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As I reached the end of my previous post you may remember the postie had just arrived with my parcels of Stylecraft Special DK yarn and I was all excited. That excitement increased considerably as I tipped out those beautiful bundles of colour; well wouldn't you get a bit stirred up at such a sight?
Monday, 13 May 2013
Round and Round the Colour Wheel
As I reached the end of my previous post you may remember the postie had just arrived with my parcels of Stylecraft Special DK yarn and I was all excited. That excitement increased considerably as I tipped out those beautiful bundles of colour; well wouldn't you get a bit stirred up at such a sight?
30 comments:
such wonderful cheering colours, beautifully put together in your ripple blanket, and how I love those baby shoes! Simply crochet has such delicious patterns, but at the moment I'm just looking not making! so it's lovely to see your handiwork! EmmaxReplyDelete
Gosh Joy you have some projects on the go, busy, busy, busy! I love that double sole so cute. That ripple blanket is coming on a treat. Thanks for checking out my little dresses, glad you liked them and the story. Jo XReplyDelete
Hi Jo - so nice to hear from you again - like Emma, you too are quick off the mark, and I'm really happy to read your lovely message, thank you!ReplyDelete
Your little girls are lovely and I really do think you are doing such great things with them; they'll remember when they get older and be so grateful to you, quite apart from the wonderful nurturing NOW that is surely encouraging them into creative thinking and doing! Well done you! Joy x
Wow Joy you said I'd been busy! I think you have won the award for busiest haha. Lots of lovely yarn, the blanket you've started in the ripple stitch looks amazing lots of bright colours and little Pika looks like the perfect model!ReplyDelete
I like the simply crochet blanket too, perfect lap size I love the flower in the middle just adds that bit of something to it.
The Grass Elf is amazing my daughter would love that she loves all things elves and fairies.
Any tips with the kitty ears would be welcomed I've come to a stop...
Hey FB - welcome back and I do appreciate your lovely remarks, thank you! You'd love Pika in real life - she's a real personality - she doesn't need to talk - she has us well trained!!!Delete
Yes the little flower granny blanket is very sweet - I won't make it much bigger now.
You may need to look into making your daughter something along the lines of the grass elf - oh no, not something else!!!
Now then - how do I explain about the kitty ears: first mark the actual sides of the body (scrap of yarn hooked in?) then DC 8 or 10 stitches for the first ear (4 for front and 4 for back of ear) whereupon you join the ear together (on the inside edge of head )with a slip stitch.
Then continue for 3 or 4 rounds on these stitches, gradually decreasing a couple of stitches near the join as you go and it should form a nice little peak at the top. Does that sound right?
Then you join in your yarn on the other side and do the same thing. It's easy to neaten up afterwards with your ends of thread. Do partially stuff body as you go and it will be easier to finish stuffing top of head and sew together middle stitches with needle and matching yarn. Let me know if this doesn't make sense? Joy x
Oh now that sounds more like it! I think I will be able to follow it ok. Will let you know how I get on.Delete
Oh don't....not more things to make for my daughter! haha x
Such bright colours they are wonderful I really am a colour junkie the brighter the better. The blanket is amazing I so envy people who can crochet properly mine is very eccentric more like one handed knitting. The faeries are loving your elves and gnomes I will have to go and check out the book. Sarah xReplyDelete
Hello again Sarah - lovely to see you back visiting again! Thank you so much for your lovely compliments - and I was wondering if you'd given yourself a fair chance with your crochet, I mean, are you being hard on yourself? Maybe you haven't had much practice at it?ReplyDelete
I was actually thinking of you when posting the elf and gnome - do check out the book for it's quite amazing the amount of choice in there Then you can make little friends for your faeries!!! Joy x
My, what a pretty blanket! All those colors are so yummy. I keep looking back to see what colors you have to give me ideas for my next project. Since I have been busy with all my quilts, I am missing crochet more and more.....especially when I see yours!!! Beautiful!ReplyDelete
Hope you have a wonderful week,
xx Shari
Oh thank you so much Shari - it pleases me no end that you are so impressed with my blanket!ReplyDelete
I have quite a few colours yet, not chosen for this blanket, that will make another more gentle easy going one but that will have to wait - can't have too many projects on the go at once, can I ! Or can I???
I understand about you missing your crochet - you produce such wonderful results with your hook and yarn, but you know, there's a time and place for everything and at the moment you are doing such a splendid job with your beautiful quilts.
I wish you a fantastic week also and happy crafting,
Joy xx
Beautiful beautiful colourful yarn! I love all your crochet in this post, just gorgeous, but I am really quite in love with those little shoes!ReplyDelete
M xReplies
How lovely to hear from you again M and thank you so much for taking the time to leave me your sweet message; I'm so glad you like what you see. Yes those little shoes are so very cute aren't they but, just be sure to use a 'substantial' weight yarn if you decide to make them. My cotton, although 8ply, is a little on the fine side. Joy xDelete
Ah - your coloured yarn really pops out and your dog sets it off just nicely. :)ReplyDelete
I've just found out my sister-in-law is pregnant so I will be on the look out for baby clothes patterns (not forgetting that I have about 3 unfinished blankets!) and I think those booties are going to go on the list.
Hello again Hazey Bee - I'm glad you looked in again, always lovely to have you for a visit and a wee chat!Delete
A new baby on the way is wonderful news - all the best to your sister-in-law and family!
I had no reason at all to make those shoes other than totally falling for their cuteness and I love baby clothes. In past years I have knit so many bootees I couldn't count them!
Simply Crochet includes so many lovely patterns in their magazine - do give them a go! Joy x
you have been busy Joy! your new rainbow blanket should keep you in a colouful mode! I see you have some lovely greens there, hard to find sometimes. The little shoes are very sweet. Also nice to have another blanket to rest with from the colour! have a good week, Heather xReplyDelete
Hello Heather, how nice to see you here again and thank you for leaving your lovely message. The colour range is quite wonderful in the Stylecraft yarn and I do like the bluey greens especially. Yes the 'flower' blanket does provide a restful break from the bright colours - all states of mind covered! I have plans for another gentle blanket with the other Stylecraft colours I bought - to keep me balanced! Joy xReplyDelete
From one Joy to another love your blog xReplyDelete
Hi JoyReplyDelete
Thank you so much for being a regular visitor to my blog I love receiving your lovely comments. Your ripple blanket is beautiful I think I might like a rainbow blanket.
Hope you are having a good week
Sue x
Hi Sue - I'm delighted that you paid me a visit and thank you so much for your lovely message.ReplyDelete
Yes, rainbow blankets are so nice and allow so much scope in the mixing and matching - maybe that'll be your next project?
My week is going well thank you and hope yours is also!
Joy x
Hi Joy, love your blog. I'm now a follower. Im a crochet addict. I try other crafts but always go back to the crochet. Like the rainbow colours, very inspiring.ReplyDelete
S xx
Hello S - I'm very happy to have you here - welcome! Thank you for your lovely message - I am an addict too - especially with this rainbow ripple - just can't wait to see how the next row of colour will look and how it will affect the overall appearance of the blanket. I think this could be dangerous!!!ReplyDelete
I'm about to look you up at your place and in the meantime I'm wishing you happy hooking times! Joy x
Hi Joy, I am so glad that your yarn arrived. You got a much bigger pile than I did. But I will have to order again. This time round I seem to have bought muted colors but they are so pretty and I am making attic 24's ripple blanket as well. I am having the dilemma now of whether to repeat my colour rows or totally randomize ( is that a word?) them. I love symetry so I will probably just repeat the same pattern over and over. I thing it would bother me if they were mixed up but it is hard to decide. It's a shame we can't attach photos to our comments. If we could I would show you my progress. We have had a lot of rain Busselton way and it is feeling rather cold at night now. Enjoy your beautiful projects.ReplyDelete
Hi Jen - lovely to hear from you again and I wish you the best with your rippling!ReplyDelete
I took a lot of time choosing my colours in the first place and then, although most times I too like 'uniformity', I decide as I go how I'm going to stripe it - but still keep to the same colour order basically. I find this keeps some excitement in the process and I just love to watch how the colour pattern develops and changes the overall appearance of the blanket.
Whichever way you choose to go - just enjoy it!
Our weather patterns have been similar to yours by the sound of it - and of course we're into Autumn now - time for mother nature to wind down, rest and prepare I guess.
Happy weekend to you! Joy x
Hello Joy, thank you for your comment on my blog. It has been lovely to meet you on the blogosphere!ReplyDelete
I can see that crochet is your thing, as well as colour and cute dogs. I love colour and one day I will finish my granny square blanket but right now, I am surrounded by fabric and quilts. I do however leap around the craft world, being a craft " floozie"....:-)
Variety does keep one fresh.
Chat again soon I hope.
Hi Joy, you have a beautiful blog! Happy mid-winter here from the South of Africa!ReplyDelete
Hi Pigtails - and thank you for dropping in and leaving your sweet message, as well as becoming a follower.ReplyDelete
We're into winter here too and having some very cold nights - but still some sunshine too most days!
Have a lovely weekend!
Joy x
Claim faucet bitcoins from CLAIM BTC Faucet. 21 to 57 satoshis per 20 mins.ReplyDelete


