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Wednesday, April 13, 2011
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text:
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CEC publishes and distributes products designed to help practitioners work more effectively in the classroom. Learn more about CEC's publications and journals.
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text:
Zhu Shijie
Born: about 1260 in Yan-shan, near Peking, China
Died: about 1320 in Not known
|Main Index
|Biographies index
Zhu Shijie is also known as Chu Shih-Chieh. Little is known about his life other than that he wrote two outstanding mathematical texts. He must have been born around the time that Qin Jiushao died, which was about the same time that Yang Hui's first texts were appearing, and he probably was not very old when Li Zhi died. Zhu was, therefore, the last of these four great thirteenth century Chinese mathematicians but it would appear from his writings that he was unaware of the work of his three famous predecessors. The birth dates and death dates we give are based solely on the dates on which Zhu's two texts appeared. However these tell us that he must have been brought up while the Nan (Southern) Sung dynasty was being defeated by the Mongols.
Kublai Khan united the whole of China in 1279 and the Yuan dynasty came to power. The capital of the new united China became Dadu (today called Beijing or Peking) which Kublai Khan had built up as a walled city with splendid palaces and government offices. The unification of north and south China would have a significant effect on Zhu's life, for it allowed him to travel throughout the whole of China, and also allowed certain mathematical expertise which was previously known only in northern China to spread through the south. What little we know of Zhu is contained in the following quotation from the preface to the second, and most famous, of his texts. The preface, written by Mo Ruo, tells us that (see [4]):-
Zhu Shijie of Yan-shan became famous as a mathematician. He travelled widely for more than twenty years and the number of those who came to be taught by him increased each day.Yan-shan was near the new capital of united China at Dadu (today called Beijing or Peking). We see from this quotation that, as we mentioned above, the stability brought by the Mongol conquest gave Zhu opportunities to travel of which he took full advantage.
We know that Zhu wrote two books, the Suanxue qimeng (Introduction to mathematical studies) published in 1299, and the Siyuan yujian (True reflections of the four unknowns) published in 1303. These are remarkable works which led to George Sarton writing that Zhu was (see [1] where this is quoted):-
... one of the greatest mathematicians of his race, of his time, and indeed of all times.The Introduction to Mathematical Studies was intended for beginners. It appears to have been lost soon after it was first published, but it must have found its way to Japan and Korea for it was used there as a mathematical textbook. It was printed in 1433 in Korea and in 1658 in Japan but a Chinese version only became available again in the nineteen century when a 1660 Korean edition was translated back into Chinese. Ruan Yuan added a preface to a new version published in 1839 which also contains contributions by Li Shanlan. Zhu's book is based, as so many Chinese mathematics books were, on the Nine Chapters on the Mathematical Art. The book contains examples of computations with fractions and decimals giving results such as 1/16 = 0.0625 and 2/16 = 0.125. Zhu also explains the rule of three, areas and volumes, and the rule of false double position. Some of his discussions extend methods from the Nine Chapters. In dealing with simultaneous equations, Zhu certainly presented improvements, giving a method essentially equivalent to Gauss's pivotal condensation.
Some of Zhu's text, however, presents ideas going far beyond Nine Chapters. He treats polynomial algebra, and polynomial equations, by the "coefficient array method" or "method of the celestial unknown" which had been developed in northern China by the earlier thirteenth century Chinese mathematicians, but up till that time had not spread to southern China. There are still questions about this aspect, however, which have not been answered satisfactorily. In particular, how much was Zhu aware of Yang Hui's work?
Zhu's second book Siyuan yujian (True reflections of the four unknowns) marks the peak of Chinese mathematics and it was a long time before mathematics in China progressed beyond it. Like Zhu's earlier text, this one also seems to have vanished at some point. It survived in China probably until the second half of the eighteenth century when it appears to have become lost. When Ruan Yuan compiled the Chouren zhuan or Biographies of astronomers and mathematicians in 1799, he failed to find Zhu's text despite his expertise in tracking down old books. However some years later Ruan Yuan found a copy of the Siyuan yujian in Zhejiang (or Chekiang) province when he was governor there. He made a hand written copy which was sent to Li Rui for editing but Li Rui died before the work could be completed. Ruan's hand written copy of the Siyuan yujian was eventually printed.
The text of the Siyuan yujian which is available today is therefore not the one which was originally published by Zhu. The problem arises since the version which Ruan Yuan discovered was [4]:-
... extremely corrupted and teeming with errors.The present version has seven prefaces, two are dated 1303 the first being written Zhao Cheng and the second by Mo Ruo and Zu Yi. Of the other prefaces, one is written by Ruan Yuan and the others by later commentators. There are various nineteenth century commentaries on the text all of which make it harder to identify Zhu's original work. Let us examine what this remarkable book contains.
Following the prefaces, which we mentioned above, there are four figures. One of these is Pascal's triangle which gives the coefficients needed to expand sums of unknowns up to the eighth power. Zhu makes no claims for originality calling it:-
... the table of the ancient method of powers up to the eighth.You can see Zhu's Pascal triangle diagram at THIS LINK.
