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Fourier Analysis and its applications
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1 Fourier Analysis and its applications Fourier analysis originated from the study of heat conduction: Jean Baptiste Joseph Fourier ( ) Fourier analysis enables a function (signal) to be decomposed into its frequency components. Wide range of applications: Spectrum analysis Digital filtering (e.g. electronics, image processing), Deconvolution Audio compression (MP3 etc.) Solving differential equations
2 Definition of Fourier series Consider a periodic function f (t) with period T = such that f (t + ) = f (t), (1) Any periodic function can be expressed as an infinite Fourier series of sin and cos functions with frequencies that are integer multiples of ω = /T = 1, the frequency of the function: f (t) = a (a n cos(nt) + b n sin(nt)), (2) n=1 where a 0, a 1,... b 1,..., b n are the Fourier coefficients.
3 Convergence Fourier Analysis Theorem Dirichlet s theorem If f (t) is periodic of period, if for π < t < π the function f (t) has a finite number of maximum and minimum values and a finite number of discontinuities, and if π π f (t)dt is finite, then the Fourier series converges to f (t) at all points where f (t) is continuous, and at discontinuities it converges to the arithmetic mean of the right-hand and left-hand limits of the function. For all practical purposes, these conditions hold and the series converges.
4 Fourier series as an expansion of orthogonal functions can be viewed as an expansion of orthogonal functions that form a complete set over any interval: π { πδm,n if m 0 sin(mt) sin(nt)dt = (3) π 0 if m = 0 π { πδm,n if m 0 cos(mt) cos(nt)dt = (4) if m = n = 0 π π π sin(mt) cos(nt)dt = 0 all integral m and n (5) From these orthogonality relations we can derive the Fourier coefficients a n and b n
5 Fourier coefficients Fourier Analysis a n = 1 π b n = 1 π π π π π f (t) cos(nt)dt (6) f (t) sin(nt)dt (7) You can prove this by substituting the Fourier series for f (t) (eqn. (2)) in to the above relations and use the orthogonality equations (eqns. (3,4,5).
6 Example - the square wave Consider the unit step function (i.e square wave): f (t) = { 1 for π < t < 0 +1 for 0 < t < π (8) Since the function is odd, all a n s are zero. The b n s are given by b n = 1 π 0 π( 1) sin(nt)dt + 1 π π = 2 π 0 = 2 [1 cos(nπ)] nπ = π sin(nt)dt = 2 nπ [ cos(nt)]π 0 { 0, n = 2, 4, 6,... 4/nπ, n = 1, 3, 5,... 0 (+1) sin(nt)dt
7 Fourier series of square wave
8 Fourier series of square wave: N=1
9 Fourier series of square wave: N=5
10 Fourier series of square wave: N=50
11 Remarks Fourier Analysis The amplitude of the high frequency sine waves falls of 1/n. Therefore convergence is slow. In general: For discontinuous functions, like the square wave, the coefficients decrease as 1/n. For continuous functions with discontinuous slopes (e.g. full wave rectifier), coefficients typically decrease as 1/n 2. Overshoot at discontinuities is called Gibbs phenomenon. In electronics, square wave pulses are common. If apparatus does not pass the high frequencies, square wave will be rounded off.
12 Fourier series of complex functions Definition of Fourier series can easily be extended to complex functions. Using the identity e ix = cos(x) + i sin(x) we can rewrite Fourier series (eqn.(2)) as f (t) = n= c n e int, (9) where (a n ib n )/2, n > 0, c n = a 0 /2 n = 0, (a n + ib n )/2 n < 0 which can be obtained by integration (10) c n = 1 π π f (t)e int dt (11)
13 Fourier series of functions with arbitrary period So far, considered functions periodic on a interval. Can easily extend to functions with any period T : Consider a periodic function f (t) with period T, and corresponding angular frequency ω = /T. Let t ωt = t/t. Then the complex Fourier series (eqn. (9)) becomes f (t) = c n e inωt, (12) where, c n = 1 T n= T /2 T /2 f (t)e inωt dt (13)
14 Fourier series of functions with arbitrary period Similarly for the Fourier series of real functions (eqn. (2)) becomes: where, f (t) = a (a n cos(nωt) + b n sin(nωt)), (14) n=1 a n = 2 T b n = 2 T T /2 T /2 T /2 T /2 f (t) cos(nωt)dt (15) f (t) sin(nωt)dt (16) Function is expressed as a series of sin and cos functions with frequencies that are integer multiples of ω, the frequency of the function.