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subset: commoncrawl


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Sunday, January 17, 2010
guess he likes muffins
The guy in from of me at the grocery store checkout had in his cart, the Chicken Little DVD, a box of coco puffs and 12 packets of strawberry muffin mix....12! You gotta wonder.
Posted by laurenrebecca at 6:45 AM
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Saturday 9 November 2013, 12pm-4.00pm at Senate House, Malet Street, London WC1E 7HU
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- Research
- Open Access
A transfer theorem and stability of Levin-Nohel integro-differential equations
- Nguyen Tien Dung1Email author
© The Author(s) 2017
- Received: 30 October 2016
- Accepted: 23 February 2017
- Published: 1 March 2017
In this paper we show a connection between Levin-Nohel integro-differential equations and ordinary functional differential equations. Based on this connection, we obtain several new conditions for the stability of the solution, including the famous 3/2 stability criterion.
- integro-differential equations
- delays
- stability
- transfer theorem
1 Introduction
It is well known that the Levin-Nohel integro-differential equations have many applications in various fields of science and engineering. This class of equations was first studied by Volterra [1] in connection with a biological application. As is well known, the explicit solutions of the Levin-Nohel equations can rarely be obtained. Therefore, it is necessary to investigate stability properties of the solution.
For the Levin-Nohel equations of convolution type with a constant delay, the stability problem was solved by Levin and Nohel [2, 3] in the 1960s when they successfully constructed a Liapunov functional. About 15 years ago, a new technique of fixed points developed for studying stability of functional differential equations. Based on this technique, many very nice results have been obtained for asymptotic stability of the non-convolution Levin-Nohel equations with a variable delay (see, for instance, [4–7]).
The rest of this paper is organized as follows. In Section 2, we formulate and prove a transfer theorem for general Levin-Nohel equations. Section 3 is devoted to a study of the stability of linear Levin-Nohel equations with several delays. The stability of quasilinear Levin-Nohel equations is discussed in Section 4. Conclusion is given in Section 5.
2 Preliminaries and the transfer theorem
Definition 1
- (i)
stable if for each \(\varepsilon> 0\) and any \(t_{0}\geq0\) there exists a \(\delta> 0\) such that \(\Vert \varphi \Vert _{t_{0}}<\delta\) and \(t\geq t_{0}\) imply \(|x(t,t_{0},\varphi)|<\varepsilon\).
- (ii)
uniformly stable if it is stable and the above δ is independent of \(t_{0}\).
- (iii)
asymptotically stable if it is stable and \(\lim_{t\to \infty}|x(t,t_{0},\varphi)|=0\).
- (iv)
uniformly asymptotically stable if it is uniformly stable and \(\lim_{t\to\infty}|x(t,t_{0},\varphi)|=0\).
Definition 2
Proposition 1
Mean value theorem for integrals
The main results of this section are stated in the following theorem.
Theorem 1
Transfer theorem
- 1.There exist functions \(h_{k}(t),k\in I\) satisfying \(0\leq h_{k}(t)\leq r_{k}(t)\) for all \(t\geq0\) and \(x(t)\) is also the solution to the following equation:$$\begin{aligned} &\dot{x}(t)+\sum_{k\in I} \biggl( \int_{t-r_{k}(t)}^{t} a_{k}(t,s)\,ds \biggr)f_{k}\bigl(x\bigl(t-h_{k}(t)\bigr)\bigr)+\sum _{k \notin I} \int_{t-r_{k}(t)}^{t} a_{k}(t,s)f_{k} \bigl(x(s)\bigr)\,ds=0, \\ &\quad t\geq0. \end{aligned}$$(7)
- 2.In addition, we assume that, for each \(k\in I\), \(f_{k}(x)=x\ \forall x\in\mathbf{R}\) andThen there exists a function \(h(t)\) such that \(0\leq h(t)\leq\max_{k\in I}r_{k}(t)\) for all \(t\geq0\) and \(x(t)\) is also the solution to the following equation:$$ \int_{t-r_{k}(t)}^{t}a_{k}(t,s)\,ds\geq0 \quad \forall t\geq0. $$(8)$$\begin{aligned} &\dot{x}(t)+ \biggl[\sum_{k\in I} \biggl( \int_{t-r_{k}(t)}^{t} a_{k}(t,s)\,ds \biggr) \biggr] x\bigl(t-h(t)\bigr)+\sum_{k \notin I} \int_{t-r_{k}(t)}^{t} a_{k}(t,s)f_{k} \bigl(x(s)\bigr)\,ds=0, \\ &\quad t\geq0. \end{aligned}$$(9)
- 1.We first note that equation (3) can be rewritten as follows:Since \(f_{k},k\in I\) are continuous functions and the kernel \(a_{k}(t,s)\) has the property (6), we can apply the mean value theorem for integrals to infer that, for each \(k\in I\), there exists \(c_{k}(t)\in (t-r_{k}(t),t)\) such that$$\begin{aligned} &\dot{x}(t)+\sum_{k\in I} \int_{t-r_{k}(t)}^{t} a_{k}(t,s)f_{k} \bigl(x(s)\bigr)\,ds+\sum_{k\notin I} \int_{t-r_{k}(t)}^{t} a_{k}(t,s)f_{k} \bigl(x(s)\bigr)\,ds=0, \\ &\quad t\geq0. \end{aligned}$$(10)Set \(h_{k}(t)=t-c_{k}(t)\), then \(0\leq h_{k}(t)\leq r_{k}(t)\) and the above relation becomes$$\int_{t-r_{k}(t)}^{t} a_{k}(t,s)f_{k} \bigl(x(s)\bigr)\,ds= \biggl( \int_{t-r_{k}(t)}^{t} a_{k}(t,s)\,ds \biggr)f_{k}\bigl(x\bigl(c_{k}(t)\bigr)\bigr). $$Inserting equalities (11) into (10) leads us to equation (7) and so the proof is complete.$$ \int_{t-r_{k}(t)}^{t} a_{k}(t,s)f_{k} \bigl(x(s)\bigr)\,ds= \biggl( \int_{t-r_{k}(t)}^{t} a_{k}(t,s)\,ds \biggr)f_{k}\bigl(x\bigl(t-h_{k}(t)\bigr)\bigr),\quad k\in I. $$(11)
- 2.Under the assumption \(f_{k}(x)=x\), \(k\in I\), equation (7) now reduces toIt follows from the facts \(0\leq h_{k}(t)\leq r_{k}(t),k\in I\), for all \(t\geq0\), that \(t-\max_{k\in I}r_{k}(t)\leq t-h_{k}(t)\leq t\) for all \(t\geq0\). As a consequence, we have$$\begin{aligned} &\dot{x}(t)+\sum_{k\in I} \biggl( \int_{t-r_{k}(t)}^{t} a_{k}(t,s)\,ds \biggr)x \bigl(t-h_{k}(t)\bigr)+\sum_{k \notin I} \int_{t-r_{k}(t)}^{t} a_{k}(t,s)f_{k} \bigl(x(s)\bigr)\,ds=0, \\ &\quad t\geq0. \end{aligned}$$(12)This, combined with the condition \(\int_{t-r_{k}(t)}^{t} a_{k}(t,s)\,ds\geq 0,k\in I\), gives us$$\min_{t-\max_{k\in I}r_{k}(t)\leq u\leq t}x(u)\leq x\bigl(t-h_{k}(t)\bigr)\leq\max _{t-\max_{k\in I}r_{k}(t)\leq u\leq t}x(u),\quad t\geq0. $$and$$\sum_{k\in I} \biggl( \int_{t-r_{k}(t)}^{t} a_{k}(t,s)\,ds \biggr)x \bigl(t-h_{k}(t)\bigr)\geq \biggl[\sum_{k\in I} \biggl( \int_{t-r_{k}(t)}^{t} a_{k}(t,s)\,ds \biggr) \biggr] \min_{t-\max_{k\in I}r_{k}(t)\leq u\leq t}x(u) $$We therefore can obtain the estimate$$\sum_{k\in I} \biggl( \int_{t-r_{k}(t)}^{t} a_{k}(t,s)\,ds \biggr)x \bigl(t-h_{k}(t)\bigr)\leq \biggl[\sum_{k\in I} \biggl( \int_{t-r_{k}(t)}^{t} a_{k}(t,s)\,ds \biggr) \biggr] \max_{t-\max_{k\in I}r_{k}(t)\leq u\leq t}x(u). $$By the intermediate value theorem there exists \(c(t)\in(t-\max_{k\in I}r_{k}(t),t)\) such that$$\begin{aligned} \min_{t-\max_{k\in I}r_{k}(t)\leq u\leq t}x(u)&\leq\frac{\sum_{k\in I} (\int_{t-r_{k}(t)}^{t} a_{k}(t,s)\,ds )x(t-h_{k}(t))}{\sum_{k\in I} (\int_{t-r_{k}(t)}^{t} a_{k}(t,s)\,ds )}\\ &\leq\max _{t-\max_{k\in I}r_{k}(t)\leq u\leq t}x(u),\quad t\geq0. \end{aligned}$$Set \(h(t)=t-c(t)\), then \(0\leq h(t)\leq\max_{k\in I}r_{k}(t)\) and the above relation becomes$$x\bigl(c(t)\bigr)= \frac{\sum_{k\in I} (\int_{t-r_{k}(t)}^{t} a_{k}(t,s)\,ds )x(t-h_{k}(t))}{\sum_{k\in I} (\int_{t-r_{k}(t)}^{t} a_{k}(t,s)\,ds )},\quad t\geq0. $$So we can finish the proof by inserting (13) into (12).$$\begin{aligned} &\sum_{k\in I} \biggl( \int_{t-r_{k}(t)}^{t} a_{k}(t,s)\,ds \biggr)x \bigl(t-h_{k}(t)\bigr) \\ &\quad = \biggl[\sum_{k\in I} \biggl( \int_{t-r_{k}(t)}^{t} a_{k}(t,s)\,ds \biggr) \biggr]x\bigl(t-h(t)\bigr),\quad t\geq0. \end{aligned}$$(13)
3 Linear Levin-Nohel equations
Proposition 2
Myshkis [14] and Yoneyama [15]
- 1.Ifthen the zero solution of (16) is uniformly stable.$$\sup_{t\geq0} \int_{t}^{t+\max_{t\geq0}h(t)}b(s)\,ds\leq\frac{3}{2} $$