There are then four preliminary problems which Zhu uses to explain his methods of using polynomials to solve problems with 1, 2, 3, and 4 unknowns. In fact Zhu uses an extension of the "coefficient array method" or "method of the celestial unknown" to polynomials with several unknowns. Zu Yi, in his preface, says that Zhu is extending to four unknowns methods for dealing with two or three unknowns:-
... that the procedure of the celestial unknown had received previously to him.After these four examples to illustrate the methods, Zhu presents 288 problems which are divided into three volumes with 24 chapters. One of the most interesting aspects of this work is that Zhu, although still using the traditional Chinese approach of presenting mathematics through practical problems, does not in any sense make his examples realistic. Rather they are simply vehicles to present the methods. Therefore Zhu does not necessarily give the simplest solution to a problem, but rather often introduces complications explicitly designed to illustrate how to handle more complicated situations. Let us illustrate by giving one of Zhu's problems.
A right-angled triangle has area 30 bu. The sum of the base and height of the triangle is 17 bu. What is the sum of the base and hypotenuse?First let us take a straightforward approach. Suppose the base is x bu, the height is y bu, and the hypotenuse is z bu. Then the given information is xy/2 = 30 and x + y = 17. Eliminating y gives the quadratic x(17 - x) = 60 or x2 - 17x + 60 = 0. Hence x = 12 or 5 but the base having the shorter length gives x = 5 bu, y = 12 bu, so z = √(52 + 122) = 13. Hence base plus hypotenuse is x + z = 18 bu. Zhu, however, wants to illustrate something more advanced than solving a quadratic equation.
Let t = z + x. Then substituting z = x - t, y = 17 - x into x2 + y2 - z2 gives
x2 - 34x + 2tx + 289 - t2 = 0. (1)But x2 -17x + 60 = 0, so substituting x2 =17x - 60 into (1) gives
0 = 229 - 17x + 2xt - t2 or x = (-229 + t2)/(-17 + 2t). Substituting this last expression for x into (1) and multiplying through by (-17 + 2t)2 gives
t4 - 34t3 + 71t2 + 3706t + 3600 = 0. (2)Although we cannot be certain that Zhu's methods are exactly what we have presented here, he certainly arrived at the equation (2). He has illustrated how to work with the four unknowns x, y, z, t and he can now illustrate how to solve a quartic equation.
Now (2) has the roots -1, -8, 18, 25 but Zhu only gives the correct answer t = z + x = 18 bu.
Here is another of Zhu's problems. It is phrased in terms of a right angled triangle, but the conditions are so artificial that he is really simply giving a system of equations. The sides of the triangle are x, y, z where z is the hypotenuse.
Given the relations 2yz = z2 + xz and 2x + 4y + 4z = x(y2 - z + x) between the sides of a right angled triangle x, y, z where z is the hypotenuse, find d = 2x + 2y.[Answer: d = 14 (Note x = 3, y = 4, z = 5)]
The following problem in the Siyuan yujian is reduced by Zhu to a polynomial equation of degree 5 (see [7] for a detailed solution as given by Zhu):-
Let d be the diameter of the circle inscribed in a right triangle (Zhu uses the relation d = x + y - z where x, y, z are as defined below). Let x, y be the lengths of the two legs and z the length of the hypotenuse of the triangle. Given that dxy = 24 and x + z = 9 find y.[Answer: y = 3]
The Siyuan yujian also contains a transformation method for the numerical solution of equations which is applied to equations up to degree 14. This is based on the method to solve polynomial equations which was rediscovered by Horner and Ruffini. Zhu also gives formulae
1 + 2 + 3 + 4 + ... + n = n(n + 1)/2,Similarly he gave the sum of
1 + 3 + 6 + 10 + ... + n(n + 1)/2 = n(n + 1)(n + 2)/6,
1 + 4 + 10 + 20 + ... + n(n + 1)(n + 2)/6 = n(n + 1)(n + 2)(n + 3)/24,
1 + 5 + 15 + 35 + ... + n(n + 1)(n + 2)(n + 3)/24 = n(n + 1)(n + 2)(n + 3)(n + 4)/120,
1 + 6 + 21 + 56 + ... + n(n + 1)(n + 2)(n + 3)(n + 4)/120 = n(n + 1)(n + 2)(n + 3)(n + 4)(n + 5)/720.
1 + 3 + 6 + 10 + ... + n(n + 1)/2 = n(n + 1)(n + 2)/6,
1 + 4 + 10 + 20 + ... + n(n + 1)(n + 2)/6 = n(n + 1)(n + 2)(n + 3)/24,
1 + 5 + 15 + 35 + ... + n(n + 1)(n + 2)(n + 3)/24 = n(n + 1)(n + 2)(n + 3)(n + 4)/120,
1 + 6 + 21 + 56 + ... + n(n + 1)(n + 2)(n + 3)(n + 4)/120 = n(n + 1)(n + 2)(n + 3)(n + 4)(n + 5)/720.
1 + 4 + 9 + 16 + 25 + 36 + ...By working out the second, third and fourth differences, Zhu solved the following problem.
1 + 5 + 14 + 30 + 55 + 91 + ...
1 + 6 + 18 + 40 + 75 + 126 + ...
1 + 8 + 30 + 80 + 175 + 336 + ...
1 + 5 + 14 + 30 + 55 + 91 + ...
1 + 6 + 18 + 40 + 75 + 126 + ...
1 + 8 + 30 + 80 + 175 + 336 + ...
