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The Centre for the Study of the Legacies of British Slavery has been established at UCL with the generous support of the Hutchins Center at Harvard. The Centre builds on two earlier projects based at UCL tracing the impact of slave-ownership on the formation of modern Britain: the ESRC-funded Legacies of British Slave-ownership project (2009-2012), and the ESRC and AHRC-funded Structure and significance of British Caribbean slave-ownership 1763-1833 (2013-2015).
Colonial slavery shaped modern Britain and we all still live with its legacies. The slave-owners were one very important means by which the fruits of slavery were transmitted to metropolitan Britain. We believe that research and analysis of this group are key to understanding the extent and the limits of slavery's role in shaping British history and leaving lasting legacies that reach into the present. We are now moving in the direction of more focused research on the lives of enslaved people in the Caribbean. This is a natural development from our work on slave-owners and estates and an exciting demonstration of our commitment to the study of the multiple legacies of slavery in the British imperial world. With growth comes necessary change. One we are most pleased to make is to our name, which we changed in May 2021 to the Centre for the Study of the Legacies of British Slavery. We also have a new logo. This name change incorporates the work we have done and charts a way forward for our new phase of research and activities on slavery and its legacies in Britain and the Caribbean.
Support the work of LBS! To keep the work of LBS going we need your assistance with funding to help cover our operational costs.
The inaugural Elsa Goveia public lecture @ UCL was given by Professor Jennifer L. Morgan on the subject of 'The Measure of their Sadness: Slavery and Private Life in the Early Black Atlantic'. Wednesday 18 May 2022, 6:00 pm–8:00 pm, Darwin Lecture Theatre, UCL. Click Full details below.
Catherine Hall, 'Racial capitalism. What's in a name?' The Hobsbawm memorial lecture, 2022. Thursday 10 February, at 18:00. Venue: Birkbeck Clore Management Centre (at Birkbeck, University of London)
Matthew Smith: Inaugural Professorial Lecture: A Troubling Freedom: Power and Memories of Slavery. Friday 4th March 2022 at Gustave Tuck Lecture Theatre, UCL. It can be seen on the UCL YouTube channel: click Full details below.
Eric Williams's book, Capitalism and Slavery, was first published in 1944. It was, and remains, of fundamental importance for the understanding of slavery in the British Caribbean and its relationship to the development of British capitalism. Penguin has just (February 2022) re-issued the book. Click full details to see more.
The Western Australian Legacies of British Slavery project, working in collaboration with LBS, is examining the importance of the legacy of British slavery for the colonisation of Western Australia. The research into Western Australian colonists and their networks aims to trace the movement of people, goods, capital, and practices from the Caribbean to the newly-established colony of Western Australia. See also the related blog on James Stirling (1791-1865), enslavement and Western Australia by Georgina Arnott, a member of the Western Australia project team.
Slavery and Resistance in Jamaican History.
On Saturday 4th December (11.00-18.00) at the British Library there was a day of practical talks and workshops from leading historians of 18th-century Jamaica. 18th-century Jamaica has been the subject of intense historical interest in recent years, as important or overlooked documents have been rediscovered, and new ways of approaching histories of slavery, resistance and freedom have been developed. This day of talks and workshops from leading writers on the period will offer practical insights on how to get started in early modern Jamaican history, and how to get the most out of the British Library's collection: links to digital resources are included on this page.
LBS Newsletters. Forthcoming events and other news: From time to time, the project sends out newsletters with details of forthcoming events and other news related to the project.
Catherine Hall awarded the highly prestigious Leverhulme Medal and Prize 2021 by the British Academy.
History Workshop Journal has published a Virtual Special Issue bringing together material on Black British histories published in the journal and History Workshop Online over roughly the last thirty years. All the articles are freely available for six months from October 2021. See also the special feature on Legacies of Slave Ownership in History Workshop Journal, 90 (2020).
LBS Blogs: The LBS project has a blog, which you can access here. After originally running between May 2013 and December 2015 we have revived the blog in November 2017. We have written about individual case studies, made comments on sources and the research process and anything else which attracts our interest. Different members of the research project contributed posts and we have also had the occasional outside contributor.
BBC Radio 4 series, 'Descendants': 'how close is each of us to the legacy of Britain's role in slavery?'.
The National Trust has just released (September 2020) its 'Interim Report on the Connections between Colonialism and Properties now in the Care of the National Trust, Including Links with Historic Slavery'.
Charlotte Riley has contributed a blog on the resulting controversy surrounding the report here.
LBS – past & present: here we have a statement, 12 June 2020, on doing reparative history and you can read an associated statement from the new Director of the Centre, Matthew Smith, on the challenges and prospects for our work. And for an interview with Matthew Smith see also The Guardian, 22 September 2020.
There is also a link to a recent statement by many leading British historians calling for a review of the Home Office Citizenship and Settlement Test and its misrepresentation of slavery and Empire.
For LBS media enquiries such as requests for interviews please contact UCL Media Relations
Office: +44 (0)20 7679 9041
In an article in the London Review of Books (23 January 2020), Catherine Hall explores the notion and practice of a 'hostile environment' for immigrants to Britain.
We are extremely pleased to announce the appointment of Professor Matthew Smith as the new Director of LBS as successor to Nick Draper, who retired as Director in September 2019. For an interview with Matthew Smith, occasioned by Black History Month, click here.
Nick Draper interviewed about LBS by Trevor Burnard.
At the beginning of 2020 we updated the LBS database and website. The updates include a large number of Jamaican inventories as well as revised and added entries for many individuals.
Recent books: On this page we will occasionally highlight recently published work which might be of interest to users of this website. Doing so does not endorse the opinions of the authors; but we mention them here because of their potential interest.
Click Full Details below for Jennifer L. Morgan, Reckoning with Slavery, Alex Renton, Blood Legacy, Diana Paton and Matthew J. Smith (eds), The Jamaica Reader, Alan Lester, Kate Boehme and Peter Mitchell, Ruling the World, Christine Walker, Jamaica Ladies, Vincent Brown, Tacky's Revolt, Kathleen Monteith, Plantation Coffee in Jamaica, 1790-1848, Julius Scott, The Common Wind, Katie Donington, The Bonds of Family, Sarah Thomas, Witnessing Slavery, Miles Ogborn, The Freedom of Speech, Christer Petley, White Fury, Daniel Livesay, Children of Uncertain Fortune, Margot Finn and Kate Smith (eds), The East India Company at Home, 1757-1857.
In Legacies of British Slave-ownership. Colonial Slavery and the Formation of Victorian Britain, published by Cambridge University Press, we re-examine the relationship between Britain and colonial slavery in a crucial period in the birth of modern Britain.
Britain's Forgotten Slave-owners, a two-part BBC programme based on LBS and presented by David Olusoga, was originally broadcast in July 2015.
When using the biographical entries in this website you may come across references to the Oxford Dictionary of National Biography, Ancestry.co.uk (or Ancestry.com), Find My Past or ScotlandsPeople. These sites require payment or subscriptions so clicking on links to them usually produce a page restricting access unless you log in. For more on this issue, click Full Details below. This also includes a note on references used in the notes on compensation claims.


