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Summary: Learn to think mathematically and develop genuine problem-solving skills with Stewart, Redlin, and Watson's COLLEGE ALGEBRA, Sixth Edition. This straightforward and easy-to-use algebra book will help you learn the fundamentals of algebra in a variety of practical ways. The book features new tools to help you succeed, such as learning objectives before each section to prepare you for what you're about to learn, and a list of formulas and key concepts after each section that help reinforce what you've learned. In addition, the book includes many real-world examples that show you how mathematics is used to model in fields like engineering, business, physics, chemistry, and biology. ...show moreSummary: Learn to think mathematically and develop genuine problem-solving skills with Stewart, Redlin, and Watson's COLLEGE ALGEBRA, Sixth Edition. This straightforward and easy-to-use algebra book will help you learn the fundamentals of algebra in a variety of practical ways. The book features new tools to help you succeed, such as learning objectives before each section to prepare you for what you're about to learn, and a list of formulas and key concepts after each section that help reinforce what you've learned. In addition, the book includes many real-world examples that show you how mathematics is used to model in fields like engineering, business, physics, chemistry, and biology. ...show less
James Stewart James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He did research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Stewart is currently Professor of Mathematics at McMaster University, and his research field is harmonic analysis. Stewart is the author of a best-selling calculus textbook series published by Cengage Learning Brooks/Cole, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS, and CALCULUS: CONCEPTS AND CONTEXTS, as well as a series of precalculus texts. Lothar Redlin Lothar Redlin grew up on Vancouver Island, received a Bachelor of Science degree from the University of Victoria, and a Ph.D. from McMaster University in 1978. He subsequently did research and taught at the University of Washington, the University of Waterloo, and California State University, Long Beach. He is currently Professor of Mathematics at The Pennsylvania State University, Abington Campus. His research field is topology. Saleem Watson Saleem Watson received his Bachelor of Science degree from Andrews University in Michigan. He did graduate studies at Dalhousie University and McMaster University, where he received his Ph.D. in 1978. He subsequently did research at the Mathematics Institute of the University of Warsaw in Poland. He also taught at The Pennsylvania State University. He is currently Professor of Mathematics at California State University, Long Beach. His research field is functional analysis.
Preface. To the Student. Are You Ready for College Algebra? Prologue: Principles of Problem Solving. P. PREREQUISITES. Modeling the Real World with Algebra. The Real Numbers. Integer Exponents and Scientific Notation. Rational Exponents and Radicals. Algebraic Expressions. Factoring. Rational Expressions. Solving Basic Equations. Chapter P Review. Chapter P Test. FOCUS ON MODELING: Making the Best Decisions. 1. EQUATIONS AND GRAPHS. The Coordinate Plane. Graphs of Equations in Two Variables; Circles. Lines. Solving Equations Graphically. Modeling with Equations. Solving Quadratic Equations. Solving Other Types of Equations. Solving Inequalities. Solving Absolute Value Equations and Inequalities. Chapter 1 Review. Chapter 1 Test. FOCUS ON MODELING: Fitting Lines to Data. 2. FUNCTIONS. Functions. Graphs of Functions. Getting Information from the Graph of a Function. Average Rate of Change of a Function. Transformations of Functions. Combining Functions. One-to-One Functions and Their Inverses. Chapter 2 Review. Chapter 2 Test. FOCUS ON MODELING: Modeling with Functions. 3. POLYNOMIAL AND RATIONAL FUNCTIONS. Quadratic Functions and Models. Polynomial Functions and Their Graphs. Dividing Polynomials. Real Zeros of Polynomials. Complex Numbers. Complex Zeros and the Fundamental Theorem of Algebra. Rational Functions. Modeling Variation. Chapter 3 Review. Chapter 3 Test. FOCUS ON MODELING: Fitting Polynomial Curves to Data. 4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. The Natural Exponential Function. Logarithmic Functions. Laws of Logarithms. Exponential and Logarithmic Equations. Modeling with Exponential and Logarithmic Functions. Chapter 4 Review. Chapter 4 Test. Cumulative Review Test: Chapters 2, 3, and 4. FOCUS ON MODELING: Fitting Exponential and Power Curves to Data. 5. SYSTEMS OF EQUATIONS AND INEQUALITIES. Systems of Linear Equations in Two Variables. Systems of Linear Equations in Several Variables. Partial Fractions. Systems of Nonlinear Equations. Systems of Inequalities. Chapter 5 Review. Chapter 5 Test. FOCUS ON MODELING: Linear Programming. 6. MATRICES AND DETERMINANTS. Matrices and Systems of Linear Equations. The Algebra of Matrices. Inverses of Matrices and Matrix Equations. Determinants and Cramer's Rules. Chapter 6 Review. Chapter 6 Test. FOCUS ON MODELING: Computer Graphics. 7. CONIC SECTIONS. Parabolas. Ellipses. Hyperbolas. Shifted Conics. Chapter 7 Review. Chapter 7 Test. Cumulative Review Test: Chapters 5, 6, and 7. FOCUS ON MODELING: Conics in Architecture. 8. SEQUENCES AND SERIES. Sequences and Summation Notation. Arithmetic Sequences. Geometric Sequences. Mathematics of Finance. Mathematical Induction. The Binomial Theorem. Chapter 8 Review. Chapter 8 Test. FOCUS ON MODELING: Modeling with Recursive Sequences. 9. PROBABILITY AND STATISTICS. Counting. Probability. Binomial Probability. Expected Value. Chapter 9 Review. Chapter 9 Test. Cumulative Review Test: Chapters 8 and 9. FOCUS ON MODELING: The Monte Carlo Method. APPENDIX A: Calculations and Calculations. APPENDIX B: Graphing with a Graphing Calculator. APPENDIX C: Using the TI-83/84 Graphing Calculator.
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College Algebra - 7 edition
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Netanyahu comes to the US, humiliates our president, insults our intelligence, treats the American people with condescension ... And asks for more weapons to commit acts of war that are deemed contrary to our national interests. Only israel is allowed to do that and get away with it. It's high time to normalize US-Israeli relations and treat Israel like any other country. Israel is not more important than Britain, France, Germany , Japan, or Saudi Arabia , for that matter. We must end this none sense before disaster befalls both countries and beyond.
If selected for publication, it will appear as soon as possible on Haaretz.com.

subset: commoncrawl


text: We're sorry, GROW YOUR OWN CHILLI PLANTER KIT is no longer available Why not try one of these instead? Cricket Match T Shirt by Stabo £18$37.67€26.15$29.29 can be personalised Funky Veg Kit by Plant Theatre £13.50$28.25€19.61$21.96 Combination Lock Bottle Stop by Whisk Hampers £15.95$33.38€23.17$25.95 Personalised Men's Morse Code T Shirt by Primitive State £18.50$38.72€26.88$30.10 can be personalised GROW YOUR OWN CHILLI PLANTER KIT by Giftaplant £17.99$37.65€26.14$29.27 5 customer reviews(5) This item is no longer available This item is not available for delivery to United States. would you like it gift-wrapped?would you like it gift-wrapped?NoYes (+ £4.75)would you like it gift-wrapped?NoYes (+ $9.94)would you like it gift-wrapped?NoYes (+ €6.90)would you like it gift-wrapped?NoYes (+ $7.73) your gift-message we're sorry we're sorry, This item is no longer available buy a gift voucher related categories express gifts > express gifts for men by Giftaplant Location: Surrey, GB read seller's profile see seller's complete range more items from this seller ROSE PEARL ANNIVERSARY £24.99$52.30€36.31$40.66 Pearl Anniversary Gift Choisya Aztec Pearl £24.99$52.30€36.31$40.66 50th Wedding Anniversary Gifts Rose Golden... £24.99$52.30€36.31$40.66 40th Wedding Anniversary Gift Rose Ruby We... £24.99$52.30€36.31$40.66 Silver Anniversary Gifts - Camellia Silver... £24.99$52.30€36.31$40.66 Ruby Anniversary Gifts - Camellia Ruby Wed... £24.99$52.30€36.31$40.66 view all you may also like PRODUCT DETAILS CUSTOMER REVIEWS DELIVERY RETURNS gift wrapping available ask seller a question save for later This indoor chilli plant kit comes complete with planter, compost, seeds and instructions to grow you own chilli plants, ideal for all chilli fans Makes wonderful living gift to send to family and friends for Birthdays, New Home and for all occasions. A great plant gift and especially if you love chilli's. This indoor plant kit comes complete with planter, compost, seeds and instructions to grow you own chilli plants. Supplied with care card and gift-tag for your personal message. made from: Supplied with chilli seed, planter and compost and instructions dimensions: H20 x W20 x 10cm product code: 204139 5 customer reviews Wed 16 Jan 2013 No comment supplied. Fri 11 Jan 2013 Practical gift came packaged well. Thu 10 Jan 2013 Great idea Well presented Mon 07 Jan 2013 Not used as yet but a nicely presented gift. Tue 01 Jan 2013 It was exactly what I was looking for but unfortunately it arrived very late and then it was broken. The company did however agree to refund straight away which was good. see all customer reviews hide some customer reviews read about our product rating system ratings guide trusted independent customer feedbackforum excellent bad good poor This product is dispatched to you by Giftaplant. MAINLAND UK order now and receive this item on or before price Standard Delivery Wednesday 8 July £6.50$13.60€9.44$10.57 NON-MAINLAND UK estimated delivery price Highlands & Islands of Scotland 2-5 working daysfrom dispatch £12.95$27.10€18.81$21.07 Northern Ireland 2-5 working daysfrom dispatch £17.95$37.57€26.08$29.21 Other UK Islands 2-5 working daysfrom dispatch £17.95$37.57€26.08$29.21 INTERNATIONAL DELIVERY estimated delivery price Not currently available for this region You have 28 days, from receipt of cancellable goods, to notify the seller if you wish to cancel your order or exchange an item. Please note: goods that are personalised, bespoke or made-to-order to your specific requirements, perishable products and personal items sold with a hygiene seal (cosmetics, underwear) in instances where the seal is broken are non-refundable, unless faulty. Read more about our returns policy.Should you choose to return or exchange your order you will need to deliver the item(s) to the UK, where this seller is based. Giftaplant's return policy


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Designers and twin sisters Coco and Breezy believe that eyewear has a heavier impact on a person's style than his or her clothing. It's this spirit that inspires the designers to create some of the loudest sunglasses we've seen. Featuring a 1970s-like acetate frame embedded with a wood grain pattern, the rustic-chic Rainy Days is confidence in in the form of frames. Make a statement with your sunnies—and please give that tired crop top a break.