If the cube law is applied to the rate of recruiting soldiers and it is found that on the first day 3 cubed are recruited, 4 cubed on the second day, and on each succeeding day the cube of a number one greater than the previous day are recruited, how many soldiers in total will have been recruited after 15 days? How many after n days?[Answer: 23400 soldiers after 15 days and n(n + 5)(n2 + 5n + 12)/4 soldiers after n days]
Article by: J J O'Connor and E F Robertson
Click on this link to see a list of the Glossary entries for this page
List of References (14 books/articles)
See this mathematician on a timeline
Mathematicians born in the same country
Additional Material in MacTutor
- Zhu's Pascal triangle diagram
Cross-references in MacTutor
- History Topics: A history of Zero
- History Topics: Overview of Chinese mathematics
- History Topics: Chinese problems
- Index of Chinese mathematics
- Chronology: 1300 to 1500
Other Web sites
- Dictionary of Scientific Biography


text:
Equal Nebraska is a grassroots group of dedicated, passionate, knowledgeable, professional individuals that come together to help other organizations across the state create and retain a community of equal access and opportunity for all citizens. We believe that an equal Nebraska is a better Nebraska and that we must work together to make that happen.
Equal Nebraska is a continuation and expansion of Equal Omaha. As a group we worked with various organizations and non-profits, bringing everyone together to ensure the passing of the Equal Employment Ordinance that would end discrimination in the workplace for the LGBT community in Omaha. The Ordinance passed, so we decided to roll up our sleeves and get back to work.
We believe equal is equal. We want all Nebraskans to have a fair chance at the good life, the better life. So, Equal Nebraska has expanded our mission and our goals, while we continue to work on equal employment, we also value voter access and the continued effort to make certain that no citizen of our state is disenfranchised from the fundamental right to vote, regardless of political affiliation.
This is currently a "site preview," barely scratching the surface of our larger plan. Our ambitions for an Equal Nebraska include a dynamic site that will be a resource for communities and individuals across the state to learn, get motivated and start participating in real change.
Change starts when citizens take notice – let's come together and make certain that Nebraska values include valuing everyone equally.


text: Endpoint security platforms have become commonplace on end-user devices and Internet-facing systems. In addition to malware and spyware protection, an enterprise-grade endpoint security platform typically provides some kind of device firewalling, intrusion prevention and data loss prevention capabilities. Symantec is the worldwide leader in enterprise protection market share for enterprises and consumers, according to Gartner. McAfee's enterprise protection platform ranks second in market share worldwide, Gartner said. Security experts say both firms have grown through extensive acquisitions over the years. CRN pits the two competitors head-to-head.


text:
Security Update: Debian Linux Kernel Local / Remote Vulnerabilitieslast updated in Categories Debian Linux, kernel, Linux distribution, Security Alert
Debian project today released a pair of security updates to plug at least ten security holes in its core called Linux kernel. Several vulnerabilities have been discovered in the Linux kernel that may lead to a denial of service or privilege escalation. This update has been rated as having important security impact.


text:
Who really knows Windows 8.1?
Windows 8.1 is FAR more than simply a new and/or improved UI Windows 8.1 "under the covers" Picking out the differences between Windows XP and Windows 8.1 or even between Windows 8 and Windows 8.1, improvements have been enormous and have remained unnoticed by a lot of people. So here's a glimpse of new… Read more
- Tags: 64-Bit, ADM, Boot, Developer, Enterprise Strategy, Gruppenrichtlinien, Hibernate, Internet Explorer 10, IT Pro, IT Professional, Maleware, Microsoft Services Broschü, Optimierung, Performance, PFE, Premier Developer Workshop, Premier Services, PSfD, RE, SDL, Secure Code, Security, Shutdown, Sicherheit, Windows 7, Windows 8, Windows 8.1, Windows Client, Windows Server 2012


text: I recently finished a route through Illinois. We have done Iowa, Wisconsin, and felt it was time to see our own state. The route takes in some of Bigdogs river to river ride, as well as some of Rhino's bridges. We rode a good deal of the Mississippi levee from just south of East St Louis to Cairo, Ill. We did this over 8 days. I know slow pace but the goal was to enjoy the scenery and see the sights. I am cleaning up the routes and will post up soon along with what will be a weak ride report since I do not have the skills that cannonshot or bigdog have when it comes to reports. Here is a video that will offer up some flavor to the ride. Strangely as it is, Illinois was not as boring as we thought! http://www.youtube.com/watch?v=Q7ZPk2J9g_s&feature=g-upl more to follow Routes are located further in. you can also find routes that were compiled by Big Dog. (thanks for that) If you have any questions PM me and I will help you sort them out.


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New York, April 11, 2014--The Committee to Protect Journalists congratulates Turkish investigative journalist and book author Ahmet Şık on being awarded UNESCO's prestigious Guillermo Cano World Press Freedom Prize. The annual prize, named after slain Colombian journalist Guillermo Cano Isaza, honors a journalist or organization that "has made an outstanding contribution to the defense of press freedom." Şık will receive the award on May 2 at UNESCO's headquarters in Paris, as part of the UNESCO celebrations for World Press Freedom Day.
"We are thrilled to congratulate Ahmet Şık on this much-deserved honor," CPJ Europe and Central Asia Program Coordinator Nina Ognianova said. "But we note that while Şık is being celebrated as a press freedom hero internationally, he is being prosecuted as a criminal at home. We call on Turkish authorities to immediately drop all charges against him and allow him to do his work without reprisal."
