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Thursday, August 8, 2013
Repost: When is your HVAC too old to repair?
Posted by Nickadeemus at 10:34 AM
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I've been wondering this about my hvac in Calgary. Do you know where I can find more information on this?ReplyDelete
In Chicago you are require a Furnace repair Services provider ..
You contact to MDB Mechanical. They provide all heating and cooling home services for your HVAC installation, tune-up or repair, you know we'll get the job done right and stand behind our work.
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Here is where to find great deals for Robby Krieger tickets. As you browse Ticketpolice, you are putting a hand on cheap tickets for Robby Krieger events including those appearing in many cities including Nashville, Indianapolis, Chicago and more. Purchase Robby Krieger tickets here at very low prices.We found 3 events sets found available in this time for 'Robby Krieger'
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Algonquian Tribes | Communities | First Nations | Ojibway Indians History | Reservations | Tribes
Rocky Boy Tribe of Chippewa Indians of Montana Needs Your Help
Rocky Boy Tribe of Chippewa Indians of Montana needs funding to establish offices at Blackfeet Reservation, Crow-Northern Cheyenne Reservation, Flathead Reservation, Fort Belknap Reservation and at Great Falls, Montana where Hill 57 Reservation is located. Our goal is to gain Tribal Recognition at Blackfeet Reservation, Crow-Northern Cheyenne Reservation, Flathead Reservation and Fort Belknap Reservation and Federal Recognition for Rocky Boys Tribe of Chippewa Indians at Great Falls with Reservation. Your donation will be greatly appreciated. Below is my paypal link where you can donate to this very important cause for survival. If you are interested in becoming a member of Rocky Boys Tribe of Chippewa Indians of Montana, you can fill out a form here . In comments box, please include your tribal affiliation. In Montana, members of Blackfeet, Crow-Northern Cheyenne, Flathead, Fort Belknap and Rocky Boys Reservation are automatically members of Rocky Boys Tribe of Chippewa Indians of Montana. However, if you are a member from another tribe (Reservation) your application will be approved if you have proof of membership from your tribe (Reservation).
Click Here To Donate
June 19, 1813 Battle of Pequereque
This is yet another battle which is considered by historians to have been a part of the Alto Peru Campaigns, or a part of the Argentine War of Independence. It was, however, just another battle between the Anishinabe Army and army of the white confederation led by England, for control of South America. It was a minor battle between 135 brave Anishinabe soldiers and nearly 200 soldiers from the white confederation. It was fought in Bolivia which means the whites were yet still trying to control land away from the Pacific Coast. Anishinabe soldiers defeated the soldiers from the white confederation. Anishinabe casualties were 3 killed and 10 wounded. White casualties were 10 killed and 20 wounded.


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2017 marks Dietsmann's 40 years anniversary
In 1977 Peter Kütemann established Dietsmann and won his first contract to provide crew for a single gas production platform in the Dutch sector of the North Sea. Peter Kütemann, as President & CEO, has since led the company through many challenges and successes. To celebrate the 40-year milestone in 2017, a book will be published detailing the history of the company. Unlike typical corporate publications, Dietsmann's history will be told in a... comic book.Read post
Dietsmann joins the SPRINT Robotics initiative
As part of its continuous efforts to implement smarter and, first and foremost, safer operations, Dietsmann recently joined the Sprint Robotics Collaborative (http://www.sprintrobotics.org) as a participant. The SPRINT Robotics Collaborative is a new, industry-driven initiative that promotes the development, availability and application of robotics techniques in the technical inspection and maintenance of capital-intensive infrastructure.Read post
Dietsmann awarded first prize in EPC-Construction category during ENI's Worldwide Safety Day 2016
During ENI's Worldwide Safety Day, which took place in Milan on 16 May 2016, Dietsmann was awarded the first prize in the EPC-Construction category.Read post
Continued efforts maintain Dietsmann's good HSE performance in 2015
The continued efforts of its employees to prevent work accidents and their disciplined safe working attitude resulted in further improvements to Dietsmann's HSE performance in 2015 - an LTIF of 0.08 for a total of 12.5 million man-hours worked and a TRIR of 0.64.Read post
Dietsmann's 4th year of commitment to the UN Global Compact initiative
In 2015 Dietsmann published its fourth annual Communication on Progress report since the Company became a signatory to the UNGC - the world's largest corporate citizenship and sustainability initiative - at the end of 2011. The UN Global Compact is both a corporate responsibility initiative and a strategic policy initiative for businesses that are committed to aligning their operations and strategies with 10 universally accepted principles in the areas of human rights, labor, the environment and anti-corruption.Read post
Dietsmann awarded continuation of General Maintenance Services contract in Libya
In March 2016 Mabruk Oil Operations awarded Dietsmann a five-year Marine Operations & Maintenance Services contract for the offshore Al Jurf site. The Al Jurf site comprises the FPSO Farwah and a platform. The contract, which will start in April 2016, is a continuation of the initial one-year contract awarded in April 2015. It includes the General Maintenance Services as well as the Fabric Maintenance, Production, Marine and Logistics Services. In carrying out this contract Dietsmann will, as always, strive to maximize local employment.Read post


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Helping Hannah: 3D Printer to the Rescue
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Published: December 19, 1993
(Page 2 of 2)
"The military will discharge members who engage in homosexual conduct, which is defined as a homosexual act, a statement that the member is homosexual or bisexual, or a marriage or attempted marriage to someone of the same gender," the guidelines issued in July said.
"An allegation or statement by another that a service member is a homosexual, alone, is not grounds for either a criminal investigation or a commander's inquiry," the guidelines said. "Only credible information that a service member engaged in homosexual conduct will form the basis for initiating an inquiry or investigation of a service member."
But gay rights groups complained that the legislation that Mr. Clinton eventually signed into law was silent on many of the provisions on what constituted credible information. Administration officials said the specific regulations to commanders -- detailed legalistic language as well as practical instructions -- would fill any gaps.
Senior Pentagon officials said the nomination on Thursday of Bobby Ray Inman, a retired admiral, to replace Mr. Aspin would probably not delay the announcement of the new regulations.
Pentagon officials have taken extraordinary steps to prevent premature disclosure of the regulations. Military and civilian officials who received a briefing on the guidelines were sworn to secrecy. Those who want to read the actual language must go to a secure reading room at the Pentagon, sign in and sign out. There are no copies to take home for leisurely perusal.
Pentagon officials involved in writing the regulations say disputes over language and illustrative scenarios and resolutions have been resolved to insure broad commander discretion in handling possible violations.
"People are quibbling over a word here or there, but at this point, I think most everyone feels we have a workable policy that meets the commitment the Administration made," said one senior military lawyer.