15 Fourier series - summary Fourier series decomposes periodic signal into its frequency components. Even discontinuous functions or functions with discontinuous slopes (where Taylor expansion fails) can be expressed in a converging Fourier series. Solving differential equations. e.g. harmonic oscillator with some periodic driving force.
16 From Fourier series to Fourier transform Concept of Fourier series can be expanded to non-periodic functions. Consider the Fourier series for functions with period T in complex representation: f (t) = n= c n e in ωt, (17) with c n = ω T /2 T /2 f (t)e in ωt dt, (18) where we have written ω = ω, since the discrete frequencies nω are separated by ω = /T.
17 From Fourier series to Fourier transform Now define c n = ω g(n ω), (19) so that g(n ω) = f (t) = 1 T /2 n= T /2 f (t)e in ωt dt, (20) ωg(n ω)e in ωt. (21) Take the limit as T. Then, n ω becomes the continuous variable ω and the summation becomes an integral as ω = /T dω.
18 Fourier Analysis time domain f (t) = 1 frequency domain g(ω) = 1 We define g(ω) to be the Fourier transform of f (t): g(ω)e iωt dω, (22) f (t)e iωt dt (23) Fourier transform F[f (t)] = g(ω) (24) inverse transform F 1 [g(ω)] = f (t) (25)
19 Remarks: Fourier Analysis As with the Fourier series, the Fourier transform is used to obtain information on the frequency spectrum. However, F[f (t)] = g(ω) is complex in general, even if f (t) is real. Fourier transform is often represented in terms of its magnitude and phase: g(ω) = g(ω) e iθ(ω), where θ = tan 1 (Im(g(ω)/Re(g(ω))). Prefactor (1/ ) of the transforms depends on convention. Here we chose them to be distributed symmetrically. Often, the Fourier transform is used to go from the time domain to the frequency domain. However, mathematically, the original transform could be considered the inverse and vice versa. Therefore, the sign in the exponential also depends on the convention.
20 The Dirac delta function If Fourier transform are consistent, then inserting f (t) into g(ω) should lead to an identity: 1 ( 1 ) g(ω) = g(ω )e iω t dω e iωt dt (26) } {{ } = f (t) [ 1 ] e i(ω ω)t dt g(ω )dω (27) The term in the square brackets [...] has to be the Dirac delta function: δ(ω ω) = 1 e i(ω ω)t dt (28)
21 The Dirac delta function Consider δ(ω ω) τ = 1 τ τ e i(ω ω)t dt = sin((ω ω)τ) π(ω ω)
22 The Dirac delta function Eqns.(27) and (28) have to hold for any function g(ω). Set g(ω) = 1: 1 = However, according to eqn. (28), δ(0) =. δ(ω ω)dω (29) Delta function is a distribution, not a function, and has only a meaning inside an integrand!
23 Properties of the Fourier transform Linearity: F[f 1 (t) + f 2 (t)] = F[f 1 (t)] + F[f 2 (t)]. Shifting: F[f (t t 0 )] = = 1 1 = e iωt 0 1 = e iωt 0 g(ω), f (t t 0 )e iωt dt f (τ)e iω(τ+t 0) dτ f (τ)e iωτ dτ where τ = t t 0. Similarly, F 1 [g(ω ω 0 )] = e iω 0t f (t)
24 Properties of the Fourier transform Scaling: Let F[f (t)] = g(ω) and α > 0. Then, F[f (αt)] = = α = 1 α g(ω/α), f (αt)e iωt dt f (t )e iωt /α dt where substitution t = αt was made. For α < 0, we obtain F[f (αt)] = 1 α g(ω/α)
25 Properties of the Fourier transform Therefore, F[f (αt)] = 1 α g(ω/α) Similarly, F 1 [g(βt)] = 1 β f (t/β). This is a crucial relation!. As function f (t) becomes more localized, its Fourier transform becomes broader in frequency domain.