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New National Taxpayer Advocate Issues First Report to Congress
Erin M. Collins, the nation's new National Taxpayer Advocate, has issued her first report to Congress, which details the series of challenges—some met, some unmet—faced by the IRS this year. The challenges ranged from the COVID-19 pandemic and the subsequent aid and relief programs, to implementation of the Taxpayer First Act.
Collins prefaced the report with an admission that her tenure got off to a rocky start.
"On March 30, 2020, I had the honor and privilege of being sworn in as the third National Taxpayer Advocate," Collins wrote. "Starting in the midst of a pandemic and witnessing IRS offices closing one by one was not the way I envisioned my role when I accepted the position, . . . but there also has been a silver lining in this experience: As I have participated in conference calls with members of my leadership team, TAS employees, and the IRS's COVID-19 response team, I have been extraordinarily impressed by their commitment and focus on the health and safety of all employees during this pandemic, while still doing as much as possible to assist taxpayers."
Collins also praised her predecessor, Nina Olson, who served from 2001-2019, and the very first National Taxpayer Advocate, Val Oveson, who served from 1998-2000. "Over the past 20 years, TAS has successfully assisted more than 4.5 million taxpayers by helping them resolve their tax problems and protecting their rights, and it has made hundreds of administrative recommendations adopted by the IRS and some 45 legislative recommendations enacted by Congress," Collins wrote.
The Taxpayer Advocate says 2020 is a year fraught with challenges.
In the report, Collins praises the IRS for quick action during the developing COVID-19 pandemic, postponing more than 300 filing, payment, and other time-sensitive deadlines. The IRS also provided relief from compliance actions under its "People First Initiative" and distributed some 160 million Economic Impact payments (EIPs). Collins says these are balanced against some areas where the IRS didn't so so well:
- Taxpayers who filed a 2019 paper return and are entitled to refunds may be in for a long wait. The IRS had to suspend the processing of paper tax returns, and as of May 16, it estimated it had a backlog of 4.7 million paper returns. Although the IRS is reopening some of its core operations, it is not clear when it can open and process all the returns sitting in mail facilities.
- Some taxpayers whose returns were mistakenly flagged by IRS processing filters are experiencing lengthy delays in receiving their refunds. All tax returns claiming refunds are passed through filters designed to detect identity theft and other types of refund fraud. As TAS has documented, some of these filters produce "false positive rates" of more than 50 percent (meaning that more than half the taxpayers whose returns are stopped by certain filters are entitled to the refunds they claimed). Affected taxpayers are often asked to mail in documentation to substantiate their claims, but the IRS has not opened or processed many of their responses, delaying their refunds.
- Taxpayers who have needed help from the IRS have had difficulty obtaining it. The IRS shut down its Accounts Management telephone lines, so taxpayers could not reach a live assistor by telephone. The IRS shut down its Taxpayer Assistance Centers, making it impossible for taxpayers to obtain in-person assistance. The IRS also shut down its mail facilities, so it was unable to log or process taxpayer responses to compliance notices.
- IRS systems prepared over 20 million notices during the pandemic that could not be mailed due to closure of notice production centers between April 8 and May 31. The IRS is mailing these notices now. However, some collection notices bear old dates and include response deadlines that often have passed. The IRS plans to include "inserts" with these notices explaining that response deadlines have been postponed, but the report expresses concern that receiving compliance notices with response deadlines that have passed will be confusing and concerning to many taxpayers who may not read the inserts.
What were the CARES Act challenges faced by taxpayers?
The report says the IRS generally did a good job in implementing the CARES Act, but here too, challenges remain:
- Individuals who did not receive some or all of their Eonomic Impact Payments may have to wait until next year to receive them. To date, the IRS has taken the position that most taxpayers who did not receive their full payments must wait until they file their 2020 income tax returns to claim the amounts as credits against their 2020 tax liabilities, even though there is no legal constraint on the IRS's ability to issue additional EIP amounts as advance refunds during 2020.
- Employers are struggling to determine whether they qualify for the Employee Retention Credit (ERC) and in what amounts. The ERC is a complex, refundable tax credit that requires employers to determine when a trade or business was fully or partially suspended by government order; the employer's number of full-time employees; what constitutes qualified wages; whether a business's operations post-COVID-19 are comparable to its pre-COVID-19 operations; and the application of aggregation rules. Despite IRS efforts to issue guidance, additional clarification is needed.
- Businesses are facing challenges when seeking to utilize the CARES Act provision that authorizes the use of net operating losses to offset taxable income in prior years (and in some cases to receive refunds). For businesses to determine the optimal application of the CARES Act provisions so they can exercise their right to pay no more than the correct amount of tax, they may need to create and run complex financial models involving multiple tax years.
What was in the National Taxpayer Advocate's 2020 filing season review?
Usually, the National Taxpayer Advocate' report to Congress includes a wrap-up on the year's income tax filing season. Since the filing and pay deadlines were extended due to the COVID-19 pandemic, filing season is still ongoing. But Collins notes that the effects of the various IRS closures and shutdowns had an enormous effect on taxpayers. Among those setbacks were:
- Due to campus and office closures, the IRS could not staff phone lines to assist callers beginning the week of March 21.
- After March 20, taxpayers no longer had access to face-to-face customer service.
- There is a large backlog of incoming mail (about 10 million pieces of mailed tax returns or correspondence sitting in trailers at IRS campuses). The IRS could not process paper returns and process or respond to other written correspondence from taxpayers.
- The IRS has sent only a very limited volume of outgoing taxpayer correspondence.
- There was a substantial reduction in Volunteer Income Tax Assistance, Tax Counseling for Elderly, and Low Income Taxpayer Clinic services.
- The National Distribution Center was shut down, depriving taxpayers of a means to acquire pre-printed forms.
Because of the IRS's limitations and the postponed filing deadline, an assessment of the filing season is necessarily incomplete. The report says TAS may provide a more thorough analysis later.
The report also takes a look at how the recommendations from the previous report to Congress were viewed by the IRS. The Internal Revenue Code gives the National Taxpayer Advocate authorization to submit administrative recommendations to the IRS Commissioner. The agency is required to respond within three months. However, in 2019 the Acting Taxpayer Advocate made 19 administrative recommendations. The IRS claims it is not required to respond to them and has made only general narrative responses.
Collins writes the intent of the federal statute is clear.
"If the National Taxpayer Advocate makes an administrative recommendation to mitigate a taxpayer problem – regardless of whether or where it has appeared in a report – the IRS should evaluate it and respond in writing so that TAS, Congress, and the taxpaying public know whether the IRS plans to implement the recommendation and, if not, why not. General narrative discussions that do not address recommendations directly fail to satisfy this objective."

subset: commoncrawl


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What is the answer to can Guinea Pigs Eat Raisins? Although guinea pigs can eat raisins, they overall have little nutritional value. They have no vitamin A and a low vitamin C content. One of their only real benefits is that they do contain fiber, which is good for your guinea pig's digestive tract. 所以, your guinea pig can eat raisins, but may not receive as many health benefits from this particular treat as from other fruits and vegetables.
是, guinea pigs can eat raisins. Because of their high sugar content, be sure to limit the amount of raisins you feed your guinea pig. You can feed your cavy raisins about one to two times per month. A good serving size is a couple of raisins at a time. When feeding your guinea pig raisins, be sure to note what other ingredients are in the raisin box. Many boxed brands have added sugar and preservatives to the raisins. As raisins are already high in sugar, they do not need any more. 也, any artificial additives are potentially dangerous to your cavy. 因此, try to feed them raisins without these extra ingredients.
As mentioned above, raisins are very high in sugars. If a cavy has a diet too high in sugars, it can lead to some serious health problems. Your guinea pig can get digestive issues, weight gain, and even diabetes from eating too much sugar. 因此, be sure to severely limit how many raisins you feed your cavy.
所以, can guinea pigs eat raisins? 是, but in great moderation. Because of their high sugar content and low nutritional value, they should only be an occasional treat for your cavy, if fed to them at all. 然而, if you monitor how often raisins are fed to your guinea pig, then they can be a tasty treat to supplement their more regular diet.


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Find out why a Claflin education is more than a means to a degree.
Office of the Registrar
The best way to get a feel for Claflin is to visit us.
Claflin students work with the best leaders in their fields.
You'll find endless opportunities here to get involved.
There is always something happening at Claflin!
Claflin is #1 in alumni giving among all HBCUs, thanks to you.
Keep up with Claflin University on social media! Here's where to follow us.


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Cleantouch POS Software is an all-in-one retail management system for shops, super stores and departmental stores. It has integrated professional accounting module with easy to maintain inventory module. Sales screen is optimized to generate invoice and apply various actions e.g. hold, recall bill / last item, save and print, print old invoices etc. quickly. Feature of auto save item in bill is... Read Full Information
Cleantouch Trading Control System by is one of the most famous accounting software in Pakistan. The software is written for small business of trading. User can track records of physical stock at multiple locations along with integrated accounting options.
Orders registers can be categorized by Pending Only, Completed Only, Canceled Only or can be printed all orders register by date. Order... Read Full Information
Features marked with an (*) are available in Professional Edition only


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Lots of kids love video games. In fact, they like them so much that they might hear something like this from mom or dad: "Enough! Find something else to do!"
It can be good advice, even if you were about to get to the next level. Why? Too much of anything is just too much. It's true that some studies have shown certain video games can improve hand–eye coordination, problem-solving skills, and the mind's ability to process information. But too much video game playing may cause problems.
It's hard to get enough active play and exercise if you're always inside playing video games. And without enough exercise, kids can become overweight.
Overdoing video games also could affect other important stuff, like friendships and how well a kid does in school. And kids who play violent video games might act more aggressively.
But here's the good news: Playing video games some of the time can be OK. Choose quality games, and limit screen time — which includes TV, computer, smartphone, tablet, and video game time combined — to a reasonable amount.
A good game will be the right one for how old you are. Games are rated like movies and your mom or dad can help figure out which ones you should use. If you can choose one that gets you up and moving, that's even better.
You might challenge your mom, dad — or even your grandma — to swing the bat in a game of baseball or try out some fancy moves in one of the dancing games. Could your grandma be a dancing queen? Time to find out!
Note: All information is for educational purposes only. For specific medical advice, diagnoses, and treatment, consult your doctor.
© 1995- The Nemours Foundation. KidsHealth® is a registered trademark of The Nemours Foundation. All rights reserved.
Images sourced by The Nemours Foundation and Getty Images.
New UsersCreate a User AccountBecome a Member |
Forgot PasswordForgot your password? Click here |


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The cost of the loan and Annual Percentage Rate (APR) depend on several factors, including state law, credit history and employment history. The APR also depends on the request loan amount and term. The loan terms are disclosed during the loan request process when you are directed to the lender's or lending partner's website. Start your loan request now!
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The terms of your loan, including the APR, fees, finance charges, and other terms are disclosed during the loan request process after you are directed to the lender's and/or lending partner's loan agreement. This information is strictly between you and the lender and/or lending partner you are connected with. Not all customers will be eligible for a loan or meet the criteria to receive the best terms or lowest interest rate.
The examples represent sample rates, are for informational purposes only, and may not reflect the actual APRs offered by your lender and/or lending partner.
If you borrowed $5,000 over a 24 month period and the loan had a 6% APR, your monthly repayments would be $221.60, with a total payback amount of $5,318.47
If you borrowed $5,000 over a 24 month period and the loan had a 15% APR, your monthly repayments would be $242.43, with a total payback amount of $5,818.40


