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Using the variational principle of Ricceri and a local mountain pass lemma, we study the existence of three distinct solutions for the following resonant Duffing-type equations with damping and perturbed term , a.e. , and without perturbed term , a.e. , .
1. Introduction
In this paper, we consider the following resonant Duffing-type equations with damping and perturbed term:
where , , and are continuous. Letting in problem (1.1) leads to
which is a common Duffing-type equation without perturbation.
The Duffing equation has been used to model the nonlinear dynamics of special types of mechanical and electrical systems. This differential equation has been named after the studies of Duffing in 1918 [1], has a cubic nonlinearity, and describes an oscillator. It is the simplest oscillator displaying catastrophic jumps of amplitude and phase when the frequency of the forcing term is taken as a gradually changing parameter. It has drawn extensive attention due to the richness of its chaotic behaviour with a variety of interesting bifurcations, torus and Arnolds tongues. The main applications have been in electronics, but it can also have applications in mechanics and in biology. For example, the brain is full of oscillators at micro and macro levels [2]. There are applications in neurology, ecology, secure communications, cryptography, chaotic synchronization, and so on. Due to the rich behaviour of these equations, recently there have been also several studies on the synchronization of two coupled Duffing equations [3, 4]. The most general forced form of the Duffing-type equation is
Recently, many authors have studied the existence of periodic solutions of the Duffing-type equation (1.3). By using various methods and techniques, such as polar coordinates, the method of upper and lower solutions and coincidence degree theory and a series of existence results of nontrivial solutions for the Duffing-type equations such as (1.3) have been obtained; we refer to [5–11] and references therein. There are also authors who studied the Duffing-type equations by using the critical point theory (see [12, 13]). In [12], by using a saddle point theorem, Tomiczek obtained the existence of a solution of the following Duffing-type system:
which is a special case of problems (1.1)-(1.2). However, to the best of our knowledge, there are few results for the existence of multiple solutions of (1.3).
Our aim in this paper is to study the variational structure of problems (1.1)-(1.2) in an appropriate space of functions and the existence of solutions for problems (1.1)-(1.2) by means of some critical point theorems. The organization of this paper is as follows. In Section 2, we shall study the variational structure of problems (1.1)-(1.2) and give some important lemmas which will be used in later section. In Section 3, by applying some critical point theorems, we establish sufficient conditions for the existence of three distinct solutions to problems (1.1)-(1.2).
2. Variational Structure
In the Sobolev space , consider the inner product
inducing the norm
We also consider the inner product
and the norm
Obviously, the norm and the norm are equivalent. So is a Hilbert space with the norm .
By Poincaré's inequality,
where , is the first eigenvalue of the problem
Usually, in order to find the solution of problems (1.1)-(1.2), we should consider the following functional , defined on :
where , .
Finding solutions of problem (1.1) is equivalent to finding critical points of in and
Lemma 2.1 (Hölder Inequality).
Let f, g , , and the conjugate number of . Then
Lemma 2.2.
Assume the following condition holds.
(f1) There exist positive constants , , and such that
Then is coercive.
Let be a sequence such that . It follows from (f1) and Hölder inequality that
which implies from that . This completes the proof.
From the proof of Lemma 2.2, we can show the following Lemma.
Lemma 2.3.
Assume that and the following condition holds.
(f2)There exist positive constants and such that
Then is coercive.
Lemma 2.4.
Assume the following condition holds.
(f3) for all .
Then is coercive.
Let be a sequence such that . Fix , from (f3), there exists such that
Denote by the set and by its complement in . Put for all . By the continuity of , we know that . Then one has
which implies that . This completes the proof.
Based on Ricceri's variational principle in [14, 15], Fan and Deng [16] obtained the following result which is a main tool used in our paper.
Lemma 2.5 (see [16]).
Suppose that is a bounded convex open subset of , , , , is a strict local minimizer of , and . Then, for small enough and any , , there exists such that for each , has at least two local minima and lying in , where , , where , and .
3. Main Results
In this section, we will prove that problems (1.1)-(1.2) have three distinct solutions by using the variational principle of Ricceri and a local mountain pass lemma.
Theorem 3.1.
Assume that (f1) holds. Suppose further that
(f4) there exists such that
(f5) there exists such that .
Then there exist and such that, for every , problem (1.1) admits at least three distinct solutions which belong to .
By Lemma 2.2, condition (f1) implies that the functional is coercive. Since is sequentially weakly lower semicontinuous (see [16, Propositions 2.5 and 2.6]), has a global minimizer . By (f5), we obtain . Let . Since is coercive, we can choose a large enough such that
Now we prove that has a strict local minimum at . By the compact embedding of into , there exists a constant such that
Choosing , it results that
Therefore, for every , it follows from (f4) that
which implies that is a strict local minimum of in with .
At this point, we can apply Lemma 2.5 taking and as perturbing terms. Then, for small enough and any , , we can obtain the following.
(i) There exists such that, for each , has two distinct local minima and satisfying
(ii) (see [16, Theorem 3.6])
Let be such that
and put . Owing to the coerciveness of , there exists such that . Since is continuous, then
Choosing , hence, for every with , one has
and when
Further, from (3.6), we have that . Since is arbitrary, letting , we can obtain that
Therefore, by (3.6) and (3.11), can be chosen small enough that
and (3.9)-(3.10) hold, for every .
For a given in the interval above, define the set of paths going from to
and consider the real number . Since and each path goes through , one has .
By (3.9) and (3.10), in the definition of , there is no need to consider the paths going through . Hence, there exists a sequence of paths such that and
Applying a general mountain pass lemma without the (PS) condition (see [17, Theorem 2.8]), there exists a sequence such that and as . Hence is a bounded sequence and, taking into account the fact that is an type mapping, admits a convergent subsequence to some . So, such turns to be a critical point of , with , hence different from and and . This completes the proof.
Taking in Theorem 3.1, we can obtain the existence of three distinct solutions for the Duffing-type equation without perturbation (1.2) as following.
Theorem 3.2.
Assume that (f1), (f4), and (f5) hold; then problem (1.2) admits at least three distinct solutions.
Together with Lemma 2.3 and Lemma 2.4, we can easily show that the following corollary.
Corollary 3.3.
Assume that (f2), (f4), and (f5) hold; then there exist and such that, for every , problem (1.1) admits at least three distinct solutions which belong to . Furthermore, problem (1.2) admits at least three distinct solutions.
Corollary 3.4.
Assume that (f3), (f4), and (f5); hold, then there exist and such that, for every , problem (1.1) admits at least three distinct solutions which belong to . Furthermore, problem (1.2) admits at least three distinct solutions.
4. Some Examples
Example 4.1.
Consider the following resonant Duffing-type equations with damping and perturbed term
where , , , , and
in which satisfy
Then there exists , for every , problem (8) admits at least three distinct solutions.
Obviously, from the definitions of and , it is easy to see that is continuous and (f1) holds. Taking , for , we have that
which implies that (f4) is satisfied. Define
Clearly, . Then we obtain that
So , which implies that (f5) is satisfied. To this end, all assumptions of Theorem 3.1 hold. By Theorem 3.1, there exists , for every , problem (8) admits at least three distinct solutions.
Example 4.2.
Let . From Example 4.1, we can obtain that the following resonant Duffing-type equations with damping:
admits at least three distinct solutions.
This work is supported by the National Natural Sciences Foundation of People's Republic of China under Grant no. 10971183.
Duffing, G: Erzwungene Schwingungen bei veränderlicher Eigenfrequenz und ihre Technische Beduetung.
Zeeman, EC: Duffing's equation in brain modelling. Bulletin of the Institute of Mathematics and Its Applications. 12(7), 207–214 (1976)
Njah, AN, Vincent, UE: Chaos synchronization between single and double wells Duffing-Van der Pol oscillators using active control. Chaos, Solitons and Fractals. 37(5), 1356–1361 (2008). Publisher Full Text
Wu, X, Cai, J, Wang, M: Global chaos synchronization of the parametrically excited Duffing oscillators by linear state error feedback control. Chaos, Solitons and Fractals. 36(1), 121–128 (2008). Publisher Full Text
Peng, L: Existence and uniqueness of periodic solutions for a kind of Duffing equation with two deviating arguments. Mathematical and Computer Modelling. 45(3-4), 378–386 (2007). Publisher Full Text
Chen, H, Li, Y: Rate of decay of stable periodic solutions of Duffing equations. Journal of Differential Equations. 236(2), 493–503 (2007). Publisher Full Text
Lazer, AC, McKenna, PJ: On the existence of stable periodic solutions of differential equations of Duffing type. Proceedings of the American Mathematical Society. 110(1), 125–133 (1990). Publisher Full Text
Du, B, Bai, C, Zhao, X: Problems of periodic solutions for a type of Duffing equation with state-dependent delay. Journal of Computational and Applied Mathematics. 233(11), 2807–2813 (2010). Publisher Full Text
Wang, Y, Ge, W: Periodic solutions for Duffing equations with a -Laplacian-like operator. Computers & Mathematics with Applications. 52(6-7), 1079–1088 (2006). PubMed Abstract | Publisher Full Text
Njoku, FI, Omari, P: Stability properties of periodic solutions of a Duffing equation in the presence of lower and upper solutions. Applied Mathematics and Computation. 135(2-3), 471–490 (2003). Publisher Full Text
Wang, Z, Xia, J, Zheng, D: Periodic solutions of Duffing equations with semi-quadratic potential and singularity. Journal of Mathematical Analysis and Applications. 321(1), 273–285 (2006). Publisher Full Text
Tomiczek, P: The Duffing equation with the potential Landesman-Lazer condition. Nonlinear Analysis: Theory, Methods & Applications. 70(2), 735–740 (2009). PubMed Abstract | Publisher Full Text
Li, Y, Zhang, T: On the existence of solutions for impulsive Duffing dynamic equations on time scales with Dirichlet boundary conditions. Abstract and Applied Analysis. 2010, (2010)
Ricceri, B: A general variational principle and some of its applications. Journal of Computational and Applied Mathematics. 113(1-2), 401–410 (2000). Publisher Full Text
Ricceri, B: Sublevel sets and global minima of coercive functionals and local minima of their perturbations. Journal of Nonlinear and Convex Analysis. 5(2), 157–168 (2004)
Fan, X, Deng, S-G: Remarks on Ricceri's variational principle and applications to the -Laplacian equations. Nonlinear Analysis. Theory, Methods & Applications. 67(11), 3064–3075 (2007). PubMed Abstract | Publisher Full Text
Willem, M: Minimax Theorems,p. x+162. Birkhäuser, Boston, Mass, USA (1996)


