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Some 800 members of the Bani Yas tribe, led by the Maktoum Family, settled at the mouth of the creek in 1833. The creek was a natural harbour and Dubai soon became a center for the fishing, pearling and sea trade.
By the turn of the 20th century Dubai was a successful port. The souk (Arabic for market) on the Deira side of the creek was the largest on the coast with 350 shops and a steady throng of visitors and businessmen. By the 1930s Dubai's population was nearly 20,000, a quarter of whom were expatriates.
In the 1950s the creek began to silt, a result perhaps of the increasing number of ships that used it. The late Ruler of Dubai, His Highness Sheikh Rashid bin Saeed Al Maktoum, decided to have the waterway dredged. It was an ambitious, costly, and visionary project. The move resulted in increased volumes of cargo handling in Dubai. Ultimately it strengthened Dubai's position as a major trading and re-export hub.
When oil was discovered in 1966, Sheikh Rashid utilized the oil revenues to spur infrastructure development in Dubai. Schools, hospitals, roads, a modern telecommunications network … the pace of development was frenetic. A new port and terminal building were built at Dubai International Airport. A runway extension that could accommodate any type of aircraft was implemented. The largest man-made harbor in the world was constructed at Jebel Ali, and a free zone was created around the port.
Dubai's formula for development was becoming evident to everyone – visionary leadership, high-quality infrastructure, an expatriate-friendly environment, zero tax on personal and corporate income and low import duties. The result was that Dubai quickly became a business and tourism hub for a region that stretches from Egypt to the Indian sub-continent and from South Africa to what are now called the CIS countries.
Since the 1960s, Sheikh Zayed bin Sultan Al Nahyan, then ruler of Abu Dhabi, and Sheikh Rashid bin Saeed Al Maktoum had dreamed of creating a federation of the Emirates in the region. Their dreams were realized in 1971 when Dubai, Abu Dhabi, Sharjah, Ajman, Umm Al Quwain, Fujairah and (in 1972) Ras Al Khaimah, joined to create the United Arab Emirates.
Under the late Sheikh Zayed, the first President of UAE, the UAE has developed into one of the richest countries in the world with a per capita GDP in excess of US$17,000 per annum.
In the 1980s and early 1990s, Dubai took a strategic decision to emerge as a major international-quality tourism destination. Investments in tourism infrastructure have paid off handsomely over the years.
Dubai is now a city that boasts unmatchable hotels, remarkable architecture and world-class entertainment and sporting events. The beautiful Burj Al Arab hotel presiding over the coastline of Jumeira beach is the world's only hotel with a seven star rating. The Emirates Towers are one of the many structures that remind us of the commercial confidence in a city that expands at a remarkable rate. Standing 350 meters high, the office tower is the tallest building in the Middle East and Europe.
Dubai also hosts major international sporting events. The Dubai Desert Classic is a major stop on the Professional Golf Association tour. The Dubai Open, an ATP tennis tournament, and the Dubai World Cup, the world's richest horse race, draw thousands every year.


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Brad Childress has one big regret about the 2010 season, his last as head coach of the Minnesota Vikings. But it's not the one that likely comes to everyone's mind first.
Roaming the hallways of the NFL.com and NFL Network offices in Culver City, Calif., on Wednesday, Childress opened up about his unceremonious departure from Minnesota last November.
The Vikings decided to fire Childress 10 games into the season for many reasons. Their 3-7 record, for one. Their embarrassing 31-3 home loss to the Green Bay Packers in Week 11, another. But perhaps the biggest reason was Childress' odd jettisoning of Randy Moss -- without telling owner Zygi Wilf first -- just four weeks after the team traded for the receiver.
"I should have gone up the chain," Childress now admits.
Childress said he had no such regrets about bringing back the Vikings' other big headliner, quarterback Brett Favre, for another season. The courting of Favre last August brought vitriol from some corners because of his age (40) and the distraction he created by missing minicamp. But the Vikings were fresh off an NFC Championship Game appearance in 2009, and Favre was the man who took them there. Childress said it was a no-brainer to chase Favre rather than go into 2010 with Tarvaris Jackson at quarterback.