Court challenges, however, could upset the carefully laid plans. Lawyers at the Pentagon and Justice Department disagree on how to deal with a Federal appeals court ruling in Washington last month that struck down the old Pentagon rules under which the Navy had dismissed a midshipman, Joseph C. Steffan, from the United States Naval Academy in Annapolis.
There is no consensus even within the Justice Department. Some officials there believe it is best to write off the past, let the appeals panel ruling stand and marshal the department's best arguments and financial resources to defend the new policy against anticipated court challenges.
Other lawyers at Justice and virtually all Pentagon officials believe it is necessary to appeal the ruling on the former policy, even though it will soon be superseded, because the constitutional challenge could undermine Mr. Clinton's new rules.
"The question is whether the President's policy could survive a Steffan-type analysis, and I have serious doubts it could," said one senior Pentagon official.
The Government has until Dec. 30 to make a decision. In an interview, Drew S. Days 3d, the Solicitor General, declined to say what action the Administration would take.
In another important case, a Federal appeals panel in San Francisco heard arguments last Thursday from Government lawyers to reject a lower court order that barred bias against homosexuals in the military.
In that case, the Government is appealing a series of decisions made by Judge Terry Hatter of Federal District Court involving an openly gay seaman, Keith Meinhold. Mr. Meinhold was discharged from the Navy in August 1992 after he admitted his homosexuality on national television.
Last January, Judge Hatter ordered Mr. Meinhold's reinstatement and ruled that the military's ban on homosexuals was unconstitutional. In September, Judge Hatter expanded that ruling, ordering the military to stop discriminating against homosexuals. But the United States Supreme Court set aside the second order in October pending the outcome of the Government's appeal, which could be several months away.


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Cat n Jack image from Inky Antics and shaded it with pencil. The image was colored with Copic Markers.
Have a happy sort of day!
Tuesday, October 14, 2014
Halloween Kitty
Posted by Michelle Pearson at 12:01 AM
Labels: Animals, Copic Markers, Fall, Halloween, Inky Antics
4 comments:
- Maxine D said...
Thanks for the smiles Michelle - this is a gorgeous card, beautifully coloured and tangled.
- October 14, 2014 at 1:32 AM
- Debbie Fisher (debbiedee) said...
L♥VE this! so rich in color and the zentangle makes it pop even more!
- October 14, 2014 at 8:21 AM
- Janeen said...
So bright and cute.
- October 14, 2014 at 8:30 AM
- Barbara Thompson said...
So stinkin cute!
- October 21, 2014 at 8:30 AM
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Personal Statement
Hello and thank you for visiting my Lybrate profile! I want to let you know that here at my office my staff and I will do our best to make you comfortable. I strongly believe in ethics; a......more
Hello and thank you for visiting my Lybrate profile! I want to let you know that here at my office my staff and I will do our best to make you comfortable. I strongly believe in ethics; as a health provider being ethical is not just a remembered value, but a strongly observed one.
More about Dr. Vasim
Dr. Vasim is one of the best Homeopaths in Sharanpur, Nashik. Doctor has been a practicing Homeopath for 13 years. Doctor studied and completed BHMS . You can consult Dr. Vasim at Asher Clinic in Sharanpur, Nashik. You can book an instant appointment online with Dr. Vasim on Lybrate.com.
Lybrate.com has a nexus of the most experienced Homeopaths in India. You will find Homeopaths with more than 35 years of experience on Lybrate.com. You can find Homeopaths online in Nashik and from across India. View the profile of medical specialists and their reviews from other patients to make an informed decision.
Lybrate.com has a nexus of the most experienced Homeopaths in India. You will find Homeopaths with more than 35 years of experience on Lybrate.com. You can find Homeopaths online in Nashik and from across India. View the profile of medical specialists and their reviews from other patients to make an informed decision.
BHMS - Motibala Medical College - 2004
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Asher ClinicShree Prakash Complex, Behind Kulkarni Garden, Sharanpur Road, Nashik Get Directions
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33 years old male from Kolkata asked
Hiy sir. My wife was suffering from hair fall issue. I was being happening since 4 month ago. She were using shampoo named these men hair fall shampoo, but not any result. please help out. Her age was: 24 Weight: 45.
M. Ch. (Plastic Surgery), MS - General Surgery, MBBS
Cosmetic/Plastic Surgeon, Delhi
Mr. lybrate-user. There are many reasons for hair fall. It is important to first examine the scalp before prescribing any treatment .We have different modalities for hair fall like mesotherapy ,PRP, etc.
21 years old male from Panchkula asked
Mere face pe bhut pimples h or muje allergy bi hoti h jisse bhut khujli hoti h dhupai bi or chote chote dane ho jante h.
MD - Homeopathy
Homeopath, Aurangabad
Following homoeopathic medicines available in homoeopathic shop. Use berberis aquifolium q sbl 20 drops in water x 1 month also apply berberis aq cream which is available in your city any company do exercise no night watching no outside food repeated (3 to 4 times) face wash with ayurvedic soap or face wash plenty fruits and vegetables.
21 years old female from Ludhiana asked
Sir I have tinnitus problem. I am taking vertin 16 mg since a month. But no positive result I got rather the pitch is increasing. As mention to take vertin 16 mg 1011 what does this 1011 indicates.
MD - Homeopathy
Homeopath, Vadodara
To treat tinnitus first we need to know the reason... wheather is it functional or there are some pathology behind it... If you have got diagnosed then share it... And to prescribe a good homeopathic medicine more details are required... But for your assurance homeopathic medicine are very good in such conditions and if given properly then can produce lasting result without any side effects...
17 years old female from Jaipur asked
I am 17 year old girl. I have been having vaginal discharge since a week. It's white thick fluid and has a faint unusual odour. Is it normal or some type of infection? Is there a medicine that I can consume for discharge?
PG Diploma in Emergency Medicine Services (PGDEMS), Bachelor of Ayurveda, Medicine and Surgery (BAMS), MD - Alternate Medicine
Ayurveda, Ghaziabad
Cook a handful of rice in a half a lit of water in an open pan. When rice is ready don't throw the residue water drink reason this water when it remains that much hot that you can consume. Drink it on adding 1 tsp of sugar. This relieves your leucorrhoea that within a week. This is one of the most common home remedies for leucorrhoea. Take pranacharya leucorest syrup 2-2 tsf twice a day. And pranacharya leucona capsule 1-1 twice a day.
A person asked
My father bp is always above 155/85. Earlier he was on cresar 40 in morning and amlovas 5 in evening. We increased the dose of cresar To 80 still even after 4 weeks the BP is either same or sometimes even more. He has hyponatremia so a diuretic I don't think should be added. Other tests are normal. Pls advise. Is Telma 80 a better choice than cresar.