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Synthesis of carbon nanotubes with and without catalyst particles
Author affiliations
1 IFW Dresden, P.O. Box 270116, 01069 Dresden, Germany
2 Technische Universität Dresden, 01062 Dresden, Germany
3 University of Oxford, Parks Road, Oxford, OX1 3PH, UK
4 West Pomeranian University of Technology, ul. Pulaskiego 10, 70-322 Szczecin, Poland
5 Nanotechnology Center, VSB Technical University of Ostrava, 17. listopadu 15, 70833 Ostrava-Poruba, Czech Republic
6 National Center for Nanomaterials Technology, POSTECH, Pohang 790-784, Republic of Korea
Citation and License
Nanoscale Research Letters 2011, 6:303 doi:10.1186/1556-276X-6-303Published: 7 April 2011
The initial development of carbon nanotube synthesis revolved heavily around the use of 3d valence transition metals such as Fe, Ni, and Co. More recently, noble metals (e.g. Au) and poor metals (e.g. In, Pb) have been shown to also yield carbon nanotubes. In addition, various ceramics and semiconductors can serve as catalytic particles suitable for tube formation and in some cases hybrid metal/metal oxide systems are possible. All-carbon systems for carbon nanotube growth without any catalytic particles have also been demonstrated. These different growth systems are briefly examined in this article and serve to highlight the breadth of avenues available for carbon nanotube synthesis.