"(Favre) had his best season ever his first year (in Minnesota)," Childress said of Favre's 33-touchdown, seven-interception campaign. "Could you do more with Brett Favre? Absolutely you could."
It's easy to criticize in hindsight, after Favre stumbled through a 24-turnover, injury-marred campaign.
"We made a conscious effort to bring everybody back," Childress said. "What did we get for it? I got fired, and (Favre) got hurt. Did I feel like he was as sharp as he could've been? No."
As for the Moss fiasco, Childress said he wanted to acquire a player who would be a difference-maker for the Vikings after they got off to a disappointing 1-2 start. They needed a player who could stretch the field while Sidney Rice recuperated from an injury.
Enter Moss. He made a difference all right, unfortunately tipping the needle in the wrong direction.
"He called me and said, 'I can't wait, I can't wait. I feel like I'm coming home again,' " Childress recalled.
Despite Moss' reputation for loafing and being a distraction, Childress believed the receiver would be more mature with 12 seasons under his belt. He believed Moss wouldn't be a distraction in the locker room.
Uh, not so much.
"We had good guys, by and large," Childress said, "(but Moss) walked in the locker room and vomited on it."
Childress had tried to develop a better locker room since becoming the Vikings' head coach in 2005. He inherited a team coming off the "Love Boat" scandal and a quarterback (Daunte Culpepper) with a bad knee and not the best work habits.
By 2010, Childress believed he had righted the Vikings ship in the character department and could afford to take on Moss. But instead of augmenting that veteran leadership with another quality veteran, the Vikings got a 1-3 record, 13 receptions and at least as many headaches from Moss' tenure.
Was Childress the perfect coach? No. But he's a smart guy who started his career with a tiny stipend to assist Gary Moeller at Illinois. That was 1979. Childress' first job in the NFL was 26 years ago in Indianapolis with Rod Dowhower. Basically, he's a football lifer.
"Coaching is what I do," he said.
And he has enjoyed much success at it, despite being vilified since Leslie Frazier took over in Minneapolis. People forget how sought after Childress was while being a part of a Philadelphia Eagles staff that went to four consecutive NFC Championship Games. Charley Casserly in Houston called him, Ted Thompson in Green Bay called him and, of course, so did the Vikings. Remember, the failure in Minnesota wasn't solely his fault. He did what so many coaches do tactically, and got a lot further than many doing it.
That might be all he needs to answer for.


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How to Use
The Blackstone River meanders through the Blackstone River Valley for 46 miles from Worcester to Providence.
The Blackstone River provided the waterpower for the birth of industry in America with its 438-foot drop over a 46-mile length.
1. Based on Map 1, how would you describe the Blackstone River Valley's location?
2. Trace the route of the Blackstone River on Map 2. Why was the river so important to the region?
3. Locate Pawtucket, Rhode Island. Why is Pawtucket considered the birthplace of the American Industrial Revolution? If needed, refer to Setting the Stage.
4. Locate Worcester, Massachusetts. What role did it play in the economy of the region in the 19th century?
* The maps on this screen have a resolution of 72 dots per inch (dpi), and therefore will print poorly. You can obtain a larger version of Map 1 and Map 2, but be aware that the files may take as much as 45 seconds to load with a 28.8K modem.


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Burgess was built on a love of yachting. Founded in 1975 by Nigel Burgess, renowned sailor and worldwide single-handed ocean racer, he created a company with an obsessive eye for detail that put clients first every time.
From our original office in London in 1975 we now span the world, with branches catering to clients in major locations. Each office is led by an exceptional individual in keeping with the belief that quality is defined by the calibre of our team. Quite simply, we believe ours to be the best there is. Meet them and judge for yourself.