MBBS, MD-General Medicine, DM - Cardiology
Cardiologist, Secunderabad
Dear Shaban, Medicine is just one component of treatment. Lifestyle modification like exercise,wt management, low salt and low fat diet, stress management, regular sleep, etc are another important component which many people ignore. What your father needs is stringent lifestyle measures. If his BP is still high we can modify his medicines.
23 years old male from Malappuram asked
I am 23 years old boy. My current height is 155 cm. Can I increase my height upto 160 cm with daily workout? This is for join navy.
DHMS (Diploma in Homeopathic Medicine and Surgery)
Homeopath, Hyderabad
Take protein rich food -eggs, milk products, seeds, pulses, dry fruits, soya milk etc. Whole grains, fruits, vegetables and greens provide carbohydrates, vitamins and minerals. Have vigorous physical exercise to improve absorption of food and blood circulation. Games like basketball, volley ball and stretch exercises like pull ups, cycling will be helpful. Chances are better for the age group up to 20 years. Homoeopathic treatment will be beneficial to you.
20 years old male from Vijayawada asked
Doctors I want to take an health diet. I must be fit and due to sun my skin tone is little dark so I want to improve my skin tone. So please suggest me Complete food table what to eat and what to not eat.
B.Sc(hons), Physics, B.H.M.S., PGDIT (software Engg)
Homeopath, Delhi
Drink fruit juice and water daily maintain good habit means no alcohol smoking and outside oily food.
36 years old female from Mumbai asked
I'm 35 years old. Unmarried.have thyroid at boarder. Not taking any medication. Height is 5'4 weight is 65 kg. Want to reduce weight by 10 kg but without loosing face loose skin.
MBBS, CCEBDM, Diploma in Diabetology
Endocrinologist, Hubli-Dharwad
Hi, what do you mean by" thyroid at border? give the test results. Looking at your height and weight, present weight is actually normal (height in cms - 100 = ideal body weight). If you still want to reduce weight, then do some exercise regularly like jogging, skipping and running or swimming. Plus reduce present caloric intake by about 500 calories per day. Thanks for the question.
31 years old female from Bangalore asked
I am 25 years old I am from bangalore last night I was doing some work unfortunate I fell down on the ground I had some kind of illness like headache.
General Physician, Mumbai
For headache take tablet paracetamol and get your vital parameters of the body checked and revert back with your findings
23 years old male from Mumbai asked
How to gain a weight faster without having any supplement or any drugs in a working time tell me if have clue 9f it thanks in advance.
Homeopath, Raebareli
Please note the followings in respect to your queries: 1. Banana and Milk -- Bananas are full of calories and contain high amount of carbohydrates and potassium that give you instant energy. Whosoever want to gain weight must eat a banana daily in the morning with a glass of warm milk. Add a teaspoon of sugar in it. Moreover, you can also have it after your meals. Note – Don't eat bananas when you are down with common cold. 2. Peanut Butter -- Peanut butter is a yummy spread for toast and bread. If you're trying to gain weight, feel free to go for this high-calorie and nutritious food. Apply it on your whole wheat bread for breakfast and see how your weight increases within a short period of time. •Besides, you can spread a spoonful of peanut butter on fruits or vegetables like banana, apple slices, fresh berries, wheat germ or applesauce. •Alternatively, a peanut butter sandwich is also a good choice. If you have any medical disease that needs to be treated.
20 years old female from Jodhpur asked
I am suffering from skin itching problem and this problem increasing day by day but not relief .I have gone through clinic tests .Tell me solution of this problem.
MD - Skin,VD & Lepxsy
Dermatologist, Hyderabad
Hello lybrate-user, use cetaphil cleansing lotion for your skin. If you have an uncontrollable sensation to scratch your skin, then you have a condition called itchy skin. There can be many causes of itchiness like dry skin, skin rashes, internal illnesses like kidney or liver disease, deficiency of iron, thyroid disorder etc. Sometimes itchy skin can also be due to irritation or allergic reaction to certain chemicals, soaps, cosmetics, pollution or sun. So to find the exact cause of itchiness is important to start right line of treatment either in the form of oral medications or topical medications. A dermatologist can give you right guidance after running certain tests on you like blood test, thyroid test, skin test or through detail biopsy of your skin. Once the exact cause of itchiness has been pinpointed, you can be successfully treated. For quick relief, some creams can help you till the exact cause of your problem is diagnosed. Get in touch with the nearest gynaecologist who can recommend some creams. Meanwhile, you can reduce the itchiness at home with the help of good moisturiser, avoiding soaps, cosmetics and other chemicals. Bathe with natural products or with cool plain water for some days, avoid scratching the skin altogether.
26 years old male from Lucknow asked
What is the treatment of smegma? Inspite if washing the area with water and soap everyday, next morning again it comes and causes itching which after washing goes away.
General Physician, Gurgaon
Hello lybrate-user, Smegma is not A disease ,its only deposition of secretions and Semen, so you clean it regularly while bathing and clean with diluted dettol water, by this cleaning you will feel comfortable. Good luck and Take care.
41 years old male from Hyderabad asked
I am 42 years old, I am diabetic. How to control sugar levels? I am using glucoryl mv2. What tablets can suggest? My sugar levels are between 210 to 240 (random)
Bachelor of Ayurveda, Medicine and Surgery (BAMS)
Ayurveda, Bundi
High end fibres in diet, regular caloric burning by exercises and 100% support of herbs needed along with your current regime. It will prevent all the complications in the offing incidental to DM and anti DM drugs.
18 years old male asked
MBBS, MBA (Healthcare)
General Physician, Delhi
take crocin pain relief one sos. get your eye sight checked, get your BP checked. take rest and good sleep. take pan d one daily for 3 days. consult if not ok.
19 years old male from Agra asked
Why my friend gets irritation and pain Everytime during flush in her vagina. She is 20 years old. She has done sex 3 to 4 times and after last time she is facing this problem. Please help.
MBBS, MS - Obstetrics and Gynaecology, DNB (Obstetrics and Gynecology)
Gynaecologist, Bangalore
These could be signs of vaginal infection or local injury. If symptoms don't settle in a week's time it is best she consults a doctor.
18 years old male from Junagadh asked
Ayurveda, Ambala
These are the methods to treat fastly pimples: • Imbalance in hormone level causes excessive sebum production and causes acne. So do not take stress and do exercise daily such as running, jogging and long breathing exercises. • Do YOGASANA daily. Especially do SINHASANA & SARVANGASANA daily. • Eat a fruit daily such as apple, banana , melon ,cucumber , avoid to eat mango , garlic , papaya and drink 7 -8 glass of water daily . • Do not touch your pimple because your finger transfer bacteria to it and make it worse. If you touch it then clean your face with water. • Take cucumber and papaya pulp .Mix it well and add 1 tablespoon Turmeric. Make a paste and apply it on face and leave it for 15 minutes. Apply one teaspoon Besan with one teaspoon of curd and a pinch of haldi (turmeric) mix it with water then apply for 15 minutes then rinse off it with water . • Steam your face to open the pores ,which in turn clear the skin .steam your face for a couple of minutes. • Take 2 teaspoon of RAKTASHODAK SYRUP of BAIDYANATH company once a day.