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Bottle 1072 - Sailboat |
Date Added: 25 April 2013
"I have built two ships for two children. They are 8 and 10 years old and are the son and daughter of the friend of my youngest daughter. After they have seen my SIB's they are both willing to build an SIB. The boy wanted a rubber boot whit an outboard motor. The girl wanted to built a sailing boot. I have made the hull of both ships and the other parts. The boy and girl have painted the parts, making the ropes on the sailing boot and welding some brass parts. The girl has punched the sails and glued it on the mast and spars. They both put see into the bottles. (very hard working for both) After they had put the parts into the bottle I helped them to get everything on the right place and in the right position. I have made the Turkish not on the bottleneck en put some seal on the cork whit my mark in it. After that I have made an oak standard for both whit their names in it. The both were very pleased whit the result and showing it to their parents and grandparents. The bottle neck opening is 18mm." Frans Dekker
Type: | Sailboat | Maker's Name: | Dekker, Frans | |
Category: | Watercraft | Made Where: | Beemster, Holland | |
Bottle Size: | 23cm x 9cm | Year Made: | 2013 | |
Bottle Type: | Unknown |
Links to Additional Information | ||
Frans Dekker, Artist |


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Slope | = | _Vertical leg_ Horizontal leg |
= | Δy Δx |
= |
For example,
If the value of y changes by 2 units when the value of x changes by 3, then the slope of that line is the number .
What does slope mean? It indicates the rate at which a change in the value of x produces a change in the value of y. 2 units of y per -- for every -- 3 units of x.
For every 3 units that line moves to the right, it will move up 2. That will be true between any two points on that line. Over 6 and up 4, over 15 and up 10. A straight line has one and only one slope. (Theorem 8.1 below.)
In each of those lines, the x-coördinate has increased by 1 unit. In the line on the left, however, the corresponding value of y has increased much more than in the line on the right. The line on the left has a greater slope than the line on the right. The value of y has changed at a much greater rate.
The tangent to a curve
In calculus, the student will see that the slope of a tangent line to a curve at a point P --
-- is the geometrical meaning of what is called the derivative. It indicates the typically non-constant rate of change of y with respect to x -- at the point of tangency.
The slope of a straight line is very definitely a topic of precalculus.
In a typical application, the x-axis represents time and the y-axis, distance. The rate of change of distance with respect to time -- the speed -- is typically not constant. The graph is not a straight line. The slope of the tangent line gives the instantaneous speed at a specific moment of time.
Which line do we say is sloping "up"? And which is sloping "down"?
Since we imagine moving along the x-axis from left to right, we say that the line on the left is sloping up, and the line on the right, down.
What is more, a line that slopes up has a positive slope. While a line that slopes down has a negative slope.
For, both the x- and y-coördinates of B are greater than the coördinates of A, so that both Δx and Δy are positive. Therefore their quotient, which is the slope, is positive.
But while the x-coördinate of D is greater than the x-coördinate of C, so that Δx is positive, the y-coördinate of D is less than the y-coördinate of C, so that Δy, 5 − 8, is negative. Therefore that quotient is negative.
Problem 1. What number is the slope of each line?
To see the answer, pass your mouse over the colored area.
To cover the answer again, click "Refresh" ("Reload").
Do the problem yourself first!
a) | b) | |||||||
3 4 |
4 3 |
c) | d) | |||||||||
− | 4 3 |
− | 3 4 |
Horizontal and vertical lines
What number is the slope of a horizontal line -- that is, a line parallel to the x-axis? And what is the slope of a vertical line?
A horizontal line has slope 0 because even though the value of x changes, the value of y does not. Δy = 0.
Δy Δx |
= | 0 Δx |
= | 0. | (Lesson 5) |
For a vertical line, however, the slope is not defined. The slope tells how the y-coördinate changes when the x-coördinate changes. But the x-coördinate does not change -- Δx = 0. A vertical line does not have a slope.
Δy Δx |
= | Δy 0 |
= | No value. | (Lesson 5) |
Problem 2.
a) Which numbered lines have a positive slope? 2 and 4.
b) Which numbered lines have a negative slope? 1 and 3.
c) What slope has the horizontal line 5? 0.
c) What slope has the vertical line 6? It does not have a slope.
Problem 3. Calculate the slope of the straight line joining the points (−1, −2) and (7, −8). And what does that slope mean?
Δy Δx |
= | −8 − (−2) 7 − (−1) |
= | −8 + 2 7 + 1 |
= | −6 8 |
= − | 3 4 |
That slope indicates the rate of change of the y-coördinate with respect to the x-coördinate. For every 4 units the x-coördinate increases, the y-coördinate decreases by 3.
Problem 4. Let y = f(x) = x2 − 1, and let two points on its graph have these x-coördinates: x1 = 3, x2 = 5. Calculate the slope of the straight line that passes through those two points.
At each of those points, f(x) will give the value of y. At x1 = 3, y1 = 32 − 1 = 8. At x2 = 5, y2= 52 − 1 = 24. Therefore the two points are (3, 8) and (5, 24). And therefore, Δy/Δx =
(24 − 8)/(5 − 3) = 16/2 = 8.
Problem 5.
Let y = f(x), and let its graph pass through two points P and Q whose x-coördinates are separated by a distance h. And let x be the x-coördinate of P.
a) What is the x-coördinate of Q? x + h
b) What are the x- and y-coördinates of P? (x, f(x))
c) What are the coördinates of Q? (x + h, f(x + h))
d) Write an expression for the slope of the straight line joining the
d) points P and Q.
f(x + h) − f(x) h |
This is the famous difference quotient of calculus. (Topic 3.) The question calculus asks is: What is the value of that slope when h is practically 0? The answer will be the slope of the tangent line at P. That slope will be the rate of change of the function at P.
See Topic 3, Problem 11.
One slope
To establish the algebraic equation of any geometrical figure, we must carry over our knowledge from plane geometry; for nothing will come of nothing. With the aid of the following theorems, we will be able to prove that the equation of a straight line may take the form y = ax + b, and that a is the slope of the line. We will do that in the following Topic.
Theorem 8.1. A straight line has one slope.
That is, whether we measure the slope by moving from point A to point B, or by moving from point C to point D, the number we obtain will be the same.
For, if we measure the slope from A to B, we will get BE/EA. While if we measure it between C and D, we will get DF/FC.
But FC is parallel to EA because they are both parallel to the x-axis;
and DA is a straight line that falls on two parallel straight lines;
therefore, the exterior angle DCF is equal to the opposite interior angle on the same side, angle BAE. (Euclid, I. 29)
Therefore the right triangles BEA, DFC are similar (Euclid, VI. 4), and therefore, proportionally,
. |
Δy Δx |
will be the same, whether we go from A to B, or from C to D. |
That is what we wanted to prove.
Problem 6. A straight line will make an angle θ with the x-axis.
Which trigonometric function of θ is its slope?
tan θ. For, a line has one slope.
"Same slope" and "parallel"
Before we state the next theorem, the student should be familiar with the logical expression if and only if.
First, if p and q are statements (sentences), then in the proposition "If p, then q," p is called the hypothesis. It is what we are given, or what we assume. There is no logic without hypotheses.
Statement q is called the conclusion. It is what we must prove on the basis of the hypothesis.
The proposition "If q, then p" is called the converse of "If p, then q." The hypothesis and conclusion are exchanged.
Finally, the proposition "p if and only if q" means: "If p, then q , and if q, then p." In other words, a proposition and its converse are both true.
For example, "A triangles is isosceles if and only if the base angles are equal." This means, "If a triangle is isosceles, then the bases angles are equal; and, conversely, if the base angles are equal, then the triangle is isosceles."
Therefore, when we prove an if and only if proposition, we must prove both a proposition and its converse.
The slope of a line is a number. Parallel is a geometrical property. The relationship between them is the next theorem.
Theorem 8.2. Two straight lines are parallel if and only if they have the same slope.
Let the straight lines L1, L2 be parallel. And let the slope of L1 be BC/CA; for a straight line has only one slope. (Theorem 1)
Draw the straight line ACF intersecting L2 at D, and draw FE perpendicular to DF.
Then the slope of the straight line L2 is EF/FD.
Then the slope of L2 is equal to the slope of L1. That is,
For, since the lines L1, L2 are parallel, and the straight line AF falls on them, the alternate angles BAC, EDF are equal (Euclid, I. 29);
therefore the right triangles BAC, EDF are similar (Euclid, VI.4),
and those sides are proportional that contain the equal angles:
Therefore the straight lines L1, L2 have the same slope.
Next, conversely, assume that those lines have the same slope:
Then the two straight lines are parallel.
For, the angles at C and F are right angles and therefore equal,
and by assumption, the sides that make them are proportional.
But if two triangles have one angle equal to one angle, and the sides that make them are proportional, then the triangles are similar,
and those angles are equal that are opposite the corresponding sides;
(Euclid, VI. 6, 4)
therefore, angle BAC is equal to angle EDF.
But angle CDG is equal to angle EDF because they are vertical angles;
(Euclid, I. 15)
therefore angle BAC is equal to angle CDG.
That is, the straight line AF falling on the straight lines L1, L2 makes the alternate angles BAC, CDG equal.
Therefore the straight line L1is parallel to the straight line L2.
(Euclid, I. 27)
Therefore two straight lines are parallel if and only if they have the same slope. Which is what we wanted to prove.
As for perpendicular lines, in Lesson 34 of Algebra we prove the following:
If two straight lines are perpendicular to one another, then the product of their slopes is −1.
That is, if the slope of one line is m, then the slope of the perpendicular line
is − | 1 m |
. |
The specification of a straight line
Finally, we can state
Theorem 8.3. A straight line may be specified by giving its slope and the coördinates of one point on it. Equivalently: Through any point there is exactly one straight line with a given slope.
Let the straight line L have slope m, and let it pass through the point P. Then L is the only straight line through P with slope m.
For, it will be impossible to draw another straight line through P parallel to L, because parallel lines do not meet.
Therefore, any two lines through P will not be parallel, and therefore they will have different slopes. (Theorem 2)
Therefore, there is only one straight line through P with a given slope.
This means that a straight line may be specified by giving its slope and the coördinates of one point on it.
Which is what we wanted to prove.
On the basis of this theorem, we will be able to prove, in the following Topic, that the equation of a line may take the form y = ax + b, where a is the slope of the line, and b is the y-intercept.
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Deputy Store Manager - Monsoon Accessorize - Derry
Ref: | MON11968 |
Salary: | Competitive |
Department: | Retail Management |
Location: | Londonderry |
Position type: | Permanent |
Hours / Duration: | 40 Hours Per Week |
Our story begins with one man and his vision, to bring vibrant colourful clothes and accessorize from faraway places to the markets of London. We are a lifestyle brand, passionate about connecting contemporary designs with a network of craftspeople and creating unique collections enabling everyone to express themselves.
We are built on a way of working we are proud of, were values and ethics go hand in hand.
We have an exciting opportunity for an experienced Deputy Store Manager, at our Derry Monsoon Accessorize Store.
Our ideal candidate would be customer focused, reflecting the passion we have for our product and the drive to create an exceptional experience for the Monsoon Accessorize customer. We value the qualities of enthusiasm, integrity, and the desire for success.
What are we looking for in you?
- A confident leader, one who will inspire the team, leading by example to make Monsoon Accessorize a great place for all who work and shop with us
- A proven track record of managing a successful retail store, delivering excellence in customer service, both personally and through their team
- Someone who demonstrates passion, drive and resilience, with a can – do approach
- Possess a creative approach, to support the store and develop the team to reach their full potential
- The ability to communicate openly and effectively
- A Solution driven Individual, with the ability to make decisions to benefit the business, with a sense of ownership to take responsibility
In this role you will
- Support the store manager in driving the overall performance of the store, through managing and developing your team, demonstrating the Monsoon Accessorize values and ensuring your store is delivering an exceptional customer experience
- Generating profit, through exceeding your KPIs, keeping P&L and controllable costs in line with budget and maximising local market opportunities
- Ensuring your team are motivated and knowledgeable, supporting everyone to achieve excellence in their roles
- Maximise commercial opportunities to drive sales within your store, implementing Visual Merchandising and Window Guidelines to a high standard
- Be flexible in your approach to your role, supporting other stores and team members to achieve a common goal
- Ensure an inclusive environment, promoting equality and kindness with your team
Joining us, your benefits would include
- A competitive salary and exciting bonus scheme
- A Staff uniform allowance – enabling you to have fun wearing our accessories
- Generous staff discount across all our brands – Accessorize, Monsoon, Monsoon Childrenswear and Monsoon Home
- An additional day's holiday to celebrate your birthday
If this all sounds great and this could be the role for you, let us know and apply today.
At Monsoon Accessorize we don't focus only on what we do, we also care about how we do it. Our values and the way we behave are important to us.
We are committed to creating a diverse and inclusive workforce and an environment where we value and respect every individual's unique contribution, enabling all of our employees to thrive and achieve their full potential.
We want to attract the broadest range of talented people and are an equal opportunity employer. We welcome applications from individuals, regardless of age, gender, ethnicity, disability, sexual orientation, gender identity, socio-economic background, religion and/or belief. We will also consider flexible working requests for all roles, unless operational requirements prevent otherwise.
We provide reasonable accommodations as needed to people with disabilities to participate in the job application or interview process, to perform essential job functions, and to receive other benefits and privileges of employment. Please contact us at firstname.lastname@example.com to request discuss any specific requirements.