- 2.Ifthen the zero solution of (16) is uniformly asymptotically stable.$$\liminf_{t\to0}b(t)>0,\qquad \sup_{t\geq0} \int_{t}^{t+\max_{t\geq 0}h(t)}b(s)\,ds< \frac{3}{2} $$
When the delay \(h(t)\) is infinite we have the following results.
Proposition 3
Graef et al. [13]
Let us now apply Propositions 2 and 3 to establish the stability conditions for the zero solution of (1).
Theorem 2
The proof of uniformly asymptotical stability can be done similarity and, hence, we omit it here. □
Remark 2
If the kernel \(a_{k}(t,s)\) satisfies the two conditions (6) and (8), then \(a_{k}(t,s)\geq0\) because of its continuity. That is why we imposed the condition \(a_{k}(t,s)\geq0\ \forall (t,s)\) in Theorem 2.
Theorem 3
By using the same arguments presented in the proof of Theorem 2, the desired result follows directly from Proposition 3. □
Remark 3
The results of Theorems 2 and 3 are well known; see e.g. [16]. We restate these results here to illustrate the usefulness of the transfer theorem. By using the transfer theorem, the proofs of Theorems 2 and 3 are very simple.
Proposition 4
Berezansky and Braverman [17]
As a product of Proposition 4, we can obtain new conditions for the exponential stability of equation (1) in the next theorem.
Theorem 4
Remark 4
Remark 5
The exponential stability of equation (1) has been recently discussed in [9]. To the best of our knowledge, that paper seems to be the first one studying the exponential stability of Levin-Nohel integro-differential equations. Theorem 4 thus is an interesting and important contribution because it provides us one more sufficient condition for the exponential stability.
Applying Theorem 4 for \(J=\{1\},\{2\}\) and \(\{1,2\}\) yields the following.
Corollary 1
- 1.\(\int_{0}^{r_{1}} a_{1}(s)\,ds>0\) and there exists \(r(t) \geq0 \), such that for sufficiently large t$$\begin{aligned} &\biggl( \int_{0}^{r_{1}} a_{1}(s)\,ds \biggr) r(t)\leq \frac{1}{e}, \\ &\limsup_{t\to\infty} \biggl( \biggl( \int_{0}^{r_{1}} a_{1}(s)\,ds+\biggl\vert \int _{0}^{r_{2}} a_{2}(s)\,ds\biggr\vert \biggr)\bigl\vert r(t)-r_{1}\bigr\vert +\frac{\vert \int_{0}^{r_{2}} a_{2}(s)\,ds\vert }{\int_{0}^{r_{1}} a_{1}(s)\,ds} \biggr)< 1. \end{aligned}$$
- 2.\(\int_{0}^{r_{2}} a_{2}(s)\,ds>0\) and there exists \(r(t) \geq0 \) such that for sufficiently large t$$\begin{aligned} &\biggl( \int_{0}^{r_{2}} a_{2}(s)\,ds \biggr) r(t)\leq \frac{1}{e}, \\ &\limsup_{t\to\infty} \biggl( \biggl(\biggl\vert \int_{0}^{r_{1}} a_{1}(s)\,ds\biggr\vert + \int_{0}^{r_{2}} a_{2}(s)\,ds \biggr)\bigl\vert r(t)-r_{2}\bigr\vert +\frac{\vert \int _{0}^{r_{1}} a_{1}(s)\,ds\vert }{\int_{0}^{r_{2}} a_{2}(s)\,ds} \biggr)< 1. \end{aligned}$$
- 3.\(\int_{0}^{r_{1}} a_{1}(s)\,ds+\int_{0}^{r_{2}} a_{2}(s)\,ds>0\) and there exists \(r(t) \geq0 \), such that for sufficiently large tThen equation (25) is exponentially stable.$$\begin{aligned} &\biggl( \int_{0}^{r_{1}} a_{1}(s)\,ds+ \int_{0}^{r_{2}} a_{2}(s)\,ds \biggr) r(t)\leq \frac{1}{e}, \\ &\limsup_{t\to\infty} \biggl(\biggl\vert \int_{0}^{r_{1}} a_{1}(s)\,ds\biggr\vert \bigl\vert r(t)-r_{1}\bigr\vert + \biggl\vert \int_{0}^{r_{2}} a_{2}(s)\,ds\biggr\vert \bigl\vert r(t)-r_{2}\bigr\vert \biggr)\\ &\quad < \frac {\int_{0}^{r_{1}} a_{1}(s)\,ds+\int_{0}^{r_{2}} a_{2}(s)\,ds}{ \vert \int_{0}^{r_{1}} a_{1}(s)\,ds\vert +\vert \int_{0}^{r_{2}} a_{2}(s)\,ds\vert }. \end{aligned}$$
4 Quasilinear Levin-Nohel equations
- (a)For each \(k\in\{N+1,\ldots,M\}\), \(g_{k}(0)=0\) and \(g_{k}(x)\) is a Lipschitz function, i.e.where \(K_{k}\) is a finite positive constant.$$ \bigl\vert g_{k}(x)-g_{k}(y)\bigr\vert \leq K_{k}\vert x-y\vert ,\quad\forall x,y\in \mathbf{R} , $$(26)
- (b)
The kernel \(a_{k}(t,s)\) is continuous and fulfils the condition (6) for any \(k\in I=\{1,2,\ldots,M\}\).
- (c)
The delays \(r_{k}(t)\), \(k\in I\) are continuous with \(t-r_{k}(t)\to\infty\) as \(t\to\infty\).
Proposition 5
Dung [18]
Theorem 5
Once again, the proof of this theorem is similar to that of Theorem 2. So we omit it here. □
We conclude this section with an example.
5 Conclusion
In this paper, we proved a transfer theorem for the Levin-Nohel equations. Because of its simplicity, the transfer theorem provides us with an effective method to investigate the stability of the Levin-Nohel equations. Each of the known stability conditions for the corresponding functional differential equations may give us a stability condition for the original Levin-Nohel equations.
By using the transfer theorem, we obtain simple proofs for some well-known results (Theorems 2 and 3) and new stability conditions (Theorems 4 and 5) for the Levin-Nohel equations.
The author would like to thank the anonymous referees for their valuable comments and for the reference to [14, 16].
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors' Affiliations
- Volterra, V: Sur la théorie mathématique des phénomès héréditaires. J. Math. Pures Appl. 7, 249-298 (1928) MATHGoogle Scholar
- Levin, JJ, Nohel, JA: On a system of integrodifferential equations occurring in reactor dynamics. J. Math. Mech. 9, 347-368 (1960) MathSciNetMATHGoogle Scholar
- Levin, JJ, Nohel, JA: On a nonlinear delay equation. J. Math. Anal. Appl. 8, 31-44 (1964) MathSciNetView ArticleMATHGoogle Scholar
- Burton, TA: Fixed points and stability of a nonconvolution equation. Proc. Am. Math. Soc. 132, 3679-3687 (2004) MathSciNetView ArticleMATHGoogle Scholar
- Burton, TA: Fixed points, stability, and harmless perturbations. Fixed Point Theory Appl. 1, 35-46 (2005) MathSciNetMATHGoogle Scholar
- Burton, TA: The case for stability by fixed point theory. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 13B(suppl), 253-263 (2006) MathSciNetGoogle Scholar
- Becker, LC, Burton, TA: Stability, fixed points and inverse of delays. Proc. R. Soc. Edinb. 136A, 245-275 (2006) MathSciNetView ArticleMATHGoogle Scholar
- Dung, NT: New stability conditions for mixed linear Levin-Nohel integro-differential equations. J. Math. Phys. 54, 082705 (2013) MathSciNetView ArticleMATHGoogle Scholar
- Dung, NT: On exponential stability of linear Levin-Nohel integro-differential equations. J. Math. Phys. 56, 022702 (2015) MathSciNetView ArticleMATHGoogle Scholar
- Halanay, A: Differential Equations: Stability, Oscillations, Time Lags. Academic Press, New York (1966) MATHGoogle Scholar
- Hale, IK, Verduyn Lunel, SM: Introduction to Functional-Differential Equations. Applied Mathematical Sciences, vol. 99. Springer, New York (1993) View ArticleMATHGoogle Scholar
- Krisztin, T: On stability properties for one-dimensional functional-differential equations. Funkc. Ekvacioj 34(2), 241-256 (1991) MathSciNetMATHGoogle Scholar
- Graef, JR, Qian, C, Zhang, B: Asymptotic behavior of solutions of differential equations with variable delays. Proc. Lond. Math. Soc. 81, 72-92 (2000) MathSciNetView ArticleMATHGoogle Scholar
- Myshkis, AD: Linear Differential Equations with Retarded Argument. Nauka, Moscow (1972) (in Russian) MATHGoogle Scholar
- Yoneyama, T: On the 3/2 stability theorem for one-dimensional delay-differential equations. J. Murh. Anal. Appl. 125, 161-173 (1987) MathSciNetView ArticleMATHGoogle Scholar
- Gusarenko, SA, Domoshnitskiı̌, AI: Asymptotic and oscillation properties of first-order linear scalar functional-differential equations. Differ. Equ. 25(12), 1480-1491 (1989) MathSciNetMATHGoogle Scholar
- Berezansky, L, Braverman, E: Explicit exponential stability conditions for linear differential equations with several delays. J. Math. Anal. Appl. 332(1), 246-264 (2007) MathSciNetView ArticleMATHGoogle Scholar
- Dung, NT: An asymptotic stability theorem for quasilinear delay differential equations with oscillating coefficients. Int. J. Math. 24(11), 1350092 (2013) 14 pp MathSciNetView ArticleMATHGoogle Scholar