subset: commoncrawl


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Brisk trade threatens slow lorises
Cambridge, UK - A little-known venomous primate may be heading towards extinction due to the high demand for its use in traditional medicine. Surveys conducted in early 2014 by Oxford Brookes University and TRAFFIC in the border area between China and Myanmar have revealed the scale of the trade in Bengal Slow Lorises.
08 Jan 2015 | News story
First vulture safe zone declared in Bangladesh
The Government of Bangladesh has declared two safe zones for Vultures where 'zero tolerance' will be shown towards using 'Diclofenac' and other harmful veterinary drugs under article 20 (1) of Wildlife (Conservation and Security) Act 2012. The designated areas are Sylhet, parts of Dhaka and Chittagong covering an area of 19,663.18 sq km (1,966,318 ha) as Vulture Safe Zone-1 and Khulna, Barisal and parts of Dhaka covering an area of 27,717.26 sq km (2,771,726 ha) as Vulture Safe Zone-2 (VSZ). …
06 Jan 2015 | News story
Communities from Southern Lao PDR share experiences on Ramsar site management
Community members from Beung Kiat Ngong Ramsar site in Champasak province recently participated in a study tour in Xe Champhone Ramsar site in Savannakhet province. Held from 10-12 December 2014, the objective of the study tour, which is one of the closing activities of the four-year long Mekong Water Dialogues projects, was for communities to share experiences on Ramsar governance and promote the Ramsar Convention principle on the wise use of wetlands. …
28 Dec 2014 | News story
SOS at World Parks Congress
It's late Monday evening at the World Parks Congress and there is a party booming outside on the lawn. Despite the late hour, upstairs in Hall 2, Pod North is crammed with people. Organised by SOS – Save Our Species, this event featured a selection of grantees presenting on their work. …
23 Dec 2014 | News story
Empowering youth with Ecosystem knowledge: Investing in Future
Youth and the next generations are the owners and beneficiaries of the present day environment conservation. Environmental and ecological problems are emerging as a major challenge in Sri Lanka and expected to get further complicated by the climate change.
23 Dec 2014 | News story
Adapt or die: lessons from Vulture Conservation in South Asia
For SOS Grantee Ananya Mukherjee, switching from dipstick technology to GPS-enabled bird-tagging was a classic case of adaptive management. Indeed it was one that allowed the larger vulture conservation project to continue working towards its objective: creating three effective Vulture Safe Zones (VSZs) on the Indian subcontinent. …
16 Dec 2014 | News story
Launch of Field Guide to Reef Fishes Volume 02
IUCN Sri Lanka launched the second volume of "Field Guide to Reef Fishes of Sri Lanka" at the Auditorium of the National Science Foundation, on December 04, 2014. Written by Mr Arjan Rajasuriya, Coordinator of IUCN Sri Lanka Marine Programmes and produced by Mangroves for the Future (MFF) Sri Lanka. This Volume 2 of Reef Fishes, adds to the comprehensive expanse of knowledge on Reef Fishes provided by Mr. Rajasuriya in his first volume (Rajasuriya, 2013). …
15 Dec 2014 | News story
Helping celebrate more than 50 years of IUCN's contribution to wildlife conservation with a magazine and free digital app
To help celebrate more than 50 years of the International Union for Conservation of Nature's (IUCN) work protecting our global natural heritage, Terre Sauvage has published a special edition of their renowned wildlife magazine. …
11 Dec 2014 | News story
Terre Sauvage Exclusive: Saving Thailand's Blood Wood
Highly prized for making reproduction Chinese furniture, Siamese Rosewood (Dalbergia cochinchinensis) is being poached to extinction in the eastern forests of Thailand. Heavily armed gangs of poachers are invading the forests, where poorly armed, under-resourced rangers are fighting a battle to protect the few trees that remain. …
04 Dec 2014 | News story
Widodo Ramono receives IUCN/WCPA Fred M. Packard Award
SOS congratulates Mr. Widodo Ramono for receiving the IUCN/WCPA Fred M. Packard Award for his long dedication and inspirational leadership in preventing Sumatran and Javan rhinos from extinction. …
02 Dec 2014 | News story


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The Surfin' Cowboy, New Craft Cocktail and Burger Bar, Opens In Capo Beach
Categories: Now Open
Well, he's surfaced, and his project was the Surfin' Cowboy, a new craft cocktail bar and restaurant in the Capistrano Beach section of Dana Point. He is the general manager and designed the drinks menu.
There have been pictures of apple bitters and bacon-infused bourbon and all manner of what people who aren't me call "mixology"; Valiante's a lover of all things agave, so expect plenty of tequilas and mezcales. Also, unbelievably for South County, the place actually stays open late--they're open 11 a.m.-2 a.m. Monday through Friday, 9 a.m.-2 a.m. Saturday, and 9 a.m.-1 a.m. Sunday.
The menu is burgers, sandwiches, bar snacks, salads and specials by Sima Ganaba, formerly of the Resort at Pelican Hill, who's been putting up pictures of her experimentation on Twitter and Facebook. There's weekend brunch, too, with omelettes and panc... uh... flapjacks.
The Surfin' Cowboy is located at 34235 Doheny Park Rd., Capistrano Beach; (949) 272-5957; thesurfincowboy.com (caution: auto-play gun sounds, and you'll get more information from their Facebook page). The restaurant opens at 11 a.m. today.
Follow Stick a Fork In It on Twitter @ocweeklyfood or on Facebook! And don't forget to download our free Best Of App here!
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Posts Tagged 'Northrop Grumman'
Nodine stands trial today
Stephen Nodine is a true Pensacola phenomenon, a rising star that soared into the Pensacola on the back of a Northrop Grumman Air Tanker and today, two years later, stands trial for murder. From 2008-2009, Nodine could do no wrong. He was billed as the politician that understood economic [...]
Viewpoint: On Tanker Contest
From: Stephen Nodine I would like to express my most sincere appreciation to all our friends and partners along the Gulf Coast who joined Mobile's fight to build America's next generation of refueling tankers here. I know we are all sickened by the way things played out: a Northrop [...]
Air tanker deal may be shot down
CQ Politics is reporting that the White House directed the Pentagon to delay procurement of air refueling tankers by five years and cancel plans for a new long-range bomber---which ends the Gulf Coast region's chances of getting Northrop Grumman Corp. to build a plant in Mobile. Read more.