Şık, a defendant in the controversial Odatv case, faces charges that stem from his unpublished book, The Imam's Army, which was highly critical of a community led by exiled charismatic cleric Fethullah Gülen. In a separate case, the journalist is criminally charged in connection with making critical remarks about the police, judges, and prosecutors involved in the Odatv case. Earlier this week, CPJ sent a letter to Prime Minister Recep Tayyip Erdoğan expressing concern about the Turkish government's recent steps to restrict the independent Turkish media.


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Wells, Hill stepping up early
He was in the batting cage taking swings and he was in the outfield shagging flies. He was joking around and smiling and looked a bit trimmer, even if he said he actually reduced his offseason workload. Blue Jays center fielder Vernon Wells arrived to camp.
One question entering camp was, "Who would replace Doc Halladay as the clear team leader?"
Over the past few years, Wells has been a clubhouse leader — there is no question about that. But, he even admitted on Wednesday that he felt like the team was only "partly" his because Halladay obviously filled the leadership role. Now, as Wells arrives in camp as the longest-tenured Jay, things are different.
Since we've been down here, it's been clear that Aaron Hill has been ready and willing to step up as a leader for this young group. Manager Cito Gaston said Hill is willing to be vocal, if needed, and he's even had the younger guys in full uniform before it's required. That, and Hill's comments to the media have already shown his feelings on this group.
"I hope these guys know what kind of opportunity they have," Hill told me on Thursday. "If I'm seeing it, I just hope that they see it. I love seeing guys really get after it and fight for it. I hate seeing young guys, or anybody, that just expects to be given something. You should always work for whatever it is — not just baseball.
"I want to see the edge, the fire in these guys' eyes, to get out there and just kick some butt."
Asked whether he or Hill were going to be the team's leader, Wells smiled.
"I've got him on that one," Wells said. "It's weird. It's one of the first times that I've felt like this is my team."
The reality is that there is plenty of room for both Wells and Hill to become veteran voices in the room for the Jays, and that is a great thing for the ballclub. With so many young players, Toronto needs some guys to fill the lead-by-example void created by Doc's departure.
Wells did have more to say…
On general manager Alex Anthopoulos: "I think he's been amazing. To come in and make the kind of changes he made in your first year as the GM is impressive. He's got a direction that he wants to take this organization in and I think everybody is on board with it and everybody is looking forward to it. It's an exciting time, even though there could be a step backwards at certain points."
On whether the Jays are rebuilding: "I think 'retooling' is a better word. We've got guys that are close. We've got some young arms that got some experience last year and it's a period of getting to where we need to be. Whether that's now or next year, we're building toward something. We're building toward an organization that can be strong for years instead of a year or two."
On working out less over the winter: "I gave my old body a chance to reover over the offseason. I did some working out, but I think now it's just a matter of gearing up for April. I think over the last couple of offseasons I've been gearing up for February and kind of wearing down."
On suggestions that his defense has declined: "I don't know. Apparently there's mathematics that can go along with catching a fly ball or something. I don't know. I just say ask the pitchers that are on the mound and ask the guys that are hitting in the box and they'll answer that question for you."
On his wrist problems: "The real pain didn't really come until about three weeks in the offseason. Once the cortisone shots and the anti-inflammatories were out of my system, it hurt to turn a wheel. So I said, 'I should probably get this looked at again. They went in and looked at it and said, 'Let's get it cleaned out.' I saw the before and after images and it was pretty neat. I got to see the inside of my wrist and it looks normal again.
"There was just fraying and it was inflamed. It was pretty ugly. I don't know. I learned some different things about the wrist and tendons and everything else that goes along in there. I'm a little smarter because of it and it's taken the slice out of my golf swing, so that's good."
On the team's expectations for 2010: "We've got guys that can play. I think it's been lost obviously with what the Yankees have been able to do, what the Red Sox have been able to do, what the Rays have been able to do in our division. We're not going to put any limitations or expectations on what we're going to do. We're going to go out and play hard and at the end of the day just look at ourselves in the mirror and say, 'You know what? We did what we could to help this team win today,' and move forward."
On late-season clubhouse issues: "I think a lot of things kind of got blown out of proportion with that. It's a family. Youre around guys for almost 200 days including Spring Training and you're going to have issues regardless of who it is. You deal with them in-house and unfortunately this got out, but I don't think it was any bigger than anything else that goes on in any other clubhouses."
On losing Roy Halladay: "It'll be different. It'll be different playing in center field and every fifth day not seeing No. 32 on the mound. But, to be honest with you, those were boring days for me. I didn't do much in the outfield. I'd yell at him sometimes, but he wouldn't hear me."
Which player is wearing these custom-made shoes?
BIRD FEED: That picture right there is the precise moment when Gaston approached Adam Lind to discuss where the young designated hitter will hit in the batting order this season. Gaston has decided to keep Lind in the No. 3 spot. As the manager told reporters, he told Lind, "Why mess with it?" Gaston also talked to Hill about keeping the second baseman in the No. 2 hole for 2010. Gaston said, "Hill is a great kid. He said, 'I'll hit anywhere, even sixth if you want." … Gaston said he will not play Wells or third baseman Edwin Encarnacion in a game until he is absolutely certain that are 100-percent recovered from the wrist surgeries they had over the winter. … Anthopoulos has been in the Dominican Republic this week scouting different players. The Jays watched Cuban first baseman Jose Julio Ruiz workout and the free agent is expected to make a decision about where to sign in the coming days. … Pitchers threw bullpen sessions on Wednesday and Gaston was impressed with what he saw from righty Dustin McGowan, who hasn't pitched in a game since July 2008 due to health woes. If McGowan proves to be a legit contender for the rotation? "That'd be a great, great surprise for us," Gaston said. … Gaston noted that Randy Ruiz (not in camp yet) and Brian Dopirak were definitely in the mix for a 1B/DH role with the Jays. If one made the team, they could be used as a DH on days when Lind played left field or at first base if Lyle Overbay needed a day off. Gaston said Ruiz and Dopirak's chances of making the team would drastically improve if the Jays felt outfielder Travis Snider needed more time in the Minors to open the year. That would necessitate moving Lind back to LF regularly. … Gaston noted that Toronto will most likely open the year with 12 pitchers and 13 position players, which has become the common breakdown for MLB clubs these days.