Chief Executive Jonathan Beckett has led Burgess to become the world's number one superyacht brokerage house. In recognition, in 2001 we became the first yacht brokerage firm ever to receive the prestigious Queen's Award
~ Experience the Burgess Difference ~


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19-year-old shot at Palm Coast birthday party
Gunman at large; victim has several previous arrests in Flagler County
PALM COAST, Fla. – Flagler County deputies are searching for a gunman after a 19-year-old man was shot in the face early Sunday morning at a large birthday party at a Palm Coast home.
The Sheriff's Office says Johnnie Thomas Jr., of Bunnell, was shot about 3 a.m. at the end of what it described as a loud party at a house on Pine Hill Lane. Thomas was taken by friends to Florida Hospital Flagler, where he was treated and released.
Thomas was arrested in April for firing a .32-caliber gun at Ralph Carter Park in Palm Coast when two groups of teens got into a brawl and with dozens of children nearby.
Thomas (pictured right in Flagler County booking photo) has been in and out of jail five times in the last five years, most recently last August on a trespass after warning charge.
Deputies say there were 75 to 100 people at the party when several gunshots were heard coming from the front of the house. Three or four shell casings were recovered at the entrance to the house.
While many scattered immediately after the shooting, several people did witness the shooting, but the gunman's identity was not known by investigators at the scene Sunday.
"This was a reckless act of violence, which endangered the lives of many. Incidents such as this need to stop before innocent lives are lost," Sheriff Jim Manfre said in a statement.
Anyone with information that could help investigators in this case is asked to contact Detective Annie Conrad at 386-586-4844 or Crime Stoppers at 888-277-TIPS (8477). Callers may remain anonymous and could be eligible for a reward up to $1,000.
Copyright 2013 by News4Jax.com. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.


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Colonial planktonic pelagic tunicate, adrift in the open ocean, forms rings and chains as it drifts with ocean currents. San Diego, California, USAStock Photo: 26833Species: Salp, Cyclosalpa affinisLocation: San Diego, California, USAFormat: Digital 3:2Other Names: salp chain, pelagic tunicateCopyright © Phillip Colla, all rights reserved worldwide.
Keywords: animal, animalia, california, chordata, creature, cyclosalpa, cyclosalpa affinis, invertebrate, jellyfish, marine, marine invertebrate, nature, notochord, ocean, oceans, outdoors, outside, pacific, pacific, pelagic tunicate, plankton, planktonic, salp, salp chain, salpida, salpidae, san diego, submarine, thalicea, thalicea, tunicate, tunicates, underwater, urochordata, usa, wildlife, zooplankton
Updated: February 23, 2020


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Cutting Edge
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Discharge at times of peak demand to avoid or reduce demand charges.
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I'm seeing progress as far as cleaning and decorating and I had my furnace repaired yesterday. I think we're going to have a white Christmas --- if the predicted rain doesn't melt all the snow.
I've been really tired, so I've been relaxing a lot these past few days!
I'm Dreaming of a White Christmas
Feeling good.........kids are home on Saturday...
Merry Christmas to all...
Feeling frustrated that I can't fall to sleep again!
I'm Dreaming of a White Christmas
I'm feeling sad for this place two years ago at this time of year there where always three or four people logged on .
This place was hoppin now it's floppin too sad.
'I will live in the Past, the Present, and the Future!' Scrooge repeated, as he scrambled out of bed. 'The Spirits of all Three shall strive within me. Oh, Jacob Marley! Heaven, and the Christmas Time be praised for this! I say it on my knees, old Jacob, on my knees!' (Charles Dickens A Christmas Carol)
There are so many guests that don't seem to join anymore!
I'm Dreaming of a White Christmas
I agree with you, Papa... I wasn't able to get on the past 2 days, I'd just get a blank page. Thought maybe the site was being updated, but now I see all these posts that were made.


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Quick Search: Choose Model and Year, then enter search topic.