17 years old male from Pune asked
I am 16 years old. I am suffering from urticaria related disease. Skin swells and becomes red after applying pressure. My doctor consulted and said its something like hives. Taking medicines since two months.. Now totally tired. Still not cured. What should I do?
General Physician, Pune
Urticaria or commonly called allergic rash is troublesome many times. The causes are complex. You never know what causes allergy. Food and drugs are the main culprits. But rarely presence of worms also can cause allergy. The psycho-somatic angle also needs to be ruled out. Too much anxiety is also responsible in some cases. Best thing is to see a good skin specialist first. And then a holistic expert. Solutions are not simple and cannot be doled out on this platform. Getting a good physician is the first important step.
21 years old male from Guwahati asked
Sometime when I got up from my bed then in front of my eyes I see fully black. Do not know why this happens. Please help me.
Fellowship in Comprehensive Ophthalmology, DOMS
Ophthalmologist, Sangrur
Hello this is due to postural hypotension which is normal phenomenon as we get up blood pools in lower extremities and circulation to brain is impaired for few seconds leading to darkness.
19 years old male from Dewas asked
I am suffering from hairfall . Generally my hair fall when I wash my hair with shampoo and when I stop washing my hair it start itching on my scalp nlWhen my scalp start itching and when I rub that place then 2 -3 hair fall on that place is it due to pollution effect or something else .plz help me advise me a bst shampoo that make my hair dense as it before and stop hairfall am suffering from hair loss ,my hair become less dense and become transparent on some places .my 10-20 hair generally fall when I use shampoo .when I not clean my hair even a day then my scalp start itching and when I rub that place then 2 -3 hair fall on that place is it due to pollution effect or something else .plz help me advice me a bst shampoo that make my hair dense as it before and stop hairloss am suffering from hairfall . Generally my hair fall when I wash my hair with shampoo and when I stop washing my hair it start itching on my scalp nlWhen my scalp start itching and when I rub that place then 2 -3 hair fall on that place is it due to pollution effect or something else .plz help me advise me a bst shampoo that make my hair dense as it before and stop hairfall am suffering from hair loss ,my hair become less dense an.
Homeopath, Mumbai
Hairloss at your age is due androgenic alopecia its a male pattern of baldness, its a progressive disorder can only be controlled, following tips can help you, avoid using helmet or cap for long duration of time. Take multivitamin daily once for atlest 3 months, drink 2 to 3 cups of green tea daily avoid using hot water for hair wash, avoid blow drying of hair, use wooden combs inplace of plastic. Do not use strong shampoo or conditioners, avoid rigorous hair massage, take homeopathy medicine jaborandi q 10 drops 3 times a day for 3 months. Scalp itching is due to sensitive skin or agressive use of shampoos is uggest take homeopathy medicine sulphur 30 4 pills twicw a day for 15 days and let me know.
23 years old male from Gurgaon asked
She went through big losses in her life after that she become I'll, body pain, lack of sleep, anxiety and much more. please suggest what to do.
MBBS, MD Psychiatry, DNB Psychiatry
Psychiatrist, Nagpur
Having problems of anxiety, inability to sleep etc are common after stressors in life. If they persist for more than 6 months or have been impairing your occupational a and functional life, treatment is recommended. Consult a good psychiatrist in your vicinity for help.
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Howard Stern Gets Slammed By Comic!
It's not all ugly, mind you.
But in the breezily readable new memoir from comic Pat Cooper called How Dare You Say How Dare Me?, the Italian firebrand Cooper -- who was a mouthy regular on the Stern show -- has this to say:
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"Howard remarried and went A-list.
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And I guess they're stuck there!
Concludes the non-punch-holding Cooper, Howard actually left his audience very gradually.
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Ouch. That's gotta hurt!
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|By PR Newswire
Article Rating:
|August 29, 2014 05:00 PM EDT
NEW YORK, Aug. 29, 2014 /PRNewswire/ -- Neuberger Berman Real Estate Securities Income Fund Inc. (NYSE MKT: NRO) has announced a distribution declaration of $0.02 per share of common stock. The distribution announced today is payable on September 30, 2014, has a record date of September 15, 2014 and has an ex-date of September 11, 2014.
Under its level distribution policy, the Fund anticipates that it will make regular monthly distributions, subject to market conditions, of $0.02 per share of common stock, unless further action is taken to determine another amount. There is no assurance that the Fund will always be able to pay a distribution of any particular size, or that a distribution will consist of only net investment income. The Fund's ability to maintain its current distribution rate will depend on a number of factors, including the stability of income received from its investments, availability of capital gains, the cost of leverage and the level of other Fund expenses.
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Neuberger Berman is a 75-year-old private, independent, employee-controlled investment manager. The firm manages equities, fixed income, private equity and hedge fund portfolios for institutions and advisors worldwide. With offices in 17 countries, Neuberger Berman's team is more than 2,000 professionals and the company was named by Pensions & Investments as a 2013 Best Place to Work in Money Management. Tenured, stable and long-term in focus, the firm fosters an investment culture of fundamental research and independent thinking. It manages $257 billion in client assets as of June 30, 2014. For more information, please visit our website at www.nb.com.
Statements made in this release that look forward in time involve risks and uncertainties and are forward-looking statements within the meaning of the Private Securities Litigation Reform Act of 1995. Such risks and uncertainties include, without limitation, the adverse effect from a decline in the securities markets or a decline in the Fund's performance, a general downturn in the economy, competition from other closed-end investment companies, changes in government policy or regulation, inability of the Fund's investment adviser to attract or retain key employees, inability of the Fund to implement its investment strategy, inability of the Fund to manage rapid expansion and unforeseen costs and other effects related to legal proceedings or investigations of governmental and self-regulatory organizations.
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DevOps is often described as a combination of technology and culture. Without both, DevOps isn't complete. However, applying the culture to outdated technology is a recipe for disaster; as response times grow and connections between teams are delayed by technology, the culture will die. A Nutanix Enterprise Cloud has many benefits that provide the needed base for a true DevOps paradigm.