26 Parseval s theorem Fourier Analysis Consider the integral I = f 1(t) f 2 (t)dt. Substitute Fourier transforms of f 1 (t) and f 2 (t): [ 1 ] [ 1 ] I = g 1 (ω)e iωt dω g 2 (ω )e iω t dω dt = = = g 1 (ω)g 2 (ω ) [ 1 ] e i(ω ω)t dt dωdω g 1 (ω)g 2 (ω )δ(ω ω)dωdω g 1 (ω)g 2 (ω)dω For f 1 (t) = f 2 (t), we obtain Parseval s theorem: f (t) 2 dt = } {{ } Power g(ω) 2 } {{ } Power spectrum dω (30)
27 Higher dimensions Fourier Analysis So far considered 1D Fourier transform. Generalization to higher dimensions as follows: 2D: 3D: F[f (x, y)] = g(k x, k y ) = 1 F[f (x, y, z)] = g(k x, k y, k z ) = ( ) = g( k) = ( 1 ) 3 2 f (x, y)e i(kx x+ky y) dxdy f (x, y, z)e i(kx x+ky y+kz z) dxdydz f ( r)e i k r d r
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Your donation will train IBD nurse specialists and provide a lifeline to people living with Crohn's or Colitis.
Refunds are at the discretion of Crohn's and Colitis UK. If you require any assistance, please call or email the team:
Address: 4, Beaumont House, Sutton Rd, St Albans AL1 5HH
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If you agree, we would also like to get in touch with you with news and updates of other ways you can make a difference in the fight against Crohn's and Colitis. Please tick below to let us know how you'd like us to send you our news and updates:
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subset: commoncrawl


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Actor #KenErics ended our marriage on the night of our wedding – Ex wife. [Swipe] 📷: SDK
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Eco Defense's bed bug treatment uses naturally-derived non-toxic ingredients like geranium oil, which is known to be a natural bug repellent, to safely help rid your home of bed bugs throughout all their life stages (eggs, nymphs and adults). Eco Defense Bed Bug Killer spray and our 3-step program will help you reclaim your home when bed bugs strike.
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Don't just kill bugs; create a bug barrier with Ortho® Home Defense Insect Killer For Indoor & Perimeter 2 with Comfort Wand®. Whether you have ants, roaches or other home-invading insects, you can count on Ortho® to keep them out. Simply plug in the Comfort Wand®, and with one touch you can kill and protect against pests.
I'd advise trying natural sprays first, like Eco Defense Bed Bug Killer or EcoRaider Bed Bug Killer. All products that we've covered for clothes and mattresses can be used safely for any other furniture.
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What would you do to draw my attention?
By Citychic
@Citychic (4071)
United States
May 27, 2009 5:19pm CST
Hey friends, so if you and I were to be on a reality show and you only had two minutes to try to get my attention. What would you do to get me to focus on you? Have fun and be creative.
1 response
@robertshay00 (446)
• United States
27 May 09
What is the reality show what doe's it containe...


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Asked in Toys
What are some unique girl games to play at a slumber party?
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What are some 11 year old party ideas?
Well, if its a boy party he can invite some friends over and do a camping theme party or eat at a kids resteraunt at the mall and check out some stores and if its a girl, you can have a spa themed slumber party and get your nails and or toes done and a facial or eat at a resteraunt at the mall and go shopping after. Good luck, and have fun!
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What are some good ideas for an 11 year olds birthday party?
some good ideas for a 11 year old birthday ideas is having a diva slumber party or having a boy girl party and take them out to the movies or even an elegant spa party . my daughter had a fashion party with a pretend beauty pageant a fashion show with makeup and clothes. and we had went swimming and had a talent show.
Asked in Actors & Actresses
What actors and actresses appeared in Scary Story Slumber Party - 2012?
The cast of Scary Story Slumber Party - 2012 includes: Takiah Coleman as Erin (segment "The Pledge") Brittany Colley as Erin (segment "Noise Complaint") Lauren Dawson as Bar Girl 4 (segment "UnLucky Night") Jessica Dole as Danielle (segment "The Slumber Party") Heather Dorff as Becca (segment "Event Invitation") Jackey Hall as Holly (segment "The Dare") Sierra Holmes as Rachel (segment "UnLucky Night") Sarah Kaminski as Hilary (segment "The Pledge") Rachael Lang as Melissa (segment "The Pledge") Brandon McPherson as Aaron (segment "Noise Complaint") Elizabeth Spaetzel as Party Girl (segment "Noise Complaint") Ashley Vetere as Jenna (segment "The Pledge") DaNae West as Kristen (segment "Bashed")
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What would an eighteen year old girl want for her birthday?
she might want to go to kids kingdom as it has different age groups to go there or she might want to have a swimming party then go somewhere for lunch afterwards or she could have a bowling party it is a good family celebration or just with friends you could have a slumber party with lots of friends and play games such as true or dare and spin the bottle here are some ideas for the presents ipad / ipad2 3ds iphone ipod 32inch plasma television i hope that helps


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Here is very interesting video in terms of cancer however from the patient and doctor point of view in one.