Page: 89
Displaying the IMEI
The IMEI (International Mobile Equipment Identity) is a serial number that permits unique identification of the hardware in mobile radio equipment. This number allows different network providers to block the telephone in the event of misuse.
Call settings (PCM telephone)
Setting call forwarding
Call forwarding allows you to forward (divert) calls
to another telephone number (e.g. to your
answering machine).
When you first access the call forwarding system, the status of all call diversions in the network is automatically queried. The individual call forwarding functions cannot be selected during this time.
Activating and deactivating call forwarding is not supported in all networks.


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GRAND FORKS, N.D. (AP) — State and local leaders in North Dakota announced Thursday plans to build a new $1.5 billion nitrogen fertilizer production facility northwest of Grand Forks.
Gov. Jack Dalrymple and Grand Forks Mayor Michael Brown were joined by others in announcing that Northern Plains Nitrogen intended to build the new facility. The plant will produce nitrogen-based fertilizers by converting natural gas into anhydrous ammonia and urea.
"This plant will utilize the increasing supplies of natural gas across the region and will provide a reliable regional supply of fertilizer while reducing producers' dependence on imported products," Dalrymple said.
The company announced plans for a study examining specifications and infrastructure needs. If complete, the plant will produce more than 600,000 tons of nitrogen per year and employ approximately 135 full-time employees.
Construction is scheduled to begin in spring 2015, with an estimated completion date in spring 2017.


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Art by Tiffin woman on exhibit in Toledo
Through September, visitors at Toledo Museum of Art can view "Zeroes and Ones," an exhibit of art inspired by video games and technology. Among the works on display are three digital pieces by Patricia Banks of Tiffin. Many friends and family members attended the opening reception in May, and Banks was interviewed on WTTF.
Having lived in Texas much of her career, the artist returned to her hometown about three years ago. While trying to cope with the harsh winter of 2013-14, she started searching for contests to enter.
"I found one at the Toledo museum, so I sent some of my digital work in there and three of them were accepted," Banks said.
The titles are "Merbaby's Treasures," "Marble Shooter" and "Golden Fish." The museum's website said three dozen artists created 70 works that included short videos and two-dimensional art, using a variety of computer techniques. Banks said she was elated to be exhibiting in the same halls with thousands of famous artists.
Raised in Tiffin, Banks said she knew at age 5 she wanted to be an artist. After graduation from Calvert High School, she enrolled in the art program at North Texas State University (now the University of North Texas). Her maternal grandparents lived in the same area, so she stayed with them during her college years and remained there to pursue her craft. She lived in New York for a few years before coming back to Tiffin.
"I took forever to get used to the cold. When I first came up here, I sat all summer long on my sister's porch, wrapped in a blanket. I was freezing to death," Banks recalled.
At NTSU, she took a special interest in portrait drawings and various kinds of sculpture – hand-cast paper, alabaster, ceramics and bronze. Banks' resume includes numerous awards dating back to 1980, and she has been featured in exhibitions in Texas, Kentucky, New York and Ohio. She holds a membership in the Museum of Computer Art in Brooklyn, New York.
About a year ago, Banks discovered the sculpture studio and foundry of James Havens in Gibsonburg. She said she was excited to find a place where she could get back to crafting her own sculptures. An instructor at Owens Community College in Toledo, Havens was instrumental in organizing the Toledo Area Sculptors Guild. Havens' bronze sculpture, "The Chaplain," can be seen at Gibsonburg's Veterans Memorial. A community in Nebraska commissioned Havens to make a similar sculpture for their town.
"I helped him make that, and he was teaching me along the way. He's kind of my mentor … I help him and he helps me," Banks said, adding, "My main focus always should have been sculpture."
Anyone who has driven through Gibsonburg probably has noticed the "art in the park" that Havens has installed. Starting in 2004, he and members of the TASG have created a new outdoor exhibit each year. It has become an attraction for art lovers. Now a member of Toledo Area Sculptors Guild, Banks soon may add one or more of her pieces to a future display in Gibsonburg.
