australian 2000, p. 23, cited in Healey 2001). Hegemony refers to the dominant classes maintenance of social and cultural domination over others (OSullivan et al. 1983). It forces people to hand over their power either consciously or unconsciously by creating a power bloc (OSullivan, p. 102). Government agencies such as Centrelink, job network centres, and training institutions, which in theory are neutral and are there to represents everybody often exercise their power to achieve hidden company outcomes. As the dominant economic class, they look after the interests of the company first and their clients needs often become secondary. Unequal power relationships that influence the manner in which people communicate with each other are easy to develop and difficult to dismantle. The exchange between senders and receivers is an active encounter in which participants frequently occupy positions of unequal power (Kress 1988, p15). Those on the receiving end feel diminished, unheard, and often defensive. Negative stereotypes on both sides are liable to increase, and self-fulfilling prophecies and conflict occurs because of ineffective communication. There is growing concern about welfare dependency and the impact this is having on the economy. There is a shift in government policy, the emphasis now is that those on welfare must accept more responsibility for their economic circumstances (Saunders 2005). Community service workers understand that participation in order to lead a rich meaningful life within the community it is necessary to have a healthy self-esteem. They are aware that social exclusion and unemployment deny people the opportunity to participate (Saunders). Approach Reading body language, paying attention to details and clear effective communication require well developed skills that human service workers need to keep in mind when working with clients. When communication, the life blood of every relationship (Bolton 1987, p. 6) is positive, it creates nurturing fulfilling relationships. As fifty-five percent of all communication consists of body language (Hargie Dickson 2004, p. 46), particular attention to non-verbal communication skills is required. Non-verbal communication such as a sneer, a sense of distain, or body language that is closed, communicates indifference, which can be as damaging as a verbal confrontation. As a human services worker it is essential that the clients your there to assist do not feel ostracised by the agencies assigned to help them. Human service workers must be conscious of non-verbal behaviour, their own and their clients because non-verbal behaviour often contains significant, misleading, and undeclared messages (Baney 2004). How people dress, their posture, eye contact and how they walk all convey meaning, and reveal to the observer a myriad of information. Cultural differences need to need recognition, studies show that African Americans and white Americans gaze in opposite directions when spoken to (Hargie 2006), Indigenous Australians also avoid eye contact. Avoid judgements because for clients to develop a healthy self-concept, judgement does not have to be verbal to be experienced. Judgement is one of the major roadblocks to successful communication (Rogers cited in Bolton 1987, p.17). Most people fear rejection and the surest way to create it in relationships with people is through judgement and criticism. Our sense of self develops through our interactions with others, we are social beings, and developing self-awareness is an important step in understanding ourselves and other people (Gamble Gamble 2008). Our self-concept and self-image is often warped and unbalanced, often how we see ourselves differs from how others see us. Our culture teaches us to repress our feelings, and many people are unaware of what emotionally, is actually occurring inside of them (Bolton 1987). A new counsellor may want to help clients avoid painful emotions, but emotional release encourages healing processes to occur (Geldard Geldard 1998, p. 50). An effective counsellor has the capacity to help their clients to feel what is happening within them, by either understanding what the client is verbally expressing, or transmitting by body language. By assisting clients whose body language maybe conveying feelings of inadequacy or inferiority, a human services worker, can bring to their clients attention factors that their clients maybe unaware of, and hence the client can begin to address them. Human service workers must be aware that giving advice can create interfere-iority complex (Bolton 1987, p. 22) and they must avoid giving advice but rather assist clients to find solutions. How something is expressed alters reactions, and those with low self-esteem often expect criticism from others, and possibly will read into statements meaning that was never there (Bolton 1987). Human service workers have the ability to reflect feelings back to the speaker, and are in a position to offer assistance that can and does make a difference in peoples lives. Building self-esteem can mean the difference between employment and continuing unemployment for a client, as a positive relationship exists between career development and the ability to communicate effectively (Bolton 1987, Gamble Gamble 2008). Therefore, human services workers are required to have skills that go beyond those of basic communication. Listening, assertion, conflict-resolution, and collaborative problem solving skills (Bolton 1987) are strengths that assist practitioners successfully negotiate interpersonal communication. As Bolton says low-level communication, leads to ineffectiveness, both at work and in personal communication, consequently by developing effective intercommunication skills it will lead to increased competence in all areas of life. Listening skills are required for successful communication, paraphrasing lets the listener know that you understand what the speaker has said. It allows the listener to comprehend the context of what the speaker said, and therefore the speaker knows understanding has been achieved. Communication skills require empathy and genuineness and need to affirm and validate peoples experiences (Kenny, 1994). Attending skills, following skills and reflective skills (Bolton 1987) are all a part of listening and allow the listener to demonstrate a clear understanding of what the speaker has conveyed. Listening allows a counsellor to bring to the attention of clients the negative self-talk they may