Measures 60 x 20 x 140 mm. Please see size chart for details. UV-protective lenses. Includes case, soft microfiber bag, and microfiber cleaning cloth.
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Fort Bend man goes missing during walk with his wife
By Robert Stanton | November 7, 2012
Photo By Fort Bend SOVicente Bonilla, 74, was reported missing after he went out for a walk with his wife on Tuesday, Nov. 6, 2012. The couple became separated and Bonilla?s wife began looking for him in their Mission Glen neighborhood.
The Fort Bend County Sheriff's Office is asking the public's help to locate an elderly man who disappeared early Tuesday morning.
Vicente Bonilla, 74, was out for a walk with his wife early Tuesday when the couple became separated, sheriff's deputies said. Bonilla's wife began looking for him in their Mission Glen neighborhood, but could not locate him.
Bonilla was last seen in the vicinity of Williwaw Drive and Mission Glen Drive. He is 5 feet 6 inches tall, weighs 150 pounds and has brown eyes and black hair. He was last seen wearing a blue hat, a gray long-sleeve shirt and blue jeans.
Anyone with information on Bonilla should contact the Fort Bend County Sheriff's Office Dispatch at 281-341-4665.


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Katrina puts cab rate request on hold
Taxi drivers say they need help with gas prices
Taxicab drivers in Corpus Christi will have to wait longer than they want to before they can get city approval for a rate increase.
Two local cab companies, Super Yellow Taxi and Green-N-Go Taxi Co., filed emergency requests on Wednesday for a temporary fare increase of $1 per trip, saying high gas prices were making the business unprofitable.
On Friday, City Manager Skip Noe said he had been busy planning for the expected arrival of 3,000 victims of Hurricane Katrina and hadn't had time to resolve the matter. He said the city attorney's office informed him that he does not have authority to grant the rate increase, but that it must be determined by the City Council. The next council meeting is scheduled for Sept. 13.
Dan Stiefel, chief executive officer of Green-N-Go, said the time frame is unreasonable.
"They won't even be able to look at this until Tuesday," he said. "Then, they'll probably figure that it's only one more week until City Council meets."
Stiefel said his drivers have walked off the job, saying gas prices are too high to make a profit driving a taxi in the city.
The current fare in the city is $2.25 for the first 1/5 mile, 45 cents for each additional mile and there is a 25-cent fuel surcharge if gas prices are above $1.50.
Contact Nick Nelson at (361) 886-3678 or HYPERLINK mailto:email@example.com email@example.com


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DIY Wedding
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Mrs. Gift Bag
By: DecoArt
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Here comes the bride on this one-of-a-kind gift bag made with craft foam and foam paint. Present it to the bride-to-be at a wedding shower for a personal touch.
DecoArt Products Required
Foam Paint
- FP12 - Silver Metallic
- 2-mm craft foam sheets: white, black, and red
- Small sharp scissors
- Craft knife
- Pencil
- Lo-temp glue gun
- Hole punch
- Curling ribbon: red and white
- White paper sack, DMD/Paper Reflections: 4 5/8" x 2 7/8" x 8 5/8"
1. Cut out wedding dress pattern and use pencil to trace it onto white craft foam. Trace heart and ribbon bow onto red foam.
2. Cut out all foam shapes. Cut 4" x 6" rectangle from red foam.
3. Glue red bow on waist of wedding dress. Center and glue dress over red rectangle.
4. Referring to photo, use Silver Metallic Foam Paint to paint buttons and scallop with dots on dress. Write "Mrs." on heart shape. Let dry.
5. Use craft knife to cut 1/4" slit just below top center of heart.
6. Refer to photo for placement. Glue dress to front of sack, centering it at sides and bottom. Fold down top of sack and punch two holes about 1" apart. Pull ends of two curling ribbons through holes in sack and tie in bow at front.
7. Curl ends of ribbon and attach heart tag to one end of ribbon by folding end of ribbon through slit and gluing layers of ribbon together.
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Join this group if you are also on Twitter! It would be great to follow a bunch of the moms that are on here through Twitter as well. Don't forget to leave your Twitter username in the comments when you join this group so we can follow each other!
Website: http://twitter.com
Location: everywhere
Members: 2014
Latest Activity: on Tuesday
Started by Kishea Green. Last reply by Crystal Green Feb 5. 2 Replies 1 Favorite
Started by Erica Gold Apr 25, 2014. 0 Replies 0 Favorites
Started by Marie Ann Novak Oct 16, 2013. 0 Replies 0 Favorites
Come find some dedicated blog readers and followers in Exposure 99% weekday blog hop. Link up all things blogging, from reviews, giveaways, twitter, facebook, G+ and many more in the linky list..
Wishing you a great week and happy mothers day celebration!! http://nzeremm.blogspot.de/2012/05/exposure-99-weekday-blog-hop-is-...
HI, I'm looking for new followers. Follow me and I follow back. www.Twitter.com/Jehancancook
what did you think of that controversial "time" magazine breastfeeding mom cover? here's what i have to say about it: http://www.tulipandthelma.com/2012/05/11/extended-breastfeeding-or-...
Great artist for commissioned paintings! http://bit.ly/JudyMStudios
No Rules Blog Hop is up and waiting for you all to link up, No crazy rues and no rquirements to follow people. Just a really fun way to get your blog out there and have some fun!
Be sure to come back by on Monday to see who's blog is in the Monday Spotlight!
Hi Michelle Spell! I checked out your site. You have good content. I'm now following you on FB. Well, I liked your page. That's the same as a follow, right? I've been blogging on my own sites for 3-4months now. Before that I had been blogging on Christian Blog.com. I think you'll like my parenting blog, Amanda's Books and More at http://abooksandmore.blogspot.com On that site you'll see my other blog links, so feel free to check them out. By the way, I've heard that my comment box on my parenting blog doesn't work. It's a free template I'm using, so it might have a glitch. Have a great day! Tina
I follow back. Just let me know you are following me from MBC
Here are my links:
Blog: http://cmsfamilyblog.com/
Facebook: http://www.facebook.com/pages/Live-And-Look-Healthy/109257605793108
Twitter: https://twitter.com/organicngreen
It's almost the weekend and that means it's time to hippity hop for new friends and followers! Woo Hoo! So come on over and join us as we find fabulous new blogs, fantastic new friends and show each other some bloggy love! Link up your blogs, facebook, twitter, google+, reviews, phenomenal posts and more! What are you waiting for? It's Finding New Friends Blog Hop time! http://jmanandmillerbug.com/2012/05/finding-new-friends-weekend-blo...
finally back to blogging and twitter and would love the followers :o) thanks so much


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This blog very nearly didn't happen today. On Tuesday evening I returned home from work and attempted to power on my crummy laptop, only to have it stubbornly refuse to co-operate. A few simple diagnostic tests revealed it to be, in what I believe is the correct technical terminology, "fucked". It's been a shambling husk for a long while now, to tell the truth, and I believe a traumatic blow it received while in transit during December may well have been the last straw. Thankfully I've been able to replace it on short notice (albeit with grave consequences for my savings account), so the planned blogging schedule can remain in effect and go ahead. Today is the second weekend of January, which means it's time for...
January Edition - Platformers!
For those of you who may have missed last week's blog in which I laid down my blogging plans for the year ahead, I'll explain briefly. Letting Off Some Steam is a monthly blog series that I'll be putting out on the second weekend of every month in 2014. Inspired by (read as: 'copied almost directly from') fellow Giant Bomb user Mento and his backlog-browsing antics, I'll be downloading a handful of titles from my own pile of digitally distributed shame and playing each of them for a little while, providing a few thoughts on each game as I go. The idea behind it is to get me to finally trawl through my enormous treasure trove of unfinished games, get a feel for them, and work out which ones I should be prioritising.
In the interest of keeping things thematically consistent for as long as is reasonably possible, I've decided to focus on one particular genre each month. For January's edition of Letting Off Some Steam, the genre is 'platformers'. The games I've chosen are And Yet It Moves, Braid, Gish, and Rayman Origins. First up, if only because my Steam catalogue is organised alphabetically by default, is And Yet It Moves.