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- Filed Under
"To everything there is a season and a time for every purpose under heaven."
So goes the familiar verse from Ecclesiastes, and the Pete Seeger song that was made an international hit in the 1960s. We are caught up in so many seasons right now. It's fall. The leaves are beautiful. I'm trying hard to notice them - really notice them - before they're gone.
It's soccer season which means we've been really busy with practices and games and we're weary - ready for it to end. But soccer season will quickly give way to the holiday season with all its joys and excitements, and also with a good measure of ...


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" BIG FUN tonight! "
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James Cameron Pushes Back 'Avatar' Sequels
Citing the complexity of writing all three scripts simultaneously, the filmmaker revealed Avatar 2 won't be released until late 2017, a year later than planned.
Citing the complexity of writing all three scripts simultaneously, the filmmaker revealed Avatar 2 won't be released until late 2017, a year later than planned.
The filmmaker gives a totally bodacious update on the status of the upcoming trilogy of Avatar sequels.
The Oscar-winning filmmaker reveals there's "nothing I need to say as an artist" that he can't say through Avatar.
Director James Cameron announces that Sigourney Weaver will return for the Avatar sequels as a new character.
But didn't she die? Looks like that doesn't matter, based on the actress' new comments.
The filmmaker offers an update on the sequels to the 2009 blockbuster, explaining, "We're still in the early stages."
The actors behind Jake Sully and Neytiri will reprise their roles for three more Avatar movies.
The filmmaker and Fox have sealed a deal to shoot the new trilogy in New Zealand, the same country where the first Avatar was filmed.
The deceased Colonel Quaritch will return to the Avatar franchise to terrorize Pandora in a role characterized as "a mix between Star Wars' Darth Vader and Arnold Schwarzenegger's Terminator character."
James Cameron will collaborate with Josh Friedman (Terminator: The Sarah Connor Chronicles), Shane Salerno (Salinger) and Rick Jaffa and Amanda Silver (Rise of the Planet of the Apes) on three Avatar sequels.
Speaking at the NAB Technology Summit on Cinema, producer Jon Landau revealed that for the Avatar sequel, director James Cameron will experiment with using performance-capture technology underwater.
Actress Sigourney Weaver revealed that director James Cameron will film her in in the three sequels to Avatar at the same time.


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Empowering orphans living in extreme poverty using our 360 degree approach to bring solutions to entire communities by developing leaders with the knowledge to develop long-term solutions.
SOAP International is a nonprofit organization dedicated to enhancing the lives of underprivileged orphans living in extreme poverty in East Africa through educational and training opportunities. These opportunities cultivate the lives of orphans who have a love of learning and desire to prosper their life and the lives of others. Through our educational and training opportunities students not only earn an education they are also mentored to become leaders in their communities. As a result, students develop a broader understanding of how to develop self-sustaining and growing improvement in the areas where our students and alumni reside. Making a donation to SOAP International will help us continue enriching the lives of orphans through education who in turn promote self-sustained human prosperity.
Monetary support is raised via fundraising events, private donations and volunteer opportunities. All monies raised are put into a single bank account designated to act as a scholarship for the students sponsored by SOAP.
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Former Child Sudanese Refugee and 'Lost Boy' Dut Aguer Bior is committed to the futures of underprivileged orphans in East Africa. Despite Dut's own struggles, he like many other refugees is remarkably generous and his endeavor is a moving story of courage, sacrifice and hope. Learn More


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Not sure if you remember this case. Back in 2006, a 13-year-old boy named Thomas White reportedly brought a gun to his middle school. He fired one round into the ceiling, and he tried shooting a principal, only the gun jammed, police allege. He was certified to stand trial as an adult, despite being very young, and has been in custody ever since.
He's 16 now. He's being evaluated to see if he's mentally competent to stand trial. Last year, a judge ruled that he wasn't.
Meanwhile, he keeps getting closer and closer to the magic age of 17. Right now, if he's found guilty, he could be put in a juvenile program, get some schooling and counseling. After he hits 17, he must be put in an adult prison. (I remember another case from southeast Missouri, last year IIRC, and another kid, just turned 17, who was being sent to a max-security prison. He killed himself a few hours before they were going to make the transfer.)
I found a really thoughtful post by a Missouri blogger, The Heartland Diary of Betty B, that talks about White's case.


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Find a Parish Near You Using Our Parish Finder
Pope Francis' Vocation Story and The Sacrament of Reconciliation
"For me, this was an experience of encounter: I found that Someone was waiting for me. Yet I do not know what happened. I can't remember. I do not know why that particular priest was there, whom I did not know, or why I felt this desire to confess. But the truth is that Someone was waiting for me. He had been waiting for me for some time. After making my confession, I felt something had changed. I was not the same. I had heard something like a voice or a call. I was convinced that I should become a priest." - Pope Francis
Read more about the encounter Pope Francis had with Jesus Christ in the Sacrament of Reconciliation here.
The Sacrament of Reconciliation
"Three conditions are necessary for Penance: contrition, which is sorrow for sin, together with a purpose of amendment; confession of sins without any omission; and satisfaction by means of good works." - St. Thomas Aquinas
Here are some resources to help you prepare for the Sacrament of Reconciliation:
Examination of Conscience Guides
USCCB - Examinations Of Conscience
National Catholic Register - Confession Guide for Adults & Confession Guide for Children
Lifeteen - Forgiveness is Waiting for You: 8 Tips for an Awesome Confession
FOCUS - Examination of Consience for College Students
Knights of Columbus PDF - A Guide to Confession
Acts of Contrition
My God, I am sorry for my sins with all my heart. In choosing to do wrong and failing to do good,
I have sinned against you whom I should love above all things. I firmly intend, with your help,
to do penance, to sin no more, and to avoid whatever leads me to sin. Our Saviour Jesus Christ suffered and died for us. In His Name, my God, have mercy. Amen.
O my God, I am heartily sorry for having offended Thee, and I detest all my sins because of Thy just punishments, but most of all because they offend Thee, my God, Who art all-good and deserving of all my love. I firmly resolve, with the help of Thy grace, to sin no more and to avoid the near occasions of sin.
Lord Jesus Christ, Son of God, have mercy on me a sinner.
"Confession heals, confession justifies, confession grants pardon of sin, all hope consists in confession; in confession there is a chance for mercy." - St. Isidore of Seville