use. Clients can then overcome barriers and create for themselves employment opportunities previously denied with knowledge, new skills, and understanding. Conclusion Human service workers are at the forefront in developing new programs aimed at increasing participation within the workforce. They are working for government and job network agencies on programs that address issues such as appearance, attitude, and communication styles. They are aware that sending solutions (Bolton 1987, p.20) rather than assisting clients to come to their own conclusions are barriers to empowerment that could undermine a clients motivation. Eighty percent of people who fail at work do so for one reason: they do not relate well to other people (Bolton 1987, p. 7). Human service workers are adopting principals, with the intention of addressing this problem. They know that with the correct assistance the downward spiral that creates unemployment, class stigma, and low income is reversible. By assisting low-income earners and unemployed people to understand how their verbal and non-verbal cues are preventing them from leading fulfilling lives can help motivate people to change. Methods learnt as a child can be undone and the barriers broken so that they can participate in a meaningful way, to live fulfilling personal and social lives, as well as gaining employment. Skill building workshops, training workshops, and counselling aimed at improving interpersonal relations are a practical solution in assisting clients to gain the skills required to communicate effectively. The flow on from that comes from learning how communication barriers lead to anger, ineffectual and damaging social relationships and that a clearer understanding will empower, and assists the disadvantaged members of society. Creating a ripple effect that will be of benefit to the wider community. Communication is our link to the rest of humanity (Gamble Gamble 2008, p.5), therefore as workers in the human services industry by helping clients to win, ultimately we all share the rewards. References Baney, J 2004, Guide to interpersonal communication. Pearson Education, Upper Saddle River, New Jersey. Barrett, G, Crossley, T Worswick, C 1999, Consumption and income inequality in Australia, Centre for Economic Policy Research, Australian National University Discussion Paper no.40. Bolton, R 1987, People skills, Simon and Schuster, NSW. Covey, SR 1989, 7 habits of highly effective people, Simon and Schuster, New York. Gamble, TK Gamble, M 2008, Communication works, McGraw-Hill, New York. Geldard, D Geldard, K 1998, Reflection of feelings, in Basic personal counselling, Prentice Hall, Frenchs Forest, pp. 49-58. Hargie, O 2006, Skill in practice: An operational model of communicative performance, in O. Hargie (ed.), The handbook of communication skills, Routledge, London, pp. 37-70. Hargie, O Dickson, D 2004, Nonverbal communication, in Skilled interpersonal communication: research theory, and practice, Routledge, London, pp. 43-66. Hartley, J 2002, Communication cultural and media studies, Routledge, London. Healey, J (ed.) 2001, The wealth divide, Issues in Society, vol 141, The Spinney Press, NSW. Howard, G 1991, Can you put it on a t-shirt? David Charles, London. Kenny, S 2007, Developing communities for the future, Thompson, Victoria. Kress, G 1988, Communication and culture, in G. Kress (ed.), Communication and culture, New South Wales University Press, NSW. OSullivan, T, Hartley, J, Saunders, D Fiske, J, 1983, Key concepts in communication, Routledge, London. Saunders, P 2005, Welfare to work in practice, in P.Saunders (ed.), Welfare to work in practice social security and participation in economic and social life, Ashgate, Hants, England, pp. 1-7. Tyler, S, Kossen, C Ryan, C, 2005, Theories of communication, in Communication: a foundation course, Pearson Education Aust., Frenchs Forest, NSW, pp. 16-26.

Albert Camus The Myth of Sisyphus Essays -- Papers Albert Camus Sisyp

Albert Camus' The Myth of Sisyphus Albert Camus' essay, 'The Myth Of Sisyphus' is an insightful analysis of the classic work, 'The Myth Of Sisyphus'. In some regards Camus' view of Sisyphus can seem quite accurate and in tune with the original text, but based on Camus' interpretation of the justness of Sisyphus' punishment, it is clear that the writer has some different ideas as well. Camus concludes that this punishment does not have the effect the Gods had intended, and ultimately the tragic hero must be seen as being 'happy'. This is his greatest departure from the intent of the original myth wherein the reader is left with the feeling that Sisyphus' punishment can be seen as appropriate and just. As his punishment for repeatedly outwitting the Gods, Sisyphus is forced to roll a great rock up a steep hill only to have it roll back down each time he reaches the top, forever condemned to repeat the process over and over again. It is this punishment that Camus is most focused on, as the topic of Sisyphus? trickery only comes up to give the reader some background on the story. It is unusual however that Camus considers this punishment as an, ?unspeakable penalty in which the whole being is exerted toward accomplishing nothing?, and at the same time assumes that; ?The struggle itself towards the heights is enough to fill a man?s heart.? The gratification that one might find through hard work could certainly be seen as an accomplishment, but it?s hard to see how this pertains to Sisyphus. Camus states that, ?the workman of today works every day in his life at the same tasks?, and that his fate is, ?no less absurd.? If a man whistles while performing his laborious job it is onl y because it is assumed that the fruits... ...l text was meant to represent. Camus states that, ?myths are made for the imagination to breathe life into them?, and he surely takes advantage of this. If it is true that Sisyphus truly owns his fate and is the master of his own ?absurd? universe, then that should be seen as his greatest punishment of all, for it does not amount to very much, and as Camus himself pointed out, ?the rock is still rolling.? Bibliography: Works Cited Bierlein, J.F. ?The Myth Of Sisyphus.? Lives Through Literature A Thematic Anthology (3rd ed.). Helane Levine Keating and Walter Levy. New Jersey: Prentice Hall, 2001. 1042-43. Camus, Albert. ?The Myth Of Sisyphus.? Lives Through Literature A Thematic Anthology (3rd ed.). Helane Levine Keating and Walter Levy. New Jersey: Prentice Hall, 2001. 1044-46.