I am watching and reading so many articles which makes me think twice or even more about the most frequently used method of 'curing' cancer as one of the most ineffective. However everyone have their own choice indeed.
Spreading these knowledge is vital for me.
Lots of love
from Margo :)


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Dave Matthews Band Tickets Quincy - WA
Dave Matthews Band in Quincy - WA Tickets - Washington
You are looking for Dave Matthews Band tickets Quincy but you find it hard to get them. You are on the right website where to buy Dave Matthews Band Quincy tickets, and without doubt you'll attend one of the hot shows in Staples Center and of course have the opportunity of seeing Dave Matthews Band right in front of you!
Dave Matthews Band Quincy Tickets December 08th, 2019
Dave Matthews Band 08/12/2019 in Quincy - WA
Dave Matthews Band Quincy - Concerts
If it happens that you aren't persuaded that Quincy Dave Matthews Band January 26th, 2020 tickets or tickets we are offering for any of the hottest performances hosted in New York, Wantagh and Sacramento are cheap, you just browse concert schedules in other website and you are going to note the difference. If it happens that you have not decided yet what performance to be on time to, we recommend for you Dave Matthews Band Quincy as the artist's performances are amongst the ones that attract fans including from Albany, West Palm Beach and Stockholm and all cities from around US. What is vital when attending Quincy Dave Matthews Band or any hottest performances of those taking place in Dallas, Berlin and San Francisco is to have a seat in VIP seats, and above all, pay competitive prices.


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Click here to read the full article.
Music and entertainment streaming platform Tidal will launch its first fashion collection with Bershka on Nov. 22.
The 10-piece reflective collection named Seeing Sounds, which is modeled by Canadian rapper Tommy Genesis in the campaign, is comprised of crop tops, bodysuits, minidresses, puffers and sportswear such as joggers and hoodies in purple, silver and black metallic colors that change colors in the light.
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The collection ranges in price from $12 to $55 and is available at Bershka stores in Italy, Spain, Portugal, Germany and the U.K. in a special section where customers can experience the Tidal app and music. In addition, each piece comes with a QR code to redeem a free three-month Tidal subscription.
"Tidal's mission is grounded in amplifying and supporting all things that have caught the cultural zeitgeist — fashion is a natural extension to this mission and we're excited to share our vision," said Tidal chief operating officer Lior Tibon. "Bershka is a forward-thinking brand that represents creativity and embraces the spirit of culture driving collaboration — making cool, wearable fashion accessible for all."
Tibon said this is "just the star" of the partnership between Tidal and Bershka. "We're looking forward to its growth."
Bershka is one of many Tidal partners, including Samsung, Mercedes-Benz, Sprint, Sonos and Barry's Bootcamp.
Inditex's Bershka Moving Into U.S. Market
Mercedes-Benz Fashion Taps M.I.A. and Tommy Genesis for Seasonless Campaign
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Sign up for WWD's Newsletter. For the latest news, follow us on Twitter, Facebook, and Instagram.


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SK grad Stinson qualifies for NCAA championship meet
Kaitlyn Stinson, a native of South Kortright, will be competing in the 2019 NCAA Division III Cross Country Championships in Louisville, Kentucky Saturday, Nov. 23.
Stinson, a graduate student at Utica College, qualified for the championship race with her 17th-place finish at the NCAA Atlantic Regional meet in Canton Saturday, Nov. 16. Stinson finished the 6K course in 23:06, good for the second-best regional finish in school history.
This marks the second straight season Stinson has qualified for the national meet. Last year, Stinson recorded the best finish for a Pioneer, earning 180th place.
Pair of OHS athletes sign NLI's
Oneonta High School seniors Teddy McGraw and Kylie McKee each officially committed to continue their athletic careers Friday, Nov. 15.
McGraw signed his national letter of intent to play baseball at Wake Forest while McKee will further her diving career at St. Bonaventure. Both schools are Division I programs.


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Yet another possibility, Ott claims, is toward pick out a single or two colours and then use dissimilarities of it. If the primary color is blue, oneself might pick out a gray-blue, a pure blue and a army paint as oneself shift in opposition to place toward place. The identical principle can be used for attractive extras. For wall paint, oneself can question the paint retail store toward develop a "tint" of a distinctive color, maybe knocking down the primary color as a result of 50 %, which the mixer will do as a result of adding white. "They can develop a lighter or darker version of it," Ott claims. "That's a superior route toward unite without inserting the identical color everywhere."