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20th Cloud Expo, taking place June 6-8, 2017, at the Javits Center in New York City, NY, will feature technical sessions from a rock star conference faculty and the leading industry players in the world. Cloud computing is now being embraced by a majority of enterprises of all sizes. Yesterday's debate about public vs. private has transformed into the reality of hybrid cloud: a recent survey shows that 74% of enterprises have a hybrid cloud strategy.
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With major technology companies and startups seriously embracing IoT strategies, now is the perfect time to attend @ThingsExpo 2016 in New York. Learn what is going on, contribute to the discussions, and ensure that your enterprise is as "IoT-Ready" as it can be! Internet of @ThingsExpo, taking place June 6-8, 2017, at the Javits Center in New York City, New York, is co-located with 20th Cloud Expo and will feature technical sessions from a rock star conference faculty and the leading industry p...
Apr. 30, 2017 08:00 PM EDT Reads: 1,746
Today we can collect lots and lots of performance data. We build beautiful dashboards and even have fancy query languages to access and transform the data. Still performance data is a secret language only a couple of people understand. The more business becomes digital the more stakeholders are interested in this data including how it relates to business. Some of these people have never used a monitoring tool before. They have a question on their mind like "How is my application doing" but no id...
Apr. 30, 2017 07:45 PM EDT Reads: 7,466
With major technology companies and startups seriously embracing Cloud strategies, now is the perfect time to attend @CloudExpo | @ThingsExpo, June 6-8, 2017, at the Javits Center in New York City, NY and October 31 - November 2, 2017, Santa Clara Convention Center, CA. Learn what is going on, contribute to the discussions, and ensure that your enterprise is on the right path to Digital Transformation.
Apr. 30, 2017 07:30 PM EDT Reads: 1,758
@GonzalezCarmen has been ranked the Number One Influencer and @ThingsExpo has been named the Number One Brand in the "M2M 2016: Top 100 Influencers and Brands" by Analytic. Onalytica analyzed tweets over the last 6 months mentioning the keywords M2M OR "Machine to Machine." They then identified the top 100 most influential brands and individuals leading the discussion on Twitter.
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Developers want to create better apps faster. Static clouds are giving way to scalable systems, with dynamic resource allocation and application monitoring. You won't hear that chant from users on any picket line, but helping developers to create better apps faster is the mission of Lee Atchison, principal cloud architect and advocate at New Relic Inc., based in San Francisco. His singular job is to understand and drive the industry in the areas of cloud architecture, microservices, scalability ...
Apr. 30, 2017 07:00 PM EDT Reads: 3,759
Five years ago development was seen as a dead-end career, now it's anything but – with an explosion in mobile and IoT initiatives increasing the demand for skilled engineers. But apart from having a ready supply of great coders, what constitutes true 'DevOps Royalty'? It'll be the ability to craft resilient architectures, supportability, security everywhere across the software lifecycle. In his keynote at @DevOpsSummit at 20th Cloud Expo, Jeffrey Scheaffer, GM and SVP, Continuous Delivery Busine...
Apr. 30, 2017 07:00 PM EDT Reads: 1,489
In his keynote at 19th Cloud Expo, Sheng Liang, co-founder and CEO of Rancher Labs, discussed the technological advances and new business opportunities created by the rapid adoption of containers. With the success of Amazon Web Services (AWS) and various open source technologies used to build private clouds, cloud computing has become an essential component of IT strategy. However, users continue to face challenges in implementing clouds, as older technologies evolve and newer ones like Docker c...
Apr. 30, 2017 07:00 PM EDT Reads: 1,430
Most technology leaders, contemporary and from the hardware era, are reshaping their businesses to do software in the hope of capturing value in IoT. Although IoT is relatively new in the market, it has already gone through many promotional terms such as IoE, IoX, SDX, Edge/Fog, Mist Compute, etc. Ultimately, irrespective of the name, it is about deriving value from independent software assets participating in an ecosystem as one comprehensive solution.
Apr. 30, 2017 06:45 PM EDT Reads: 779
SYS-CON Events announced today that T-Mobile will exhibit at SYS-CON's 20th International Cloud Expo®, which will take place on June 6-8, 2017, at the Javits Center in New York City, NY. As America's Un-carrier, T-Mobile US, Inc., is redefining the way consumers and businesses buy wireless services through leading product and service innovation. The Company's advanced nationwide 4G LTE network delivers outstanding wireless experiences to 67.4 million customers who are unwilling to compromise on ...
Apr. 30, 2017 06:15 PM EDT Reads: 1,663
The 20th International Cloud Expo has announced that its Call for Papers is open. Cloud Expo, to be held June 6-8, 2017, at the Javits Center in New York City, brings together Cloud Computing, Big Data, Internet of Things, DevOps, Containers, Microservices and WebRTC to one location. With cloud computing driving a higher percentage of enterprise IT budgets every year, it becomes increasingly important to plant your flag in this fast-expanding business opportunity. Submit your speaking proposal ...
Apr. 30, 2017 05:30 PM EDT Reads: 1,829
SYS-CON Events announced today that CollabNet, a global leader in enterprise software development, release automation and DevOps solutions, will be a Bronze Sponsor of SYS-CON's 20th International Cloud Expo®, taking place from June 6-8, 2017, at the Javits Center in New York City, NY. CollabNet offers a broad range of solutions with the mission of helping modern organizations deliver quality software at speed. The company's latest innovation, the DevOps Lifecycle Manager (DLM), supports Value S...
Apr. 30, 2017 05:15 PM EDT Reads: 1,531
Cybersecurity is a critical component of software development in many industries including medical devices. However, code is not always written to be robust or secure from the unknown or the unexpected. This gap can make medical devices susceptible to cybersecurity attacks ranging from compromised personal health information to life-sustaining treatment. In his session at @ThingsExpo, Clark Fortney, Software Engineer at Battelle, will discuss how programming oversight using key methods can incre...
Apr. 30, 2017 05:15 PM EDT Reads: 4,233
SYS-CON Events announced today that Hitachi, the leading provider the Internet of Things and Digital Transformation, will exhibit at SYS-CON's 20th International Cloud Expo®, which will take place on June 6-8, 2017, at the Javits Center in New York City, NY. Hitachi Data Systems, a wholly owned subsidiary of Hitachi, Ltd., offers an integrated portfolio of services and solutions that enable digital transformation through enhanced data management, governance, mobility and analytics. We help globa...