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Last Updated on August 2, 2023 by GeeksGod
The financial markets are not very easy to handle and to trade. The Forex market is the biggest of those with more than 2 trillion dollars exchanged on a daily basis. But, there is a way to make profit out of all those transaction with forex trading and this is the goal of this course. Indeed, if you :
– Are someone who is interested in forex trading but never actually started
– Always wanted to learn how to generate profits on those markets and work from home
– Want to Learn and understand different styles of trading
– Simply want to launch your trading career
Then this course is definitely for you. Indeed, this course will teach you everything you need to know to launch your trading career in no time. From choosing the right broker to opening your first trade this course has all the information that you need to be able to succed in the trading world.
The structure of the course
This course is made to help you enter the trading world step by step. Indeed, each part of the course is here to help you learn new concepts and also to help you achieve your goal of becoming a trader. From choosing the right broker to downloading MT4, talking about different types of analysis and many other things, you are never left alone in your learning. In other words, by the end of this course you will have your broker account set, all the platforms downloaded and everything else ready so you will be able to focus only on the trading and not thinking about anything else.
Also, this course will give you an introduction to different trading strategies since the main goal is to help you create your own trading plan. You will have all the required knowledge in trading money management analyze and any other field that is required to help you become a better trader. Also, there is a lot of practice in this course and this is one of the reasons why it's definitely a good choice to learn the basics of trading with it.
For who is this course designed
This course is designed for people that have no prior knowledge of trading but who want to learn how to enter the Forex trading world. Also, everybody who is simply interested to learn in general about trading, finances and all the basics of those will definitely love this course. Indeed, this course offers a lot of very valuable information about different markets and about different trading styles that it could very useful to know in the trading world but also for personnel purposes.
Why should I take this course
The main reason is that it will give a complete introduction to the biggest financial market. Then, by understanding how this market works you will be able to understand how to generate an income from it. Not only this course will offer you the opportunity to have another stream of income but you will also be able to learn different ways that you can use to be able to limit your risk in this market.
There is no risk involved in taking this course
This course comes with a 100% satisfaction guarantee, this means that if your are not happy with what you have learned, you have 30 days to get a complete refund with no questions asked. Also, if there is any concept that you find complicated or you are just not able to understand, you can directly contact me and it will be my pleasure to support you in your learning.
This means that you can either learn amazing skills that can be very useful in your professional or everyday life or you can simply try the course and if you don't like it for any reason ask for a refund.
You can't lose with this type of offer !!
This is why more than 130 000 students have already took the course !! Don't wait anymore
ENROL NOW and start learning today 🙂


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More than half a century after they invented the concept, Volvo Construction Equipment recently celebrated the production of the 75,000th articulated hauler. Having produced more than half of the articulated haulers ever made, a staggering 50,000 Volvo haulers are still in regular use around the world.
The 75,000th machine – one of the new generation A45G full suspension models – rolled off the production line in late June at the factory where the first machine – the DDR631 or 'Gravel Charlie' – was made, in Braås, Sweden. And although Volvo articulated haulers can be found all over the world, the 75,000th machine is staying relatively local, going to Norwegian customer Leonhard Nilsen & Sønner AS.
In typically Swedish style, the landmark 75,000 articulated hauler was marked modestly – with factory workers celebrating the achievement with ice creams. Then it was back to work, to meet the demand that is seeing Volvo take a bigger lick of the articulated hauler market.
It's no surprise to see why Volvo CE has made more articulated haulers than all other competitors put together. Over the last 51 years, the models have increased in size and sophistication. The first 15 tonne capacity machine built in 1966 can fit into the haul body of the A60H – Volvo flagship 55 tonne articulated hauler.
More than half a decade of experience is built into every Volvo machine. A high hitch gives better stability and ground clearance, hydro-mechanical steering offers high speed stability, while 100% dog clutches and automatic switching between 6X4 and 6X6 drive not only powers through any conditions, but does so with minimal wear and maximum fuel efficiency.
"There's no question that we have the best product, says Esbjörn Fritzell, Vice President of Volvo CE' Trucks business platform. "The fact that so many of our haulers are still working around the world is a testament to their usefulness and durability – it's almost impossible to kill a Volvo articulated hauler!"
While it took a while for the world to fully appreciate the benefits of articulated haulers, the machines are now in demand as never before, finding work as production machines in mines and on all types of infrastructure projects. This is driving the trend for larger machines – such as the newly introduced 41 tonne class size of the 75,000th machine, the A45G. Volvo CE's A60H is the largest on the market, and can deliver 40% higher production than Volvo's previous largest machine – the A40G – with hardly any increase in the ongoing cost of ownership.
"There's not many companies can say that they are still the market leaders half a century after they invented a concept," says Håkan Ask, business platform leader for Trucks at Volvo CE. "Having made 75,000 machines we are still showing the way, building more productive and fuel-efficient machines that are the envy of the industry."
Head of Brand, Marketing and Corporate Communication
Regions Asia and China
Volvo Construction Equipment
E-mail: email@example.com
Head of Strategic Communications
Volvo Construction Equipment
Email: firstname.lastname@example.com