text:
Ringtones For At And T Phones
- (Ringtone (song)) Internet Leaks is the third EP from "Weird Al" Yankovic. It was released digitally on August 25, 2009, although all of the songs were initially released as separate digital singles between October 2008 and August 2009.
- A sound made by a mobile phone when an incoming call is received
- A ringtone or ring tone is the sound made by a telephone to indicate an incoming call or text message. Not literally a tone, the term is most often used today to refer to customizable sounds used on mobile phones.
- (Ringtone (film)) Ringtone is a 2010 Malayalam film by Ajmal starring Suresh Gopi, Bala and debutant Megha Nair.
- Used in the context of general equities. Conjunctions used in an order, market summary, or trade recap that signify a bid or an offer, respectively. See: On.
- (phone) telephone: electronic equipment that converts sound into electrical signals that can be transmitted over distances and then converts received signals back into sounds; "I talked to him on the telephone"
- (phone) call: get or try to get into communication (with someone) by telephone; "I tried to call you all night"; "Take two aspirin and call me in the morning"
- A speech sound; the smallest discrete segment of sound in a stream of speech
- (phone) (phonetics) an individual sound unit of speech without concern as to whether or not it is a phoneme of some language
For Things Beyond
Things beyond, I know they are
I do not need to see
The things inside the treasures hid
The secrets that I keep
The things beyond the bridges burned
And those I wish I'd saved
For things above a thousand tongues
The angels and the saints
The chaos of love
The fury of life
The chaos of love
The fury of life
For Things Beyond - Gileah
At times, It's hard to keep faith alive, but when certain people come into your life and leave footprints behind, they were put there for a reason. I am slowly coming to grips with the true meaning of life and the pursuit of happiness. As time has shown me, happiness is something you can't go searching for alone.. you have to let time, and God show you the right path to take. Sara for instance, (the girl pictured in this photo) she is someone who means the world to me. I would do anything for her and I consider her my best friend. God brought her into my life to help me through hard times, and make the good times great. Of course I am there for her also, and its people like her, that bring great joy into my life. Her mother is also an amazing person. While I was bickering with my mom, she was kind enough to let me stay in her home for a whole week. She is a blessing and I appreciate her so much, I feel like I met her for a reason and it explains why Sara is such a great human being. Then there is Chris. Through all of these hard times I've been going through, he has been there for me no matter what. He is unbelievable. I am grateful for him and I'm pretty sure I love him.
I am so lucky to have such great people in my life, and for this I thank God for all he has given to me.
McDonnell Douglas DC-10-30 Fed-Ex preparing for take-off on 28L at PDX.
McDonnell Douglas DC-10-30 Fed-Ex preparing for take-off on 28L at PDX.
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I adore to be spoiled and loved! I like nice guys who know how to treat a girl. Smart people with good sense of humor.. Strong, sure of themselves and protective men, thats what im looking for :)


text:
I was studying Political Science a couple of days ago when I read a paragraph about Democracy vs. Non-Democracy which stated that the majority of States on a global level are non-democratic regimes, and that they frequently include the highest population rates around the world. This was not exactly news for me but, sometimes, reading a certain known fact on a book or an article makes it suddenly and disturbingly clear for you. It is as if you had seen the same information before behind a frosted glass or a dirty window and, all of a sudden, you're seeing it through the cleanest glass or water surface. And it hits you with massive strength.
There are no airbags when it counts to realising that we live in a world where the majority of States does not recognise its citizens their basic, fundamental human rights. It is so easy for us to imagine a simple, carefree life in a safe, free society – that comfort and liberty have been there since the date of our birth. We have never been stopped from saying or writing what we think, we have never been stopped from having driving lessons because we are women, we have never been stopped from going to school because our Government does not want us to have an education. It is hard to step out of one's shoes and imagine life "on the other side" – but I see it as a big box divided by a central glass window. It is not any glass window; it is a one-way mirror, like those you find in interrogation rooms. A one-way mirror is partially reflective and partially transparent; when you light one side and keep the other in the dark, it allows viewing from the darkened side but not from the other side. And so I picture all these people that live on one side of the box, a chock-full of men and women and children who are looking at the other half through the one-way mirror, watching individuals on the other side living their lives freely and carelessly. On their side, however, things do not work the same way – and the people who live in the first half, the so-called better half, simply do not see them.
This is bull**** of course, if you feel like swearing a little. Everyday we see and hear news on TV about how someone else has been blown up by a bomb somewhere in the Middle East, or how war is going on in Syria, or how a fatal disease is once again making its way through Sub-Saharan Africa, or how an ethnic minority is once again being slaughtered in Burma. We see and hear and, yet, it is as if we are blind and deaf. We carry on eating supper and living our free, careless lives. So, in a way, it is as if there is a one-way mirror separating the North from the South. But it is worse than that, because this mirror is imaginary: it is in all our heads; in each of us.
Nevertheless, being immune to any effect these news might have on us – there is still a breach in our blidness and deafness. That is the trivializing of violence. Hannah Arendt spoke of the "banality of evil", and coining the term from my own personal perspective, I can only say that this is probably a good definition of the society we live in. We have become so used to violence that we are no longer shocked by watching children on TV being trained by ISIL to become future assassins. There are numerous theories on why this happens: violent videogames, violent TV series, violent books, violent wars, violent attacks, too much talk about terrorism and death and violence. Truth is, we are being pumped violence and death and bloody images and sceneries from a very young age. We grow up hearing about it, we grow up seeing it, in a way that, by the time we should actually be motivated to do something to fight it, we are simply insensitive to its gory effects.
This is a tendency we must fight. The moment we stop feeling shocked with the sight of children being given AK-47s and taught how to kill, is the moment we cease to be deeply, spiritually motivated to act – in such a way that we will no longer have the urgent, unavoidable need to do something to stop it. If you look at these children on TV and do not feel your stomach clench or your guts wrap in a sudden nausea; if you do not feel tears coming to your eyes or if you simply do not have this nuclear, instinctive red flag that tells you there is something wrong with that picture… then you have banalized evil inside you. And there is nothing more dangerous than that. "All that is required for evil to prevail is for good men to do nothing". Or like Martin Luther King Jr. put it, "Our lives begin to end the day we become silent about things that matter".
It is time to de-banalize evil, to turn it back into the monster it is. We all love the Joker, but villains in real life are not in any way lovable. They are not actors performing behind a TV screen; evil must not be seen as a temporary distraction, it mustn't be seen as entertainment. Let's make it a monster again, let us feel shocked and scared and sad and uncomfortable about it. It is the only way to ensure that, when we see news like this, when we darken the other side of the mirror and finally watch what is happening on "the other side", we will finally realise that one part of the box cannot live in a dream while the other part is living in a nightmare.
Let us destroy the wall that divides us. And let us face the monster as it is: evil, as a force to be reckoned with, as a fight to be fought, as a challenge to be overcome. Only light can drive out darkness. Let's destroy the one-way mirror.


text:
Dataface — Dataface: Put a face on your databaseby millegratie & 1 other
No comment on this link yet.
Founded in late 2003 and heartquartered in France, we are non-profit and independant.
We believe in the open web, think internet services should be sustainable, build for the long term.
While we are re-launching the service, we only accept new members through invitation.
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the 21/01/2007 at 07:14
the 09/01/2007 at 20:24


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A Team Japan ant dribbles up the pitch with an eye on goal during the Ant World Cup, held at the Kashihara City Insectarium in Nara Prefecture on May 26. (Mainichi)
I don't know what else to say but are they crazy or are they crazy??
The Camponotus obscuripes ants, known as Muneaka-oari in Japanese, measured between 7 and 12 mm long. They played using a 1 cm ball on a pitch 20 by 30 cm.
In the wild, the ants recognize enemies by their pheromones. The organizers of the game used this natural ability to make the ants "ant-agonize" each other, by feeding the Japanese team with Kagoshima pork and the Brazilian team with spare ribs in order to alter the ants' pheromones.
Technorati Tags: World Cup, Soccer, Ants Cup, Football, Insects, Games


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CMS understands the challenge of filling a senior or mid-level healthcare management job. Searching for just the right combination of experience and leadership qualities in a permanent candidate may take months and no one can afford their organization to stop functioning in the meantime. A talented temporary manager is vital during these searches, and CMS is skilled at locating the best interim managers to bridge the gap in leadership during a permanent search.
Our interim candidates are seasoned professionals who have the experience to perform the necessary duties and knowledge of the field that can't be easily taught to a temporary employee. They don't need a long-term commitment and we attract them with a competition compensation package and solid support along the way. We seek and foster the best of the best, assuring our clients that our candidates will exceed their expectations. As with all of our contract employees, CMS handles the day-to-day management of their employment, leaving you and your organization free to continue your business of providing quality healthcare.
Continuum Medical Staffing offers our clients many benefits as we:
- Meet your staffing needs with the right healthcare professional
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Let CMS be the staffing partner you need to run your healthcare organization seamlessly during transitions with interim and permanent management. Contact one of our interim recruiters today and tell us what you need right now.