The Influence of Temperature in the Forward Osmosis Process

Chapter FourMathematical Model Chapter Four THEORETICAL ANALYSISMA andMathematical Modeling Purpose of the survey is to probe of temperature as a factor that influences the conveyance of H2O across the membrane in FO procedure. The steady-state theoretical accounts have been developed to foretell H2O i ¬Ã¢â‚¬Å¡ux (JouleTungsten) as map of temperature (Thymine) and bulk concentration (C) ( i.e. Draw and Feed concentration ) . It was besides study the consequence of temperature on some belongingss, such as Solute diffusion coefficient (CalciferolSecond) , Mass transportation coefficient (K) , Permeability coefficient (A) and Solute electric resistance (Km) . 4.1 Osmotic Pressure The osmotic force per unit area (?) of a solution depends on the concentration of dissolved ions in solution and the temperature of solution, and can be computed by utilizing Va n't Hoff equation: WhereNis the van’t Hoff factor ( histories for the figure of single atoms of a compound dissolved in the solution ) ,?is the osmotic coefficient,Cis the molar concentration ( molar concentration ) of the solution,Roentgenis the gas invariable andThymineis the absolute temperature of the solution. The van’t Hoff factor is introduced to cover divergences from ideal solution behaviour that include finite volume occupied by solute molecules and their common attractive force as in new wave derWaals attractive force ( Howard, 2003 ) . Table 4.1 show osmotic coefficients (?) for a figure of solutes of physiological importance ( Khudair, 2011 ) . For all solutes?depends on the substance and on its concentration. As the concentration of any solute attacks zero its value of?attacks 1. In ideal solution,?= 1 ( Glass tone, 1974 ) . Table 4.1 Osmotic Coefficients (?) and Van’t Hoff Factor ( N ) for a Number of SolutesSubstanceVan’t Hoff Factor (N)Osmotic Coefficients ( ? )NaCl20.93KCl20.92HCl20.95New hampshire4Chlorine220.92NaHCO320.96CaCl230.86MgCl230.89Sodium2So430.74MgSO420.58Glucose11.01Sucrose11.024.2 Concentration Polarization 4.2.1 External Concentration Polarization Concentration polarisation ( CP ) is the accretion of solutes near the membrane surface and has inauspicious effects on membrane public presentation. The i ¬Ã¢â‚¬Å¡ux of H2O through the membrane brings feed H2O ( incorporating H2O and solute ) to the membrane surface, and as clean H2O i ¬Ã¢â‚¬Å¡ows through the membrane, the solutes accumulate near the membrane surface. Equations for concentration polarisation can be derived from i ¬?lm theory and mass balances. Harmonizing to i ¬?lm theory, a boundary bed signifiers at the surface of the membrane. Water and solutes move through the boundary bed toward the membrane surface. As H2O base on ballss through the membrane, the solute concentration at the membrane surface additions. The concentration gradient in the boundary bed leads to diffusion of solutes back toward the majority provender H2O. During uninterrupted operation, a steady-state status is reached in which the solute concentration at the membrane surface is changeless w ith regard to clip because the convective i ¬Ã¢â‚¬Å¡ow of solutes toward the membrane is balanced by the diffusing i ¬Ã¢â‚¬Å¡ow of solutes off from the surface. A mass balance can be developed at the membrane surface as follows: Mass accretion = mass in ? mass out ( 4.2 ) With no accretion of mass at steady province, the solute i ¬Ã¢â‚¬Å¡ux toward the membrane surface must be balanced by i ¬Ã¢â‚¬Å¡uxes of solute i ¬Ã¢â‚¬Å¡owing off from the membrane ( due to diffusion ) and through the membrane ( into the permeate ) as follows: WhereMeteris mass of solute,Jouletungstenis the experimental permeate H2O flux,Tis clip,CalciferolSecondis the diffusion coefficient of the solute,omegathe distance perpendicular to membrane surface,Cpeis the solute concentration in the permeate andE‘is the surface country of membrane. Equation 4.3 applies non merely at the membrane surface but besides at any plane in the boundary bed because the net solute i ¬Ã¢â‚¬Å¡ux must be changeless throughout the boundary bed to forestall the accretion of solute anyplace within that bed ( the last term in equation 4.3 represents the solute that must go through through the boundary bed and the membrane to stop up in the permeate ) . Rearranging and incorporating equation 4.3 across the thickness of the boundary bed with the boundary conditions C ( 0 ) = CMeterand C ( ?Bacillus) = CF, cell, where CF, cellis the concentration of provender cell solution and CMeteris the concentration at the membrane surface, are done in the undermentioned equations: Integration outputs WhereKis the mass transportation coefficient and?Bacillusthickness of the boundary bed, rearranging the equation 4.6 when utilizing the van’t Hoff equation the eventually theoretical account from the concentrative external concentration polarisation at each permeate flux, could be calculated utilizing: Where?F, Bis the osmotic force per unit areas of feed solution at the majority and?F, mis the osmotic force per unit areas of the provender solution at the surface membrane. Note