Last winter, Banks could not get to the foundry or to her studio at the Tiffin home of her niece. Having done digital art for a number of years, Banks decided to work in that medium until the weather improved. That was how she found the art museum's contest online.
Banks' website (fineartbypjbanks.weebly.com) has samples of her "Madonna and Child" series of limited edition prints and another series, "Highly Admirable People." The latter is a collection of drawings of people such as Mother Theresa, Gandhi, Einstein, Nelson Mandela, Helen Keller, Crazy Horse, John F. Kennedy and Martin Luther King Jr. The artist explained she does the portraits by using a group of photographs to complete a composite. They are called derivative art because she derives information from multiple pictures. Banks compares her method to what a screenwriter does to adapt a book into a movie script.
"I did a friend of mine, and I took pictures all around him. Then I sat with all these pictures. It's intimidating to try to draw somebody when they're sitting there for hours and hours, so I just use the photographs. But I consider that original work," Banks said. "Mostly, I take pictures of my art so I can exhibit them. You always have to have pictures."
She also had two photographs chosen for the Tiffin Art Guild's 2014 photography contest. No matter what the medium, Banks said people and animals are her favorite subjects. When she came back to Tiffin, Banks met Mark Levans and made arrangements with him to make prints of her art. Her digital pieces have nature, mythology and fantasy themes.
With the help of technology and her new-found connections, Banks said she wants to continue creating art "as long as my feet and hands work."
To learn more or purchase art by Patricia Banks, visit www.fineartbypjbanks.weebly.com. The Toledo Area Sculptors Guild has a Facebook page with information about that group.


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Wondering if anyone knows of any secret creams that would work best for eczema.
My nearly 10 month old daughter gets it a little on the bad side. So far I've used Pentatin mixed with Vaseline. I smear ti all over and so far it's prevented any flair ups....
Started by Amanda on 01/11/2009 in Moms Under 30
Last update on 01/12/2009 by Josephine


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Abstract linear spaces
|Algebra index
|History Topics Index
Cartesian geometry, introduced by Fermat and Descartes around 1636, had a very large influence on mathematics bringing algebraic methods into geometry. By the middle of the 19th Century however there was some dissatisfaction with these coordinate methods and people began to search for direct methods, i.e. methods of synthetic geometry which were coordinate free.
It is possible however to trace the beginning of the vector concept back to the beginning of the 19th Century with the work of Bolzano. In 1804 he published a work on the foundations of elementary geometry Betrachtungen über einige Gegenstände der Elementargoemetrie Ⓣ. Bolzano, in this book, considers points, lines and planes as undefined elements and defines operations on them. This is an important step in the axiomatisation of geometry and an early move towards the necessary abstraction for the concept of a linear space to arise.
The move away from coordinate geometry was mainly due to the work of Poncelet and Chasles who were the founders of synthetic geometry. The parallel development in analysis was to move from spaces of concrete objects such as sequence spaces towards abstract linear spaces. Instead of substitutions defined by matrices, abstract linear operators must be defined on abstract linear spaces.
In 1827 Möbius published Der barycentrische Calcul Ⓣ a geometrical book which studies transformations of lines and conics. The novel feature of this work is the introduction of barycentric coordinates. Given any triangle ABC then if weights a, b and c are placed at A, B and C respectively then a point P, the centre of gravity, is determined. Möbius showed that every point P in the plane is determined by the homogeneous coordinates [a,b,c], the weights required to be placed at A, B and C to give the centre of gravity at P. The importance here is that Möbius was considering directed quantities, an early appearence of vectors.
In 1837 Möbius published a book on statics in which he clearly states the idea of resolving a vector quantity along two specified axes.
Between these two works of Möbius, a geometrical work by Bellavitis was published in 1832 which also contains vector type quantities. His basic objects are line segments AB and he considers AB and BA as two distinct objects. He defines two line segments as 'equipollent' if they are equal and parallel, so, in modern notation, two line segments are equipollent if they represent the same vector. Bellavitis then defines the 'equipollent sum of line segments' and obtains an 'equipollent calculus' which is essentially a vector space.