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Sometimes, all it takes to become famous is to get just one market call right. What sets apart truly successful investors, however, is their ability to shift gears as market conditions change and continue to find ways to reap profits from their portfolios. It's tough to keep an open mind about your investing philosophy, but if you can, you'll be able to take advantage of whatever situations you face and more effectively protect your assets when times get tough.
Changing your mind
In the latest edition of The Motley Fool's Rule Your Retirement newsletter, Foolish fund expert Amanda Kish takes a close look at the struggling economic environment. Noting how several economic indicators are flashing warning signs of a possible double-dip recession, Kish looks at how some of the money managers she tracks are planning to make money despite the potential for a long period of slow or no growth.
One such manager is John Paulson, who is famous for having made huge financial bets against the mortgage securities market. After the housing bubble's collapse, the investments Paulson made panned out in pay dirt. Yet what's most remarkable about Paulson's success is that in searching for smart investment opportunities, he turned to the same industry he bet against previously.
In particular, Paulson recently counted JPMorgan Chase, Citigroup
There's no doubt that it takes determination to turn away from a strategy that made you billions. But being able to evaluate investment opportunities with an objective mind is a skill you'll need if you want to avoid seeing hard-earned paper profits go up in smoke when the investing climate changes.
Rolling with the punches
Not all money managers are able to change gears when their investment strategies go bad. Take Bill Miller, for instance, of Legg Mason Value Trust fame. His fund went an amazing 15 consecutive years of beating the S&P 500, taking full advantage of bull markets while limiting its losses when the tech bubble burst.
But Miller's streak came to an end in 2006, and he's struggled ever since to regain his lost success. Suffering a devastating 55% loss during 2008, Miller's value strategy didn't work with Sears Holdings
It's true that sticking with a winning strategy through tough times can be smart in the long run. But if you can anticipate how markets will change, you can gain an even bigger edge by finding ways to adapt to them.
Look both ways
That's why great investors never stop trying to learn. Whether it's poring through annual reports like Warren Buffett does or exploring the latest exchange-traded fund, you can only gain by looking into new investing strategies and finding out more about the companies that interest you.
The resources at the Fool's Rule Your Retirement service can help you in your ongoing quest for knowledge. In addition to Amanda's commentary, you'll find tips on financial planning, understanding deflation, and how real estate investments can help you fill out your portfolio. Best of all, we offer those resources free of charge to new subscribers for 30 days, with no further obligation.
The key, though, is that even when the economy is slow and the overall stock market stays flat, you can still make money. By staying vigilant about learning about investing, you'll be better able to pinpoint the specific investments that will perform the best.
See more about turning your hard-earned savings into retirement riches. The experts at Rule Your Retirement can show you the way, and a 30-day free trial is just a click away.
Tune in every Monday and Wednesday for Dan's columns on retirement, investing, and personal finance.
Fool contributor Dan Caplinger enjoys playing locksmith and searching for hidden treasure. He doesn't own shares of the companies mentioned in this article. Electronic Arts is a Motley Fool Stock Advisor recommendation. Try any of our Foolish newsletters today, free for 30 days. You'll never have to retire without the Fool's disclosure policy.


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Raising Voices: To Social Media or Not To Social Media
- HomeRaising Voices: To Social Media or Not To Social Media
Raising Voices: To Social Media or Not To Social MediaNovember 9, 2015 No Comments » For Authors, Writing Advice Amanda Hester
Jiovanni joins again for this week's edition of Raising Voices. Today he is discussing his thoughts on the effects of social media. We'd love to hear your thoughts.
What if one day you walked into a restaurant and it was almost completely silent; the only noise was the sound of text alerts and other app sounds? If social media continues the way it has been for the last couple decades, this is a likely scenario you will see in the future. Technology is ever advancing; as humans, we have gone from the wheel to be able to predict the weather, cure diseases, and create artificial intelligence. Also, not everything humans create is ever perfect or flawless. I want to look specifically at the smartphone, not on the phone itself, but what people use it for and the effects it has on us as a whole.
Let's look at some pros about the use of the smartphone before we start dogging it. Telephones were originally created to be communication devices. The man who made the telephone, Alexander Graham Bell, didn't think he was going to be playing Pac-man on it or something irrelevant to communication. Being able to communicate with someone over a distance in real time, I believe, was one of the greatest breakthroughs in technology for humans. Over time, as our knowledge expands, we've been able to turn the telephone into the cellular phone. It's so much better and can do many more things on it, but as the saying goes,
"Bigger isn't necessarily better."
Now let's look at the many cons about the smartphone. The smartphone allows for easy access to social media sites such as Facebook and Twitter, which in turn have their own effects on people. Social media sites such as Facebook and Twitter promote text slang for example; your is turned into "ur". I believe the constant use of text slang on these social media sites seriously affects the grammar of younger people of today's society.
The big point I want to address is face-to-face communication skills today. People are so used to talking to each other through technology that it's starting to hurt our social skills. Having social media skills is crucial to everyday life. Social skills can be used to make you appear better during a job interview, with personal relationships, and more. Because people communicate so frequently using technology, eventually people could stop interacting with one another altogether!
Now let's just quickly go over the good reasons why having a smartphone outweighs the bad reasons. With your phone, you can contact people in real time, exchange information and other important things.Now let's go over the cons of people using smartphones. Social skills start to diminish due to constant communication through social media sites, and slowly but surely it's affecting grammar. Now, I've given the good reasons and the bad reasons for using a smartphone. What is more important? Communication or social and grammar skills?
I believe communication, social, and grammar skills are all important, which is why I think phones with talking and texting should be enough for people. When you want to check Facebook or Twitter, wait until you go home and just check it on your computer two or three times a day. People are using social apps nearly 24/7, and this frequent use of social media through smartphones is what is affecting people as a whole so greatly.
Overall, having communication isn't a bad thing, but maybe the constant use of communication through the smartphone is a bad thing. If everyone just had phones with talk and text capabilities, would we still have these ever growing problems today?
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No more reality shows for Aishwarya Sakhuja
The actor says she now wants to focus only on fiction shows.tv Updated: Jul 09, 2016 18:21 IST
Actor Aishwarya Sakhuja has participated in two reality shows, and loved every bit of her experience. However, now she wishes to return to television soaps and focus on her acting.
"I really want to act now because I have been out of action for two years. It was not a deliberate attempt to stay out of fiction but it happened nonetheless.
Read: Jennifer Winget is Kushal Tandon's psycho girlfriend in new show Beyhadh
"I am an actor and I got the celebrity tag because I could act. So, I think it is about time to relive my acting skills. Not to mention that I had a great time doing reality shows," says Sakhuja, who became famous after playing the role of Tosti in the show Saas Bina Sasural before she moved on to do Nach Baliye in 2013 and later in 2015 and adventure reality show Khatron Ke Khiladi earlier this year.
Read: Aishwarya Sakhuja is on the lookout
The actor will soon be seen in a finite comedy series and feels the format of limited shows is a good option.
"Finite series really work right now. Who has the time to sit down and watch a story go on and on? I think it's time we start making more finite series," she says.
Follow @htshowbiz for more.
First Published: Jul 09, 2016 18:21 IST


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Mater's Junkyard Jamboree Line
Mater has gone all out to decorate his line. He has put lots of different things from his various shorts (Mater's Tall Tales) out for you to enjoy looking at while in line.
My husband and I had always used the handicapped entrance but on our last trip there was no line for MJJ! We decided to stop and just go in and look at Mater's display of memorabilia and take pictures. It was something we had wanted to do but with the crowds we could not do it before this. We could see bits of it from the handicapped line but not all of it. Also it was impossible to get pictures with the crowds. I do not expect the lines to stay this short for long. I'm sure once the holiday comes the crowds and long lines will return.
Here are our pictures!