And Yet It Moves
Three of the four games on this month's Letting Off Some Steam can collectively be described as 'platformers with a gimmick'. The first of these, Broken Rules's And Yet It Moves, stands out from the crowd by way of its world-rotating mechanic. At any given time, the player can rotate the whole level clockwise or anticlockwise in ninety-degree increments, turning previously impassable walls into floors in order to open new pathways. It's a neat mechanic, and in the half-hour of the game that I played, the developers seemed to get a fair bit of mileage out of it. Objects and creatures in the world can also be manipulated in this way, creating physics-based puzzles that punctuate the precarious platforming. Aesthetically the game is a bit of an oddity, and not necessarily in an endearing way. The 'torn paper' visuals are striking and unique, but not exactly easy on the eye, and the ambient beat-boxed soundtrack didn't sit well with me. That being said, it seems a cool little game, and providing it doesn't outstay its welcome, I can see myself playing through it in full over the course of a few evenings later in the year.
If the gimmick of And Yet It Moves is making the world go round, then Braid's gimmick is rewinding time. Considered by some to be the original 'indie darling', Braid was adored by Ryan Davises and Soulja Boys alike when it was released in 2008. Having played through the game's first two worlds earlier today, I'm beginning to understand why. It feels great to play thanks to some agreeable platforming physics, and unlike And Yet It Moves, which seems to rest on the laurels of its core mechanic, Braid seems keen to force the player to constantly re-think their approach by piling on new permutations to the established rules at regular intervals. The narrative is pretty well married to the action too, focusing on the themes of learning from one's mistakes, and longing to be able to undo what is already done. I'll definitely be returning to this one later in the year in order to play through the remaining worlds, although I'm not sure I've got enough lateral thinking in me to pick up all of the game's fiendishly out-of-reach puzzle pieces.
On to our third platformer with a gimmick. Gish is a conceptually interesting puzzle platformer in that its eponymous ball-of-tar hero doesn't control like your average jumping protagonist. Instead, Gish has several different states of being, clever manipulation of which is required to navigate the game's myriad hazards and pitfalls. Make him sticky and he'll cling to surfaces, make him more slippery and he'll slide through tight spaces, and make him more dense and he'll be able to destroy crumbling brickwork and crush enemies. It's a cool concept that's pretty well executed from what I've seen of the game (which is the first five levels, if you're wondering), although there were a few moments along the way where I felt the traversal was a little too 'hit-and-hope' and lacking in real control. Visually it's a treat thanks to Edmund McMillen's trademark art style, and I loved the jazzy saxophone breaks in its soundtrack. Whether or not I come back to Gish is largely dependent on how many levels it has, I think - I was already tiring of it after a half-hour session. If it's not a long game I may consider returning to it, but if it goes on beyond a couple of hours I think I'd find it very difficult to persevere.
Rayman Origins
Rayman Origins very nearly didn't make it into this blog, because it wasn't actually in my list of games to play. I'd previously confined it to a neglected corner of my Steam library titled 'Can't Run', on account of it being a stuttering choppy mess on my previous laptop. I was originally going to cover Toki Tori, which is really more a puzzle game than a bona fide platformer, but decided to take a gamble and see if the Limbless Wonder would run any better on my new PC. And whaddaya know, it runs smooth as butter. I'm finally in a position where I can enjoy the gorgeous art direction and revel in the fast, loose and fluid platforming gameplay. As someone who played a lot of the first Rayman game back on my original PlayStation, there's something about the game's mechanics and structure that appeals to my inner seven-year-old and puts a big ol' nostalgic smile on my face. I played about half an hour of Rayman Origins, which took me through the first five levels and did more than enough to convince me that I need to make this a high priority title. I'll probably have to hook up my Xbox 360 controller as I'm not keen on playing platformers with a keyboard, but I cannot wait to sink my teeth deeper into this beautiful, crazy adventure.
I think that's going to do it for this month's Letting Off Some Steam. Out of these four, I'm pretty sure it's Rayman Origins that'll end up on the Gaming Agenda for February. Braid and And Yet It Moves are also likely candidates for full playthroughs before the year is out, but I'm not sure I'll be returning to Gish in a hurry. Next weekend I'll be putting together a more considered opinion piece, most likely related to the time I've recently spent with the two Zelda titles A Link Between Worlds and Link's Awakening, and more broadly the franchise as a whole. Also, be on the lookout for the start of a new serial blog, which is likely to land mid-week. Thanks for reading guys, take care and I'll see you around.
Currently playing - The Legend of Zelda: Link's Awakening DX (3DS)


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Karma 2-Piece Putter Grip$1.99Finally, Karma brings its renown combination of superior value and premium performance to long and belly putters! Works great on most long putter shafts. Does not conform to the Rules of Golf. Learn More
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Back to the Future
Emma Langman explores the usefulness of some of the Quality tools that have been around since the 50s for gathering requirements, tackling repeat problems, or innovating more efficiently as a team.
Voice of the Customer
Barb Spurway, Tracy Bowman discuss Voice of the Customer (VoC), a Total Quality Management/ Lean Manufacturing concept helping teams build quality products from the customers' perspective.
Building SOLID Foundations
Nat Pryce, Steve Freeman advise on design principles useful to create code structures with objects that fit together and communicate, and where the capabilities and the information flow are explicit.
Stop That! Questioning Dogmatic Programming
Doug Hiebert questions conventional wisdom that is taken for granted when writing code, and presents alternatives by way of before-and-after examples.
Managing JavaScript Complexity
Jarrod Overson presents ways to quantify and reduce JavaScript complexity as well as some of the techniques the experts use to create maintainable JavaScript.
Programming, Only Better
Bodil Stokke keynotes on the FP languages for writing bug free, fault tolerant code that help building simple, concurrent and reusable software.
Testing the Hard Stuff and Staying Sane
John Hughes discusses automated testing techniques that can catch more code defects, with war stories from the likes of Ericsson, Volvo Cars, and Basho Technologies.
Using Static Analysis with Grails
Jeff Beck shows how to use Codenarc, Cobertura, JSLint, and other tools to perform static analysis on Grails applications.
Reasonable Code with F#
Mike Falanga shows several C# and F# solutions to common programming problems, comparing how well each language enhances the ability to draw accurate conclusions about the code.
Making Software Development Make Sense to Everyone
Jen Myers discusses the need to make software development attractive and accessible to a larger audience, improving the overall development and learning process in order to have better programmers.
Surviving Big JavaScript Projects
Anton Kovalyov provides an inside look into a large JavaScript project, presenting techniques for maintaining code quality while allowing the team to push lots of changes every day.
Robust Software - Dotting the I's and Crossing the T's
Chris Oldwood discusses what it takes to create robust software: correct error detection and recovery, testing systemic effects, app monitoring and configuration.


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Welcome to the Kitchener Rangers Ticket Marketplace!
Connecting Rangers ticket buyers and sellers! Register to sell your tickets by visiting the Ticket Marketplace Registration page.
Once your tickets have been sold, please email Treena Hennessey or call 519-576-3700 ext 221, during regular business hours, to remove your posting.
2015-16 Season Ticket Package
(Sec, Row, Seat) 12 N 14, 15
I am selling all game tickets for the 2015-16 season (not surrendering membership). Please email me at email@example.com if interested.


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Apple aapl -0.1263823064770932% Apple Inc. U.S.: Nasdaq USD126.44 -0.16 -0.1263823064770932% /Date(1435870800080-0500)/ Volume (Delayed 15m) : 26810454 AFTER HOURS USD126.34 -0.0999999999999943 -0.07908889591901297% Volume (Delayed 15m) : 400498 P/E Ratio 15.629171817058097 Market Cap 728424620100.17 Dividend Yield 1.6450490351154698% Rev. per Employee 2287920 More quote details and news » and Samsung Electronics aren't the only big beneficiaries of the shift to mobile computing. Out of the limelight, Taiwan Semiconductor Manufacturing, 2330.tw 0.9594417793283908% Taiwan Semiconductor Manufacturing Co. Ltd. ADS U.S.: NYSE USD23.15 0.22 0.9594417793283908% /Date(1435870941929-0500)/ Volume (Delayed 15m) : 7833400 AFTER HOURS USD23.15 % Volume (Delayed 15m) : 51491 P/E Ratio 12.48516880595405 Market Cap 118720178792.141 Dividend Yield 3.143257019438445% Rev. per Employee 708134 More quote details and news » or TSMC (ticker: 2330.Taiwan), controls about half of the world's $40 billion-plus customized-chip business. The semiconductor-foundry operator profits not only from the rise and rise of Apple and Samsung but from their increasingly fierce rivalry.
"It doesn't really matter if it is a Broadcom BRCM 0.7321772639691715% Broadcom Corp. U.S.: Nasdaq USD52.28 0.38 0.7321772639691715% /Date(1435870800103-0500)/ Volume (Delayed 15m) : 5195657 AFTER HOURS USD52.28 % Volume (Delayed 15m) : 74741 P/E Ratio 45.92813845207766 Market Cap 31470887224.1601 Dividend Yield 1.0711553175210407% Rev. per Employee 798310 More quote details and news » [BRCM] connectivity chip that enables Wi-Fi, bluetooth and GPS in smartphones or Qualcomm's QCOM 0.3338632750397456% Qualcomm Inc. U.S.: Nasdaq USD63.11 0.21 0.3338632750397456% /Date(1435870800018-0500)/ Volume (Delayed 15m) : 9701040 AFTER HOURS USD63.23 0.119999999999997 0.19014419267944857% Volume (Delayed 15m) : 1601788 P/E Ratio 14.954976303317535 Market Cap 102879462382.911 Dividend Yield 3.042307082871177% Rev. per Employee 878307 More quote details and news » [QCOM] 4G LTE chip. The chances are that it is being made by TSMC," says Credit Suisse's Randy Abrams. Clearly, TSMC has a huge opportunity in the post-PC era. "The PC industry, where Intel INTC 1.242544731610338% Intel Corp. U.S.: Nasdaq USD30.555 0.375 1.242544731610338% /Date(1435870800207-0500)/ Volume (Delayed 15m) : 26804419 AFTER HOURS USD30.55 -0.004999999999999 -0.016363933889707086% Volume (Delayed 15m) : 300804 P/E Ratio 12.947033898305085 Market Cap 144952921447.754 Dividend Yield 3.1418753068237604% Rev. per Employee 523777 More quote details and news » [INTC] was the core chip supplier, was a 350 million-units-a-year market," notes HSBC's Steven Pelayo. "Mobile phones and tablets are a 1.7 billion-units-a-year market. There is no Intel inside any of those devices. TSMC is the Intel to a smartphone world that's growing 30% to 40% a year while the PC market is stagnant," he says.