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At the height of his career, former Cardinal Theodore McCarrick was one of the most influential leaders of the Catholic Church in the U.S., heading the Archdiocese of Washington, D.C. Last week, he became the first U.S. Cardinal to be criminally charged with a sexual crime against a minor, making the 91-year-old the highest-ranking Catholic Church official in the country to face criminal charges for clergy sexual abuse.
The fact that McCarrick sexually molested adults and children was already known: A Vatican investigation confirmed the abuse. He'd been defrocked in 2019.
Mitchell Garabedian has settled more than 2,000 clergy sex abuse cases over the past 20-plus years and is the lawyer representing an abuse survivor in a current civil case against McCarrick.
"Cardinal McCarrick was one of the most powerful and influential cardinals in the world. He hobnobbed with presidents: George W. Bush, President Ford, President Carter, President Clinton," Garabedian says. "He was very influential, very powerful, and Cardinal McCarrick right now is a defendant in a criminal case, thanks to the courage of a brave clergy sexual abuse victim."
Late last year, the Vatican released a report detailing both abuses committed by McCarrick and how various internal church investigations into those abuses had begun and then stalled over the years.
"The Catholic Church recognizes that prevention of sexual abuse is an ongoing effort that includes pastoral care and outreach to survivors, reporting allegations to civil authorities, background checks, education and training on keeping children and youth safe, and the implementation of child protection policies at the local level," a spokesperson for the U.S. Conference of Catholic Bishops said in a statement to NPR.
They went on to say: "We have made much progress, but we also know that the painful experience of survivors calls us to continual improvement."
Mitchell Garabedian spoke to All Things Considered's Mary Louise Kelly about whether he's seen progress in the way the U.S. justice system has prosecuted these cases, if there's difficulty in building a defense against allegations that may be decades old and if the Church itself has begun to take meaningful action to end systemic abuse.
This interview has been edited for length and clarity.
Interview Highlights
On whether he thinks law enforcement is now more willing to go after top church officials
Oh, without a doubt. I think that some of the laws have changed, allowing the prosecution. There's been a seismic change in the attitude that this is no longer a priest who can't be touched, who must be taken care of, who couldn't possibly have done this, or it's an anomaly. I think the attitude is this is a priest and he's using the veil of morality to act immoral. I believe that the prosecutors and police are now looking into these cases — because of the momentum created by clergy sexual abuse victims coming forward — more closely. There's no doubt in my mind.
On whether survivors coming forward after decades have passed complicates building a legal case
Victims of sexual abuse — in the clergy, sexual abuse — do not come forward, usually, till they're at least 45 years or older. It's not unusual at all for someone to call me and say, "I was sexually abused by a priest. I'm 75 years old, or I'm 82 years old, and I want to proceed with a claim." So I'm used to old cases coming forward. But if you dig hard enough, if you look hard enough, you'll see that there is evidence, there is corroboration, and you pursue that evidence and corroboration and you support your client's claim with that evidence and corroboration. So you don't let the age of a case or age of a claim deter you in any way. You just keep moving forward.
On how the Catholic Church's 2020 report on its internal McCarrick investigation is a PR move more than meaningful action
This report was a forced report. The Church is a master at spin control. They tried not to incriminate anyone else, or as few people as possible. Where have they been in decades — for decades and decades since the 1980s? In the 1980s, a woman wrote to cardinals in the papal nuncio stating that McCarrick had been sexually abusing children. So why didn't they bring that to light in the 1980s and 1990s and thereafter so that children could be protected? The Catholic Church is all about the Catholic Church. It's all about the size of its bank accounts, it's not about the safety and welfare of children. And now victims are coming to me saying they were abused in the 1990s by priests, by the janitor, by the deacon. So the evidence, to me, is that the Catholic Church has not changed.
On how the delay to investigate proves the Church's commitment to itself over people
It took them more than 40 years to produce a report. Whatever happened to "Call the police," send it to the police? They could have sent it to the police in [the] 1980s, 1990s. I believe, in a Vatican report, there are at least 17 reports, 17 individuals, sexually abused by Cardinal McCarrick. And Bishop [Edward] Hughes, Bishop [John M.] Smith, saw him sexually abusing children, and now here we are far more than 40 years later and they're first talking about it? This shows you how the Catholic Church is concerned about itself and not about the safety and welfare of children. It speaks volumes.
On whether he's discouraged about the work so many years later
Oh, no, I'm not discouraged. I'm doing my work. We're making advances. I get calls of gratitude from clients I've represented 20 years ago saying, "You know, you really helped me out in my life, and you were right. This wasn't my fault." And it's not any sexual abuse victims fault that they were sexually abused, but these are the damages victims feel often. And I'd like to add that many victims call me and they take the weight off their shoulders and they become survivors as opposed to victims.
Ayen Bior and Courtney Dorning produced and edited this story for broadcast. Cyrena Touros adapted it for the web with help from Jason DeRose. contributed to this story
Copyright 2023 NPR. To see more, visit https://www.npr.org.


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Daniel Pink (or just Dan Pink), a proponent of human drive, is hell-bent on motivation and changing the workplace, and he has an impressive resume, to say the least.
Besides being a bestselling author, with works translated into numerous languages, he has served in the White House "as chief speechwriter to Vice President Al Gore."
The video above is fascinatingly interesting! I literally couldn't pull myself away, and its also a must watch, because of the awesome animations!


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May Allah make siraj Wahhaj better
Click Here
A Message from Imam Siraj himself:
As Salamu Alaikum, Dear Brothers and Sisters!May Allah cure him and grant him sabr...
It is well known now that I have been suffering from hypertension. Al Hamdulillah, I have been working with it for a while now, and insha'Allah it's pretty much under control. As a result of being thoroughly checked by the competent doctors in Atlanta , I have been recently diagnosed with prostate cancer. Al Hamdulillah, inna lillahi wa inna ilaihi rajiun. (All Praise is for Allah. Truly, to Allah we belong and truly, to Him we shall return.)
My diagnosis is not as bad as it sounds on the surface. Many men have been cured from prostate cancer. My doctors are very optimistic about my cure, and so am I. Insha'Allah the treatment should last about two months. But you and I know that the cure is in the Hands of Allah. If Allah heals me, I will be very grateful. If Allah doesn't heal me, then I will be patient and happily accept my fate. This is the way of the Believers. I am looking forward to full recovery and getting back to work in the not-too-distant future, insha'Allah.
Many people will ask the question, what can we do? Don't waste your time feeling sorry for me. Make du'a. But don't just make du'a for me. There are a lot of Muslims, men and women, with cancer (and other diseases). Make du'a for them also. There are so many among the elderly, who need our help, make du'a for them. There are so many Muslims who have lost their jobs, lost their homes, make du'a for them! Beyond the prayers, go visit the sick, those in prison, and others in need.
Get involved more with Islamic work. Support organizations like MANA, ISNA, ICNA, MAS, CAIR, SIFCA, the community in association with Imam Warith Deen Mohammed, the community of Imam Jamil Al Amin, etc. Support good brothers and sisters, like Mauri' Saalakhan of the Peace and Justice Foundation. Support Islamic education and schools. If you want to help Imam Siraj, then help support his Masjid, Masjid At-Taqwa, in Brooklyn, New York and all the other struggling Masjids throughout America.
Every challenge we face in life presents us with many opportunities for growth. With a heightened awareness and sensitivity about health-related issues, I will feel better when we, as an ummah, learn more about our health. We have to be very careful about the foods we consume! I urge all of us to cultivate healthy appetites such that we begin to love and crave foods that are good FOR us and eliminate foods that are not. I intend with Allah's help to share information with you in the coming weeks about our health.
On behalf of MANA, I encourage you to lend your support to our growing Organization. Every MANA project is structured to strengthen American Muslim communities. The SHARE Centers, Healthy Marriage Initiative, Community Reentry Program, and Healing and Reconciliation Project all need input and active service urgently. Please contact the MANA office to find out more and look for regular updates in our newsletters, insha'Allah.
In closing, I am humbled and very thankful for all the prayers, and well wishes of the Muslims, and am very appreciative for all the help extended to me and my family in the past. Alhamdulillah! I am also overwhelmed with gratitude that a number of you want to lend financial support, and have asked how you can do that. Online donations can be made here, or feel free to correspond with me directly at Siraj Wahhaj, P.O. Box 312264, Atlanta, GA 31131.
Thank you kindly. May Allah guide and protect us all.
Your brother in faith,
Imam Siraj Wahhaj
May Allah make siraj Wahhaj better
ameen at the dua
May Allah SWT Grant a speedy recovery back to good health inshAllah
Ameen to the adiya!
MashaAllah ur patience .ssss.......Hatsoff Mr Imam Siraj..!
May Allah Give u healthy wealthy Life
Read "YA Hayu Ya QAYUM Br REHMATIKA ASTAGHISU"
SubhanAllah, may Allah grant him shifa


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[youtube http://www.youtube.com/watch?v=NT1tZmGvFfY&w=615&h=461]
It seems almost unthinkable that Jim Henson's Fraggle Rock, his landmark children's program about several different species living underground and in worlds beyond, could be turning 30 this year. Lasting four seasons and 96 episodes (not to mention an animated spinoff) in the mid-'80s, the adventures of Gobo, Mokey, Wembley, Boober, and Red are still very much in the minds of people young and old alike. Who doesn't know to dance their cares away? Now, you can relive all the wonder and excitement with the Fraggle Rock 30th Anniversary Collection on DVD.
Carefree Fraggles, dutiful Doozers, clueless Gords, and a puppet dog named Sprocket are all in the set, as is that great explorer Travelling Matt with his mighty mustache. The set includes all 96 episodes, two full discs of special features, a new comic book adventure, and a Red Fraggle mini-plush. Wanna know the best part? We're giving one away! All you have to do is enter our contest and wait. You can even head to our Facebook, Twitter, and Google+ pages to get yourself extra chances to win. Make sure you enter by midnight on May 21st, though, or no amount of dancing will take away the worry of missing out.
And, of course, you should check out Ben Folds Five's video for "Do It Anyway" featuring the Fraggles (and Chris Hardwick). There might also be more Fragglicious fun coming soon on the Nerdist Channel…
[youtube http://www.youtube.com/watch?v=mEyrfFwf3rI&w=615&h=346]
(Oh, and in case you missed it, see the Nerdist Channel's exclusive clip from the DVD set with puppeteer Jerry Juhl interviewing Gobo by clicking here)