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Distilled 1967 bottled 2008 aged 40 years in oak casks.
Jim McEwans Celtic Heartlands:
70cl limited edition of 523 bottles.
Decanter shape bottle, Presented in a Black Leather case with silver writing
Jim McEwan's Celtic Heartlands deliberately stands out from the crowd; these are not standard bottlings, These stimulate the mind with their amazing complexity and originality.
With over 40 years in the whisky industry, starting as an apprentice cooper at the age of 15 means that there is very little that Jim McEwan does not know about single malt scotch whisky.
He has been recognised three times as Distiller of the Year, amongst a myriad of other accolades including Industry Leader of the Year (Malt Advocate) and Personality of the Year (Whisky Magazine).
Tomatin Whisky Tasting Notes Distillery Style
Nose : Rich and malty. Honey, vanilla, Kendal mintcake!
Palate : Smooth and rich. Malty, spicy, cream fudge.
Finish : Gentle and spicy.
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There Are No Excuses Quote
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The Shadow Chasers conducted an investigation of TS in West Winfield. The team conducted a full site analysis with a variety of technology. After reviewing 42 hours of video, 7 hours of audio and more than 300 pictures only minimal results were attained.
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St. Anthony's given high marks for heart attack care
OSF HealthCare Saint Anthony Medical Center has received the American College of Cardiology's NCDR ACTION Registry Platinum Performance Achievement Award for 2017, one of only 193 hospitals nationwide to receive the honor.
The award recognizes the medical center's commitment and success in implementing a higher standard of care for heart attack patients, and signifies that OSF HealthCare Saint Anthony has reached an aggressive goal of treating these patients to standard levels of care, as outlined by the American College of Cardiology/American Heart Association.
"This recognition is the result of focused teamwork and commitment by our caregivers and leaders to provide patients with the fastest and most effective care possible," said Dr. Thomas Isaacson, Vice President of Cardiovascular Medical Services – OSF HealthCare Cardiovascular Institute. "For our community, this distinction means they have access to a local hospital that is in a very elite group nationwide. Our patients can absolutely expect safe, highest quality care for a life threatening incident."
The Center for Disease Control estimates that over 700,000 Americans suffer a heart attack each year. A heart attack occurs when a blood clot in a coronary artery blocks blood flow to the heart muscle. Treatment guidelines include administering aspirin upon arrival, timely restoration of blood flow to the blocked artery, and cardiac rehabilitation, among others.
–OSF HealthCare


text:
Wasted all my Banana Juice trying to learn Cart Revolution. At one point I was completely naked, including cart, literally the only items on me were the quest ones, and yet he still didn't teach me.
What should I do? This is extremely frustrating.
Kreuzbube wrote:What level is your character and what class is it? What items do you have as quest items?
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text:
Welcome to Southern OOAKS. Ooaks means "One Of A Kind Sculpt" All designs are unique and hand sculpted without the use of molds. Here under the old ooak tree you will also find my jewelry designs, needle felt designs and any other item that my muse has whispered to me to design. Come and sit a spell!!
Wednesday, March 2, 2011
Wednesday WIP-clay beads
7 comments:
These are looking great!ReplyDelete
Just gorgeous!ReplyDelete
Too Cute! I bought some clay but at the moment only have some shapes formed, wondering if I'll pursue... these are great!!ReplyDelete
- AnonymousMarch 2, 2011 at 11:56 PM
You have been chosen to receive the Awesome Blog Award!ReplyDelete
Laurie @ http://kottagecreations.blogspot.com
These are turning out beautifully- as usual, I'm on tenterhooks to see where you're going with them! So COOL!ReplyDelete
Love the little oinkers, but that beautiful face in the middle of the top row is my favourite, that soft, knowing smile......ReplyDelete
These are great! I love the faces at the top. :) Have a wonderful weekend! xox PamReplyDelete


text:
Water treatment
extended embed settings
0.30 0.25 0.20 0.15 0.10 0.05 0.00 Y = 0.0469X + 0.0282 R 2 = 0.92 0 2 4 6 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 Y = 0.0097X + 0.0211 R 2 = 0.9726 0 10 20 30 40 A Figure A3-2 Suspend solids (m g /l) by Standard M ethod B Suspend Solid (m g /l) by Standard M ethod Standard curve for suspended solids (mgl -1 ) versus absorbance at 810 nm in samples taken from effluents of CGF pilot units (A) and Full scale plants (B). Samples were taking again from CGF effluents and were analysed for SS with both Gooch and spectrophometric methods. The obtained results were used to validate spectrophometric method. Descriptive statistics of data originated from pilot plant samples are presented in table A3-1. These data have a lineal regression given by the equation Y = 0.047X + 0.028 (r 2 = 0.92), in which Y and X are suspended solid values obtained by the spectrophometric and Gooch methods respectively. The data originated from full-scale plants have a lineal regression given by the equation Y = 0.0097X + 0.0211 (r 2 = 0.97). Table A3-1 Descriptive statistics of SS measurements (mgl -1 ) with samples taken from effluents of CGF pilot units using both Gooch and spectrophometric methods. Descriptive Statistic Method Gooch Spectrophometric Mean 2.82 2.75 Standard Deviation 2.46 2.50 Minimum 0.40 0.10 Maximum 12 11 Data (number) 58 58 Based on the results obtained with samples from both pilot and full-scale plants the spectrophometric method was used for SS measurements with samples having low turbidity values, below 20 NTU. Comparison between the statistical evaluation for gravimetric and spectrophometric methods was made with t-student test verifying that the slope of these line will be 1. The result with 5% of statistical significance level indicate that does not exist statistic evidence for disprove the hypothesis. Applying the same test and statistical significance level, the result indicated that does not exist statistical evidence for deny that the Y intercepted was 0. In others words, with 5% of statistical significance level, both procedures can be used to estimate SS concentrations. Furthermore, the adopted spectrophometric method can be used for the determination of suspended solids when great amount of analyses are required because is faster than the volumetric procedure described and recommended in the Standard Methods. References APHA, AWWA and WPCF, (1989). Satandard Methods for the Examination of Water and Wastewater. Joint Editorial Board. Washington, DC 20005. USA. Sawyer, C.; McCarty, P., and Parkin, G, (1994). Chemistry for Environmental Engineering, McGraw Hill International Editions, Fourth edition. USA. Krawzyk, D. and Gonglewski, N, (1959). Sewage and industrial wastewater, Vol. 31, Pp 1159-1164. A3-2
Annex 4: Example of F-Test (Analysis of Variance) application This example presents an application of F-Test (Analysis of Variance) to mean suspended solids (SS) removal efficiencies in DyGF units during Phase I, Period I, of this research work. The statistical model used is the randomised block design as represented by equation A4-1.(Vargas, 1991) Yij = µ + τi + βj + εij (A4-1) Y ij: SS removal efficiencies in i-treatment levels (i = 1,2,3, because three DyGF filtration rates were tested during Period I) with j-blocks (j = 1,2,3,4,.......,33, because there were b = 33 blocks, sampling sessions or repetitions per each filtration rate during Period I). µ: Mean SS removal efficiency of all Y ij values, without distinguishing between treatment levels. τ i : Effect due to i-treatment level. In this case i takes values between 1 and 3. τ i represents D y GF filtration rate i tested during Period I: τ 1 . = 0.9mh -1 , τ 2 = 1.3 mh -1 , and τ 3 = 1.4 mh -1 , (t = 3). β j : Effect due to block j of observed values in each sampling session, with j changing from 1 to b, b = 33 SS-sampling sessions during Period I. ε ij : Random variation associated with the i-treatment level in the j-block of observed values (the experimental error) The basic assumption (null hypothesis) used to apply the model described in the equation A4-1 is that all observed values during test runs, divided among several groups according to treatment levels and sampling sessions, are all from the same population. This means that there are not statistically significant differences between the group means. In this case the null (H o ) and the alternate (H a ) hypotheses are as follows. H 0 : τ 1 = τ 2 = τ 3, Ha: τ i ≠ τ k (i≠k), filtration Rate differences in DyGF units do not imply statistically significant differences in the mean SS-removal efficiencies of all DyGF units, Vs, filtration Rate differences in DyGF units does imply statistically significant differences in at least a pair of DyGF mean SS-removal efficiencies. The process to accept or reject the null hypothesis (H o ), with an established level of significance (α), involves the F-Test, after the British statistician, Sir Ronald A. Fisher, who developed the method called analysis of variance (ANOVA) on which the F-test rests (Fisher, 1947, quoted by Mesa, 1999; Rowntree, 1981). The calculations required by the ANOVA technique to decide about Ho are summarised in the table A.4-1 Table A4-1 Summary of Analysis of Variance (ANOVA) with the randomised blocks design. Source of Variation Degrees of Freedom Sum of squares (SS) Mean square (MS) F c Treatment (between) t –1 SSTreat SSTreat/(t –1) = MSTreat MSTreat / MSE Blocks (between) b – 1 SSBlocks SSBlocks/(b – 1) = MSBlocks MSBlocks / MSE Error (within) (t –1)(b –1) SSE SSE/((t –1)(b –1)) = MSE Total tb - 1 SST H 0 is rejected when F c > F (α, t-1, (t-1)(b-1)), where F (α, t-1, (t-1)(b-1)) is the F-distribution with t-1 and (t-1)(b-1) degrees of freedom for the numerator and denominator respectively. α is the significance level of the test. A general notation for the observed data used in this example is shown in the table A.4-2. A4-1
Development and Evaluation of Multi
ACKNOWLEDGEMENTS To my supervisor,
ABBREVIATIONS ABNT: Acuavalle: ACV:
SOCs: Synthetic Organic Chemicals S
u c V V f Vs uniformity coefficient
1 INTRODUCTION Water is essential f
Table 1.2 Access to WS&S in Colombi
Table 1.5 Safe drinking water cover
1.2 Multiple Barriers Strategy and
adjustment, are among the technolog
On January 14, 1829, Simpson's on
With increasing life expectancy, en
Table 2.2 Treatments steps recommen
In table 2.3, WHO guideline values
2.5 The Slow Sand Filtration Proces
When the particles are very close t
in which p 0 is the clean media por
Yao et al (1971) related the remova
compensate for the increase in the
can be applied, but intermittent op
Table 2.4 Comparison of design crit
Although accepted as indirect indic
50% when the temperature falls from
Figure 2.9 Flow diagram of the wate
ut higher running costs, since more
Headloss and flow control. Final he
Figure 2.13 Influence of flow condi
Operation and maintenance (O & M).
in parallel (Galvis, 1983; Smet et
cleaning simple, DyGF should behave
case of Dortmund (Germany), the HGF
Table 2.9 Data about three experien
Some points of discussion about HGF
and 600-800 NTU) and different filt
the HGF units of Aesch (see table 2
in spite of the low removal efficie
order to overcome the water quality
full-scale units. In this research,
in the case of UGFL. Initially, it
• Bigger and better-instrumented
l Figure 3.7 Plan view of Cinara's
The present research work was divid
Table 3.1. Design parameters, grave
Figure 3.9. Piezometer distribution
were used to collect samples for DO
were poured into a funnel using fil
H 0 : H a : Treatment levels workin
3.2 Results and Specific Discussion
3.2.2 Dynamic gravel filtration (Dy
Mean faecal coliform removal effici
Table 3.10 Comparative analysis of
DyGF-A had flow reductions in the r
The experimental data used to produ
Previous observations were further
ates (figure 3.17 B). However, at t
Longer "initial-ripening" perio
Table 3.17. Descriptive statistics
100 Filtration rate = 0.3 mh -1 100
After the present experience, faeca
nature of the organic matter and th
Table 3.24 Comparative analyses of
188.8.131.52. Filtration run lengths and
deep bed filter (data not included
and operational considerations Pard
than in sand samples from other SSF
Step dose tracer tests were made at
for HGFS and from 3 to 5 for HGF. T
Constant and declining filtration r
The efficiency levels summarised be
Surface area of CGF and SSF units.
community based organisations and l
systems. All these systems were fed
Parts of the suburban settlements o
Figure 4.2. Layout of Retiro MSF pl
Traditionally, in the WS&S of Colom
Photo 4.10. Partial cleaning activi
Figure 4.3 Location of full-scale M
126.96.36.199 Main characteristics of mul
Figure 4.4 Layout of Restrepo MSF p
Figure 4.6 Layout of Javeriana MSF
Figure 4.9 Layout of Cañasgordas M
Figure 4.11. Layout of Ceylan MSF p
Table 4.4 Descriptive statistics fo
Water sources in the coffee region
Filterability results seem to under
Table 4.8 Mean removal efficiencies
The length of this ripening period
in Peru (Pardon, 1989) and Colombia
Photo 4.24 Drainage facilities in u
the Cauca Valley. This is not the c
Pardon (1989) reports similar evide
ecame formally established as WS en
Models for assessing construction q
MSF system can then be calculated o
5.7 Cost Model for the Cali Area an
Table 5.8. Annual labour costs due
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text: Sheila Sue Arends, 65, of Jewell, passed away on Monday, Nov. 6, at Mary Greeley Medical Center in Ames. Funeral services were held Monday, Nov. 13, at Grandon Funeral and Cremation Care. Burial was at Lawn Hill Cemetery in rural Stanhope. Memorial contributions may be directed to Baptist Children's Home, Ind.