"I as well notify persons if they're likely toward do their wall within just this color, move two or three hues lighter for your ceiling so it doesn't seem to be together with a sore thumb considering that oneself painted it white," claims Keith Wardlaw of Furthermore Progressive Structure within just Kansas Metropolis, Missouri. Paint decks can as well be a superior enthusiasm resource for finding colours that get the job done well with each other.
Rooms out of the sightline of other rooms are superior destinations for likely wild. Discover bedrooms, powder rooms, kids rooms and any other place encapsulated as a result of four partitions are excellent destinations toward indulge, claims Carl Mattison, an Atlanta-based designer. "If oneself convert the corner and move into a tiny powder lavatory, which oneself don't move within just all the time, who cares? Paint it black!" It functions, Mattison claims, "because it's its personalized tiny box."


text:
Tay Cities Deal funding could pave the way for ambitious projects
A £200 million Tay Cities Deal funding boost could spark a bright future for St Andrews University's green energy centre.
A £200 million Tay Cities Deal funding boost could spark a bright future for St Andrews University's green energy centre.
Fife's health service is facing a near £20 million budget cut by the end of the financial year.
Thieves have stolen more than £800 raised to buy Christmas dinner for vulnerable children.
A five-year-old girl offered to give her toys to Santa as a community rallied round to save Christmas for hundreds of Fife youngsters.
The final signing of the Tay Cities Deal has been hailed as long-awaited good news for north east Fife.
Staff shortages should not be used as a reason to justify removing out-of-hours GP cover from North East Fife, an MSP has insisted.
Fife Council has been accused of acting as if it really does have public money to burn by spending more than £8,500 on Friday night's spectacular fireworks display in Glenrothes.
NHS Fife has said it is considering a community's bid to get involved in the decision over out-of-hours GP cover.
A Fife community has launched an 11th hour bid to halt the closure of its local out-of-hours GP service.
Police investigating a large-scale disturbance in Thornton hope to gather useful information from a separate operation.


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The network has a new type of malware that uses the computing power of cloud servers for mining cryptocurrency. The peculiarity of the virus is that it is not detected by security systems.
Researchers at the California-based cyber-security company Palo Alto Networks have published a report on the malicious group of Rocke scripts attacking cloud infrastructure objects. Once on the server, the virus gains administrative control and removes all security related components. Then the script injects code that uses Monero mining server capacity.
Investigating infected servers running Linux, experts found that the virus had successfully removed five different programs for the security of cloud servers. Among them, products of the largest cloud service providers in China – Alibaba and Tencent.
According to experts, Rocke exploits vulnerabilities in Apache Struts 2, Oracle WebLogic and Adobe ColdFusion software. A shell script called "a7" is loaded onto the server, which disables anti-mining software and hides its presence by disabling security systems.
"As far as we know, this is the first family of viruses that has the unique ability to impact and remove cloud infrastructure security products," the researchers said.
It is worth noting that Monero still retains the title of the most popular cryptocurrency among hackers. Last week a study was published, the authors of which concluded that at least 4.32% of all Monero tokens in circulation were mined using cryptojacking.
In October, Monero developers launched a special site to combat this phenomenon. The resource contains information on how to remove XMR viruses from your computer. However, just a month later, the Israeli company Check Point Software Technologies spoke about the malicious miner KingMiner, which evolves so that it cannot be detected.


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Jason & Jaymi
It would be without hesitation that we would recommend Rykon. It was our experience that the Rykon team committed to getting to know us as people, as well as clients, which allowed them to guide us seamlessly through the process in a manner that suited our needs. Their method of project management and organization is exemplary and lends itself to a completely transparent and trustworthy process. Concerns and anxieties are normal when building a home, but Rykon was responsive to our every question. The end result was a beautiful home that we are proud of. If we ever build again, it will be with Rykon.
Join The Journey!
Become another happy home owner! Let us help you along the way.