that the advocate is positive, he pointed out that ?F, m& A ; gt ; ?F, B. The draw solution in touch with the permeate side of membrane is the being diluted at the permeate membrane interface by the permeating H2O ( Moody and Kessler, 1976 ) . This is called diluted external CP. Both dilutive external CP phenomena cut down and concentrative the effectual osmotic driving force. A dilutive external CP modulus be identified as above, merely In the present instance, the concentration of the majority greater than concentration of the draw solution at the membrane surface ( i.e. ?D, B& A ; gt ; ?D, m) ( Cath et al. , 2006 ) : Where?D, mis the osmotic force per unit areas of the draw solution at the membrane surface and?D, Bis the osmotic force per unit areas of draw solution at the majority. The general equation depicting H2O conveyance in FO, RO, and PRO is ( Cath et al. , 2006 ) : Where,Athe H2O permeableness invariable of the membrane, ? the contemplation coefficient, and a?† P is the applied force per unit area. For FO, a?† P is zero ; for RO, a?† P & A ; gt ; a?† ? ; and for PRO, a?† ? & A ; gt ; a?† P ( see figure 4.1 ) . Figure 4.1 Direction and magnitude of H2O as a map of ?P. To pattern the flux public presentation of the forward osmosis procedure in the presence of external concentration polarisation, we start with the flux equation for forward osmosis, given as We assume that the salt does non traverse membrane, the osmotic contemplation coefficient (?) , assume equal 1. Equation 4.10 predicts Flux as maps of driving force merely in the absence dilutive external concentration polarisation or concentrative, which may to be valid merely if the permeating flux is excessively low. When higher flux rates, must be modified to include this equation both the dilutive external concentration polarisation and concentrative: Figure 4.2 ( a ) shows this phenomenon with a dense symmetric membrane ( McCutcheon and Elimelech, 2006 ) . 4.2.2 Internal Concentration Polarization If the porousness support bed of asymmetric membrane confronting feed solution, as is the instance in force per unit area retarded osmosis ( PRO ) , Polarization bed is established along interior of heavy active bed as H2O and solute propagate the porousness bed ( Figure 4.2 ( B ) ) . This is referred to as concentrative internal concentration polarisation, this phenomenon is similar to concentrative external concentration polarisation, except that it takes topographic point within the porous bed, and therefore, can non be underestimated by cross flow ( Lee et al, 1981 ) Obtained look patterning this phenomenon in force per unit area retarded osmosis ( Loeb et al. 1997 ) . This equation describes internal concentration polarisation ( ICP ) the effects and how it links to H2O flux, salt permeableness coefficient ( B ) and H2O permeableness coefficient: WhereKmis the opposition to solute diffusion within the membrane porous support bed,Kmis defined as WhereSecondthe membrane structural parametric quantity,?mis the thickness,?is the tortuousness and?is the porousness of the support bed,Kmis a step how easy it can be dissolved widespread support inside and outside Layer, and hence is a step of the strength of ICP. We maintain the usage of theKmterm due to convention established in old surveies on internal concentration polarisation. Salt permeableness coefficient ( B ) is about negligible compared with the other footings in the equation 4.12. Therefore, we ignore salt flux in the way of H2O flux and any transition of salt from the permeate ( draw solution ) side ( Gray et al. , 2006 ) . Therefore, flux can be solved for implicitly from equation 4.12: The exponential term in equation 4.14 is the rectification factor that could be considered the concentrative internal concentration polarisation modulus, defined as Where ?F, Iis the osmotic force per unit area of the feed solution on the interior of the active bed within the porous support. The positive advocate indicates that ?F, I& A ; gt ; ?F, B, or that the consequence is concentrative. Substitute Equation 4.8 into 4.14 to obtain an analytical theoretical account for the impact of internal and external concentration polarisation on H2O flux: All the footings in equation 4.16 are readily determined through computations or experiments. From equation we can cipher the flux of H2O through the membrane where feeding solution is placed against asymmetric support bed and the draw solution on the active bed. In forward osmosis applications for desalinization and H2O intervention, the active bed of the membrane faces the provender solution and the porous support bed faces the draw solution ( Kessler and Moody, 1976 ) . As H2O permeates the active bed, the draw solution within the porous infrastructure becomes diluted. This is referred to as dilutive internal concentration polarisation ( Figure 4.2 ( degree Celsius ) ) . ( Loeb et al, 1997 ) Descriptions likewise flux behaviour in the development of forward osmosis: When presuming that B = 0 ( i.e. , the salt permeableness is negligible ) and the equation 4.17 is agreement, are acquiring an inexplicit equation