TSMC-made chips enable smartphone and tablet makers to penetrate emerging markets with affordable models. "Most of the smartphones sold this year will be low-end Android phones in emerging markets," notes CLSA's Bruce Lu. These phones, he says, may use cheap components and Google's (GOOG) free Android software, but "they have to use high-end chips" like TSMC's to offer consumers performance comparable to an iPhone or the Samsung Galaxy.
Another big plus: Because of their legal battles over patents, Apple (AAPL) is cutting its reliance on Samsung (5390.Korea) for chips. TSMC has been working on a new Apple chip for over a year and Apple-designed chips could start rolling out from TSMC's fabrication plants early next year. If Apple gives TSMC all its business, the contract could account for nearly 20% of the foundry giant's sales. That "makes the difference between TSMC growing at 10% a year or 20% a year over the next three years," says Abrams. Chip makers generally are growing at about 3% annually and fabricators at 7%.
Investors are on to TSMC's potential, but there is still some room for the shares to gain. The stock has risen 39% over the past year and trades at 14 times this year's earnings. After reporting $17 billion in revenue last year, TSMC is expected to top $20 billion this year and $24 billion next. Earnings are projected to rise 11% this year to $6.2 billion and jump 26% next. CLSA's Lu has a price target of 20 New Taiwan dollars ($4.05) on the shares, 16% above last week's level. HSBC's Paleyo foresees a 10.5% gain.
TSMC is so successful that Samsung and Intel are trying to push into its market. But being a pure-play chip maker that doesn't design its own wares or make other products gives TSMC advantages. Samsung, a huge producer of smartphones and tablets, has to overcome a lot of conflicts to win chip business from rivals. Intel has its own issues with rival ARM Holdings ARMH -1.1979695431472082% ARM Holdings PLC ADS U.S.: Nasdaq USD48.66 -0.59 -1.1979695431472082% /Date(1435870800227-0500)/ Volume (Delayed 15m) : 1471965 AFTER HOURS USD48.66 % Volume (Delayed 15m) : 5896 P/E Ratio 51.7935071846727 Market Cap 22784723240.1251 Dividend Yield 0.8580517879161529% Rev. per Employee 406774 More quote details and news » (ARMH) whose designs power most mobile processors, although ARM doesn't make its own chips. "How much does Intel want to help ARM by manufacturing their chips?" asks Abrams.
There are worries about TSMC's margins given its 40% capital expenditure-to-sales ratio and big depreciation costs on its new $5 billion factories. So far, so good. Last year it produced a 48.6% gross margin, above its typical 48% rate. Clearly, "TSMC has shown that it can pass through higher costs because of its technology leadership," Pelayo says. That's a lot like Apple and Samsung.
A Hiss
Asian stocks finished the week mixed. China welcomes the Year of the Snake.
ASSIF SHAMEEN covers Asian markets from Singapore.
E-mail: email@example.com


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About 25 House Democrats are undecided on how they will vote. They want firm assurances from the Senate that they will pass the same health care bill. So far, Senate Democratic leaders have 41 votes, and they need 51 to pass the bill through a process called reconciliation.
President Obama has ratcheted up the pressure on undecided Democrats, personally reaching out to those party members in the House who are still undecided or are vowing to vote "No."
In an interview with Fox News Wednesday, the president appealed to the constituents of conservative House Democrats to urge them to vote "Yes."
"What I can tell you is that the vote that's taken in the House will be a vote for health care reform. And if people vote yes, whatever form that takes, that is going to be a vote for health care reform. And I don't think we should pretend otherwise," Obama said in an interview with Fox News' Bret Baier. "If they don't, if they vote against, then they're going to be voting against health care reform and they're going to be voting in favor of the status quo.
"So Washington gets very concerned about these procedural issues in Congress. This is always an issue that's -- whether Republicans are in charge or Democrats in charge -- when Republicans are in charge, Democrats constantly complain that the majority was not giving them an opportunity, et cetera," he added.
The president was referring to the controversy surrounding the parliamentary procedure Democrats may use if they cannot get the 216 votes they need.
The earliest the bill could be passed at this point is Sunday as the Congressional Budget Office has yet to release its cost estimate.
If they are not able to garner enough votes, Democratic leaders have hinted they may employ a parliamentary maneuver dubbed as "deem and pass."
The controversial procedure would allow House members to vote on health care changes without ever voting directly on the Senate bill. In this case, the House would vote on a "fix it" measure that would make changes to the Senate health care bill and then automatically, in the process, pass the bill without actually having to vote on it.
The procedure has been used 20 times over the last 30 years by both Democrats and Republicans, often on technical or unpopular measures like raising the debt limit, but never on one as big as health care reform.
Vice President Biden joked about the difficulties of tackling the health care bill at the annual Radio-TV Correspondents dinner Wednesday evening.
"Trying to negotiate a lasting peace between the Palestinians and Israelis is tough. But it was a hell of a nice break from health care," Biden quipped.
Members of Congress are under increasing pressure from all sides on the health care bill. Altmire has not only received calls from the president, he was confronted by tea party activists at his office, demanding an answer on how he will vote.
At the same time, some union leaders are telling wavering Democrats that if they vote against the health care bill, they might not get any union support in November's mid-term election.
"We're telling them that we supported them on that basis and if they can't stand up for their promises, then we have to consider what else we can do," said Andy Stern, president of the Service Employees International Union.
Others are making a much darker prediction about what the health care debate could do to Obama's presidency.


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On the auspicious occasion of Dussehra and Vijaya Dashami, Bollywood celebrities like Amitabh Bachchan, Karan Johar, Bipasha Basu, Anupam Kher took to twitter to wish their fans all the good wishes and best in life. They wish good health, prosperity and lots of happiness to one and all. H
Chokra Jawaan (Ishaqzaade) Full Song feat Sunidhi Chauhan & Vishal Dadlani - HQ
sunidhi chauhan
The music legend Manna Dey is no more but he has left behind for us valuable treasure, his music and songs which will glow in our heart forever. His musical journey is very commendable. Manna Dey has landed his voice for many Bollywood actors and worked with many noted filmmakers of Bollywoo
Singer Sunidhi Chauhan is spotted with a baby bump recently. Going by the latest photo of Sunidhi, it can be assumed that she is pregnant with her first baby. Last year, Sunidhi entered into matrimony with her childhood friend and composer Hitesh Sonik. Recently, she has put on lots of we
Latest Bollywood News
- Kareena Kapoor poses with Channing Tatum in London
- Shashank Vyas aka Jagya walks out of 'Balika Vadhu'
- Sunny Deol starrer 'Mohalla Assi' release halted by court
- Sunny Leone to play cameo in Akshay Kumar's 'Singh Is Bling'
- John Abraham-starrer 'Welcome Back' to finally release on September 4


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- Brian Windhorst, ESPN.com
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LAS VEGAS -- Southern Nevada is hot, flat and crowded with the NBA at this time of year. For the Cleveland Cavaliers, there's no place to hide.
As the team formerly known as a championship contender slips from the shock stage to acceptance of what happened last week, it is having to do it publicly and painfully in the glare of attention at the Las Vegas Summer League.
In the midst of trying to pick up the pieces, the Cavs are suddenly staring at one of the league's toughest conundrums, one that nearly every franchise faces once a decade or so. How can they rebuild? How should they rebuild? How can they sell the rebuilding process?
The questions are unpleasant and the answers are complicated for reasons the Cavs can't control and reasons they can.
The anger stage of LeBron James' departure was no doubt the sharpest in Cleveland.
Even before the first batch of burning James jerseys had cooled or the giant Nike Witness mural started to come down, team owner Dan Gilbert's stinging open letter to fans hit the media. The attack of James' character in the hours after he announced his intention to sign with the Miami Heat was the most prolific moment.
But the true low point for the team was hearing and then reading about how James was actively recruiting free agents for his new team: putting the full-court press on friend Mike Miller, meeting Derek Fisher at the airport and calling up to tug Mr. Cavalier Zydrunas Ilgauskas to South Beach.
The Cavs had privately been disappointed over the last two years about the lack of intensity James put into their free-agent processes, last year feeling like they lost out on Trevor Ariza because James refused to commit to the future when Ariza called to ask him about it. In fairness, James was just telling free agents the truth even if it was costly to his team in the short run.
Then there was waiting the eight days for James to announce his plans. As information has slipped out, it now seems James wasn't wrestling with the decision as much as he was in talks with a production company and a talent agency about when his primetime special could be scheduled.
The Cavs spent that first week of free agency attempting to set up plans for the team when James re-signed. They were in the mix to sign Miller, they were involved in sign-and-trade talks to add complementary pieces. Yes, there was a backup plan, but it was not in action. The Cavs were moving forward believing James was going to be with them.