Apr. 30, 2017 05:00 PM EDT Reads: 1,659


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Top Class Food: How To Make The Perfect Cheese Board
54 Yummy Vineyard Wedding Cakes And Cheese Towers | HappyWedd.com
cocktail hour cheese platter - lovely arrangement. This works beautifully for an cocktail hour. Gives the feeling of a cornucopia which I love. http://pinterest.com/pin/149252175124097821/
Holiday Entertaining: Perfecting the Cheese Board
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Cheese Table


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History of India's Midday Meal Horrors
The recent mid day meal tragedy in Bihar and Madhubani has brought the controversial government scheme back in focus. Started in the 60's in the state of Tamil Nadu, the idea to give incentive to children to attend schools, at the same time providing them healthy food to strike down the problem of mal-nutrition, has always looked promising, especially on paper. India's mid-day meal scheme is one the biggest of its kind in the world, covering more than 60 million children. With no functional government solution to uplift them from poverty and destitution, and the ever increasing food prices have made poor families rely on this scheme to ensure their children get that one square meal a day. But the scheme has been plagued with instances of corruption, mis-management and lax health & safety guidelines, with previous incidents of food poisoning too, but none as deadly as the Bihar horror. Lets us take a look at the chequered past of the Midday Meal Scheme.
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Higher Computing Science 2015/16 SQA Specimen, Past and Hodder Gibson Model Papers
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Higher Computing Science 2015/16 SQA Specimen, Past and Hodder Gibson Model Papers by SQAAccept no imitations! Practise for your exams on the genuine Higher Specimen Paper and 2015 Past Paper from the Scottish Qualifications Authority, and three specially-commissioned Hodder Gibson Model Papers. - Discover how to get your best grade with answers checked by senior examiners - Prepare for your exams with study skills guidance sections - Gain vital extra marks and avoid common mistakes with examiner tips
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I'm sure some of those weirdos would not mind to much, bunch of Pervects.
Oh well.
UFO documentaries do not cure the common cold as far as I know.
Now were all the old members went I don't know. Told you this internet thing was just a fad.
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In January 2017 Public Opinion Research Centre investigated, how Czech citizens evaluate material living conditions of their households and economic situation in the Czech Republic. During January 2017 comparable surveys on this theme were carried out also in Poland and Hungary, and in the end of November 2017 also in Slovakia.
>> Full text is available in Czech only <<
Všechny zprávy z tohoto výzkumu:Â NS_1701


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Veronika Scott, founder and CEO of The Empowerment Plan, has built an organization that began around a single idea: to design a coat specifically for the homeless. The coat is self-heated, waterproof, and transforms into a sleeping bag at night. That idea has now transformed into a system of empowerment in which homeless women are paid to learn how to produce coats for people living on the streets, giving them an opportunity to earn money, find a place to live, and gain back their independence for themselves and their families.
Scott takes audiences on her journey from being on track to becoming a top product designer to dedicating her life to the empowerment of others through her own non-profit organization. Scott shares anecdotes from her time at a homeless shelter in Detroit where she conducted the research for her coat prototype. She also shares how her idea for creating a coat for the homeless led her to hiring the homeless. Audiences will leave with knowledge about homelessness and what can be done to help this growing population.
11:00am - Registration and Networking
11:45am - Lunch
12:30pm - Veronika Scott
1:30pm - Program Ends
About NOW
The TMA Network Of Women fosters female leadership by providing the premier business development and networking group for women in the corporate renewal industry. NOW focuses on programming and networking opportunities specifically targeted to the interests of TMA's female membership base.
Requests for refunds must be made in writing no later than 48 hours prior to the date of the event (e-mail is acceptable). No cancellations will be accepted within 48 hours of the event. Substitutions are allowed and must be submitted in writing (e-mail is acceptable). The substitute must be from the same firm as the original registrant and, if the substitute is not a TMA Member, the difference in registration fee will be required. Please note that if you register for the event after the cancellation deadline has passed, you will not be eligible for a refund should you need to cancel your registration. The cancellation policy applies to all registrants regardless of when the registration is submitted. Registrants who fail to attend the event and do not provide written notice in accordance with these policies and deadlines are responsible for full payment.


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Pep Guardiola defended Sergio Aguero after the Argentina striker missed a series of chances in Manchester City's 1-1 Premier League draw against Liverpool on Sunday.
Aguero was on target, equalising with a close-range finish from Kevin De Bruyne's low right-wing cross to cancel out James Milner's penalty, but he wasted three opportunities to score the winner in the closing minutes at the Etihad Stadium.
City and Liverpool shared the points after a breathless encounter and Guardiola felt the injured Brazilian forward Gabriel Jesus could have made a difference had he been paired with Aguero.
"When you play with [Yaya] Toure, [David] Silva and De Bruyne alongside two 19-year-olds [Leroy Sane and Raheem Sterling] and Aguero upfront - they all want to attack," Guardiola told reporters.
"I can only imagine what it would have been like had Jesus and Aguero had both been on the pitch in the final few minutes.
"I played football for 11 years and scored 11 goals. One goal a year. Can you imagine me giving advice about scoring goals? I leave the box work for the players."
We'd have liked the full three points. But it's always great to see this team always going for more. C'mon, City!— Sergio Kun Aguero (@aguerosergiokun) March 19, 2017
John Stones impressed at the back for City, with a series of vital blocks helping to keep Liverpool's attack out, and Guardiola was effusive in his praise for the English centre-back.
"John Stones has more personality than everybody here in this room," Guardiola said. "More balls than everybody. I love this kind of player.
"I am delighted to have him. He has been under pressure. The people criticise him. But it is not easy to play central defence with this manager. I don't want long balls and passes down the channel. I want him 40 metres back to build up the play.
"With all his huge amount of mistakes, I love him."
This game was so intense!What a pity we couldn't win ... #SoManyChances #LS19 #inSané #MCILIV @premierleague pic.twitter.com/K1wi80xqpD— Leroy Sané (@LeroySane19) March 19, 2017
Guardiola was delighted with the response of his players after the disappointment of their Champions League last-16 exit following a 3-1 loss at Monaco on Wednesday.
"We lived a tough two days after being out of the Champions League, our mood and what happened in Monaco," Guardiola said. "In the first half we were what we are, and in the second half again and again and again how many chances we missed, it was tough, and playing against a team like Liverpool who were all week preparing for the game.
"How they fight until the last moment, how they put absolutely everything that they had on the pitch. Sometimes you play important games but you are just focused on that and your mood is okay.