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Mark Morgenstein
Director of Media Relations, The Public Interest Network
[email protected]
Director of Media Relations, The Public Interest Network
[email protected]
Environment America
One day, three decisions — all of which may have far-reaching effects on plastic pollution in the United States.
In California, the "straw bill" (AB 1884) passed the state Assembly. The bill is now one Gov. Jerry Brown signature away from becoming law. Once signed, California would be the first state to require dine-in and full service restaurants to give customers single-use plastic straws only upon request.
Every day in the United States, people throw away about 175 million plastic straws, and many of those straws end up in or near the ocean.
"Nothing we use for a few minutes should be allowed to pollute our rivers and oceans for hundreds of years—especially items we don't really need," said Dan Jacobson, state director of Environment California, which was a driving force in getting the bill passed.
On the Atlantic coast, Gov. Phil Murphy of New Jersey also made a statement against single-use plastics. He vetoed a bill (A 3267) fast-tracked by retailers that would have placed a statewide 5-cent fee on single-use plastic bags, while simultaneously preventing local action. Instead, New Jersey's cities and towns will have the freedom to pursue bans and heftier fees on plastic bags, while the state reconsiders what a statewide ban might look like in the future.
"Gov. Murphy made the right call to veto legislation that would have preempted cities and towns from banning plastic bags," said Doug O'Malley, director of Environment New Jersey.
"Plastics bags are a scourge on our ecosystems and communities. We need to choose wildlife over waste."
Single-use plastic bags are one of the most common single-use plastics found in the environment. Every day, Americans throw away an estimated 300 million, and less than five percent of those bags are recycled.
Not to be outdone by the east or west coast, corporate America responded from the heartland. Cincinnati-based Kroger Co., America's largest grocery-only chain, announced its plan to phase out single-use plastic bags and transition to reusable bags by 2025 in all its stores, starting with Seattle-based subsidiary QFC in 2019.
"Kroger's commitment is a big step forward in the Wildlife Over Waste movement." said Steve Blackledge, senior conservation director for Environment America. "We've known for decades that plastic pollution is harming wildlife, and we've been reminded of this recently — whether seeing horrifying video of a turtle with a plastic straw lodged in its nostril, or the images of several dozen plastic bags being removed from the bellies of whales."
This is the latest socially-responsible action from Kroger. In another recent zero waste- related initiative, Kroger set a goal to divert 90 percent of its waste from landfills by 2020.
Alex Truelove, U.S. PIRG's Zero Waste campaign director, concluded, "Individual, targeted policies to reduce plastic pollution may seem inconsequential, but these statements across the country today prove that we're all working together towards the same objective. Together, we can make a real difference."


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Toroidal chaos is quite rare in 3D autonomous continuous systems. Apart the toroidal system produced by Otto Rössler in 1979 but which does not produce chaotic behaviors, the system by Bo Deng could be one of the very first to produce toroidal chaos. What is quite interesting in this attractor is that there is a unique folding mechanism : this is thus unimodal chaos.
The system
This is a set of three ordinary differential equations reading as [1]
This system produces a toroidal chaotic attractor (Fig.1) with parameter values as a=3, b=0.8, c=1, d=0.1, m=0.05, , R=10, , , , and . A sketch of the attractor is shown in Fig. 2.
A Poincaré section revealing the single folding is shown in Fig. 3.
[1] Bo Deng, Constructing homoclinic orbits and chaotic attractors, International Journal of Bifurcation & Chaos, 4, 823-841, 1994.


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Nashville session ace Kenny Greenberg on playing with 10 music legends
Nashville session ace Kenny Greenberg on playing with 10 music legends
During country superstar Kenny Chesney's current Brothers Of The Sun tour (a co-headline extravaganza with fellow chart-topper Tim McGraw), concertgoers are treated to hit after hit after hit. But they're getting something else, too – a whole lot of rock guitar crunch, courtesy of ace axeman Kenny Greenberg, who joined Chesney's band in May.
"Putting rock 'n' roll guitar on country records has become sort of a trademark of mine," says Greenberg, a Cleveland native, raised on the music of Jimi Hendrix and the Allman Brothers Band, who moved to Nasvhille at the age of 21. "My first few years in town, I was playing on some records and doing some producing. But then one day a producer named Tony Brown, who was the head of MCA, told me, 'You know, you should play rock guitar on some of our country records.' He got me on some stuff, and things exploded from there."
Since then, Greenberg, who was recently named Guitarist Of The Year by the Academy Of Country Music, has racked up hundreds of sessions and established himself as one of Nashville's first-call players. The list of names on Greenberg's CV is fairly mind-boggling, but we cherry-picked an even 10 to ask him about.
"The acclaim and everything that comes with doing what I do is fantastic," says Greenberg. "But the best things are the relationships and the learning experiences. If you're lucky enough to sit in the studio with great artists, something's bound to rub off on you. You just have to keep your eyes and ears open."
Joan Baez
"This guy named Wally Wilson, who's now a record executive, was my songwriting mentor. We were in a band together that nobody ever heard of, The King Snakes, and one day he said to me, 'Kenny, I've got a friend who knows Joan Baez. You and I are going to get on a plane, we're going to go meet her, and by God, we're going to talk her into letting us record her record.' And, of course, I said, 'What?!' [laughs] The whole thing sounded crazy.
"So we flew to San Francisco, went to Joan Baez's house, and he talked her into letting us make records with her. He's just that kind of a guy.
"It was fucking unbelievable! Joan had the best stories of anybody I've heard. I did two records with her, and at one point I even got to play on stage with her. It was the Newport Folk Festival, and it just so happened to be a tribute show to her. Her usual guitar player couldn't make it, so I did the gig. Talk about incredible. She's an icon, somebody who's really made an important mark on society."
Brooks & Dunn
"I played on Kix Brooks' solo record, before he was even in Brooks & Dunn, and that was kind of a pivotal moment for me. But when Brooks & Dunn formed and I started playing on their albums, things really started happening. Working with them really put me on the map as a country session guy.
There's a couple of songs of theirs, Ain't Nothing 'bout You and Only In America, that were very big for me – Ain't Nothing 'bout You, in particular, because it's got a real rock 'n' roll rhythm guitar thing going on. The rock guitar was prominently featured.
The song Red Dirt Road is another really cool one for me because I played slide on that. The whole Brooks & Dunn era really did wonders for my career. They're great guys, great friends of mine – totally amazing people."
Kenny Chesney
"The thing about Kenny Chesney is, he knows exactly who his audience is, and he knows how his songs should go. When you go into the studio with an artist, there's always varying degrees of how involved he or she is going to be. With Kenny, he's involved as much as is humanly possible. You can count on it.
"He picks really great songs, and he writes really great songs – right there, that makes it a lot easier for me. A guitarist always wants to play on something amazing – it's inspiring. You sit down with Kenny and he'll tell you what he wants. He might not describe it note-for-note, but he'll give you the feeling of what he's looking for. And you know that if he stops you, if he says, 'No, that's not it,' he'll always be right. He's totally tuned in to his audience. It's weird.
"A great guy. Unpretentious, no bullshit – the real deal. And we've become friends. I can't say enough about the guy."
Sheryl Crow
"I just played on a couple of songs for her new record. Sheryl is such an all-around talent. She's a record producer, no doubt about it. She knows her way around a studio, she knows about all about guitars, and has a great understanding of amplifiers and gear.
"What's funny is, she was talking about this being her 'Nashville record' – that's kind of how she's viewing it in the marketplace. Somebody in the studio said to her – and I think this was a great observation – 'You know, Sheryl, here in Nashville we've been trying to make Sheryl Crow records for the last 15 years!' [laughs] She got a big kick out of that.
"But it's true. We're all trying to get those sounds on My Favorite Mistake. I can't tell you how many sessions I've been on where somebody brought that song up as a reference. Or Every Day Is a Winding Road – what a sound on that one, too.
"Her new stuff is classic Sheryl Crow. She's very comfortable with who she is, and writes great songs. I was totally honored to be asked to be part of what she's doing."
Etta James
"Amazing! An amazing experience. What's strange is, I played on her album Seven Year Itch, and then on her follow-up, Stickin' To My Guns, she recorded one of my songs, Cry Like A Rainy Day, but I didn't play on that.
"Working with Etta James was definitely a highlight for me. She was getting on in years by the time I worked with her, and of course she had a history of drug addiction. But when you sat and talked with her, all of that stuff just disappeared. She was the nicest person in the world. Smart, too. I think she was a very smart lady with a lot of demons.
"Barry Beckett was the producer on the records, and he was a huge influence on me. He influenced anybody who was ever in the studio with him. He was a Muscle Shoals guy, so working with him was very educational.
"And Steve Cropper, too! Oh, man, I was scared to death. This was before I really broke into the scene, and there I am with Steve Cropper. What do they need me for, you know?"
Toby Keith
"He's extremely knowledgeable about the history of music. I'll be in the studio with him, and he can name you every song – who wrote it, produced, he'll quote you lyrics. It doesn't matter if it's Roger Miller, Hoyt Axton, Willie Nelson, David Allen Coe – you name it, he knows it. So I said to him one day, 'Toby, you love all those songs, you should do some of them.' So we formed a band and booked a gig in New York. He didn't want to use his own name, though, so called it The Incognito Banditos.
"We recorded ourselves. On his last couple of albums, there's some extra songs, which is us as the Incognito Banditos. I got to be the producer on those songs.
"I've played on Toby's records for the last 10 years. He's a sharp guy. He's the record label, the songwriter, the artist, but in every respect he's exactly the way he seems – laid-back and easygoing. But the important thing is, his songs are great, which makes it extremely easy for me."
Willie Nelson
"My favorite thing about recording about Willie Nelson actually happened on my birthday. I remember it was a Sunday and they couldn't get everybody to come in to work, but I went in and we recorded a version of Dylan's Gotta Serve Somebody.
"I remember sitting across from Willie – he was in a booth with his old Baldwin amp, and I was out on the floor – and we were just trading licks on guitar. There I am, it's my birthday, I'm playing Gotta Serve Somebody with Willie Nelson, and I just thought… It don't get any better than this!" [laughs]
Lionel Richie
"I think I played on eight tracks or nine tracks on the Tuskegee record, and let me tell you, it was an incredible experience. And the best thing was watching just watching Lionel Richie sing. Everything he did was so effortless.
"There were all of these guest stars on the album – Kenny Chesney, Willie Nelson, all of these big artists – and of course, everybody was there to sing a different song with Lionel. He would come in, tell everybody what he wanted, and while we were playing, he'd go to the mic and sing… and he sounded just like he did 30 years ago! I couldn't believe it.
"A natural singer, and just the nicest guy in the world."
Bob Seger
"I've done two records and a tour with Bob Seger, and I can honestly say, learned a lot about playing rock 'n' roll guitar from him.
"He's a super upbeat guy who likes to laugh. What I didn't know at first was, on a lot of his records, he either came up with the guitar parts or he played them. When I recorded with him, it was the same thing. I'd play something and he'd go, 'Yeah, I like that, but… ' and then he'd take the guitar and play something incredible. He's got great ideas. He's real garage band raw. If I played something too sophisticated, he'd be like, 'Naw, that needs to be more angry.' He'll sit there and play you this real Detroit rock, gritty and dirty stuff. You just watch him and go, 'Man, I can't believe what I'm hearing.'
He's similar to Chesney in the way that he really knows how he wants his songs to sound. Such an ear and instinct. The song That Strut – he played all those parts in the studio. So when we rehearsed it for a tour, he took my guitar and said, 'No, here's how we did it when I recorded it.' I'm standing there thinking, 'Wow, I'm watching Bob Seger show me how to play the guitar.'
"He's super-nice about it... but he's always right."
Tricia Yearwood
"She's one of the best singers in country music. She recorded one of my songs called Bring Me All Your Lovin', and I got to play on it. That was one of my first songs. Being in the studio and playing the guitar, and listening to Tricia Yearwood on my headphones singing a song that I wrote – that was pretty cool!"