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The Washington Post | The Oregonian | The Pioneer Log
Before he allowed Lewis & Clark Law School's newspaper to publish an article about Chief Justice John Roberts' visit to the school, Dean Robert Klonoff submitted it to the Supreme Court with "a note that said 'Please let me know if it meets with your approval,'" Robert Barnes reports.
The request — unnecessary, Barnes writes — caused The Pioneer Log to go to press without the story.
Klonoff apologized, telling Oregonian reporter Scott Learn he thought a court request to approve other materials relating to the visit applied to the newspaper as well.
"A justice's visit is especially prestigious for a law school," Barnes writes, "and deference is often extended even when not sought."
"I understand the desire of the law school to appease the chief justice because it's a big feather in their cap," Adam Goldstein of the Student Press Law Center told Learn. "But the law does not recognize a metaphysical state of, 'it (the press) is usually free, most of the time.'"
Zibby Pillote and Anthony Ruiz, the Pioneer Log's editor-in-chief and sports editor, respectively, note in a piece about the fracas that the paper doesn't have a "dedicated faculty advisor" this semester, and that of all the classes in the Rhetoric and Media Studies Department, "none are explicitly related to journalism. This means that there are no dedicated classes on journalistic law or writing practices at LC."
Several editors and writers at The Pioneer Log have stressed the importance of an academic experience for writers and editors, and have expressed disappointment in the lack of academic support offered by the College. It is the position of The Pioneer Log that LC should invest in the journalistic education of its students in order to prevent future "misunderstandings" as well as demonstrate a continued support of free student press.
Related: University of Pittsburgh student government clamps down on press access after unflattering stories (SPLC)


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Worksite Marketing
Worksite Marketing is the distribution channel of insurance products at the work place. This includes complementing any existing coverages by employers for its employees. This distribution channel focuses on employees who wish to purchase additional insurance. Marketing of these products are jointly facilitated through the employees' respective employer at no obligation and no cost to the employer . Premiums are usually paid through Salary Deduction.


text: IBD scholarship empowers students By guest blogger Marie Waine As a university student, I know how challenging school can be: managing money, meeting new friends, keeping up grades and trying to figure out the future. I can¹t imagine what it¹s like to do all this while facing any other pressures, let alone an illness with no known cause or cure. That¹s why I was inspired when I heard about a scholarship specifically designed for students with inflammatory bowel disease (IBD), who are striving to achieve their personal and academic goals despite their condition. The Crohn's and Colitis Foundation of Canada (CCFC) and AbbVie have teamed up to bring an IBD scholarship program for anyone living with IBD and is entering or already in a Canadian post-education institution. There are seven, one-time scholarships of up to $5000 available to support students to continue their education. Inspiring, unstoppable: Clinton Shard, past-winner of the IBD Scholarship and student at Capilano University, British Columbia. ••• Clinton Shard knows what it's like to struggle with Crohn's. The Business student at Capilano University in Vancouver, British Columbia is a past winner of the IBD scholarship. Clinton was diagnosed with Crohn's when he was 12 years old and has faced the challenge of overcoming the many obstacles that living with a chronic illness presents. But he wasn't going to let his illness stop him from attending university. IBD causes inflammation in the intestines due to an abnormal reaction of the body's immune system. It can result in very uncomfortable symptoms, many medical procedures and long hospital stays. And unfortunately, there is currently no cure. Some sobering statistics: • Canada has one of the highest number of reported cases of IBD in the world and many of these diagnoses (20-30%) are to youth under the age of 20. Unfortunately this disease ends up taking a toll on their schooling. • A survey conducted by the CCFC showed 69 % of people who were diagnosed with IBD when they were young were delayed in completing post-secondary education. The IBD scholarship programs aims to provide the opportunity to keep students inspired despite their disease. Do you know a youth who should apply for this scholarship? All he or she needs to do is share how they've reached their life goals while battling IBD. By sharing stories, IBD sufferers can create awareness of the disease and help to reduce stigma surrounding it. The deadline for applications is June 30, 2013. Simply visit the IBD Scholarship web site. And if you have a friend, neighbour, perhaps a colleague at work whose child could benefit from this $5,000 scholarship, do forward this blog post. Who knows, you could just help a determined youth get through school! You might also like:Oct. 21 is the Day of the Mammogram: Have you... 4 things you'll learn about Canadian health... Teens can get fit for free this summer Get a free workout at GoodLife on National He... 2015 World Health Day to focus on food safety


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Narrow your search
The Boston Acoustics TVee One natural-sounding upgrade to your current TV's sound that costs considerably less than its competitors.
The Boston Acoustics TVee sound bars offer a sonic upgrade to flat-panel televisions and can be wall mounted.
The Boston Acoustic TVee Model 25 is a competent, but unexceptional, sound bar with some design flaws that make it not quite worth its premium price tag.
Bethesda's head of marketing told GameSpot that Fallout 4's Boston setting was set many years ago.
Some brilliant YouTube spark has cut footage of Boston Dynamics' humanoid robots performing feats of strength and agility to "Scarface (Push it to the Limit)."
The ride-sharing service says the data, compiled in a way that protects driver and rider privacy, can be used to reduce congestion, expand transportation options and even identify potholes.
A Boston Uber driver who allegedly attacked a woman is charged with rape, kidnapping and two counts of assault and battery.
Twenty-five years after the cult hit monster movie, Bacon is set to produce and star in a TV reboot.
The ride-sharing giant's new safety advisory board along with other related efforts show the company is heeding security concerns.
It might not have spent time officially in geostationary transfer orbit, but Blue Origin's New Shepard rocket successfully landed after a trip to space. That's big news for anyone hoping for a ride toward the stars someday, since reusable rockets mean much cheaper costs for commercial space flight.