for the flux of H2O permeating: Here, ?D, Bis now corrected by the dilutive internal concentration polarisation modulus, given by Where ?D, Iis the concentration of the draw solution on the interior of the active bed within the porous support. The negative advocate because the H2O flux is in the way off from the membrane active bed surface, In other words, the concentration polarisation consequence in our instance is dilutive, intending that ?D, I& A ; lt ; ?D, Bby replacing equation 4.7 into 4.18, we get The footings in equation 4.20 are mensurable system conditions and membrane parametric quantities. Note that here ; dilutive internal concentration polarisation is coupled with concentrative external concentration polarisation, whereas in the equation 4.16, concentrative internal concentration polarisation was coupled with dilutive external concentration polarisation. In each of these instances, the external concentration polarisation and internal concentration polarisation moduli all contribute negatively to the overall osmotic drive force. The negative part of each addition with higher flux, which suggests a self-limiting flux behaviour, this implies that increasing osmotic drive force will supply decreasing additions in flux ( Tang et al. , 2010 ) . Figure 4.2 Illustration of osmotic driving force profiles for osmosis through several membrane types and orientations, integrating both internal and external concentration polarisation. ( a ) The profile illustrates concentrative and dilutive external CP. ( B ) PRO manner ; the profile illustrates concentrative internal CP and dilutive external CP. ( degree Celsius ) FO manner ; the profile illustrates dilutive internal CP and concentrative external CP (McCutcheon and Elimelech, 2006 ) . In this hunt if taking transmembrane temperature difference into history, the temperature being next to membrane surface will besides differ from that in bulk solution due to the happening of heat transportation. Hence, utilizing van’t Hoff jurisprudence for computation of osmotic force per unit area requires the temperature points to be purely in line with the concentration points as WhereC,TDandTFis the concentration, temperature draw and temperature, with the inferiors F, cell ( feed cell solution ) and D, cell ( draw cell solution ) . The theoretical account to foretell H2O i ¬Ã¢â‚¬Å¡ux can be rewritten to a modii ¬?ed by replacing equation 4.21 and 4.22 in 4.20, we get Figure 4.3 gives the conventional illustration of the concentration and temperature proi ¬?les in FO procedure operated under active bed – provender solution ( AL–FS ) . Figure 4.3Conventional diagram of mass and heat i ¬Ã¢â‚¬Å¡ux proi ¬?les within boundary bed and membrane during FO procedure under AL–FS manner in the presence of temperature difference ( TF, cell& A ; gt ; TD, cell) . 4.3 Heat Flux Heat transportation from the solution to the membrane surface across the boundary bed in the side of the membrane faculty imposes a opposition to mass reassign The temperature at the membrane surface is lower than the corresponding value at the majority stage. This affects negatively the drive force for mass transportation. Under steady province conditions, derived from the heat balance, the heat transportation in the single compartments of system is represented by the undermentioned equation: In which Q denotes the heat flux, and the inferiors FS – BL, m and DS – BL represent feed solution boundary bed, membrane and draw solution boundary bed. By stipulating the equation 4.24, we obtain WhereHis the single heat transportation coefi ¬?cient,CPthe specii ¬?c heat of H2O,?tungstenthe H2O denseness. Rearranging the equation 4.25 gives expressed looks of temperature near the membrane surfaces as ( Zhong et al. , 2012 ) It is sensible to dei ¬?ne the temperature at interface of SL and AL by averaging theThymineF, mandThymineD, m 4.4 Heat Transfer Coefficients The finding of heat transportation coefi ¬?cientHis developed on the footing of the correlativity between Nusselt, Reynolds and Prandtl figure ( Holman, 2009 ) . For the laminar flow: For the disruptive flow: WhereNu=hL/? , Pr =CPhosphorus µ/? ,and.Nu is the Nusselt figure,Rheniumthe Reynolds figure andPraseodymiumthe Prandtl figure. TheCPhosphorusis the specii ¬?c heat,Literlength of the channel, µthe dynamic viscousness, and ? the thermic conduction of NaCl solution. The value µis obtained harmonizing to µ = , in which?is the solution denseness, and?the kinematic viscousness. The dependance of?on temperature can be described by Where And are the thermic conduction of H2O at temperature T and 298.15 K. The heat transportation coefficientHcalculated by Where happenNufrom equation 4.29 or 4.30 The overall heat transportation coefficientHmof FO membrane embodies the thermic conduction of both liquid-phase H2O go throughing the micro pores and the solid-phase membrane 4.5 Mass Transfer Coefficient The mass transportation coefficient is a map of provender flow rate, cell geometry and solute system. Generalized correlativities of mass transportation, which have been used by several writers ( Sourirajan, 1970 ) , suggest