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"Mapping Maciunas" at Stendhal Gallery
Stendhal Gallery is pleased to announce the exhibition, "George Maciunas" featuring the Fluxus maestros' lifelong interest in the production of charts and diagrams to historicize, clarify and advance the experimental art of his time.
Throughout his life, Maciunas prided himself in the creation of "learning machines," taking the form of elaborate charts documenting key eras of history and art. Maciunas himself was a learning machine, having studied art, graphic design and architecture at Cooper Union (1949-1952), architecture and musicology at the Carnegie Institute of Technology in Pittsburg (1952-1954) and art history at the Institute of Fine Arts at New York University (1955-1960).
As a student, Maciunas had developed charts, such as his, "Chronology of Russian History: Oct. 3, 1914-1934" (1953-1954), to further his perspective of the subject. In 1958, he turned his attention to an "Atlas of Prehistoric Chinese Art." Attending N. Y. U., Maciunas even drew up several, "History of Art Charts." As a student of history, art, and art charts, Maciunas described his diagrams as a "recategorization of all fields of knowledge according to a more logical system."
These charts had educational and creative purposes. "It is very easy to locate all present art forms within the categories," Maciunas stated," and find categories for which no art examples exist yet." The charts also had a promotional purpose in demonstrating that Fluxus was heir to a number of 20th century avant-garde movements continuing a subversive artistic subculture.
As a proselytizer of the contemporary avant-garde, birthing difficult performative works and unpretentious objects incomprehensible to the public as artistic statements, Maciunas was forced to position these new activities into a context the public could find precedents and comfort.
The documentation of Fluxus personalities and events lead to the creation of Maciunas' "Diagram of Historical Development of FluxusŠ" (1973), arguably a masterwork, which posits Fluxus in a continuum of radical art history brought center stage by Dada, Marcel Duchamp and John Cage.
Setting his sights on more practical matters, Maciunas undertook a 1968-1969 grant supported by the Carnegie Corporation of New York to improve arts education in the United States. His research for "Proposals for Art Education," resulted in a series of charts and diagrams including "Contemporary Man" and a "Curriculum Plan" for both art majors and non-major programs.
Maciunas' diagram for "Contemporary Man" pits "Literate Man" (Plato, Darwin, Harpo Marx) against "Post-Literate Man" (Cezanne, Joyce, Groucho Marx). His view of humanity is expressed as a struggle between the hedgehog (obstinate, determined) and the fox (curious, quick, skeptical). This is one of Maciunas' most far reaching charts, ranging beyond art and cultural history to express universal approaches to thought and practice.
In his detailed chart for "Curriculum Plan," Maciunas cites areas of arts education training in "Object Art," "Environmental Art," "Graphic Art (& Design)," and "Aural Art." The chart, collaged by Maciunas, is itself a work of art, composed of similar graphic elements found in Fluxus publications.
Maciunas makes clear his devotion to charts, diagrams and atlases, devoting a separate section to them in his resume. The rejection of a 1976 grant to the Guggenheim Foundation to work on a "Diagram of History of the Avant-Garde, Particularly its Development from Futurism, Dada, Duchamp, Surrealism, John Cage to Happenings, Events and Fluxus," affirmed his commitment to a lifetime pursuit of learning until shortly before his death.
Utopian planner and urban pioneer, leader of a cultural avant-garde, scholar, graphic designer, architect, Maciunas by necessity prioritized and categorized the various components of his life. These obsessions and passions are made manifest in the charts and diagrams on display at Stendhal Gallery.
By John Held Jr.


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The Kathryn W. Davis Village is COA's "greenest" housing complex. The houses in the village are heated by a biomass pellet boiler system and are incredibly energy efficient. All six houses have a living room, kitchen, and dining area on the ground floor, replete with vibrant color schemes and comfy furniture. Upstairs, two floors house eight residents in large student rooms with communal bathrooms boasting composting toilets.
More information on the story and sustainable efforts behind Kathryn W. Davis Village is available here.


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We also recognise that the decisions financial practitioners make on how to invest beneficiaries' money entrusted to them shapes the society they will live in. Further, we argue that the differentiation between 'shareholders' and 'stakeholders' which is often produced to justify the status quo is inherently false. Today, the majority of shares are owned (through savings and pensions) by the very people who make up what we think of as societal stakeholders. That the majority of these same stakeholders perceive the 'system' to have failed them is becoming increasingly clear around the developed world and has been noted by many, most recently here by the Prime Minister.
I propose in my paper entitled "The Why Question", that the current 'professional' understanding of investment theory which seems to frame the financial world almost as entirely separate from the real world that ordinary investors and beneficiaries live and work in was a main contributory factor to the crises in 2008 and the increasing level of public distrust towards business and finance that resulted from it, and which is threatening the sustainability of the free market model.