In 1814 Argand had represented the complex numbers as points on the plane, that is as ordered pairs of real numbers. Hamilton represented the complex numbers as a two dimensional vector space over the reals although of course he did not use these general abstract terms. He presented these results in a paper to the Irish Academy in 1833. He spent the next 10 years of his life trying to define a multiplication on the 3-dimensional vector space over the reals. Hamilton's quaternions, published in 1843, was an important example of a 4-dimensional vector space but, particularly with Tait's work on quaternions published in 1873, there was to be some competition between vector and quaternion methods.
You can see a picture of the plaque commemorating where Hamilton discovered the Quaternions at THIS LINK and a (fanciful) engraving of when he carved the rules at THIS LINK.
In 1857 Cayley introduced matrix algebras, helping the move towards more general abstract systems by adding to the different types of structural laws being studied. In 1858 Cayley noticed that the quaternions could be represented by matrices.
In 1867 Laguerre wrote a letter to Hermite Sur le calcul des systèmes linéaires Ⓣ. His systèmes linéaires is a table of coefficients of a system of linear equations denoted by a single upper-case letter and Laguerre defines addition, subtraction and multiplication of of these linear sysyems. In this work Laguerre aims to unify algebraic systems such as complex numbers, Hamilton's quaternions and notions introduced by Galois and by Cauchy.
Laguerre's work on linear systems was followed up by a paper by Carvallo in 1891. In this paper he defines operators on vector functions and draws a clear distinction between operators and matrices.
To understand the difference between the notions of an operator and a matrix, it suffices to say that, if one changes the coordinate system, one obtains a different matrix to represent the same vector function, but the same operator.Another mathematician who was moving towards geometry without coordinates was Grassmann. His work is highly original but the notion of barycentric coordinates introduced by Möbius was his main motivation. Grassmann's contribution Die Ausdehnungslehre Ⓣ appeared in several different versions. The first was in 1844 but it was a very difficult work to read, and clearly did not find favour with mathematicians, so Grassmann tried to produce a more readable version which appeared in 1862. Clebsch inspired Grassmann to work on this new version.
Grassmann studied an algebra whose elements are not specified, so are abstract quantities. He considers systems of elements on which he defines a formal operation of addition, scalar multiplication and multiplication. He starts with undefined elements which he calls 'simple quantities' and generates more complex quantities using specified rules.
But ... I go further, since I call these not just quantities but simple quantities. There are other quantities which are themselves compounded quantities and whose characteristics are as distinct relative to each other as the characteristics of the different simple quantities are to each other. These quantities come about through addition of higher forms ...His work contains the familiar laws of vector spaces but, since he also has a multiplication defined, his structures satisfy the properties of what are today called algebras. The precise structures are now known as Grassmann algebras. The ideas of linearly independent and linearly dependent sets of elements are clearly contained in Grassmann's work as is the idea of dimension (although he does not use the term). The scalar product also appears in Grassmann's 1844 work.
Grassmann's 1862 version of Die Ausdehnungslehre Ⓣ has a long introduction in which Grassmann gives a summary of his theory. In this introduction he also defends his formal methods which had clearly been objected to by a number of mathematicians. Grassmann's justification comes very close to saying that he is setting up an axiomatic theory and this shows that he is well ahead of his time.
Cauchy and Saint-Venant have some claims to have invented similar systems to Grassmann. Saint-Venant's claim is a fair one since he published a work in 1845 in which he multiples line segments in an analogous way to Grassmann. In fact when Grassmann read Saint-Venant's paper he realised that Saint-Venant had not read his 1844 work and sent two copies of the relevant parts to Cauchy, asking him to pass one copy to Saint-Venant.