that the Sherwood figure,Sh,is related to the Reynolds figure,Re,and Schmidt figure,Sc,as: For the laminar flow: For the disruptive flow: Whereand.Shis the Sherwood figure,Scandiumthe Schmidt figure andvitamin DHis the hydraulic diameter, the hydraulic diameter is dei ¬?ned as Where tungsten and h the channel breadth and channel tallness severally. The parametric quantities,CalciferolSecondand?rely strongly on temperature, which can be quantitatively determined by empirical equations below. For aqueous electrolyte like NaCl,CalciferolSecondvalue of the ions is presented by ( Beijing, 1988 ) Where N ±is the absolute valley of ions ( i.e. N ±=1 ) , and ? ±is the tantamount conduction of Na+and Cl–ions, estimated as ( 4.40 ) In which( 5.1Ãâ€"10-3m2/? for Na ions ; 7.64Ãâ€"10-3m2/? for chloride ions ) is the mention tantamount conduction at 298.15 K ; temperature coefficient,,forSodium+, and,,for, severally. The empirical equations were employed to gauge kinematic viscousness of NaCl solution as Whereis the H2O viscousness at temperature T, expressed as In whichvitamin E= 0.12,degree Fahrenheit= -0.44,-ˆ= -3.713,I=2.792 are the fitting parametric quantities,CSecondthe NaCl molar concentration, andThymineRoentgenthe normalized temperature. There is besides another manner to cipher diffusion coefficient in the liquid stage of a dilute solution can be estimated by the Stokes – Einstein equation if the solute radius is clearly larger than the solvent radius WhereKBacillusis the Boltzmann invariable, T ( K ) is the absolute temperature,  µ is the dynamic viscousness of the liquid and ROis the radius of the solute. To cipher diffusion coefficients in aqueous solutions predict that diffusion coefficients really linearly with temperature and reciprocally with viscousness. Indeed, harmonizing to Li and Gregory, ( 1974 ) . In instance of the stokes – Einstein relation the diffusion coefficientD ( T )at a temperatureThymineis given as Where D( TO)is the diffusion coefficient at a mention temperatureThymineOand µ ( T )and µ ( TO)are the dynamic viscousnesss at temperaturesThymineandThymineO, severally. Note that temperatures are given in Kelvin. Finally the mass transportation coefficient K calculated by WhereShdiscovery from equation 4.36 or 4.37 4.6 Water Permeability Coefficient The equation ciphering pure H2O permeableness coefi ¬?cient A for FO procedure is derived from the theoretical account ; thereby the H2O i ¬Ã¢â‚¬Å¡ux of rearward osmosis procedure is predicted ( Baker, 2004 ) WhereCtungstenis the H2O molar concentration,Volttungstenthe molar volume of H2O,Calciferoleffthe effectual H2O molecule diffusivity within the pores of active bed of the FO membrane Wherevitamin DSecond( 4AO) andvitamin DPhosphorus( 7.2AO) are the diameter of H2O molecule and pore, and D the evident diffusivity, which is given as Along with H2O dynamic viscousness (  µw ) predicted by There is besides another manner to cipher membrane permeableness ( A ) i ¬Ã¢â‚¬Å¡at-sheet bench-scale RO trial system was used to find the H2O permeableness coefi ¬?cient ( A ) of the CTA membrane. A membrane voucher holding an effectual surface country of 64 centimeter2was the active bed of the membrane confronting the provender solution. Mesh spacers placed in the provender channel enhanced the turbulency of the ultrapure H2O provender watercourse. A hard-hitting positive supplanting pump was used to recirculate the provender solution at 12 L/h. The FO membrane H2O permeableness coefi ¬?cient ( A ) was determined utilizing ( Lee et al. , 1981 ) . Where is the osmotic force per unit area difference across the membrane and ?P is the hydraulic force per unit area difference across the membrane. Because ultrapure H2O was used as the provender solution, was zero during the experiments. Pressure was increased from 1 saloon to 2 saloon. Pressure was held changeless at each increase for continuance of 3 h. Water i ¬Ã¢â‚¬Å¡ux through the membrane was calculated based on the increasing weight of the permeant H2O on an analytical balance. The temperature was held changeless at 25OC. See figure 4.4 Figure 4.4 Flux vs. force per unit area and the swill is representedH2O permeableness coefi ¬?cient ( A ) . 4.7 Recovery Percentage The recovery factor measures how much of the provender is recovered as permeate. It is reported as a per centum ( Al-Alawy, 2000 ) . The recovery of the membrane was calculated by spliting the overall of permeate rate by the provender rate solution. Recovery, or transition, is defined by: WhereVoltPhosphorusis the overall permeate volume andVoltFis the provender volume solution. Figure 4.5 the flow chart of patterning FO H2O flux at different temperature matrixes. 1

The Advantages and Disadvantages of Spell Checkers