GARFOOSE SIGHTING: Blue Jays reliever Dirk Hayhurst, who has been banished to the disabled list with a bum right shoulder, emerged from the training room and showed off his upcoming book to reporters today. "The Bullpen Gospels" hits book stores on March 30 and is definitely worth a read. I read it over the offseason and enjoyed it. I wouldn't keep mentioning it if I thought it wasn't good. I swear.
QUOTEABLE: "I think they're capable of doing it. Expected to do it? No, I wouldn't put that on them. I think they're going to get pitched differently. They're certainly going to get a lot of respect." Gaston, asked if Hill and Lind are expected to repeat last year's performances
CLUBHOUSE CONFIDENTIAL: The daily workout schedule sheet once again include a "Quote of the Day" for players to ponder as they headed out to the fields for practice. Today's quote: "The difference between genius and stupidity is that genius has its limits."
ANSWER: The shoes belong to none other than Adam Lind. He said they were made for him for the All-Star Game, which he had a chance to attend last year as a Final Vote candidate. Lind did not wind up winning the vote, but he received the cool kicks anyway.
For complete Blue Jays coverage this spring, make sure you're reading bluejays.com and following me on Twitter at @MLBastian. You can also find spring photos on TwitPic.com.
12 Comments
Do you really think Snider might end up in AAA to start the year? What would you put the chances at?
I can't believe you only have 2 comments on this post. If you read the Toronto Star and Globe + Mail, and/or all the blogs like Bluebird Banter, Tao Of Stieb, and the Drunks, everyone is using your spring training stuff. Come on Jays fans, show some love to MLBastian, and lend some posts to this site. It's the place to be for the preseason.
Thanks for the updates, I'm here daily. I think the Jays are on the right track.
Bastian, important question for you. You said you read Hayhurst's book "The Bullpen Gospels", but have you read the classic book by Dave Stieb "Tomorrow I'll be Perfect". I have a beauty paperback copy that sits right on top of my toilet.
I really just don't understand how Cito Gaston is still a manager at the major league level. It's almost not even considered that Bautista could be a bench player (which he should be) and Randy Ruiz takes a seat for HIM? The only way Dopirak or Ruiz get at bats is if Snider starts the year in AAA, where he has absolutely no place being?
How long before he starts talking about wanting AA to trade with the Cubs for Kevin Millar? I know this year doesn't mean anything, but it would be nice to see a shot given to Ruiz or Dopirak instead of unquestioned lead off privileges given to a bench player.
Ok before we all go anti-Cito like some other blogs out there right now lets sit back and think about this for a second. 1. What is the goal of the Blue Jays for 2010? Its to continue to develop some young players to build a core around for the future. What do Jose Bautista, Randy Ruiz and Brian Dopirak have to do with this process? Nothing, right? so does it really matter if Bautista is getting bats over Randy Ruiz or Brian Dopirak? no… Cito has been given a sub par lineup to work with, and there are only 3 players right now I can think of that will be here when (if) the team is back to contention say 3 or 4 years down the line. Adam Lind, Aaron Hill, and Travis Snider (Wells too but lets not talk about him right now). Also there are many young pitchers they have to look out for. So for a sucessfull season in my eyes, and for Cito to do a good job this year, we will see Lind, Hill, and eventually Snider all hitting in a productive situation. He must also provide the best defence possible for those young pitchers to work in. That is where Jose Bautista comes in. His defence is right feild last year was very good. He may not be a "leadoff hitter" but really what else does Cito have to work with? Cito is here to teach the young players about winning and being a Major League baseball player, and I think he will do a fine job with that. Lind and Hill both have had career seasons playing for him, im excited to see what he can do with some of the other players.
Wells a leader? I guess that is why he SHOWED UP EARLY to camp like some of the others, NOT! At 20+ million a year, Bastian needs to start asking Wells the hard questions.
I think it's great that Hill is willing to step up and lead this group of youngsters. I especially like his comment about not wanting to see anyone taking anything for granted. I think that's extremely important with a young team and players like Snider who got caught up with the whole thing last year leading him into a slump.
Also, I really don't care for all the Wells hate. Is it Wells' fault for accepting a contract he was offered? If you're going to throw some hate, throw it at JP for that ridiculous contract. That said, Wells didn't have a great season last year and definitely needs to improve his numbers this year. I'm sure Wells is going to be a leader but I'm not convinced it's going to be "his team". I'm more inclined to think it'll be Hill's team.