"We were sad and that is why I am so, so happy, it's one of the days I am proud the most being coach and being coach of those guys. More than ever I want to help the club, if I am able and if they want to stay with me, to put in the next years to be there with the next step forward."
|Rashford starts Manchester derby for United, Gabriel Jesus on City bench
|´Overrated´ Pogba and Balotelli have been lucky, says Cassano
|Atletico Madrid not afraid of Real Madrid, Torres claims
|Chelsea captain Terry wanted at Bournemouth
|Schneiderlin fires ´revenge´ warning to Chelsea
|Dortmund-themed cast cheers Bartra as recovery continues
|Barton betting ban was ´shortest possible sanction´ - FA
|Eriksen insists Tottenham can still win Premier League
|Liverpool confirm Gerrard will take over Under-18s
|Albania fined by FIFA after crowd unrest in Italy
|Bartomeu to stand trial over Neymar transfer after appeal is rejected
|Sanchez the only Arsenal player who would get in Tottenham team, says Henry
|Clement confident of Swansea survival
|Aguero bemoans City´s bad luck in ´tough year´
|Barcelona tried to lower Suarez price after Chiellini bite, claims ex-Liverpool CEO
|Allegri refusing to let Monaco be a distraction in Juve´s title bid
|Being benched not a problem for Aguero
|Bayern Munich sign Coman from Juventus for €35m
|Cavani, Mbappe and Griezmann among nominees for UNFP awards
|Roma stalwart De Rossi reflects on ´wrong´ career choices
|Pep didn´t do his homework on English football, Grant claims
|Verratti: I´d be angry if I played for Monaco
|Sakho injury could be cruciate damage - Allardyce
|Guardiola: I´m a better manager since joining Manchester City
|Barcelona to report Malaga president to anti-violence commission after controversial Twitter post
|Go fourth and prosper? Guardiola and Mourinho wrestling to lift Manchester horizons
|Liverpool present new kit and crest to mark 125th anniversary
|Manchester United captain Rooney vows to ´prove people wrong´ amid talk over future
|Eto´o reveals Mourinho´s Champions League final masterstroke
|Serbia well on the way to Russia 2018, but Stankovic highlights domestic difficulties
|Mourinho unhappy with Smalling, Jones but insists defenders have Manchester United future
|Pachuca 1 Tigres UANL 0 (2-1 agg): Alonso´s men win Champions League title
|Copa Libertadores Review: Brawl erupts after Palmeiras beat Penarol
|Madrid star Isco: This could be the best form of my career
|Mascherano scores first Barcelona goal... in his 319th appearance
|James: Five cup finals in LaLiga for Real Madrid
|Zidane hails phenomenal Isco as Madrid stay level with Barca
|Beating Bayern like this is ´madness´ - Tuchel
|Moyes: Sunderland deserved something against Middlesbrough
|Battle-scarred Arsenal star Sanchez takes to social media following last-gasp win
|Sakho injury could bring end to Palace loan spell - Allardyce
|Campbell expects extra ´spice´ in crucial north London derby
|The challenge is to keep going - Pochettino delighted as Spurs hunt Chelsea
|The target is clear - Wenger confident of Arsenal´s top four chances
|If my grandmother had wheels, she´d be a bicycle - Luis Enrique won´t lean on Malaga in title race
|Ancelotti feels Bayern only have themselves to blame for Dortmund defeat
|Guardiola: If Man City miss out on Champions League we will adapt
|He can play in 10 positions – Guardiola marvels over United star Pogba
|Kane´s focus on Tottenham not Chelsea in title run-in
|Deportivo La Coruna 2 Real Madrid 6: Six appeal gets Zidane´s men back on track
|Chelsea continue FA Youth Cup dominance by thumping City
|Paris Saint-Germain 5 Monaco 0: Emery´s men thrash youthful visitors
|Alcacer honoured to play alongside ´unique´ Messi
|Crystal Palace 0 Tottenham 1: Eriksen ensures Spurs remain in title hunt
|Arsenal 1 Leicester City 0: Huth own goal keeps Arsenal in top four race
|Bayern Munich 2 Borussia Dortmund 3: Dembele fires BVB into DFB-Pokal final
|Middlesbrough 1 Sunderland 0: De Roon keeps faint survival hopes alive
|Barcelona 7 Osasuna 1: Messi at the double to pile pressure on Madrid
|Bauza hits out at AFA leadership: They know nothing about football
|Infantino confirms use of VAR at 2018 World Cup
|Van der Vaart tips Alli to become ´true great´
|Ibrahimovic will fight to save career - Mourinho
|Chelsea visited by HMRC officers as part of fraud investigation
|Wenger admits Mbappe already out of Arsenal´s financial reach
|AFC Champions League Review: Urawa batter Wanderers to reach last 16
|Kongolo signs Feyenoord renewal
|Xavi denies claiming Guardiola will move for Alli
|Mourinho: Finishing above Guardiola means nothing
|Silva doubtful for City but Aguero ready to face United in Manchester derby
|Pogba ruled out of Manchester derby
|Taylor gets two-game ban for Coleman challenge
|Betting ban effectively forces me into retirement - Barton
|Gignac: I´d die before I signed for PSG
|Barton banned for 18 months over betting breaches
|Messi only plays well for Barcelona - Romario
|Bruno ordered to return to prison
|David Moyes charged by FA over reporter ´slap´ comment
|West Ham involved in HMRC probe into suspected tax fraud in football
|Ronaldo out of Real Madrid clash with Deportivo
|Champions League final in Monaco sights, says Glik
|Vardy made right call in snubbing Arsenal - Shakespeare
|James wants Real Madrid stay, says wife
|Copa Libertadores Review: Iquique beat Zamora in seven-goal thriller
|Pochettino hits back at ´enemy´ Xavi over Alli speculation
|Mourinho: City favourites for top four, not United
|Sanchez won´t be sold to Premier League rival, insists Arsenal boss Wenger
|Simeone: Atletico have four finals after Villarreal loss
|Goals are his life - Chelsea boss Conte delighted to see Costa back on target
|Puel praises former pupil Hazard after Chelsea defeat
|Carrasco suffers collarbone injury in Villarreal defeat
|I have a squad of great men - Conte lauds Chelsea toughness in Southampton win
|A massive step - Cahill, Hazard confident on Chelsea´s title charge
|Borussia Monchengladbach 1 Eintracht Frankfurt 1 (aet, 6-7 pens): Hradecky and Hrgota heroes
|Atletico Madrid 0 Villarreal 1: Late Soriano strike downs Simeone´s side
|Wolves 0 Huddersfield Town 1: Brown seals play-off spot for Terriers
|Angers 2 Guingamp 0: Letellier saves hosts from penalty injustice
|Niasse red card overturned after Hull City appeal
|Chelsea 4 Southampton 2: Hazard, Cahill and Costa move Conte´s men a step closer
|Ramos receives one-match ban for Messi foul in El Clasico
|AFC Champions League Review: Paulinho at the double in Guangzhou Evergrande rout
|United need Griezmann - Silvestre backs proven goalscorer to emulate Rooney
|Roma can achieve great things - Serie A club can join Europe´s elite, claims Monchi
|Mourinho: Manchester derby not about me and Guardiola
|Cavani extends PSG contract until 2020
|Amsterdam ArenA to be renamed after Johan Cruyff
|Surgery all that matters for Ibrahimovic - Mourinho realistic on United star´s future
|Ibrahimovic should join me in MLS - Schweinsteiger
|I cannot guarantee anything - Pochettino puts Alli future aside for Spurs title charge
|Emery expecting full-strength Monaco for semi-final
|Schweinsteiger has no regrets over Manchester United move
|Sanchez a slow starter - Wenger
|Zidane would not change Clasico approach
|Sahin signs Dortmund contract extension
|Luis Enrique wishes Barcelona had Madrid´s extra games