text:
Another day, another climate change conference, this time its at the Scottish National Football Stadium, Hampden Park. I am Chairing the event and I set off at 6 am to get there in time.
The event goes well and the debate is encouraging, but I still can't help get the feeling that not everyone gets this yet.
Evan Williams from the Scottish Environmental Protection Unit does a good impression of Al Gore by utilising a lot of data from 'an unconventional truth', and its a very good way of getting the message across.


text:
I can't believe it's already time for my 4th blogoversary. Last year I changed my blog name from Sky's Book Corner to Simona's Corner of Dreams. I'm really happy I made this change, because there are so many book corners out there now and on top of that I'm not just a book corner, I blog about travel, lifestyle and other things as well. I thought I'd play around with my blog name a little bit and this is the result:
What do you think, is this me or not?! ;)
I asked my readers to describe my blog/instagram/photos in three words. Here are the words:
- Books
- Fashion
- Travel
- Fun
- Lighthearted
- Sweet
- Pretty
- Cosy
- Lifestyle
- Summer
- Sunshine
- Unique
- Diverse
Books and travel were mentioned a lot.
How would you describe my blog?
I'm very grateful for these 4 years, for all the opportunities and for all the people I have met, you know who you are! LOVE YOU and THANK YOU!!!
Here is a little giveaway to say thank you:
The first prize is a 10$ gift card from Amazon.
Another gift card from Amazon, this one is for 15$.
This beauty set contains a soap from L'Occitane, a lip balm from L'Occitane, a lip glass from Tarte and a jewellery bag from Thomas Sabo.


text:
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text:
av:link SH27 Lightweight Headphones
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A pair of stereo headphones with foam earpads, adjustable headband and great sound reproduction. Ideal for audio tours.
- Adjustable headband
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- Mylar speakers with foam earpads
- 0.9m cable
SH27 Lightweight Stereo Headphones


text:
Tameka "Tiny" Harris has many roles and she looks amazing in every one of them. The savvy businesswoman and fierce mom gives SBH the inside scoop on her mane style moves.
Tiny switches up her look often and now she's rocking her Natural curls. How does she get the look? "I actually don't do much," shares the singer. "I'll just wash my hair, wet it, saturate it down with a product, just let it air dry and 'poof' it out. Sometimes I'll swing my hair over and wear it heavier on one side."
We've seen Tiny rock various shades from red to her current color, blonde. Tiny dishes on her golden tresses: " I like blonde but I'm very funny about blonde hair. The color blonde that I'm wearing now is not the color I want to be," says Tiny. "I like blonde—ice blonde—but I know it's very damaging so I'm a little concerned that [going that light] would take away from my curls."
Tiny shares when she feels the most beautiful: "When I'm just wearing my face at home, relaxing with my kids, being a mother and being around family and friends who know me and really love me for me," says Tiny.


text:
The Goals of the Liberty Dollar
And how it intends to achieve them
To put a powerful proactive symbol in the hands of the people that builds consensus every time the Liberty Dollar changes hands.
To educate the people about the our country's monetary system and how they can protect themselves and their money.
To issue an honest medium of exchange that maintains it purchasing power.
To help the American people preserve their wealth and alleviate some of the pain and suffering from a monetary crisis.
Liberty Dollar intends to achieve these goals slowly. This is to say that the success of the Liberty Dollar is designed to be a gradual, evolutionary process rather than a costly and destructive revolutionary process.
This evolution begins with education, as one person shares the Liberty Dollar with another person. The process continues when you use the Liberty Dollar for day to day transactions. And it accelerates when you become a Liberty Associate.
Every time you convert a US dollar into a Liberty Dollar, our country is one dollar closer to a sound monetary system. Sure, that may seem like an infinitesimal bit of progress, but that is exactly how evolution happens.
The simple, peaceful, private action of converting US dollars into Liberty Dollars is making a vote for returning our country to value based economy - one dollar at a time. It's a vote that - unlike a vote in the electoral process - really counts.
You will like the feeling of the Silver Liberty in your hand and that your Liberty Dollars are backed by and redeemable for .999 fine silver. You'll like the feeling of knowing that you took action that counts. The Liberty Dollar is not owned by the Federal Reserve. It is owned by the people who use it.
American Liberty Dollar has grown from a small group of dedicated Americans into a large national organization by good people like yourself choosing to protect the purchasing power of their money with the Liberty Dollar and continues to expand in a truly decentralized fashion. You are invited to become a Liberty Associate. You will be doing what is right and making money too.


text:
2. Make a confession.
4. Favorite color? For clothing I am always a sucker for shades of pink and burgundy. BUT, lately I've really liked some of the beachy colors. For the house I love the natural colors or the beachy blues and corals. So my tastes are shifting a little bit.
5. Can you drive?
1) People who drive while talking on their cell phone and clearly should not try doing more than one thing at a time.
2) People who think they know everything about everything and are too busy to listen so they try to tell you what you are about to say, or they do not remember anything you say because they were never listening in he first place because they thought they had your situation all sized up. (I do love it when they find out they were wrong though. That's fun to watch.)
3) When my family forgets to close and lock our security door.
8. Something you miss.
9. What song is stuck in your head at the moment?
11. Favorite band.
12. Something you're excited for.
13. Favorite movie.