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Our mission is to help students become biblically competent, academically proficient, spiritually formed and culturally engaged servant leaders, shaped to be a transforming force in the church, community and world.
Stay connected to our community and help the next generation of Christian leaders become agents of positive change, whether they're serving across the street or across an ocean.
Multnomah Bible College and Biblical Seminary hosted the Northwest Commission on Colleges and Universities (NWCCU) accreditation visitation team on April 19-21, 2006. The team of evaluators is made up of seven people who met with school administrators, seminary and college faculty, and some students and staff.
"This site visit represents the final step Multnomah must take before being granted initial accreditation," said Dr. Wayne Strickland, academic dean and vice president of Multnomah. "We haven't earned the additional accreditation yet, but we anticipate an answer in July at the next commission meeting where they will vote on our accreditation. Until then,we are still in the 'candidacy' phase."
The evaluators were Ms. Natalee Vick from Seattle Pacific University, Mr. Joseph Subbiondo (Chair) from California Institute of Integral Studies, Dr. Terry Mazurak from Albertson College of Idaho, Dr. Phil Alletto from Dixie State College of Utah, and Mr. Rick Gagnier and Dr. Sneh Veena from Heritage University. Dr. Ronald Baker, Executive Vice President of NWCCU, served as liaison during the visit.
Multnomah Bible College is currently fully accredited by The Association for Biblical Higher Education (ABHE) and licensed to grant degrees by the Oregon Degree Authorization Office. The ABHE is the national accrediting association for evangelical colleges that include a substantial requirement for biblical instruction and student ministry requirements. The Council for Higher Education (CHEA), the national accrediting organization, approves the ABHE. The federal Department of Education also recognizes ABHE accreditation.
The Seminary is fully accredited by The Association of Theological Schools (ATS), the national accrediting association of seminaries and theological schools in the United States and Canada.
For more information, call the Multnomah Promotions and Communications department at 503.251.6452 or firstname.lastname@example.com.


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A close family member of one of Detroit's most influential religious leaders was shot to death Monday night inside his home.
Dwayne Green, the brother-in-law of Bishop Charles Ellis, of Greater Grace Temple, was killed.
"He was a family man, a great guy and this is going to an awful void that has to be filled," Ellis said.
Ellis said Green's cousins found him laying on the ground bleeding from a gunshot wound.
"Dwayne was more than a brother, he was our maintenance manager for 15 years here and we're going to miss him," Ellis said. "I am going to need some time, I am so used to helping others through these painful times. Sometimes the physician needs healing himself and all of us, especially my wife and her father, need time to wrap our heads around this."
Green leaves behind a son who attends Jackson College and a daughter who lives in Atlanta.
Bishop Ellis tweeted this Monday night:
@bishopche3: "Pray for My wife Crisette & fam. Her brother shot dead a few hours ago at home in apparent break-in. He supervised our church maint staff."