New Home Testimonials
For the past 12 years Travelers Insurance Company of Canada has been pleased to be associated with Rykon Construction Management. Rykon Construction Management is
After spending 30-40 minutes with Kim Barnstable, we felt very comfortable about seriously considering Rykon to build our retirement home in the Okanagan. Kim


text:
- 4 007
- 1 620 048 841
Breakfast Club Power 105.1 FM
United States
Joined Sep 18, 2013
Listen: 6am - 10am
Listen: 7am - 10am Saturdays
Twitter: @Power1051
Twitter: @BreakfastClubAM
- Themaskedtalker 3 hours ago
CTG must be heartbroken that Kamala Harris was exposed
- James 3 hours ago
This is some bitchassness
- Sadiki Akil 3 hours ago
Dope interview!
- CORITOENTERTAINMENT BISHOP 3 hours ago
The only thing Envy had to say was bye and that's unfortunate cause Dr. Umar REALLY is a special guest that's in the building who's always dropping REAL facts. Too REAL for Envy's taste.
- frank mills 3 hours ago
I get the entertainment business thing where you have to separate yourself to standout. But there is something different about this Charlamane the god kid. He is super unlikable in his nature that I can't watch him.
- BWIN HUBS 3 hours ago
Nothing but a culture vulture. 👎🏿
- Views And Vibez 3 hours ago
32:07 the look on envys face shows how he feels .. his face is so slappable 😂 tryna rush my mans 🤦🏽♂
- Twisted Logic 3 hours ago
Pump the breaks, he didn't say he was going to date Black women. He said "No More White women". That doesn't mean black woman by default. There's Asian, Latino, Middle Eastern, Indian...etc. Contrary to what the US would want many of us to believe, women around the globe are attracted to black men. Sad part is few ever travel far enough to find that out. If he did he'd know why he's so hated and envied by so many men of other ethnicities. It's not about what he has, it's about what he is. All this to say AB is a jerk but he has more than 2 options.
- Deven Troutt 3 hours ago
Obama got me a cell phone and some extra money on my income tax return... And he took money off my tax return cuz i aint have insurance.
- justina wood 3 hours ago
So why haven't they reported on juice at all
- jdmsir231 3 hours ago
Damn when he said wuddup wuddup wuddup shit broke my heart all over again.
- Adam James 3 hours ago
He def just wants money
- Kboss1 3 hours ago
How do you watch a movie that repeatedly says the proper pronunciation of a word and still leave the movie saying ThAYYYYNOOS. Nigga its THAN...OOS. How are you chastising dudes for not watching the movie and you've seen it and cant get the main villain's name right and then say you're a fan. In every adaptation of Thanos not once has someone said 'oh no it thaaayyyynnoos" even Stan Lee says 'Thann...os' geeze
- dexter simmons 3 hours ago
yo yo yo yo yo..........lol
- Gul Dukat 3 hours ago
and religion we need to say god isn't good for black people either... God has no plans for any of us because he doesn't exist.
- Toby Palmore 3 hours ago
🔥🔥🔥🔥🔥 very interesting
- Bad Azz662 3 hours ago
Nothing gets the toxic energy flowing than this fraud..Now y'all gone cash app him more money to spend on strippers and still produce no school. A fool will always follow powerful words and still be blind to the in action that these words provide. We are so straved for adequate black leadership that we will blindly follow any fool that talk like he knows something..I am so glad I can think for myself and see that this dude is robbin his own people by playing on our fears.
- TangOJ9 3 hours ago
- Cheyondra 3 hours ago
I hope y'all asked him about when he's gonna build his school!! ASK HIM WHAT HE DID WITH THOSE MILLIONS OF DOLLARS❗❗❗
- Mike Jones 3 hours ago
They are going to get him for that oil comment
- Adam James 3 hours ago
He just likes to hear himself talk lol
- T-rev 4 hours ago
Don't get trick off in these streets💯💪🏾
- Frank Blanco 4 hours ago
Billy boy back at it
- Savy Dayz 4 hours ago
This brother makes alot of sense
- Wilberth Ruiz 4 hours ago
Yang and the yanggang understand that the system needs to be for the people by the people. Large diverse coalition is the future Democrats need to wake up and drop Biden warren and Pete those Corp backed candidates will not succeed. He has been the only one I think besides Bernie that talks about people like people
- blaque301 4 hours ago
@13:48 he fanned himself 🏳🌈
- Flower 4 hours ago
Tariq such a wise guy
- abdul smith 4 hours ago
Yep that's like deleting SODA from your diet. Smartest thing I've heard from this dude!!!