And then he was gone.
Eight days into free agency the Cavs suddenly had $12 million in salary-cap space they weren't planning to have. But by then most of the top 15 free agents in the mega class, especially the guy everyone considered No. 1, were committed elsewhere.
Then there was this: "I PERSONALLY GUARANTEE THAT THE CLEVELAND CAVALIERS WILL WIN AN NBA CHAMPIONSHIP BEFORE THE SELF-TITLED FORMER 'KING' WINS ONE."
That wasn't the part of Gilbert's letter that got him in trouble with NBA commissioner David Stern and cost him $100,000. Stern was more upset with the "cowardly betrayal" and "shocking act of disloyalty from our home grown 'chosen one' sends the exact opposite lesson of what we would want our children to learn" lines.
But that was the core reason of why fan groups actually attempted to start campaigns to pay the billionaire's fine for him. His willingness to fire back with confidence won him supporters in the franchise's, and the region's, time of crisis. It was something to cling to and there's reason to believe it -- Gilbert has backed up nearly everything he's promised since buying the team in 2005.
In the unrelenting heat of Vegas, though, reality is here. The Cavs see it as they watch their summer league team attempt to install new coach Byron Scott's running offense, a system for which they don't have the personnel right now. They hear it when they talk to agents about their clients and the troubles recruiting them to what is left of the team. They feel it in the glares of other executives as they know teams see them as desperate.
The Cavs' first attempt at a roster addition came the same day Ilgauskas ended his career in Cleveland by signing with Miami, as they signed Kyle Lowry to an offer sheet. A defensive specialist who would fit in Scott's system, it seemed like a good way to start. Until the Rockets matched the deal roughly 12 hours later.
The truth, whether the team and its fans are prepared to admit it, is the Cavs cannot rebuild quickly or on the fly. They will not be competing with the Heat for the championship this season and more than likely not next season either. After being one of the focus points of the NBA since making the Finals in 2007, the national television games and late postseason runs are done for now.
The first step in this admission was agreeing to a sign-and-trade deal with the Heat for James, giving him the contract he wanted because the four draft picks and the $14.5 million trade exception were badly needed assets. The deal was done by new general manager Chris Grant, who put it together knowing he's got to be more interested in the development of assets and draft picks than winning games right now.
Even as the team looked at its options -- from signing Josh Childress to trading for Al Jefferson -- none seemed to be correct for what was needed. That's a retro-fitting that promises to be painful especially as James racks up his numbers in Florida.
It isn't yet clear if Gilbert is going to be willing to buy into it. His venomous letter and his all-out attempts to win by spending massive amounts on payroll over the last three years being the prime examples.
He's often said that it "costs more to lose than it does to win" in defending his spending. But to win, the Cavs may have to lose for a while and rebuild through the draft and trade market.
Just like the summer's hot sun, there doesn't seem to be any clear way to avoid it.
Brian Windhorst covers the Cavs for the Cleveland Plain Dealer.
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7/14/2010 - NBA Cleveland Cavaliers


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Hi , WordPress Support,
Iknow I should not be worrying you with this Problem BUT I have a Blog which is operated by you ,but was organized through Solobis. The problem I have is I cannot load up my Sites. Being either the Dashboard or the actual Blog Itself . When you click 0n either site to load it , you just watch and wait? ....And nothing happens.
I have emailed Solobis Support twice concerning this problem and have still not recieved a reply. I am desperate to find out just where I go from here. My Site for the Dashboard is: http:fossie09.solobis.net/wp-login.php
Thanks Everyone,
Donald Foster


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A apparatus 10,110,170 is provided that measures the speed of sound and/or vortical disturbances propagating in a single phase fluid flow and/or multiphase mixture to determine parameters, such as mixture quality, particle size, vapor/mass ratio, liquid/vapor ratio, mass flow rate, enthalpy and volumetric flow rate of the flow in a pipe, by measuring acoustic and/or dynamic pressures. The apparatus includes a spatial array of unsteady pressure sensors 15-18 placed at predetermined axial locations x1-xN disposed axially along the pipe 14. The pressure sensors 15-18 provide acoustic pressure signals P1(t)-PN(t) to a signal processing unit 30 which determines the speed of sound amix propagating through of the process flow 12 flowing in the pipe 14. The pressure sensors are piezoelectric film sensors that are clamped onto the outer surface of the pipe at the respective axial location.
1. An apparatus for measuring at least one parameter of a process flow flowing within a pipe, the apparatus comprising:
at least two strain sensors disposable about an outer circumference of the pipe at different axial locations along the pipe, each of the strain sensors providing a respective strain signal indicative of a pressure disturbance within the pipe at a corresponding axial position, each of the strain sensors comprising:
a strap, and
a piezoelectric film material having a pair of conductors disposed on opposing surfaces thereof whereby the piezoelectric film material is attached to the strap which transfers the strain of the pipe to the piezoelectric film material; and
a signal processor, responsive to said strain signals, for determining the slope of an acoustic ridge in the k-w plane to provide a signal indicative of at least one parameter of the process flow flowing within the pipe.
2. The apparatus of
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19. The apparatus of
20. The apparatus of
21. The apparatus of
22. The apparatus of
23. A strain sensor comprising:
a strap disposable about an outer circumference of a pipe, and
a piezoelectric film material having a pair of conductors disposed on opposing surfaces thereof, the piezoelectric film material having a thickness greater than 8 mm, wherein the piezoelectric film material is attached to the strap which transfers the strain of the pipe to the piezoelectric film material to thereby provide a strain measurement indicative of a pressure disturbance within the pipe.
24. The sensor of
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35. An apparatus for measuring at least one parameter of a process flow flowing within a pipe, the apparatus comprising:
at least three strain sensors disposable about an outer circumference of the pipe at different axial locations along the pipe, each of the strain sensors providing a respective strain signal indicative of a pressure disturbance within the pipe at a corresponding axial position, each of the strain sensors comprising:
a strap, and
a piezoelectric film material having a pair of conductors disposed on opposing surfaces thereof whereby the piezoelectric film material is attached to the strap which transfers the strain of the pipe to the piezoelectric film material; and
a signal processor, responsive to said strain signals, which provides a signal indicative of at least one parameter of the process flow flowing within the pipe.
36. The apparatus of
37. The apparatus of
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This application claims the benefit of U.S. Provisional Application No. 60/425,436, filed Nov. 12, 2002; and U.S. Provisional Application No. 60/426,724, filed Nov. 15, 2002, all of which are incorporated herein by reference in their entirety.
This invention relates to an apparatus for measuring the parameters of a single phase and/or multiphase flow, and more particularly to an apparatus having an array of piezoelectric film sensors clamped onto a process flow pipe for measuring the speed of sound and/or vortical disturbances propagating in a single phase and/or multiphase flow to determine parameters, such as mixture quality, particle size, vapor/mass ratio, liquid/vapor ratio, mass flow rate, enthalpy and volumetric flow rate of the flow in the pipe, for example, by measuring acoustic and/or dynamic pressures.
Numerous technologies have been implemented to measure volumetric and mass flow rates of fluids in industrial processes. Some of the more common approaches are based upon ultrasonic time of flight and/or Doppler effects, Coriolis effects, rotating wheels, electromagnetic induction, and pressure differentials. Each of these techniques has certain drawbacks. For example, invasive techniques that rely on insertion of a probe into the flow, or geometry changes in the pipe, may be disruptive to the process and prone to clogging. Other methods such as ultrasonics may be susceptible to air or stratified flow. Meters that use rotating wheels or moving parts are subject to reliability issues. Coriolis meters are limited when pipe diameters become large due to the increase in force required to vibrate the pipe.
One such process fluid is a saturated vapor/liquid fluid mixture (e.g., steam). It would be advantageous to be able to measure the vapor quality of this fluid mixture. Vapor quality of a saturated vapor/liquid mixture is defined as ratio of the mass of the vapor phase to the total mass of the mixture. Saturated mixtures exist at temperatures and pressures at which liquid and vapor phases coexist. The temperatures and pressures at which the liquid and vapor phases coexist lie under the "vapor bubble" on a phase diagram. The collection of points known as the saturated liquid line and the collections of points known as the saturated vapor line define the vapor bubble. These two lines connect at, what is termed, the critical point. Saturated mixtures exist only under the vapor bubble. For pressures and temperatures outside of the vapor bubble, the fluid exists as a single phase and the properties of that fluid, such as density, enthalpy, internal energy, etc., are uniquely defined by the pressure and temperature. For common fluids, such as water, these properties are tabulated as functions of pressure and temperatures and are available through a variety of references including a website hosted by NIST (ref: http://webbook.nist.gov/chemistry/fluid/).
For fluids at pressures and temperatures that lie within the vapor bubble, the fluids represent mixtures of the liquid and vapor phase. Although the properties of both the vapor and liquid phases are well defined (and tabulated for known substances), the properties of the mixture are no longer uniquely defined as functions of pressure and temperature. In order to define the averaged properties of a saturated mixture, the ratio of the vapor and liquid components of the mixture must be defined. The quality of the mixture, in addition to the pressure and temperature, must be defined to uniquely determine the properties of the mixture.
Measuring the average properties of a single or multi-phase process flow is important in many industrial application since it is the mass averaged properties of the working fluid that enter directly into monitoring the thermodynamic performance of many processes. For example, it is the difference in the flux of enthalpy of the steam mixture flowing into and exiting from a turbine that determines the maximum mechanical work that can be extracted from the working fluid, and thus is critical to determining component efficiency. However, if the steam entering or exiting the turbine were saturated, pressure and temperature measurement would not sufficient to determine the specific enthalpy, but rather, a measure of the quality of the steam would be required to uniquely define the thermodynamic properties of the saturated steam mixture.