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October 16, 2008
Mark Stampini
One of the fastest rising prospects in the state of Florida is Pahokee High School cornerback Jarvis Byrd. The 5 foot 10, 175-pound Byrd has seen two new teams contact him recently. "Maryland I have been hearing from them a lot," said Byrd. "Iowa State has offered me and I am supposed to go on an official visit next weekend when they play Texas A&M."When did Maryland come into the picture?"They came in two weeks ago. They are going to watch more film of me and then they may offer me. The head coach has to watch my film."Are you still in contact with FAU?"I still talk to Coach Williams, and I should be going on a visit in January down there."What other schools are you talking a lot to?"Colorado State and Michigan."What did Michigan have to say?"They want to see me raise my test scores and see some more film on me. Coach Smith came down two weeks ago because Brandin (Hawthorne) and Vincent (Smith) have already committed to them. When they were talking to them I got a call to talk to Coach Smith. I talked to him for a good long time."Byrd is a lock down corner that also excels in special teams. He just always seems to be around the ball whether it be an interception or a blocked kick. ...More... To continue reading this article you must be a member. Sign Up Now!
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Personal Liberty Poll
Many Americans have been led to believe that certain catastrophic circumstances are unlikely to occur or that, if they do occur, they are simply not survivable. They believe that preparation for these events is pointless — that one should place them out of mind and think happy thoughts. There are even some preppers who sermonize over the absolute futility of defensive planning where such disasters are concerned. These people are not really survivalists at all, but what are commonly referred to as "doomers."
Sadly, an element of the human psyche revels in the idea of the insurmountable scenario. Some people actually get excited over the clearing of the proverbial human slate, eager for the fulfillment of Armageddon.
I suspect that such people truly feel limited in their ability to survive, and that they perhaps fear the exposure of their own shortcomings and weaknesses. Instead of accepting these weaknesses as a personal reality and attempting to overcome them, they choose to project their vulnerabilities on the rest of the world, claiming: "If I could not survive this, neither could you!" By labeling the rest of humanity as incapable, they can avoid internal self-reproach and the shame of being frightened.
Reality is filled with horrors: some emotionally threatening and some physically threatening. Every once in a while, an event combines the two in a devastating crescendo, the likes of which are rarely seen in history. Yet the fundamental hazards of this one extraordinary and terrible moment are essentially the same as those in any other day.
We face death and psychological defeat daily. This is an unavoidable part of life; anything could happen. Usually, we get over it and set out into the world anyway. To avoid submitting to defeat before even making the attempt to face the day, we treat catastrophe as evident, supplant initial fear with force of will and move forward regardless of the scope of the obstacle in our wake, and are secure in the possibility of victory despite any odds.
In this article, I will examine some of the disaster situations commonly given doom status. With a little insight and research, we can prepare to overcome such seemingly intractable calamities.
The Bomb: What To Expect
First, we must recognize the very real threat of a nuclear-related incident on American soil. Though the immediate dangers of the Cold War appear to have subsided and though globalists seem to be more interested in keeping most of the world intact for themselves rather than ruling over a radioactive dust heap, I suspect that we will within our lifetimes see at the very least a limited thermonuclear event. Beyond the predictable scenario of false flag, the United States is growing increasingly at odds with known nuclear powers, including Russia, China and North Korea. Just last week, Russian officials openly indicated they have no qualms over the use of nukes in response to a conventional threat.
This statement was made in reference to American "global first strike systems" being established in nations on the periphery of Russia's borders.
Under certain circumstances, a nuclear event also has sociopolitical advantages for the ruling class.
Imagine the impression of an actual mushroom cloud over just one U.S. city burned into our collective psyche. Imagine the fear, panic and ignorant reactionary thinking this would cause. There are very few things in this world that are quite as formidable, and the elites are well aware of the advantages inherent in engineering such an occurrence. That is why survivalists and those in the liberty movement should fully expect this ace to be cast to the table at some point in the move toward total globalization.
In the case of a false-flag event, two types of attacks are probable. Both are small — at least when compared to the strike of an intercontinental ballistic missile (ICBM) — but still capable of severe destruction.
Low-yield nuclear explosion: If a false flag is being initiated using a nuclear device, it will probably range in size from 1 kt (kiloton yield) to 25 kt. To understand what this means, examine the bombing of Hiroshima, whose explosion was around 15 kt. A smaller device is more likely because a larger, more complex bomb would be difficult to effectively blame on terrorists and would arouse suspicion.
The blast radius of the Hiroshima bombing was only about 1 mile. Most of the deaths associated with that attack were caused not by the explosion, but by radiation poisoning from the resulting fallout.
Should a similar-sized device detonate, mass fires should be anticipated in areas just outside the blast area where buildings are still relatively undamaged, making perfect kindling for burning wreckage launched into the atmosphere by the detonation. This would cause at least another 4-mile to 5-mile swath of destruction in a densely populated environment.
Fallout from the device would depend on the direction and the strength of the wind at the time of detonation, but could travel for miles beyond the epicenter. Fallout is created when dust from the center of the explosion is irradiated, then carried along wind and weather patterns. The dust emits the radiation it was originally exposed to, and too much contact with it can cause illness or death. Fallout is at its worst if a dust cloud combines with precipitation. This rain cleans the dust out of the sky, but also concentrates it and dumps it on the ground.
Dirty bomb: "Dirty bomb" is a term used for a device made of conventional explosives that is designed to contaminate an area with radioactive material. It does not produce a thermonuclear blast, but it does create some fallout. Though no device of this type has ever been used on a population (unless you count Fukushima), U.S. military analysis has designated it as low-risk and determined its radiation output to be negligible. Any fallout poisoning in water and food supplies is still a serious threat. And the use of a dirty bomb would, of course, inspire mass hysteria, if only due to its relation to nuclear weapons.
One should also not discount the use of a high-grade missile attack, especially an upper atmospheric electromagnetic pulse (EMP).
The preparations for a major attack and a smaller attack are similar.
How To Prepare
The first step in preparing for a nuclear attack is to not be there when the bomb goes off. Avoid living in the middle of a major population center if possible. Most survivalists are aware of the danger of close proximity to the city, whether during a nuclear attack or an economic collapse, and have already taken precautions. Most steps advised herein will be in response to fallout, instead of the blast, being that fallout is the most prominent threat to the survivalist.
Home reinforcement: It takes about two weeks for the radiation in fallout to dissipate to levels safe for humans. During the two-week period, it will be necessary for everyone to stay indoors at all times. Some shelter is better than none at all, but a basement or cellar would be a distinct advantage. Stockpile barrier materials for at least the base of the first floor of the house.
The minimum requirement to effectively reduce gamma radiation to 50 percent of levels outside the home is 22 cm of wood, 8.4 cm of earth, 5cm of brick or concrete, or 2 cm of steel. Cover windows seal them with plastic. Home nuclear, biological and chemical (NBC) air filtration systems are available; but they can be rather expensive.
If you have no basement and you cannot afford to fortify the entire bottom floor, then you will need to create a safe room somewhere in the center of the building with enough protection to absorb radiation. Radiation is cumulative, meaning your body absorbs and collects it over time. Too much absorption causes radiation sickness.
Detection: Radiation is not visible or detectable with our normal senses. Fallout in rain can sometimes appear as a murky film covering surfaces, but that does not mean radiation is present. The only way to detect radioactivity is with a Geiger counter. Having a Geiger counter would be a major advantage in the event of a nuclear attack or other radiological incident.
Food, water and hygiene: It is a given that all survivalists should have a ready supply of food and water, easily accessible in a protected area of the home. Freeze-dried and dehydrated goods are an excellent option because of their 10- to 15-year shelf life. Cooking indoors without ample ventilation can create some problems, but the use of a propane stove for short periods should not cause any harm to the air quality of a shelter.
The human body needs at least two liters of water per day. Store enough water for drinking during the two-week fallout period. Double that amount to have enough water for sanitation purposes. Also, if you are a reasonable distance from the attack and have time before the fallout reaches your location, be sure to fill up all containers, bathtubs and sinks with as much water as possible from the tap. Even if pressure is still available during fallout, the water could be exposed and undrinkable. After the two-week danger period, all water taken from open sources should be filtered to remove any possible fallout particles.
Soap and sponges must be stored for washing purposes, and staying clean should be a priority. Bathroom sanitation is difficult in a fallout scenario. Waste water from cooking and washing can be saved and poured into you home toilet for a single flush if water pressure is lost, but a better option would be a survival or hunters toilet with heavy waste liners and deodorant chemicals. Remember, you won't be able to walk outside for two weeks. A 3-foot hole in the woods is not an option. Dumping refuse outside can be done as long as exposure time is kept to less than 30 minutes, although you will have to rigorously wash off dust and contaminates before coming back inside.
Protecting health: No plan or shelter is perfect. Radiation exposure will be a possibility, especially without an expensive NBC air filtration unit. Gas masks with extra filters should be made available to everyone in the home.
Symptoms of radiation injury include: nausea, diarrhea, light burns on the skin, blistering and increased loss of hair. Radiation burns should be washed with clean water only — no soaps or chemicals — and dressed with fresh bandages. Clothing should not be pulled away from severe radiation burns; and blisters should be left alone, not punctured.
One item that helps greatly in preventing the effects of radiation exposure is the ingestion of potassium iodate, which fills the thyroid and blocks radioactive iodine expelled into the atmosphere from being absorbed. Up to 99 percent of all radiation-induced thyroid damage can be prevented by taking potassium iodate pills. Potassium iodate is available from numerous online vendors and is very affordable.
Protecting electronics from EMP: An EMP is a natural byproduct of a thermonuclear explosion. It creates a powerful electromagnetic field that induces high voltages in electrical conductors and fries most electronics with transistors or computer chips whether they are plugged in or not. Some weapons called high-altitude electromagnetic pulse (HEMP) devices are designed specifically to explode in the upper atmosphere and disable an area's power grid.
Certain electronics, including solar-power generators and other gear, would be very valuable in a survival scenario; and losing said equipment could be detrimental. Protecting it from an EMP blast is a high priority. Even if your gear is stored inside your home, it can be fried by an EMP (though a basement can help). So what is the survivalist to do? Building a Faraday cage is your best option.
A Faraday cage is a box constructed out of conductive materials (like copper mesh), which absorb and then ground the EMP, keeping it away from your sensitive electronic goods. A Faraday cage can be any size and is inexpensive to make. In a pinch, an old microwave can actually serve as a Faraday cage; but it is better to build one.
After The Storm Has Passed
When two weeks have passed, any radiation should have dissipated to tolerable levels. Eventually, rain will clear away remaining fallout dust, which — though no longer a major threat — can still have long-term health effects. Some precautions may be necessary when returning to your outdoor survival routine.
Fresh crops: When gardening, scraping off the top two inches of surface soil removes about 90 percent of all fallout from your garden. This soil should be stored in steel drums far away from your food-producing area. Some pre-existing crops exposed to the fallout can still be saved, depending on their type and stage of growth.
Hunting: Game exposed to some radioactivity can still be consumed, as long as it is prepared properly. All fur should be washed before skinning. Because radiation collects in bone marrow, all meat near the bones should be avoided and bone marrow should not be consumed. All organs should be avoided as well. If an animal looks terribly sick, it is best not to eat it.
Burying the dead: Deal with bodies exposed to radiation carefully. Wrap them in plastic and bury them well away from crop-producing land.
Supporting immunity: Exposure to radiation can do considerable damage to the human immune system and decrease white blood cell count. It is also likely you will not have access to conventional medical supplies, such as antibiotics, to deal with this problem. (If you have a source for antibiotics, store as much as you can now.)
Some herbal supplements can help stimulate immune system health and protect you from adverse reactions. Eastern herbs include: astragalus, ligustrum, codonopsis, reishi, and shiitake. Another, caterpillar fungus, has been shown to protect the bone marrow and digestive functions in mice from radiation. Western herbs include cat's claw, echinacea and elderberry. These herbs can be taken in pill form; but if you find them in an organic tea, this would be preferable. The body absorbs only a small fraction of herbs through digestion; but teas have the added bonus of being breathable, meaning the vapors can enter the lungs absorbing 80 percent of their contents into the blood stream.
Treating the sick: For perhaps a month after an attack, you may run across people who survived the blast and the fallout but are extremely ill from exposure. Under normal conditions, radiation poisoning would require hospital care, blood transfusions, antibiotics and bone marrow transplants. These will probably not be available options. There is little that can be done under such limits except holistic treatments for nausea and diarrhea, so that the patient might retain some liquids; the cleanly dressing of wounds; and the consumption of the immunity-boosting herbs mentioned above. Be prepared for some people to die despite your best efforts. Those who did not plan ahead as you did will be subject to the toss of the dice, and luck is a fickle ally.
We've all seen movies and read books of nuclear holocaust, and the utter despair it could conceivably initiate. Of course, nuclear attack should not be underestimated — far from it. However, rarely in these films or fictional accounts do you see characters who prepared beforehand, who had readied themselves physically and psychologically for the aftermath. This is a symptom of the common assumption that one "cannot survive" nuclear attack and that, even if he did, he would be better off dead. I tend to disagree, and so do the U.S. Army and the Russian military, which have undergone extensive planning and written detailed manuals for soldiers on nuclear survival.
With the correct mindset and the right knowledge, any catastrophe is survivable, including "the bomb." Futility arises only when a man decides for himself that he is not capable. To endure, one must make himself a master of his circumstances, rather than a slave to them. This concept is at the heart of all survival.
–Brandon Smith