The Advantages and Disadvantages of Spell Checkers A spell checker is a computer application that identifies possible misspellings in a text by referring to the accepted spellings in a database. Also called  spell check, spell-checker, spellchecker and  spelling checker. Most spell checkers function as part of a larger program, such as a word processor or search engine. Examples and Observations Dont they teach you how to spell these days?No, I answer. They teach us to use spell-check.(Jodi Picoult,  House Rules.  Simon Schuster, 2010) Spell Checkers and the Brain Psychologists have found that when we work with computers, we often fall victim to two cognitive ailmentscomplacency and biasthat can undercut our performance and lead to mistakes. Automation complacency occurs when a computer lulls us into a false sense of security. . . .Most of us have experienced complacency when at a computer. In using e-mail or word-processing software, we become less proficient proofreaders when we know that a spell-checker is at work. (Nicholas Carr, All Can Be Lost: The Risk of Putting Our Knowledge in the Hands of Machines. The Atlantic, October 2013)[W]hen it comes to autocorrect, spellcheck, and their ilk, those who would blame digital technology for language decay are not entirely wrong. Our brains seem to become less vigilant when we know a grammatical safety net will catch us. A 2005 study found that students who got a high score on the verbal section of either the SAT or the Gmat missed twice as many errors proofreading a letter in Microsoft Word with the program’s squiggly colored lines highlighting likely mistakes as they did when the spell-check software was turned off. (Joe Pinsker, Punctuated Equilibrium. The Atlantic, July-August 2014) Microsofts Spellchecker Microsofts language experts also track word requests, as well as frequently corrected words, to assess whether those words should be added to the Speller dictionary (Speller is the trademark name of Microsofts spell-checker). One recent request was pleather, meaning a plastic faux leather, which was added because of a lobbying effort by the group People for the Ethical Treatment of Animals. If youve got the latest goods from Microsoft, pleather shouldnt get a red squiggly.In other cases, real words are intentionally kept out of the programs dictionary. A calender is a machine used for a specialized manufacturing process. But most people see calender as a misspelling of calendar. The wordsmiths at Microsoft have decided to keep calender out of the programs dictionary, figuring that at the end of the day its more useful to fix so many misspelled calendars, than it is to cater to the sensibilities of a small subset of the population who happen to know of, and want to write about, calend ers. Similar homophones (computer people call them common confusables) include words like rime, kame, quire, and leman. (David Wolman, Righting the Mother Tongue. Collins, 2008) The Limitations of Spellcheckers In fact, you have to be quite good at spelling and reading in order to use a spellchecker effectively. Typically, if you have misspelled a word the spellchecker will offer a list of alternatives. Unless your initial attempt is reasonably close to the correct spelling, you are unlikely to be offered sensible alternatives, and, even if you are, you have to be able to make sense of what is on offer. You and your pupils also have to be aware of the limitations of spellcheckers. First, you may correctly spell a word but simply use the wrong one; for example, After I had eaten my super I went straight to bed. A spellchecker will not spot that it should be supper not super (did you spot the mistake?). Second, the spellchecker does not recognize some perfectly acceptable words. (David Waugh and Wendy Jolliffe, English 5-11: A Guide for Teachers, 2nd ed. Routledge, 2013) Spellcheckers for Writers With Learning Disabilities Spellcheckers have revolutionised the lives of many dyslexic people and come to the rescue of beleaguered editors. Some snags still arise, as when homophones are used incorrectly. The speech option spellchecker can overcome these difficulties by giving definitions and using them in sentences for clarification and meaning. Some find it helpful if the spellchecker is turned off when they are doing the first draft of a piece of writing, otherwise the frequent interruptions (because of their many spelling errors) interfere with their train of thought.(Philomena Ott, Teaching Children with Dyslexia: A Practical Guide. Routledge, 2007) The Lighter Side of Spellcheckers This apology was printed in the Observers For the Record column on March 26, 2006: A paragraph in the article below fell victim to the curse of the electronic spellchecker. Old Mutual became Old Metal, Axa Framlingon became Axe Framlington and Alliance Pimco became Aliens Pico.The Rev. Ian Elston was thinking ahead to Christmas services when his computer spell-checker changed the gifts of the Wise Men to golf, frankincense and myrrh. (Ken Smith, Day of the Dead. HeraldScotland, November 4, 2013)

Anti-Federalist Argument essays