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Charlotte Bobcats @ Houston 4/9/10
The Bobcats had a lot more to gain than the Houston Rockets in this one. With Miami dropping a surprising loss against the Pistons on the same evening, Charlotte could have inched within a game of the East's sixth seed with a win in Texas but the Rockets had other plans. Behind a tremendous fourth quarter scoring burst from PG Aaron Brooks, Houston sent the Bobcats packing 97-90. Bobcats drop to 42-37, still two games back of Miami.
AP recap here | Box score here
They Just Aren't The Same Without Him
Stephen Jackson has his well-documented faults (not to mention a very suspect, very expensive contract) but this was another game that shows us just how valuable JAX is to the Charlotte Bobcats success. For all of Gerald Wallace's efforts this season (All-Star selection, rebounding boost), Stephen Jackson is clearly Charlotte's MVP.
Coach Larry Brown made good on his promise to rest Jackson as the team closes in on the postseason. Brown stated that he wasn't worried about Playoff seeding now that they've clinched, he's more worried about being effective once they start playing. I can't argue with that logic. Seeing the team play without Stephen Jackson tonight was a nice reminder.
Bobcats also rested Tyrus Thomas (thumb) and didn't dress Theo Ratliff, who is still away on a personal matter. Charlotte will need them all healthy and ready for the Playoffs.
A Few Positives From a Tough Loss
- Tyson Chandler. As terrible as Tyson was for four fifths of the season, he's picking an awfully good time to return to form. Chandler with another big defensive game: 12 rebounds and 5 blocks to go along with 7 points. Two of those points were collected on, you are not going to believe this, a NON-DUNK! I saw it with my own eyes, folks. First points of the game. Tyson backs in Luis Scola, turns and rattles in a fadeaway 5-footer. In related news, an image of Jesus was seen in a Smuckers jar last night in Bessemer City, NC.
- D.J. looks confident. His numbers weren't as good as they were against New Orleans but I like the body language. He had a nice open court stop & pop in the first half that wouldn't have taken much less made earlier in the year.
- Larry Hughes looks better. Hughes stepped in and did a decent job as Jackson's replacement going 5-13 for 16 points. My take on The Great Hughes-Graham Debate of 2010 goes like this: Coach Brown knows what Graham is going to give him. He's a given. Brown is intrigued enough with Hughes and his abilities as a proven dynamic NBA scoring guard that he's willing to gamble with him now in order to have another major scoring asset come Playoff time. That's a good gamble to make because the 'Cats will need all the scoring they can get.
Some Rockets Observations
- Shane Battier wore a green Masters jacket on the bench. I swear I'm not making this up. Something gives me the feeling that Battier and Ron Artest never hung out in the offseason.
- I wonder how strange it is for Rick Adlemen to watch Gerald Wallace today, almost ten years after he let the raw draft prospect languish at the end of Sacramento's bench? Did Adlemen ever guess that this guy might one day be an All-Star, a legitimate post threat and one of the League's top rebounders?
- Chase Buddinger = Adam Morrison gone right. In fact, Buddinger shouldn't even be compared to white wing players at all. He's got incredible athleticism that allows him to go to the basket when his outside shot isn't falling. After Chase elevated and threw one down on Tyson Chandler, Chandler seemed more confused than upset. It was like he just witnessed a Pug best a Cheetah in a footrace.
- The Rockets must lead the league in "Undersized Players." It seems everybody on the team is giving up a few inches or a few pounds at their respective positions: Kurt Lowry, Aaron Brooks, Luis Scola, Chuck Hayes, Kevin Martin, etc.
- Speaking of Chuck Hayes, he's officially listed as the team's starting center and he's a maximum 6'5″ although he's listed an inch taller but he's built like a cement truck. Always a fan of undersized big men. Charles Barkley, LJ, and now Craig Smith and Hayes. Gotta love 'em.
Only three games left and then we got Playoffs baby!


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"A profusion of color! This scene called me to create it to splash onto a wall in a flurry of textures, shadows and visual delights. To me, it's my impression of God's summer indulgence, His profligacy, draped on canvas." Julie
This piece is #1 of a 3-part tryptic
(Your purchase of all 3 will bring a 15% discount.)
The tryptic is part of my series: "God's Profligacy of Seasons"
Winter ~ Spring ~ Summer ~ Autumn
Limited edition of only 30, each piece is digitally signed and numbered.
My process: "I distilled my photo down digitally to unveil the essence of summer's warm colorful profusion, by artfully altering, simplifying and softening it down to its inner glory.
Free and safe shipping!
Printing and shipping time varies based on size and presentation, usually between 10-17 days.
All prints are digitally signed and numbered.
All art pieces are as (very) limited editions of 60 or less.
Canvas Wrap - Image is vibrantly printed on textured canvas cloth, sealed to a fade-resistant satin finish, and stretched tight around a wood stretcher-frame. Depth of stretcher 1.5-2.0" depending on size. Made in USA.
Canvas Wrap Framed - Imagine this image "floating" in a studio frame dark enough to bring out these glorious colors. For this art, the frame can be included as part of this and not as a separate purchase. It is 2" deep from the wall and made of strong black wood with 2 large comb hangers. Made in the USA.
Artistic Variations Available - Anything is possible! I can transform this into color versions to work beautifully with your space and style. Prices for these variations are very reasonable. Email your request.
We'll Frame it For You - The above product's frame can be ordered right here on this page. For other art on this site is a separate sale, see our Framing page. Any styles and sizes! From a 60x40" wrapped canvas floating in a studio frame to an 11x14" printed on metal, we'll create just the right look for your space.
Email your requests: firstname.lastname@example.com


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Holidays in the Italian Alps & Dolomites AD Travel has years of experience offering tourist incoming services and winter holidays for individuals, families and groups who wish to visit the best resorts the Italian Alps and Dolomites have to offer. Need a hand? Contact us Organised tours AD Travel plans and organises excursions and tours in some of the most beautiful placess around the Italian Alps. Discover them on foot, by bike, on the Bernina Train or relaxing at a thermal spa! Organise a group tour Making dreams come true For generations our family has worked in tourism and we are dedicated to helping people to discover the best our territory has to offer and to love and appreciate it as we do. - Samanta Antonioli
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text: Jacfico theme has a built-in: Unlimited possibilities to change the color, background color, pattern of almost every element or the area Drag and drop Content Builder (new) 130+ shortcodes Shortcodes generator built in WYSIWYG editor 3 built-in sliders (Revolution slider and ShowBiz inclusive ). 15 custom widgets 9 Predefined color variations. Over 480 vector font icons (new) Animation engine (animation site element on page scroll) (new) One click switch between strecheched and boxed layout. Custom skinable menu with icons Custom post types for sliders and portfolio Support for custom post formats (image, video, audio, aside, quote, chat, link) Sophisticated, well organized , fully rebrandable admin panel with a lot of options Custom SEO support Widget logic system (you decide which widgets will be displayed on which pages) Support for Opengraph Google Fonts, Adobe Edge and FontsSquirel Support (6 additional font@face fonts included in package) Translations ready (.po file included) …and much more


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Coming from I-270 |
Copyright © 19882000 Microsoft Corp. and/or its suppliers. All rights reserved. http://www.microsoft.com/streets
© Copyright 1999 by Geographic Data Technology, Inc. All rights reserved. © 1999
Navigation Technologies. All rights reserved. This data includes information taken with
permission from Canadian authorities © Her Majesty the Queen in Right of Canada. ©
Copyright 1999 by Compusearch Micromarketing Data and Systems Ltd.


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On the SitePoint PHP blog editor Bruno Skvorc has written up a post that talks about why a string is called a "string" going back through the history of the term and discovering its origins.
Why is a string called a string? Have you ever given this some thought? We never use such a word in contexts other than programming for a set of letters sticking together, and yet – in programming it's as pervasive as the word "variable". Why is that, and where does it come from?To find out, we have to tackle some related terms first. History lesson time!
He starts with these related terms including "font", "uppercase" and "lowercase". He talks about the printing process and how the "stringing together" of the series of characters might have been how customers using the press were charged. He then shifts over to the academic world for background there relating to a series of numbers and letters used in decision problems. The term caught on and showed up in several other academic papers over the years ending up eventually in programming language definitions and examples.


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Call us to talk to a Registered Nurse
For Healthcare Questions call 1.866.KINDRED
Not only is our clinical approach patient-centered, but so is everything else about you and your loved one's experience while you're with us. At Kindred, we feel that we must provide a patient experience that is second to none.
We welcome your feedback so we can better meet your needs, so please reach out to any of our team members when you need us. Your voice is a critical part of our effort to provide the best experience possible.
Kindred Hospital provides or assists you and your loved ones in obtaining interpretation or translation services as necessary and addresses the need of those with vision, speech, hearing and cognitive impairments.
To read the information above in multiple languages, click here.
To read the entire communications policy, click here.


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History books set the end of the Middles Ages in Europe as the 15th century, an age of extremely important and historical political and social events. The invention of the printing press, Columbus' voyage to America and the expulsion of the Sephardic Jews from Spain, first, and the annihilation of the Moriscos afterwards, are only some of the most highlighted milestones in history text books. Nevertheless, civil history is made up of events that differ greatly from the big scientific and political events. In Andalusia, the 15th century was the century of the plague epidemics. Seville, Malaga and Granada witnessed thousands of their inhabitants die while Isabel and Ferdinand tried to finish their conquest of Al Andalus.
In Cordova, the year 1488 is the darkest year of the late 15th century due to the Bubonic plague which devastated the city. Only a few years after having been the center of the Christian court, the city suffered from an illness of which little was known until the recent publication in Anuario de Estudios Medievales (Medieval Studies Yearly) by University of Cordova professor Margarita Cabrera. Her research was carried out based on notarial documents and bundles of papers held in the Archivo Histórico Provincial (Historical County Archives) and according to which the deaths from the plague reached their peak in the summer months of 1488.
The city shut down, the nobility ran off to die in the countryside, and meanwhile the notaries public could not keep up with writing up all the wills. In fact, according to Margarita Cabrera there is a remarkable difference in the number of wills in the summer months (in June alone 129 were drawn up and in July another 73) and the normal number in other times (an average of about 5.75 per month). Furthermore, the research established two means of infection of the plague based on the documents. The first, through normal trade relations between Cordova and Seville, affected by the plague in 1486 and 1487, and the other, through contact with the Muslim prisoners taken after the conquest of Malaga in 1487.
According to Professor Cabrera, based on the writings of the chroniclers of that time such as Andrés Bernáldez, the consequence of that epidemic was a truly "demographic catastrophe" in a city with a population at the time of approximately 25,000. Bernáldez reported 15,000 deaths, although experts consider this number somewhat exaggerated. However it was, what is clear is that the plague did not discriminate between social classes or religions, although Margarita Cabrera found interesting cases of survivors such as that of the juror Sancho de Clavijo, who in spite of spending months caring for his sick family managed to survive the illness.