text:
Read this tip to make your life smarter, better, faster and wiser. LifeTips is the place to go when you need to know about Junkyard Parts and other Junk Yard topics.
Many junk yards let customers pull their own junkyard auto parts. This helps keep costs down and assures the customer they are getting the part they really need. Many junkyards also organize their yards by car make and model, so if you're searching for a Chevy part, they can point you right in the direction of the Chevy junk yard area. Before you begin there are some things to remember as you head out to pull your own junkyard auto parts.
· Always wear closed toe shoes for safety.
· Usually junkyards won't allow anyone under the age of 18 on the lot.
· Bring your own tools to pull parts.
· Cars should be on stands or stable before you pull parts.
· Ask for help if you can't remove a part by yourself, most junkyards offer help with tricky or dangerous removals.
· Never climb on vehicles, especially if they are stacked or unstable.
Pulling your own junkyard auto parts is easy if you follow these simple safety rules! Find a junk yard that will let you pull your own parts and save big.
|Guru Spotlight
|Lynne Christen


text:
Pokki 0.250
Create Desktop Apps With Pokki.
Pokki by SweetLabs, Inc. is an application platform for creating desktop applications using HTML5, CSS3 and JavaScript. Pokki 0.250 uses Chromium internally, meaning layout and rendering is powered by WebKit and JavaScript is powered by V8 – giving you the latest and greatest of HTML5. If you are a front-end web developer, you are also a Pokki [pokki0.250.exe] developer! Beyond the standard HTML5 features you are accustomed to, Pokki - 0.73MB gives you a set special JavaScript APIs and events, a window for your application called a popup, and an invisible background window for notifications called a background page. Pokki 0.250 also takes care of all the " desktop" stuff you don' t want to think about, like memory management and installers, so you can focus purely on application development.
What is new in official Pokki 0.250 software version? - . What is expected in the future? Newly-made Pokki 0.251 be downloaded from current page, we also looking forward to unconfirmed 0.252 release build. You may download Pokki_PokkiSetup.exe directly, estimated download time by ISDN or CDMA [~128 kbit/s] is 0:00:41. Just write the reviews of the Pokki. System requirements are unspecified. Program has been scanned and verified by the several antivirus and anti-spyware applications and Pokki found to be clean. No guide or Pokki tutorial available. The following languages are supported by Pokki: English.


text:
Lewes, DE -- (SBWIRE) -- 08/06/2013 -- LeadingStockAlerts is a financial marketing firm that specializes in assisting the underserved small cap and micro-cap stock community. Our Today's Focus is on: Alcatel Lucent SA (ADR) (NYSE:ALU), MGM Resorts International (NYSE:MGM), Pfizer Inc. (NYSE:PFE), Sirius XM Radio Inc (NASDAQ:SIRI)
Alcatel Lucent SA (ADR) (NYSE:ALU) plunged -3.50% to $2.54 during the mid-day trading hours with the total traded volume of 15.12 million shares. ALU has positive weekly performance of 19.55% and its year to date performance is 89.21%. Alcatel Lucent SA is a France based company that proposes solutions used by service providers, businesses, and governments worldwide to offer voice, data, and video services to their own customers.
Has ALU Found The Bottom And Ready To Gain Momentum? Find Out Here
MGM Resorts International (NYSE:MGM) jumped +3.63% to $17.15 in the mid-day trading hours with the total traded volume of 12.91 million shares more than the average volume of 8.66 million shares. MGM has market cap of 8.39 billion and its beta value stands at 3.70 times. MGM Resorts International is a holding company. The Company is a hospitality company.
For How Long MGM will Fight for Profitability? Read This Trend Analysis report
Pfizer Inc. (NYSE:PFE) gained +0.14% to $29.22 in the mid-day with the total traded volume of 11.21 million shares. Its fifty two week range was $23.55-$31.15. The total market capitalization remained $207.33 billion. Company's current year earnings per share grew with 18.90% while the five year EPS growth rate was +1.30%.
For How Long PFE Gloss will Attract Investors? Find out via this report
Sirius XM Radio Inc (NASDAQ:SIRI) soared +0.53% to $3.81 during the mid-day trading session with the total traded volume of 10.18 million shares. SIRI has earnings per share of $0.07 and its price to earnings ratio is 51.12. Sirius XM Radio Inc. broadcasts its music, sports, entertainment, comedy, talk, news, traffic and weather channels in the United States on a subscription fee basis through its two satellite radio systems.
Will SIRI Continue To Move Higher? Find Out Here
About LeadingStockAlerts:
LeadingStockAlerts is a financial marketing firm that specializes in assisting the underserved small cap and micro-cap stock community.
Our site has been the clear choice for today's investors and day-traders. As one of the internet's premiere financial destinations, we offer the investment community some of the market's leading emerging opportunities. Using a balanced combination of industry experience and high-tech offerings, this site keeps you ahead of the curve and ahead of the bell.
DO NOT BASE ANY INVESTMENT DECISION UPON ANY MATERIALS FOUND ON THIS REPORT OR WEBSITE. We are not registered as a securities broker-dealer or an investment adviser either with the U.S. Securities and Exchange Commission (the "SEC") or with any state securities regulatory authority. We are neither licensed nor qualified to provide investment advice.
The information contained in our report should be viewed as commercial advertisement and is not intended to be investment advice. The report is not provided to any particular individual with a view toward their individual circumstances. The information contained in our report is not an offer to buy or sell securities. We distribute opinions, comments and information free of charge exclusively to individuals who wish to receive them.
Read Full Disclaimer at: http://leadingstockalerts.com/disclaimer/


text:
POLICE are urging residents to help them track down thieves who are stealing paving stones from streets at the dead of night.
A spate of thefts has been recorded in the Plungington area of Preston over the past few months.
PC Jenny Coupe, the area's community beat manager, is asking people in the area to be "extra observant" and to report any suspicious people or vehicles.
The thefts have been happening late at night in streets in the neighbourhood, with flag stones being lifted and removed.
Anyone with information ring 101.


text:
Reese Caldwell has a secret weapon - she talks with her dead twin brother. Together they hunt the scum of the earth, child killers and rapists, and take justice into their own hands. When a world renowned psychic medium unexpectantly enters Reese's life, she is confronted with hiding her secret and compelled to find her brother's long lost murderer.
The_Read_Aholic May 09, 2018
Why are they wearing such warm clothes in summer. Bring those skirts and crop tops out!
Anna90Alex Nov 11, 2017
Its reallt bad when twins get seperated. Here two of them are close too..
GotTheStyles Apr 02, 2017
Random but my brothers name is Rhys, pronounced the same as this. Boring fact of the day. Everyone can sleep easy knowing this.
pensandnibs May 28, 2016
I'm guessing Luke died. STOP I JUST DEVELOPED A CRUSH ON HIM.
JenniferAnnLewis Jun 29, 2016
Love it already! I enjoy how much you make us like Luke in just one chapter so that when we know he isn't coming home, we are super saddened. At least I am! Reading on!
PennyZee Jul 25, 2015
Excellent chapter! Reese should have listened to that feeling she had about her brother. Some call it your sixth sense, some refer to it as that little voice speaking to you.


text:
A pair of former members of Burlington Country Club returned to the course on Thursday and had great success in the Golf Association of Philadelphia�s 109th Open Championship.
Joe April and Jack Wallace finished 1-2 atop the leaderboard to qualify for the Open Championship on July 17 at Waynesborough Country Club in Paoli, Pa.
April, a member at Burlington (par 70, 6,725 yards) from 2008-11, earned medalist honors with a 4-under-par 66, while Wallace, a former Rancocas Valley High School standout, settled for a 3-under 67 to top the field of 98 players.
Ironically, both April and Wallace now play out of the Philadelphia Cricket Club. When April set the competitive course record of 63 at Burlington in 2006 as a non-member, he was playing with Wallace.
Both golfers made the turn at 4 under and at one point Wallace got to 5 under. However, a couple of poor chips eliminated any thoughts of the course record.
�Yes (I was thinking about it),� said Wallace, who now lives in Plymouth Meeting, Pa., in a GAP news release. �I had four birdies on the front and it could have easily been six or seven.��
Wallace, was a member of Burlington from 1994-2011, and his father David is still a member.
Zach Arsenault, a former Shawnee High School standout, playing out of Little Mill Country Club snagged one of the 20 spots for the Open Championship with an even-par 70.
Riverton basketball
7th/8th grade girls: Spitting Llamos (Shelby Young 6) topped The Michaels Development Co. (Jaden Shontz 2).
6th grade & under boys: Delran FOP 230 had four points from Brian Vanettan in a 25-19 win over Southern United Title, LLC (Kevin Fifield 9).


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The head of TransCanada Corp. says he's still optimistic about Canada's liquefied natural gas export prospects.
Russ Girling made the comments Thursday at an investment conference in Whistler.
He says the company sees an emerging window of demand opportunity in 2022 for the Shell-backed LNG Canada project to go forward.
Girling says he expects to hear a decision in the next year or so.
(The Canadian Press)


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It's almost here! The 2015 South County Bridal Show is happening this Sunday, January 4, from 11 a.m. to 4 p.m. Held at The Towers in Narragansett, RI, the show promises an array of South County's top wedding vendors, including Matunuck Oyster Bar, Coast Guard House Restaurant, Susan Sancomb Photography, Weedweavers florist and many more! A variety of door prizes, including a wedding gown, will be given away throughout the day. Order your tickets online now and save: tickets are $13 in advance but will be $15 at the door.
Photo Credit: Courtesy of South County Tourism Council


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These stunning Pom Pom's are VIBRANT and will put a smile on everyone's face no matter where you decide to use them. You can hang them above a child's bed, or in a dark corner of your living room to add a bit of sparkle, or use them as a decoration at your birthday party. The paper decorations will also look absolutely LOVELY in a window as a Christmas decoration.To create a perfect festive look mix and match all colors and sizes. To create a softer more girly look choose the pale pink and white paper decorations.The royal blue and black pom pom's creates a beautiful classic and serious look, and the CUTE white bells are just perfect for Christmas.
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