Anti-Federalist Argument essays We beat the odds and won a war to gain finally gain control of our land. The formation of our government is now our job as an independent country. Many leaders of our new nation feel its necessary to rush into forming a document to serve as the backbone of our nation. I feel that our government is too young and inexperienced to form a reliable set of laws. Rushing into things would cause things to be overlooked and forgotten. Also if our government were to make such laws without the consent of the people it would be going against everything our country stands for. I believe a poor constitution would fail to preserve the rights and powers of citizens, represent the people in government, grant the states certain rights, establish liberties for men, limit the governments powers and have the ability to change throughout time. The constitution says the government will hold all major powers and it is not up to the citizen to change the countrys method of establishing courts, vote on taxes or decide how to spend funding. The government is too large. All men have unalienable rights and in this new country of ours a simple document shouldnt outline what a citizen can and cannot do. I believe that in this new constitution citizens will not have adequate representation. For example, you cannot a select few people to represent a large state and look out for the best interest of everyone. The representative needs to come from the same background of the people they are representing, understand the citizens beliefs and concerns, but should be well educated enough to know what's possible and best for his people. I believe more middle class representatives would be appropriate because of the fact that they are down to earth and realize what the general public wants/needs. I think the only way to fix the problem of misrepresentation would be to have enough representatives that correspond with the numerous social classes and different t...

Developing Writing Skills Essay Example | Topics and Well Written Essays - 1250 words

Developing Writing Skills - Essay Example My gretest wekness in writing hs lwys been to pln, write, nd revise n essy. In generl I lck bsic knowledge bout how to pproch writing nd the writing process s whole. Prticulrly, I hve difficulty in developing n essy in the following res: () generting content, (b) creting nd orgnizing structure for compositions, (c) formulting gols nd higher plns, (d) quickly nd efficiently executing the mechnicl spects of writing, nd (e) revising text nd reformulting gols. Generting content for n essy typiclly begins with brinstorming. During this pre-writing phse, writers tke time to reflect on their topic, select n udience, nd develop ides. Skilled writing depends, in lrge prt, on student's bility to pln before composing during this phse. My wekness is tht I do not spend much time prepring to write. Insted, I often begin writing s soon s I m given n ssignment with little or no preprtion. Furthermore, I tend to rely on n ssocitive technique wherein I simply write whtever comes to mind. Beginning to write immeditely fter receiving n ssignment does not llow dequte gol setting or plnning--two importnt techniques pplied by successful writers. Subsequently, I pper unsure of wht to do when I m given time to pln. Sometimes I do not regrd strtegies in the prewriting phse s vluble tools nd fil to utilize meningful techniques to become successful writer. I lso experience difficulty when ttempting to generte content nd orgnize structure for compositions. This problem my be ttributed to their under-utiliztion of strtegies for retrieving useful informtion. Thus, sometimes I view writing ssignment s question/nswer tsk involving little preprtion. Formulting gols nd objectives, strtegy tht experienced writers use to pln nd execute higher-level writing skills, is third re of difficulty for me. Writing cn be chrcterized s problem-solving tsk tht includes identifying gols for writing s well s the mens to chieve them. During nd fter writing, these gols re ssessed to determine whether student needs to redefine the gols or continue with the writing process. In my writing strtegy I choose from list of gols tht I feel my pper should ccomplish nd thn I brek the writing tsk into severl prts: () generte product nd process gols, (b) develop notes, (c) orgnize notes, (d) write nd continue the process of plnning, nd (e) evlute success t obtining gols. fter being tught the gol-setting strtegy, I meet the gols I hve set for my essys 90% of the time. My strength in writing is tht I m ble to quickly nd effectively execute the mechnicl spects of writing. Specificlly, in comprison to my peers, I mke considerbly more spelling, cpitliztion, nd punctution errors in compositions, nd my hndwriting is less legible. Bsic skills like spelling, grmmr, nd hndwriting re usully not tught t the high school level. I lso think tht my strength in writing is in formtion sentences. I hve well-developed sense of sentence style nd produce long nd completed sentences. Thus, the repetition of simple sentences nd frequent use of run-on sentences re not common for my style. For exmple, I edit for the conventions of writing s they proceed with composing their ides nd during the post-writing stge for refinement. nother re of difficulty in writing for me is the revision of my writing. The revision process is n

Econometric Regression Analysis Assignment Example | Topics and Well Written Essays - 500 words

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