However, rather typically of Cauchy, in 1853 he published Sur les clefs algébrique Ⓣ in Comptes Rendus which describes a formal symbolic method which coincides with that of Grassmann's method (but makes no reference to Grassmann). Grassmann complained to the Académie des Sciences that his work had priority over Cauchy's and, in 1854, a committee was set up to investigate who had priority. We still await the committee's report!
The first to see the importance of Grassmann's work was Hankel. In 1867 he wrote a paper Theorie der complexen Zahlensysteme Ⓣ concerning formal systems where combination of the symbols are abstractly defined. He credits Grassmann's Die Ausdehnungslehre Ⓣ as giving the foundation for his work.
The first to give an axiomatic definition of a real linear space was Peano in a book published in Torino in 1888. He credits Leibniz, Möbius's 1827 work, Grassmann's 1844 work and Hamilton's work on quaternions as providing ideas which led him to his formal calculus.
Peano's 1888 book Calcolo geometrico secondo l'Ausdehnungslehre di H. Grassmann preceduto dalle operazioni della logica deduttiva Ⓣ is remarkable. It gives the basic calculus of set operation introducing the modern notation ∩, ∪, ∈ for intersection, union and is an element of. It was many years before this notation was to become accepted, in fact Peano's book seems to have had very little influence for many years. It is equally remarkable for containing an almost modern introduction to linear spaces and linear algebra.
In Chapter IX of the book Peano gives axioms for a linear space.
It is hard to believe that Peano writes the following in 1888. It could almost come from a 1988 book! The first is for equality of elements
Peano goes on to state the existence of a zero object 0 and says that 0a = 0, that a - b means a + (-b) and states it is easy to show that a - a = 0 and 0 + a = a.
1. (a = b) if and only if (b = a), if (a = b) and (b = c) then (a = c).
2. The sum of two objects a and b is defined, i.e. an object is defined denoted by a + b, also belonging to the system, which satisfies:
If (a = b) then (a + c = b + c), a + b = b + a, a + (b + c) = (a + b) + c,
and the common value of the last equality is denoted by a + b + c.
3. If a is an object of the system and m a positive integer, then we understand by ma the sum of m objects equal to a. It is easy to see that for objects a, b, ... of the system and positive integers m, n, ... one has
If (a = b) then (ma = mb), m(a+b) = ma+mb, (m+n)a = ma+na,
m(na) = mna, 1a = a.
We suppose that for any real number m the notation ma has a meaning such that the preceeding equations are valid.
Peano defines a linear system to be any system of objects satisfying his four conditions. He goes on to define dependent objects and independent objects. He then defines dimension.
Definition: The number of the dimensions of a linear system is the maximal number of linearly independent objects in the system.He proves that finite dimensional spaces have a basis and gives examples of infinite dimensional linear spaces. Peano considers entire functions f(x) of a variable x, defines the sum of f1(x) and f2(x) and the product of f(x) by a real number m. He says:-
If one considers only functions of degree n, then these functions form a linear system with n + 1 dimensions, the entire functions of arbitrary degree form a linear system with infinitely many dimensions.Peano defines linear operators on a linear space, shows that by using coordinates one obtains a matrix. He defines the sum and product of linear operators.
In the 1890's Pincherle worked on a formal theory of linear operators on an infinite dimensional vector space. However Pincherle did not base his work on that of Peano, rather on the abstract operator theory of Leibniz and d'Alembert. Like so much work in this area it had very little immediate impact and axiomatic infinite dimensional vector spaces were not studied again until Banach and his associates took up the topic in the 1920's.
Although never attaining the level of abstraction which Peano had achieved, Hilbert and his student Schmidt looked at infinite dimensional spaces of functions in 1904. Schmidt introduced a move towards abstraction in 1908 introducing geometrical language into Hilbert space theory. The fully axiomatic approach appeared in Banach's 1920 doctoral dissertation.