Note that once the quality and pressure (or temperature) of a saturated mixture is defined, the thermodynamic properties of the mixture are defined through mixing laws provided the properties of the liquid and vapor sates are known. For example, measuring speed of sound enables one to determine quality, which in turn enables one to calculate enthalpy, density, and other properties of the mixture. In addition to measuring the specific enthalpy, a measurement of the total mass is also, in general, required to determine the flux of enthalpy.
There are many other situations where knowing the quality of a saturated mixture is beneficial. For example, in a steam power plant, the quality of the steam within the steam turbine affects blade life. Generally it is desired to operate so the quality is as high as possible throughout the turbine to minimize liquid water drops that will erode the metal blades. Knowing the quality at the turbine inlet and exhaust (or at the exhaust only if the inlet is super-heated) provides a means to monitor the quality throughout the turbine. Also, to monitor plant performance so that it can be operated at optimum conditions and to identify degradation effects, the steam turbine thermal performance must be known. This requires the fluid enthalpy at the inlet and exhaust of each turbine to be known. If the fluid at either or both locations is saturated, pressure and temperature measurements alone will not be enough to determine the enthalpy. However if an additional measurement of quality is made the enthalpy is then defined. In addition, there may be other applications in refrigeration cycles.
The ability to measure the flow rate and composition of the saturated vapor/liquid mixtures within the conduits is an important aspect of any system or strategy design to optimize the performance of a system based on saturated vapor/liquid mixtures. The industry recognizes this, and has been developing a wide variety of technologies to perform this measurement. These include probe based devices, sampling devices, venturis and ultrasonic devices
This invention provides an apparatus and method to measure homogeneous and/or non-homogeneous fluids used in industrial systems having various working fluids to determine various parameters of the process fluid, such as the volumetric flow of the fluid, the consistency or composition of the fluid, the density of the fluid, the Mach number of the fluid, the size of particle flowing through the fluid, the air/mass ratio of the fluid and/or the percentage of entrained air/gas within a liquid or slurry.
Here a novel approach to flow measurements is proposed which utilizes a non-intrusive, externally mounted sensing element that requires no moving parts and is highly reliable. This approach is based upon signal correlation and/or array processing techniques of unsteady pressure measurements induced in an array of externally mounted sensors. The piezo-film sensors clamped onto the outer surface of a pipe provides circumferential averaging of the unsteady pressures within the pipe and provide an inexpensive solution to accurately measuring the unsteady pressures. The piezo-film also have the advantage of being able to wrap around a substantial portion of the outer circumference of the pipe to provide circumferential averaging of the unsteady pressures with the pipe.
Objects of the present invention include an apparatus having an array of piezoelectric film sensors clamped axially spaced to the outer surface of the pipe for measuring the unsteady pressures of a single and multi-phase process flows within a pipe to determine at least one parameter of the process flow.
According to the present invention, an apparatus for measuring at least one parameter of a process flow flowing within a pipe. The apparatus includes at least two pressure sensors clamped onto the outer surface of the pipe at different axial locations along the pipe. Each of the pressure sensors provides a respective pressure signal indicative of a pressure disturbance within the pipe at a corresponding axial position. Each of the pressure sensors includes a strap and a piezoelectric film sensor attached to the strap. A signal processor, responsive to said pressure signals, provides a signal indicative of at least one parameter of the process flow flowing within the pipe.
The foregoing and other objects, features and advantages of the present invention will become more apparent in light of the following detailed description of exemplary embodiments thereof.
The file of this patent contains at least one drawing(s)/photograph(s) executed in color. Copies of this patent with color drawing(s)/photograph(s) will be provided by the Office upon request and payment of the necessary fee.
Referring to
In an embodiment of the present invention shown in
Generally, the first technique measures unsteady pressures created by acoustical disturbances propagating through the flow 12 to determine the speed of sound (SOS) propagating through the flow. Knowing the pressure and/or temperature of the flow and the speed of sound of the acoustical disturbances, the processing unit 24 can determine the mass flow rate, the consistency of the mixture (i.e., the mass/air ratio, the mass/liquid ratio, the liquid/air ratio), the volumetric flow rate, the density of the mixture, the enthalpy of the mixture, the Mach number of the mixture, the size of the particles within a mixture, and other parameters, which will be described in greater detail hereinafter.
The apparatus in
The second technique measures the velocities associated with unsteady flow fields and/or pressure disturbances created by vortical disturbances or "eddies" 118 to determine the velocity of the flow 12. The pressure sensors 18-21 measure the unsteady pressures P1-P4 created by the vortical disturbances as these disturbances convect within the flow 12 through the pipe 14 in a known manner, as shown in
In one embodiment of the present invention as shown in
As best shown in
Piezoelectric film ("piezofilm"), like piezoelectric material, is a dynamic material that develops an electrical charge proportional to a change in mechanical stress. Consequently, the piezoelectric material measures the strain induced within the pipe 14 due to unsteady pressure variations (e.g., vortical and/or acoustical) within the process mixture 12. Strain within the pipe is transduced to an output voltage or current by the attached piezoelectric sensor. The piezoelectrical material or film may be formed of a polymer, such as polarized fluoropolymer, polyvinylidene fluoride (PVDF).
The thickness of the piezoelectric film 32 may be in the range of 8 um to approximately 110 um. The thickness is dependent on the degree of sensitivity desired or needed to measure the unsteady pressures within the pipe 14. The sensitivity of the sensor 30 increases as the thickness of the piezoelectric film increases.
The advantages of this technique of clamping the PVDF sensor 30 onto the outer surface of the pipe 14 are the following:
As shown in
As shown in
Referring to
While the piezoelectric film sensor 30 was mounted to the outer surface of the straps 72, the present invention contemplates the piezoelectric film sensor may be mounted to the inner surface of the strap, thereby resulting in the piezoelectric sensor being disposed between the strap and the outer surface of the pipe 14.
While the present invention illustrates separate covers for each sensor, the present invention contemplates a single cover that covers all the sensors.
Referring to
The type of unsteady pressure measurement being made determines the spacing of the sensors. Measurement of unsteady vortical pressures require sensors spacing less than the coherence length of the vortical disturbances which is typically on the order of a pipe diameter. Correlation or array processing of the unsteady vortical pressure measurements between sensors is used to determine the bulk flow rate of the process mixture, which will be described in greater detail hereinafter.
Mass flow rates and other parameters are determined by measuring the speed of sound propagating within the process mixture 12. These parameters are determined by correlating or array processing unsteady pressure variations created by acoustic disturbances within the process mixture. In this case, the wavelength of the measured acoustic signal determines the sensor spacing. The desired wavelength of the measured acoustic signal is dependent upon the dispersion of particles in the mixture flow, which is dependent on the particle size. The larger the particle size is the longer the sensing device of the aperture.
As described hereinbefore, the apparatus 110 of the present invention may be configured and programmed to measure and process the detected unsteady pressures P1(t)-PN(t) created by acoustic waves and/or vortical disturbances, respectively, propagating through the mixture to determine parameters of the mixture flow 12. One such apparatus 10 is shown in
In accordance with the present invention, the speed of sound propagating through the process flow 12 is measured by passively listening to the flow with an array of unsteady pressure sensors to determine the speed at which one-dimensional compression waves propagate through the flow 12 contained within the pipe 14.
As shown in
The frequency signals P1(ω)-PN(ω) are fed to amix-Mx Calculation Logic 138 which provides a signal to line 40 indicative of the speed of sound of the multiphase mixture amix (discussed more hereinafter). The amix signal is provided to map (or equation) logic 142, which converts amix to a percent composition of a mixture and provides a % Comp signal to line 44 indicative thereof (as discussed hereinafter). Also, if the Mach number Mx is not negligible and is desired, the calculation logic 138 may also provide a signal Mx to line 46 indicative of the Mach number Mx.
More specifically, for planar one-dimensional acoustic waves in a homogenous mixture, it is known that the acoustic pressure field P(x,t) at a location x along the pipe 14, where the wavelength λ of the acoustic waves to be measured is long compared to the diameter d of the pipe 14 (i.e., λ/d>>1), may be expressed as a superposition of a right traveling wave and a left traveling wave, as follows:
The data from the array of sensors 115-118 may be processed in any domain, including the frequency/spatial domain, the temporal/spatial domain, the temporal/wave-number domain or the wave-number/frequency (k-ω) domain. As such, any known array processing technique in any of these or other related domains may be used if desired, similar to the techniques used in the fields of SONAR and RADAR.
Also, some or all of the functions within the signal processing unit 130 may be implemented in software (using a microprocessor or computer) and/or firmware, or may be implemented using analog and/or digital hardware, having sufficient memory, interfaces, and capacity to perform the functions described herein.
Acoustic pressure sensors 115-118 sense acoustic pressure signals that, as measured, are lower frequency (and longer wavelength) signals than those used for ultrasonic probes of the prior art, and thus the current invention is more tolerant to inhomogeneities in the flow, such as time and space domain inhomogeneities within the flow.