|Ancelotti unhappy with Ribery performances
|Rooney´s Manchester United future ´doesn´t look good´
|Bale a doubt for Champions League semis with calf injury
|Luis Enrique reiterates wish for Messi to end career at Barcelona
|Tuchel relies on Reus to lead Dortmund past Bayern
|Hazard not right for Chelsea captaincy
|Pogba might regret leaving Juventus - Barzagli
|Wenger in jovial mood over Arsenal future
|Wenger dismisses Giroud to Marseille talk
|Xavi expects Guardiola to make Alli move
|Sanchez would be a good signing for Bayern – Matthaus
|Hazard in no rush to sign Chelsea renewal amid ongoing Real Madrid links
|Fernandez rules out Neymar exit, plays down Dybala talk
|Herrera talks up Manchester derby importance
|Maradona doubts Argentina World Cup qualification without Messi
|Messi, Iniesta to renew deals soon – Fernandez
|Benitez unsure over Newcastle future after promotion
|Premier League win with Chelsea would be Conte´s greatest moment
|Toure wants derby day tonic for faltering Manchester City


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Unformatted text preview: HISTORY OF MATHEMATICS – LECTURE 12 – MONDAY 18TH OCTOBER Blaise Pascal At first glance one may think that the relatively small mathematical output of Blaise Pascal (1623‐1662) is due to the fact that he died at the age of 39. However a closer look at his life reveals a more complicated explanation, starting with the fact that he was educated by his father, Etienne, who expressly prohibited him from studying mathematics until the age of 15. Etienne was forced to change his mind though when Blaise started showing a great intuitive knowledge of geometry, and within a short time of being given a copy of Euclid's Elements he had fully understood the initial 32 properties. So talented was the young Pascal that when Etienne was invited to the weekly meetings of Marin Mersenne (see Lecture 11), he took Blaise along. In 1640, still only 16, Blaise presented a paper Essay pour les coniques, to the distinguished members of Mersenne's circle which stated a number of new results concerning a hexagon inscribed inside a circle. One result states that given a hexagon with vertices A, B, C, D, E, F inscribed inside a circle, then if we extend the lengths of the sides, then the intersection of lines AB and DE, AF and CD, BC and EF lie on the same line. Pascal's next productive period occurred between 1651 and 1654, culminating with the publication of Traité du Triangle Arithmétique, which contains his famous triangle. Pascal's Triangle Properties of Pascal's Triangle There are many interesting patterns in the triangle, including the fact that if the numbers are written so as to form a right triangle rather than an equilateral triangle then the diagonal elements sum to the values of the Fibonacci numbers. However the most important feature is when a binomial term such as x + y is raised to a positive integer power, then by the binomial theorem we have where the values of ai are exactly the numbers in the nth row (starting from n=0) of Pascal's triangle. The numbers also help us determine the solution to combinatorial problems, where a selection of k unordered objects is selected from a total of n objects. The answer is ak = !
! ! Pascal's Triangle and Perfect Numbers Pascal and Probability Theory Pascal, along with Fermat, was instrumental in developing probability theory in the 17th century. Their interest was sparked by letters sent by the Flemish gentleman, the Chevalier de Méré, who enjoyed gambling, and wished to know more about the theoretical aspects of his favorite games, in particular the two below. Game 1: Roll a single die 4 times and bet on getting a six. One may naively assume that since the chance of getting a 6 in a single throw is 1 out of 6, it therefore follows that the chance of getting a 6 in four rolls is four times 1 out of 6; i.e. 2 out of 3. Game 2: Roll two dice 24 times and bet on getting a double six. Again, one might initially believe that since the chance of getting a double six in one roll is 1 out of 36, it follows that the chances of getting a double six in 24 rolls is 24 times 1 out of 36; i.e. 2 out of 3. Pascal's life took a very different course starting in November 1654, when a riding accident almost led to hisdeath. From then on Pascal devoted himself to religion, and he became a popular writer on the issues of the day. He did however turn his attention back to mathematics for a brief period in 1658, during which he believed that by solving various problems involving a cycloid it would distract him from the toothache from which he was suffering. He extended the work of Gilles Personne de Roberval (1602‐1675), who first solved the problem of finding the area generated by a circle of radius r moving along a flat surface in 1634. This prompted Descartes to say of the result that "It is a pretty one, which I had not noticed before, but [one] which would cause no difficulty to any moderately skilled geometer." Mathematical Induction While the use of induction as a method of proof was first applied by Franceco Maurolico (1494‐1575), it was Pascal who first used the method that it is familiar today. Consequence XII in the Triangle Arithmétique states that 1 1
Pascal's proof reads as follows: "Although this proposition has an infinite number of cases, I will give a rather short demonstration by supposing two lemmas. The first one, which is self‐evident, is that the proposition occurs in the second base [i.e. when n = 1]. The second one is that if the proposition is true for an arbitrary base, it will necessarily be true in the next base. From which it is clear that it will necessarily be true in all bases, because it is true in the second base by the first lemma; hence by means of the second lemma, it is true in the third base, hence in the fourth base, and so on to infinity. It is therefore only necessary to prove the second lemma." This is the process that we call mathematical induction today, and amounts to three steps: i) Showing that the result holds for the initial case (usually when n = 0 or n = 1). ii) Assuming that the result holds when n = k, and writing out the consequence. iii) Using the hypothesis in ii) to show that the result holds when n = k + 1. Ex. Ex. Note: Since the time of Pascal a lot of work has been done on induction (sometimes called "weak induction"), and we now use strong induction, the axiom of choice, and the well‐ordering principle as methods of proof, which are all mathematically equivalent to the original form. Strong induction involves replacing step ii) with the assumption that the result holds for all values of n less than or equal to some value k. Ex. Prove that every postage of 12 cents or more can be formed using 4‐cent and 5‐cent stamps. ...
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This note was uploaded on 09/22/2011 for the course MAC 2311 taught by Professor Evinson during the Spring '08 term at University of Central Florida.
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text: Thanks so much for stopping by today! I would like to share with you a few sets of cards that are PERFECT for your guided reading block! These cards are great for students that are ready to stretch words, blends words and those working on identifying sounds (beginning, medial and final). Below … [Read more...]