Thats a bunch of BS burt. What time do you show up for work if your told to be there monday morning at 9? 7 AM on a saturday? What is he doing wrong if he shows up on time? I know, some players show up early, great, if that works for them; Wells said himself he was putting too much pressure on himself to perform in February. Give the man a break. Of course everyone was disappointed with his stats last season but there is no need to get on someone for showing up on time. If he showed up ten days early you'd probably say he's trying to hard to be a leader. I usually don't disagree with you but I think you are way off base here… and I'm throwing over to first to pick you off! Hah
It's easy for Wells to talk the talk, but let's see if he walks the walk. So far, in his first test he isn't. I agree with Burt, Wells should have shown up a couple of weeks ago like Hill, Lind and others. There really is no excuse for him showing up one or two days before the mandatory reporting day-not if he is expecting to be a leader.
My take is Hill will become the leader, not Wells, and there is no way in hell this team is ever Well's team. Well's ego just always gets in his way.
As much as the success of the Jays this year depends on the whether or not Hill and Lind can perform to the same level they did last year, so much of it rides on Wells' shoulders. He obviously won't put up numbers close to his contract year, but if he can at least be effective and drive-in runs from the heart of the order, it will be a huge boost for the offence. If he is injury troubled and struggles to drive-in clutch runs again, it could be a long season. Hill and Lind should produce numbers that are somewhat close to last year, and if Wells can get his **** together it will go a long way towards winning a few more games than expected. I'm not saying if Wells, Hill and Lind all are hitting well we have a playoff shot, but could be the difference between a mediocre season and a big dissapointment.
Maybe this season means nothing to some people, but personally, I want to see the Jays at least try to put out the most competitive team possible. Saying "it doesn't matter" doesn't cut it for me. Randy Ruiz lost some weight, and apparently he is an option for the OF. Overbay is a better option for leadoff in my opinion, I strongly believe he will bounce back in a contract year and revert closer to his 2006 numbers. Cito already wants Wells hitting cleanup, fine, whatever. But I think Ruiz deserves a shot in the 5 hole, you never know where you'll find a late bloomer, and I don't know what else he had to do both last season and in winterball. I can't support a manager that literally turns our team into a one line joke after seriously batting Kevin Millar in the cleanup spot, or starting him at 3rd. He seems to have absolutely no clue what being a clean up hitter should entail.


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Abyss: The Wraiths of Eden
What do you need help on? Cancel X
40% off - limited time offer! Low introductory pricing ends soon! Plunge into an endlesslyenthralling sea adventure!Ready to strap on your oxygen mask? Famed underwater explorer Robert Marceau has disappeared under mysterious circumstances, and now hisfiancee must descend to the gloomy depths of the ocean to find him. Venture into unknown and unsettling waters to investigate the sunken city of Eden, now controlled by demons, find hidden objects and confront eerie sea monsters in this heart-pounding quest to save a missing diver!TRY IT FREE, THEN UNLOCK THE FULL ADVENTURE FROM WITHIN THE GAME! - 40 dazzling and exotic underwater locations- 16 unique hidden object scenes to search- 22 mini-games, including an unusual Domino game- Three difficulty modes: casual, advanced and expert- In-depth Strategy Guide- Game Center Support- iPhone 5 support ____________________________ ? Get new G5 games for up to 40% off! Sign up for the G5 newsletter now! www.g5e.com/e-mail ? ____________________________ ??? G5 Games - New game apps every week ! ??? Collect them all! Search for "g5" in iTunes! Adventure: ? Games Navigator By G5 Games ? Nightmares from the Deep: The Cursed Heart, Collectors Edition ? Whisper of Fear: The Cursed Doll ? Lost Souls: Enchanted Paintings ? Special Enquiry Detail: The Hand that Feeds Strategy: ? Virtual City Playground ? Doomsday Preppers ? Build-a-lot 3: Passport to Europe ? The Island: Castaway ? Supermarket Mania 2 ____________________________ VISIT US: www.g5e.com WATCH US: www.youtube.com/g5enter FIND US: www.facebook.com/g5games FOLLOW US: www.twitter.com/g5games
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Aspen body a mystery murder victim for 33 years
A couple was hunting for mushrooms on Aug. 18, 1979 when they found him lying on the ground seven miles from the tiny ghost town of Lenado, which is about 20 miles from Aspen.
The body was found 218 feet below the road embankment and was partially covered with tree limbs, the Aspen Times Weekly had reported days later.
He had a bullet hole in his right eye socket; another in his chest. His body was decomposing. Authorities estimated it had been lying there for up to 18 days. It had rained extensively in the area.
He had dirty blond hair. He was 6-feet tall and weighed about 170 pounds, according to accounts in The Aspen Times.
His pockets seemed to be turned out. He had glasses in his shirt pocket.
Someone may have stolen his wallet in a robbery or took his identification to make it harder for authorities to solve the case.
The man became John Doe.
One of the most critical facts in solving a murder case is knowing the victim's identity.
Once you know who someone is you can speak with co-workers, friends and family to find out who they spent time with, who may have had a motive to harm them and details about routines of their life.
Such clues can break a case.
Without them, investigators over the years at the Pitkin County Sheriff's Department have tried to be creative in solving this John Doe case.