It is within the scope of the present invention that the pressure sensor spacing may be known or arbitrary and that as few as two sensors are required if certain information is known about the acoustic properties of the process flow 12. The pressure sensors are spaced sufficiently such that the entire length of the array (aperture) is at least a significant fraction of the measured wavelength of the acoustic waves being measured. The acoustic wavelength to be measured in a mixture is a function of at least the size and mass of the droplets/particles, and the viscosity of the vapor. The greater the size and mass of the droplets and/or the less viscous the vapor, the greater the spacing of the sensors is needed. Conversely, the smaller the size and mass of the droplets/particles and/or the more viscous the vapor, the shorter the spacing of the sensors is needed. For single phase flow, the acoustic wavelength is a function of the type or characteristics of flow 12.
Assuming that the droplets/particles of the mixture are small enough and the acoustic frequencies and the frequencies of perturbations associated with the acoustics are low enough for the droplets/particles of liquid to exhibit negligible slip (both steady and unsteady), the sound speed can be assumed to be substantially non-dispersive (that is constant with frequency) and the volumetric phase fraction of the mixture could be determined through the Wood equation:
For one-dimensional waves propagating, the compliance introduced by the pipe (in this case a circular tube of modulus E, radius R and wall thickness t) reduces the measured sound speed from the infinite dimensional sound speed. The effect of the conduit is given by the following relationship:
Utilizing the relations above for a vapor/liquid mixture, the speed at which sound travels within the representative vapor/liquid mixture is a function of vapor/liquid mass ratio. The effect of increasing liquid fraction, i.e. decreasing vapor/liquid ratio, is to decrease the sound speed. Physically, adding liquid droplets effectively mass loads the mixture, while not appreciably changing the compressibility of the air. Over the parameter range of interest, the relation between mixture sound speed and vapor/liquid ratio is well behaved and monatomic.
While the calibration curves based on predictions from first principles are encouraging, using empirical data mapping from sound speed to vapor/liquid ratio may result in improved accuracy of the present invention to measure the vapor/liquid fractions of the mixture.
The sound speed increases with increasing frequency and asymptotes toward a constant value. The sound speed asymptote at higher frequency is essentially the sound speed of air only with no influence of the suspended liquid droplets. Also, it is apparent that the sound speed of the vapor/liquid mixture has not reached the quasi-steady limit at the lowest frequency for which sound speed was measured. The sound speed is continuing to decrease at the lower frequency limit. An important discovery of the present invention is that the speed at which sound propagates through droplets suspended in a continuous vapor is said to be dispersive. As defined herein, the speed at which acoustic waves propagate through dispersive mixtures varies with frequency.
Measuring the sound speed of a saturated vapor/liquid mixture 12 at progressively lower and lower frequencies becomes inherently less accurate as the total length of the array of pressure sensors 115-118 (Δxaperture), which define the aperture of the array, becomes small compared to the wavelength of the acoustics. In general, the aperture should be at least a significant fraction of a wavelength of the sound speed of interest. Consequently, longer arrays are used to resolve sound speeds at lower frequencies, which will be described in greater detail hereinafter. As shown in
For accurately measuring sound speeds at ultra-low frequencies, the data suggests that utilizing a quasi-steady model to interpret the relationship between sound speed, measured at frequencies above those at which the quasi-steady model is applicable, and the liquid-to-vapor ratio would be problematic, and may, in fact, be impractical. Thus, the key to understanding and interpreting the composition of vapor/liquid mixtures through sound speed measurements lies in the dispersive characteristics of the vapor/liquid mixture, which is described in greater detail in U.S. patent application Ser. No. 10/412,839, filed Apr. 10, 2003; U.S. patent application Ser. No. 10/349,716, filed Jan. 3, 2003; and U.S. patent application Ser. No. 10/376,427, filed Feb. 26, 2003, which are all incorporated herein by reference.
In accordance with the present invention the dispersive nature of the system utilizes a first principles model of the interaction between the vapor and liquid droplets. This model is viewed as being representative of a class of models that seek to account for dispersive effects. Other models could be used to account for dispersive effects without altering the intent of this disclosure (for example, see the paper titled "Viscous Attenuation of Acoustic Waves in Suspensions" by R. L. Gibson, Jr. and M. N. Toks�z), which is incorporated herein by reference. The model allows for slip between the local velocity of the continuous vapor phase and that of the droplets. The drag force on the droplets by the continuous vapor is modeled by a force proportional to the difference between the local vapor velocity and that of the liquid droplets and is balanced by inertial force:
The apparatus 10 further includes the ability to measure of volumetric flow rate of the mixture by comparing the difference of the speed of one dimensional sound waves propagating with and against the mean flow.
This method of determining the volumetric flow rate of the flow 12 relies on the interaction of the mean flow with the acoustic pressure field. The interaction results in sound waves propagating with the mean flow traveling at the speed of sound (if the vapor/liquid mixture were not flowing) plus the convection velocity and, conversely, sound waves traveling against the mean flow propagating at the speed of sound minus the convection velocity. That is,
The practicality of using this method to determine the mean flow is predicated on the ability to resolve the sound speed in both directions with sufficient accuracy to determine the volumetric flow.
For the sound speed measurement, the apparatus 10 utilizes similar processing algorithms as those employed herein before, and described in greater detail hereinafter. The temporal and spatial frequency content of sound propagating within the pipe 14 is related through a dispersion relationship.
Referring to
2) Characterizing the convective ridge of the vortical disturbances using an array of unsteady pressure sensors.
The overwhelming majority of industrial process flows involve turbulent flow. Turbulent fluctuations within the process flow govern many of the flow properties of practical interest including the pressure drop, heat transfer, and mixing. For engineering applications, considering only the time-averaged properties of turbulent flows is often sufficient for design purposes. For sonar flow metering technology, understanding the time-averaged velocity profile in turbulent flow provides a means to interpret the relationship between speed at which coherent structures convect and the volumetrically averaged flow rate.
From the saturated vapor/liquid mixture mechanics perspective, this method relies on the ability of the apparatus 10 to isolate the convective pressure field (which convects at or near the mean velocity of the saturated vapor/liquid mixture) from the acoustic pressure field (which propagates at the at the speed of sound). In this sense, the velocity measurement is independent of the sound speed measurement.
For turbulent flows 12, the time-averaged axial velocity varies with radial position from zero at the wall to a maximum at the centerline of the pipe 14. The flow near the wall is characterized by steep velocity gradients and transitions to relatively uniform core flow near the center of the pipe 14.
From a volumetric flow measurement perspective, the volumetrically averaged flow velocity is of interest. The volumetrically averaged flow velocity, defined as V=Q/A, is a useful, but arbitrarily defined property of the flow. Here, A is the cross sectional area of the tube and Q is the volumetric flow rate. In fact, given the velocity profile within the tube, little flow is actually moving at this speed.
Turbulent pipe flows 12 are highly complex flows. Predicting the details of any turbulent flow is problematic, however, much is known regarding the statistical properties of the flow. For instance, turbulent flows contain self-generating, coherent vortical structures often termed "turbulent eddies". The maximum length scale of these eddies is set by the diameter of the pipe 14. These structures remain coherent for several tube diameters downstream, eventually breaking down into progressively smaller eddies until the energy is dissipated by viscous effects.
Experimental investigations have established that eddies generated within turbulent boundary layers convect at roughly 80% of maximum flow velocity. For tube flows, this implies that turbulent eddies will convect at approximately the volumetrically averaged flow velocity within the pipe 14. The precise relationship between the convection speed of turbulent eddies and the flow rate for each class of meters can be calibrated empirically as described below.
The apparatus 170 of
Referring to
The apparatus 170 of the present invention measures velocities associated with unsteady flow fields and/or pressure disturbances represented by 188 associated therewith relating to turbulent eddies (or vortical flow fields), inhomogeneities in the flow, or any other properties of the flow, liquid, vapor, or pressure, having time varying or stochastic properties that are manifested at least in part in the form of unsteady pressures. The vortical flow fields are generated within the flow of the pipe 14 by a variety of non-discrete sources such as remote machinery, pumps, valves, elbows, as well as the fluid or mixture flow itself. It is this last source, the fluid flowing within the pipe, that is a generic source of vortical flow fields primarily caused by the shear forces between the flow 12 and the wall of the tube that assures a minimum level of disturbances for which the present invention takes unique advantage. The flow generated vortical flow fields generally increase with mean flow velocity and do not occur at any predeterminable frequency. As such, no external discrete vortex-generating source is required within the present invention and thus may operate using passive detection. It is within the scope of the present that the pressure sensor spacing may be known or arbitrary and that as few as two sensors are required if certain information is known about the acoustic properties of the system as will be more fully described herein below.
The vortical flow fields 188 are, in general, comprised of pressure disturbances having a wide variation in length scales and which have a variety of coherence length scales such as that described in the reference "Sound and Sources of Sound", A. P. Dowling et al, Halsted Press, 1983, which is incorporated by reference to the extend of understanding the invention. Certain of these vortical flow fields 188 convect at or near, or related to the mean velocity of at least one of the elements within a mixture flowing through the pipe 14. The vortical pressure disturbances 188 that contain information regarding convection velocity have temporal and spatial length scales as well as coherence length scales that differ from other disturbances in the flow. The present invention utilizes these properties to preferentially select disturbances of a desired axial length scale and coherence length scale as will be more fully described hereinafter. For illustrative purposes, the terms vortical flow field and vortical pressure field will be used to describe the above-described group of unsteady pressure fields having temporal and spatial length and coherence scales described herein.
Also, some or all of the functions within the signal processing unit 174 may be implemented in software (using a microprocessor or computer) and/or firmware, or may be implemented using analog and/or digital hardware, having sufficient memory, interfaces, and capacity to perform the functions described herein.