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FTSE gains for second dayComment on this story
London - Britain's top share index rose on Thursday, with investors' risk appetite rising after minutes of the US central bank's latest policy meeting suggested it would be more cautious in raising rates than expected.
The blue-chip FTSE 100 index rose 0.8 percent to 6,685.37 points by 10:00 SA time after gaining 0.7 percent in the previous session.
The index is still down nearly 1 percent this year after surging 14 percent in 2013.
Cyclical shares were broadly in demand, with the UK banking index rising 1.1 percent and miners up 0.9 percent as the Federal Reserve minutes prompted a shift in expectations of when US interest rates will start to rise.
Trading interest-rate futures showed expectations of a first rate hike had been pushed out by about six weeks, to July 2015.
"The market probably got a little bit ahead of itself in terms of expectations of the timing of the first rate rise. The market is taking (the Fed minutes) into account and that's positive for sentiment," said Henk Potts, equity strategist at Barclays Wealth.
The FTSE 100 was also supported by strong gains recorded by some individual shares following their announcements.
Retailer Marks & Spencer gained 2.6 percent, the biggest percentage gainer on the FTSE 100, after signs its turnaround programme may finally be gaining traction.
Its fourth quarter results showed an improvement in the sales falls suffered by its main non-food division.
Royal Bank of Scotland climbed more than 2 percent after it said it had agreed to pay 1.5 billion pounds ($2.5 billion) to cancel an arrangement that gives the government priority over dividends, clearing an obstacle to the lender's eventual privatisation.
"The agreement ... is a welcome step in the road to RBS becoming a normal bank with the ability to pay dividends to shareholders, which should help in making the share a more attractive proposition to investors," Espírito Santo Investment Bank said in a note.
Despite rising for two straight sessions, analysts said the stock market remained vulnerable due to lingering geopolitical tension in Ukraine and concerns about growth in China, the world's biggest metals consumer and the second-biggest economy.
Chinese Premier Li Keqiang ruled out major stimulus to fight short-term dips in growth, even as big falls in imports and exports data reinforced forecasts that the world's second-largest economy has slowed notably at the start of 2014.
Li stressed on Thursday that job creation was the government's policy priority, telling an investment forum it did not matter if growth came in a little below the official target of 7.5 percent.
Charts showed the FTSE 100 had slipped into a short-term range, with resistance at 6,700 and support at around 6,500.
"The strength of the long-term trend still implies that any break is likely to be to the upside, but the fact that the index is struggling to get away from the lows is still a cause for concern," Charles Stanley technical analyst Bill McNamara said. - Reuters
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