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Race name: Summer Solstice Urban Adventure Race
Date/time: Saturday, June 21st, 2014 @ 5pm
Registration/price: $30-50 per person
Location: start/finish at NW Personal Training (various locations in downtown Vancouver, WA)
Events offered: Adventure race; costume contest
Number of runners: 180
Beneficiary: Clark County Food Bank
I'll be honest, as fun as it sounded when Marilyn invited me to do the Summer Solstice obstacle course race, I almost chickened out at the last minute! I wasn't sure what to expect with this kind of race, but I'm so glad I did it because I had a BLAST! It was so much fun, and really well organized. I loved the shirts and all the swag, I can't wait for my free cupcake! Plus, the race organizers did an amazing job creating a fun, exciting, low pressure atmosphere for the event. It was awesome that this race could be as long/short, challenging/easy as each team chose for it to be. Setting it up like that really made it accessible to every type of runner, which is great for slow people like me! It was fun figuring out each clue, though I appreciated that cross streets were given for harder, lesser-known locations. I think my favorite obstacle had to be at Bad Monkey Bicycle, I laughed the entire time I pushed Marilyn around on a skateboard! I also liked the keg rolling at Dirty Hands Brewing and getting pink streaks in my hair at Beige Blond. I definitely did NOT enjoy the mealworms at Main Event! Thank goodness Mechell stepped up for our team because there was no way I was eating those! The party afterwards continued the fun with delicious food, beer, and raffle prizes. As good as the band was, I couldn't really chat with people while they were playing, and that was frustrating because there were so many fun people at the event! This event is being added to my annual race calendar, and I can't wait to start planning costumes for next year!


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Q: When can I start treating my shoreline for new cattail growth?
Charlie – Bottineau, ND
A: When the wall of cattails comes between you and your recreational pond or lake, it's time to retake control of your shoreline! Once the cattails are 18 inches above the water's surface, you can start treating the new growth.
Here's how we recommend managing cattails:
Set Boundaries
Not all cattails are bad. They provide a habitat for wildlife, like amphibians, insects, birds and fish. Their below-the-ground rhizomes stop soil erosion. And their green strap-like foliage, which stands 3 to 10 feet tall, adds beachfront privacy. So rather than totally eradicate cattails from your pond or lake, set boundaries for them and treat them when they stray.
Chemical Control
The most common way to control cattails is to apply an EPA-registered herbicide like Shoreline Defense® with a pressurized pond sprayer to the foliage of actively growing plants. The product is absorbed by the weed, ultimately killing it all the way down to its roots. It's a perfect solution for beaches, shorelines or anywhere emergent weeds grow.
Physical Removal
Once the herbicide has had a chance to fully soak into the cattail's root system, the plant will turn brown and become limp. At this point, you should remove the stalks. Why? Those dead cattails and decomposing foliage will turn into muck—which will act as a fertilizer for next season's cattails. Cut the stalks using The Pond Guy® Weed Cutter and or the Jenlis Weed Razer™ Pro at the base of the plants, allowing for easier removal with your Rake.
Stay in Control
Cattails have extensive root systems, and so staying on top of their growth is key to preventing them from turning into a cattail wall—and taking over your shoreline!
Pond Talk: What critters live in your stand of cattails?
Filed under: Cattails, Emergent Weeds, Pond & Lake, Season-Long Control | Tagged: controlling cattails, how to get rid of cattails, how to kill cattails, kill cattails, kill weeds, prevent cattails, weed cutter |


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Nevirapine is associated with a 30% decrease in contraceptive hormone levels in pharmacokinetic (PK) studies. Adequately powered studies have not previously been conducted to assess clinical outcomes, such as ovulation, in women receiving concomitant oral contraception and nevirapine.
At the 3rd International Workshop on HIV and Women, Kavita Nanda from FHI 360 presented findings from a study comparing ovulation rates in women receiving combined oral contraceptives (COCs) with nevirapine-containing ART and COCs alone.
This was a non-randomised clinical trial of HIV positive women aged 18-35 years who had regular menstruation, were sexually active, and had no medical contraindications to COC use. It was conducted in South Africa and Uganda between June 2009 and May 2011.
The study enrolled 196 women receiving nevirapine-containing ART and 207 women currently ineligible (> 350 cells/mm3) as a COC-only control group. All women received COCs containing 30 mg of ethinyl estradiol and 300 mg of norgestrel. The investigators estimated ovulation weekly serum progesterone (>10 nmol/L was considered presumptive evidence of ovulation) in the first two treatment cycles. Participants took COCs for at least one cycle before their ovulation assessment. They were tested for pregnancy monthly for 24 weeks.
Women were a median of 29 years of age; most women were in the normal range for BMI and had been pregnant before.
The investigators found no statistically significant differences in ovulation rates between the two groups: 26% of the ART and 16% of COC-only groups ovulated in the first cycle; 18% of ART and 19% of COC-only ovulated in the second and 11% of ART and 12% of COC-only ovulated in both cycles. The unadjusted odds ratio (OR) for ovulation in the ART group compared with the COC-only group was 1.4 (95% CI 0.85-2.18), p=0.2.
Women receiving COCs at baseline were 62% less likely to ovulate during follow up, OR 0.38 (0.2-0.7), p=0.002. Older age (29-32 years) halved the likelihood of ovulation, OR 0.51 (0.27-0.98), p=0.04.
There were nine pregnancies in each group, giving pregnancy rates of 10 per 100 woman years (95% CI 5-19) for each group. Women who missed three or more pills in a row were 17 times more likely to get pregnant; OR 16.76 (3.15-89.24), p=0.001. Self reported adherence and condom use did not differ between the two groups.
Adverse events were no different between the groups; three were serious but unrelated to the study medication (malaria, cellulitis and fracture), all in COC-only group.
Dr Nanda also gave a good overview of what is important with drug interactions with contraceptives at this meeting.