In particular, in the processing unit 174, the pressure signal P1(t) on the line 190 is provided to a positive input of a summer 200 and the pressure signal P2(t) on the line 191 is provided to a negative input of the summer 200. The output of the summer 200 is provided to line 204 indicative of the difference between the two pressure signals P1,P2 (e.g., P1-P2=Pas1).
The pressure sensors 180,182 together with the summer 200 create a spatial filter 176. The line 204 is fed to bandpass filter 208, which passes a predetermined passband of frequencies and attenuates frequencies outside the passband. In accordance with the present invention, the passband of the filter 208 is set to filter out (or attenuate) the dc portion and the high frequency portion of the input signals and to pass the frequencies therebetween. Other passbands may be used in other embodiments, if desired. Passband filter 208 provides a filtered signal Pasf 1 on a line 212 to Cross-Correlation Logic 216, described hereinafter.
The pressure signal P3(t) on the line 192 is provided to a positive input of a summer 202 and the pressure signal P4(t) on the line 193 is provided to a negative input of the summer 202. The pressure sensors 83,84 together with the summer 202 create a spatial filter 178. The output of the summer 202 is provided on a line 206 indicative of the difference between the two pressure signals P3,P4 (e.g., P3-P4=Pas2). The line 206 is fed to a bandpass filter 210, similar to the bandpass filter 108 discussed hereinbefore, which passes frequencies within the passband and attenuates frequencies outside the passband. The filter 210 provides a filtered signal Pasf 2 on a line 214 to the Cross-Correlation Logic 216. The signs on the summers 200,202 may be swapped if desired, provided the signs of both summers are swapped together. In addition, the pressure signals P1,P2,P3,P4 may be scaled prior to presentation to the summers 200,202.
The Cross-Correlation Logic 216 calculates a known time domain cross-correlation between the signals Pasf1 and Pasf2 on the lines 212,214, respectively, and provides an output signal on a line 218 indicative of the time delay τ it takes for an vortical flow field 188 (or vortex, stochastic, or vortical structure, field, disturbance or perturbation within the flow) to propagate from one sensing region 176 to the other sensing region 178. Such vortical flow disturbances, as is known, are coherent dynamic conditions that can occur in the flow which substantially decay (by a predetermined amount) over a predetermined distance (or coherence length) and convect (or flow) at or near the average velocity of the fluid flow. As described above, the vortical flow field 188 also has a stochastic or vortical pressure disturbance associated with it. In general, the vortical flow disturbances 188 are distributed throughout the flow, particularly in high shear regions, such as boundary layers (e.g., along the inner wall of the tube 14) and are shown herein as discrete vortical flow fields 188. Because the vortical flow fields (and the associated pressure disturbance) convect at or near the mean flow velocity, the propagation time delay τ is related to the velocity of the flow by the distance ΔX between the measurement regions 176,178, as discussed hereinafter.
Referring to
The present invention uses temporal and spatial filtering to precondition the pressure signals to effectively filter out the acoustic pressure disturbances Pacoustic and other long wavelength (compared to the sensor spacing) pressure disturbances in the tube 14 at the two sensing regions 176,178 and retain a substantial portion of the vortical pressure disturbances Pvortical associated with the vortical flow field 188 and any other short wavelength (compared to the sensor spacing) low frequency pressure disturbances Pother. In accordance with the present invention, if the low frequency pressure disturbances Pother are small, they will not substantially impair the measurement accuracy of Pvortical.
The second technique of determining the convection velocity of the vortical disturbances within the flow 12 is by characterizing the convective ridge of the vortical disturbances using an array of unsteady pressure sensors, similar to that shown in U.S. patent application Ser. No. 09/729,994, filed Dec. 4, 2000, entitled "Method and Apparatus for Determining the Flow Velocity Within a Pipe", which is incorporated herein by reference.
The sonar flow metering methodology uses the convection velocity of coherent structure with turbulent pipe flows 12 to determine the volumetric flow rate. The convection velocity of these eddies 188 is determined by applying sonar arraying processing techniques to determine the speed at which the eddies convect past an axial array of unsteady pressure measurements distributed along the pipe 14.
The sonar-based algorithms determine the speed of the eddies 188 by characterizing both the temporal and spatially frequency characteristics of the flow field. For a train of coherent eddies convecting past a fixed array of sensors, the temporal and spatial frequency content of pressure fluctuations are related through the following relationship:
In sonar array processing, the spatial/temporal frequency content of time stationary sound fields are often displayed using "k-ω plots". K-ω plots are essentially three-dimensional power spectra in which the power of a sound field is decomposed into bins corresponding to specific spatial wave numbers and temporal frequencies. On a k-ω plot, the power associated with a pressure field convecting with the flow is distributed in regions, which satisfies the dispersion relationship developed above. This region is termed "the convective ridge" (Beranek, 1992) and the slope of this ridge on a k-w plot indicates the convective velocity of the pressure field. This suggests that the convective velocity of turbulent eddies, and hence flow rate within a tube, can be determined by constructing a k-ω plot from the output of a phased array of sensor and identifying the slope of the convective ridge.
The k-w plot shown in
The present invention will now be described with reference to
Another embodiment of the present invention include a pressure sensor such as pipe strain sensors, accelerometers, velocity sensors or displacement sensors, discussed hereinafter, that are mounted onto a strap to enable the pressure sensor to be clamped onto the pipe. The sensors may be removable or permanently attached via known mechanical techniques such as mechanical fastener, spring loaded, clamped, clam shell arrangement, strapping or other equivalents. These certain types of pressure sensors, it may be desirable for the pipe 12 to exhibit a certain amount of pipe compliance.
Instead of single point pressure sensors 18-21, at the axial locations along the pipe 12, two or more pressure sensors may be used around the circumference of the pipe 12 at each of the axial locations. The signals from the pressure sensors around the circumference at a given axial location may be averaged to provide a cross-sectional (or circumference) averaged unsteady acoustic pressure measurement. Other numbers of acoustic pressure sensors and annular spacing may be used. Averaging multiple annular pressure sensors reduces noises from disturbances and pipe vibrations and other sources of noise not related to the one-dimensional acoustic pressure waves in the pipe 12, thereby creating a spatial array of pressure sensors to help characterize the one-dimensional sound field within the pipe 12.
The pressure sensors 18-21 of
In certain embodiments of the present invention, a piezo-electronic pressure transducer may be used as one or more of the pressure sensors 15-18 and it may measure the unsteady (or dynamic or ac) pressure variations inside the tube 14 by measuring the pressure levels inside of the tube. In an embodiment of the present invention, the sensors 14 comprise pressure sensors manufactured by PCB Piezotronics. In one pressure sensor there are integrated circuit piezoelectric voltage mode-type sensors that feature built-in microelectronic amplifiers, and convert the high-impedance charge into a low-impedance voltage output. Specifically, a Model 106B manufactured by PCB Piezotronics is used which is a high sensitivity, acceleration compensated integrated circuit piezoelectric quartz pressure sensor suitable for measuring low pressure acoustic phenomena in hydraulic and pneumatic systems. It has the unique capability to measure small pressure changes of less than 0.001 psi under high static conditions. The 106B has a 300 mV/psi sensitivity and a resolution of 91 dB (0.0001 psi).
The pressure sensors incorporate a built-in MOSFET microelectronic amplifier to convert the high-impedance charge output into a low-impedance voltage signal. The sensor is powered from a constant-current source and can operate over long coaxial or ribbon cable without signal degradation. The low-impedance voltage signal is not affected by triboelectric cable noise or insulation resistance-degrading contaminants. Power to operate integrated circuit piezoelectric sensors generally takes the form of a low-cost, 24 to 27 VDC, 2 to 20 mA constant-current supply. A data acquisition system of the present invention may incorporate constant-current power for directly powering integrated circuit piezoelectric sensors.
Most piezoelectric pressure sensors are constructed with either compression mode quartz crystals preloaded in a rigid housing, or unconstrained tourmaline crystals. These designs give the sensors microsecond response times and resonant frequencies in the hundreds of kHz, with minimal overshoot or ringing. Small diaphragm diameters ensure spatial resolution of narrow shock waves.
The output characteristic of piezoelectric pressure sensor systems is that of an AC-coupled system, where repetitive signals decay until there is an equal area above and below the original base line. As magnitude levels of the monitored event fluctuate, the output remains stabilized around the base line with the positive and negative areas of the curve remaining equal.
It is also within the scope of the present invention that any strain sensing technique may be used to measure the variations in strain in the pipe, such as highly sensitive piezoelectric, electronic or electric, strain gages and piezo-resistive strain gages attached to the pipe 12. Other strain gages include resistive foil type gages having a race track configuration similar to that disclosed U.S. patent application Ser. No. 09/344,094, filed Jun. 25, 1999, now U.S. Pat. No. 6,354,147, which is incorporated herein by reference. The invention also contemplates strain gages being disposed about a predetermined portion of the circumference of pipe 12. The axial placement of and separation distance ΔX1, ΔX2 between the strain sensors are determined as described herein above.
It is also within the scope of the present invention that any other strain sensing technique may be used to measure the variations in strain in the tube, such as highly sensitive piezoelectric, electronic or electric, strain gages attached to or embedded in the tube 14.
It should be understood that any of the features, characteristics, alternatives or modifications described regarding a particular embodiment herein may also be applied, used, or incorporated with any other embodiment described herein.
Although the invention has been described and illustrated with respect to exemplary embodiments thereof, the foregoing and various other additions and omissions may be made therein and thereto without departing from the spirit and scope of the present invention.
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