- Keysha Jones 4 hours ago
I here for Dr. Umar and I agree with him 100% about what he says abouts interracial relationship and about the black man
- Robert Mugabe 4 hours ago
Hard to figure out why black women worship white men so much[ especially when you hear stuff like this ].
- OMAR NOIR 4 hours ago
We need a man like this in our community. Don't have to agree and follow everything he says, however whatever he says from his educated stand point will spark conversation between other educated black folks. Which will equal up to finding solutions and working towards a better tomorrow! Thank you sir, and shout out to the Breakfast Club for also shedding light on these subjects🙌🏾🙏🏾
- H Mahdi 4 hours ago
What a joke 🤦🏽♂🤦🏽♂🤦🏽♂🤦🏽♂🤦🏽♂🤦🏽♂
- Vidale Martin 4 hours ago
REAL TALK.......ALL races have these conversations collectively behind closed doors.....Umar just says It In public. What's Wrong With Black People For The 1st Since MLK Death......Being 100% For Us??? There are more black people fighting Umar, Jay-Z etc....than white people. C**ns
- Br33zy M 4 hours ago
Isn't Dr Umar contradicting himself by giving creds to Jay? "He should create his own NFL instead of working with the whites..", thats what Dr Umar should say to be consistent🤣
- Othon Pedro 4 hours ago
Vodoo, Witchcraft. That's a very Narrow vision of Africa. I'm pretty sure , that they would use sangoma or witchcraft on the foreigners invaders then on you French.
- Henry Savoy 4 hours ago
When a male sounding like a female.
- Shakieta K. 4 hours ago
Envy... 😑
- Marcus Johnson 4 hours ago
Envy bout the green guys not the black ones lol he was ready to go
- ILHS ! 4 hours ago
- Lee Soulsby 4 hours ago
Dr Umar is full of shit
- Mimi Brown 4 hours ago
Sorry bruh... I've listened to both sides and the right has nothing to offer me. This dude is a fraud.... Byron Allen can't speak up for us because he's married to a white woman?
- Selma 4 hours ago
- Bizzy Bone 4 hours ago
this man seem like a fraud to me fr
- Notaregular Person 4 hours ago
48:23 Ima sit there and entertain y'all but I'm not going to sit there and die for y'all.. Rs don't drown in the waves especially no one else's wave 12-14-19 Free 69
- Andy Murray 4 hours ago
we foreva in bidnizz wit drake
- Gerrod Elston 4 hours ago
I'm not sold yet. Don't think i ever will. But when he announced the interview i made a slick comment. Still not a believer but he came through. I know he felt on top of the world after that. Just hope he understands he will feel 10 times up there if he explains what n is going on and comes through
- Elton Waldick 4 hours ago
Did he just say irregardless?
- Don Doe 4 hours ago
Thanks for an amazingly relevant interview.
- Legendary Productions 4 hours ago
Yeah social media really exposes you to the world around you
- PJ 4 hours ago
Fat Joe call Em the GOAT🐐
- Erica Jones 4 hours ago
Camille Cosby is Biracial by the way.
- Truth hurts 4 hours ago
Dr who????
- Danny 4 hours ago
Charlemagne's comment section is just a bunch of hypocrital racist black people. As a white person trying to better myself everyday, be a good human being, and help others, I think all of your mentalities are way out of line and you guys should rethink your ignorant opinions and stop feeding the fire with your blind hatred.
- Shaw Carter 4 hours ago
Lmao envy mad cuz he was tlkn bout his ugly ass white woman... son he wanna get umar outta there
- Trevon Laflure 4 hours ago
he makes you think about how messed up we are as black people. Black men marry black women , teach your children about financial education , and try to spread love to your black brothers and sisters and don't be so quick to judge . Peace & Lovemy black brothers and sister ✌🏿✊🏿
- Alexander Williams 4 hours ago
Y'all go along with anything this dude is a scam where is the school?
- FrankieTheWop 4 hours ago
These two friend didnt know each others last names when they were trying to dime each other out.
- Body Guard 4 hours ago
Well Suck To Be Them Men LoL 😂😂😂
- cali kid 4 hours ago
envy really tried to cut the interview at 32 minutes
- minister b. Williams 4 hours ago
Am I the only one who can tell Envy is not enthused by Umar Johnson, I love it
- FASHIONSFLYEST 4 hours ago
can we get more respected fashion people on this show this like her 3rd time on here. yawn.
- JudgedBy12 4 hours ago
I am at a minute and 22 seconds and thinkin this niggah retarded! Does this get any better?