Nanda K et al. Nevirapine-containing ART does not reduce combined oral contraceptive effectiveness: results from South Africa and Uganda. 3rd International Workshop on HIV & Women, 14-15 January 2013, Toronto, Canada. Oral abstract O_03.
Links to other websites are current at date of posting but not maintained.


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Thank you so much Ashley for showcasing your lovely llama quilt with such an adorable bunch of onlookers. I just love the finished quilt and it looks like the llamas do too :)
The llama fabric is available in my store here.
Fantastic photos of a great quilt made with cool fabrics. Thanks to both of you for this inspiational quilt!
Seriously too funny! Great quilt but it was always going to be :-)
How stinkin' cute are those Llamas!! Fantastic photo shoot! I was literally laughing out loud :)
Lol, the only thing I thought of when I saw the photos, was that I hope they didn't spit on it:)
Just too fabulous!
Photo number three made me laugh out loud. Which is BAD because I am supposed to be working. At work. Looking very serious!
Awesome pictures!
Oh my! I saw these on pinterest and couldn't believe the cuteness! What a beautiful quilt and how creative of FITF to capture them all together! I am in LOVE with your llamas and your donkeys (with boots), is there any way you could design a fabric with horses (or ponies)? I love horses, but all the horse fabrics are usually cheesy. I love your style (mondern and still cute as can be), so I am sure you could them justice!
Hysterical! I love the third one especially. What a riot.
Now who's going to take a pic of your Brr fabrics with a Polar bear?! Ashley has set the bar high!


text: Autoplay Chapter 7 - Part 8: Part 8 - 27th day of Sivan Podcast: Subscribe to SIE Daily Tanya with Manis Friedman Podcasts Audio RSS iTunes Stitcher By Manis Friedman More from Manis Friedman | RSS © Copyright, all rights reserved. If you enjoyed this article, we encourage you to distribute it further, provided that you comply with Chabad.org's copyright policy. More in this section 08:45 Chapter 7 - Part 9 10:07 Chapter 7 - Part 10 18:36 Chapter 8 05:24 Chapter 9 - Part 1 10:44 Chapter 9 - Part 2 View All » You may also be interested in... What Is the Tanya About? 20 Comments The Tanya: The "One-Size-Fits-All" Manual for... 9 Comments Practical Spirituality An Overview of Tanya Watch (1:42:32) 44 Comments Is Tanya Too Demanding? 15 Comments Start a Discussion 1000 characters remaining Include Subject Name Location Post Anonymously Email * will not be published Email me when new comments are posted. Please send me Chabad.org's weekly Magazine and periodic emails. We will not share your email address. Posting Guidelines Cancel Submit


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John Scofield has turned the corner from journeyman jazz guitarist to become one of the most inventive and witty players on the contemporary scene.
This date, his first for the Blue Note label, builds on a discography following several recordings for the Gramavision label, and also progresses this contemporary jazz music into an individualism that can only bode well for his future efforts. Teamed with the rising-star saxophonist Joe Lovano and the bulletproof rhythm team of bassist Charlie Haden and drummer Jack DeJohnette, Scofield is emerging as a player of distinction on the electric guitar, and a composer whose mirthful ideas add spark and vigor to his newfound musical setting.
In this co-production with Peter Erskine, Sco has found his melodic stride in making music that is bright and clever without being overly intellectual, retaining a soulful quality enriched by the deep-rooted, bluesy tenor sax of Lovano. What is most refreshing is that this music has broken free of clichés from the earlier original fusion movement, and what Scofield might have accomplished prior. "Farmacology" is an excellent example of this, more in the hard bop vein and echoing both ringing country twang and the unique voicings of Ornette Coleman.
There's rambling neo-bop and good-time fun in the unison of guitar and tenor sax during "Wabash III," a lighter, elegant, but free and melodic tone in 6/8 time for "Flower Power," and squeaky clean, sweet, easygoing swing demonstrated on "Since You Asked." Haden and DeJohnette are so well matched as a rhythm team that it's easy to take them for granted, while hard to ignore their brilliance. They load up on New Orleans-style blues while Scofield doles out amusing and fractured lines for "So Sue Me," collectively move to a sleek and sneaky stance on "Let's Say We Did," and rip up a driven, forceful neo-bop for the linear melody of the witty "Stranger to the Light."
Even though it's a first-time issue on CD, there are three bonus tracks, including the soul song shuffle "Time and Tide," a free, loose association that identifies "Be Hear Now," and the big-time, rock & roll-flavored, squawky "Fat Lip." It's hard to fathom this being anything other than a sustainable new direction for Scofield's music, one that he can enhance as bandmembers come and go in the not too distant future.
Michael G. Nastos ~ AllMusicGuide
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text: Wednesday, September 12, 2012 New Legal Resources Address Expert/Fact Witnesses and Other Legal Matters APTA recently developed additional general information for members who may act in the capacity of a fact or expert witness. Reviewing the witness resources may assist in being better prepared when faced with receiving a subpoena or a request to act as a witness. Myriad legal issues come into play and the resources serve to provide information on topics such as qualifications of an expert, compensation, and discovery. APTA also provides a general information page to house existing materials that address a variety of legal matters, such as contracts, informed consent, and advertising. The expert/fact witness resources were developed in response to RC 22-12, a motion passed by the House of Delegates in June. Comments Hi I would like information on how I can become an expert witness. Do you have any links or con ed courses that I can take Posted by Bianca guzman on 9/4/2017 8:46 PM