Article by: J J O'Connor and E F Robertson


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Frau Andrea Moll
Glasstr. 1
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Herr Alexandre Stienon
Sprachen: Deutsch, Englisch, Französisch
The HRDC is one of the seven leading research and development centers of the Saint-Gobain Group, HRDC is active in the main sector Innovative Materials. 220 colleagues from 10 nations develop, industrialize and optimize new products. Protecting these innovations by patents and trademarks is also a priority.
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Professor, Edinburgh Napier University
Earthwatchers investigated how rehabilitation of mangrove forests can slow erosion and support marine life in Gazi Bay, Kenya.
Earthwatch scientist Dr. Mark Huxham studies ecosystem functions and fish community structure and manages a major coastal mangrove restoration in Kenya.
Says Dr. Huxham: "My background is in marine and theoretical ecology. Like many other academic ecologists, I have become increasingly concerned about how we can use science to answer real questions of major importance to people, especially those who rely most directly on natural resources. This, combined with the fantastic opportunity to collaborate with people from Kenya and around the globe in a fascinating environment, is why I am working on this project."
"We believe that the surest route to successful mangrove conservation is to give local people direct benefits from our activities. They will then protect their mangroves," Dr. Huxham told Earthwatch. "Our research and restoration activities must therefore blend scientific excellence with equal measures of community benefits."
With support from the community and Earthwatch volunteers, twenty thousand mangrove trees have been planted in Gazi Bay since 2004. Dr. Huxham and his team have trained postgraduate students and scientists from the area, as well as from further afield - Madagascar, Tanzania, and Mozambique - on procedures and protocols of mangrove reforestation and monitoring. Two Ph.D. students have been completely funded through the project.
Earthwatch scientist Dr. Huxham studies ecosystem functions and fish community structure and manages a major coastal mangrove restoration in Kenya.
The Earthwatch research team worked to restore mangroves with local people from Gazi village in Kenya.


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And I don't mind you calling me for legitimate emergencies. It's part of the job, and I signed up for it.
My office message still says "We're closed, please call back during regular office hours for routine matters."
So please stop leaving messages like:
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At 8:30 a.m. tomorrow morning the phones will be rolled back, and you can start hassling Mary and Annie for questions about your tests, appointments, insurance authorizations, good shopping deals, safe ways to hang lights, and a myriad of other questions.
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Lancashire Bishop, Rt Rev. Julian Henderson has issued his Easter message.
The message is included in full below, along with a video which was recorded the day after the terrible events in Brussels.
Here is the full message.
I'm writing this Easter message the day after the devastating bombings in Brussels … a solemn reminder, like in Paris and Ankara and other less well known places in the world, that nowadays nowhere is safe and evil knows no boundaries.
Life is very uncertain. We could have been at Brussels airport or on the metro.
The world is not as God originally intended it to be and needs to be made new and redeemed. Sin has the power to disrupt and destroy lives.
Our hearts go out to the bereaved families and those injured, with both the assurance of our love and prayers and the Good Friday and Easter assurance that God and good will win the day.
It looked on that first Good Friday as if evil had triumphed, as Jesus, the Son of God; God in human form on earth, was crucified as a condemned criminal. There is no clearer picture of defeat.
But in God's eternal purposes it was a glorious victory as, using the familiar words of the Prayer Book, 'Jesus made there a full, perfect and sufficient sacrifice, oblation and satisfaction for the sins of the whole world' and the effectiveness of that sacrifice was confirmed three days later when God raised Him from the dead on that first Easter morning.
His resurrection was God saying His death had achieved what had been intended.
I know that many struggle to believe in so extraordinary a claim, but it has been and is a mainstream Christian belief for 2000 years and I argue that by looking at the evidence it is more reasonable to believe than to not believe.
As Christians we are people of hope, even in the darkest of moments, and so whatever your circumstances this Easter time, I pray that you will be drawn to put your hope and trust in Jesus Christ and find Him to be the Saviour, the Friend, the Lord He longs to be to all humankind. And it is in that sense that I wish you all a very happy Easter.


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