- Minstrel Mikell 4 hours ago
Just years ago he was clowning Tyler and Jay. Sounds like he's pandering for donations more than anything, should have just spoke more on the school than being PR for them.
- Addy G 4 hours ago
Breakfast club have alot of interviews with people who eventually die.
- will ellis 4 hours ago
- barbie doll 4 hours ago
Fine self
- Good Life 4 hours ago
Charlemagne so fucking good at wat he do I hope he outgrow the breakfast club cause envy damn sure can't relate to black people at all
- DEAN ABDUS-SALAAM 4 hours ago
- Queen Sagittarius86 4 hours ago
My first time watching the interview since Nip passed, I just couldn't find myself to watch it.. this still feels so unreal.. damn it's really some cold hearted people in this world, like whyyy take this beautiful man away from us 😔😇 we love you forever NIP
- StressFreeCity 4 hours ago
They sometimes give dumbass idiot rappers who can barely express themselves in English a full hour. But Umar Johnson who is trying to uplift the black community as a whole gets only 40 mins because bum ass Envy doesn't Rock with him.This man has saved countless black children from being put into special ED and being given ADHD meds and so much more, and bum ass envy wants to cut the interview short. Not everyone is ready for the truth and not every black person will ride with you. But Umar is still out here fighting for ppl who wouldn't do the same for him. That's a leader right there. He's found his purpose in life. Shoutout to Charlemagne for advocating for UJ to be brought back on the show.
- Uzair 4 hours ago
Different mentality
- Royston Moses 4 hours ago
We call it biltong in South Africa
- Chris Miramontes 4 hours ago
He's a lone wolf bruh.
- Robert Griggs 4 hours ago
So other races accept sexual a little better? Crazy, that dude is a real peice of shit
- ja-meal acree 4 hours ago
It's a shame that Mr Johnson still selling this race bating.THE BREAKFAST CLUB SOLD BLACK FOLKS OUT!
- more2me100 4 hours ago
As a black woman I have committed my life to becoming a clinical psychologist so that I can make my community a better community as a whole. Im not in it for the money I just want to leave this world a better place. As a college student it has been difficult for me along the way but I am determined to reach my goals!!!
- Jereme Juniel 4 hours ago
I dont know what PWI is so I'll just guess it stands for private white institution lol
- SweetTea 4 hours ago
Dr Umar. ✊🏾✊🏾✊🏾✊🏾✊🏾✊🏾
- MrJaytheking 4 hours ago
I didn't even know Angela Yee was even there 😂😂
- D'Ajee Kiera 4 hours ago
ALL FACTS! He's such a God sent King! He is the truth.. period! Every black person needed to support Dr. Umar Johnson, he is one of the few REAL leaders we have left! Rant over.
- Vicdemone2k 4 hours ago
Did this nigga just say "irregardless"?
- Eze Congco Dancehall Grung 4 hours ago
All boy school and all girls school breed gays
- Shaneka D 4 hours ago
For us that follow and support Dr. Umar, we already know this. Keep spreading the knowledge...We support you brother
- BM32 4 hours ago
Nigga ate a bad falaafal and want to blame voodoom
- KELLA Official 4 hours ago
This is the best interview ever on the breakfast club
- Amy LoLo 4 hours ago
I've missed Dr.Umar
- Antonio Perry 4 hours ago
They gone get him.....
- big daddy 4 hours ago
dame talking a different language here
- LaQuissa Sapp 4 hours ago
When I see this it just reminds me of that time the DC Young Fly roasted her on Instagram it's my favorite clip 😂😂 but I love her
- Waithira Maingi 4 hours ago
Slim not slim no more🤭 hottest 90s rnb though
- Leria Figueroa 4 hours ago
Omg😂😂😂 exactly you said it yourself 1) why still hate on Em. You inside now that Em won this even before throwing the diss because 2 you said yourself he is one of greatest lyricist of all time so everybody knows better than to diss Em... that's why nobody has come cose...
- Hustle Bankz 4 hours ago
This need a million views all black people please share this on your Facebook if u have a fb group pin this to the top of your group
- Dzawanda Ronald 4 hours ago
The African American negro will never amount to nothing nor change he's lost and will never be found only s few will understand & support this man's vision the rest are just lost .Here you have a man trying to open your eyes but still the hate is unbelievable but like what he said he's not here to save everyone. Some black folk are way too lost & confused to understand his masseage they've been so indoctrinated by their masters they'd rather see this man hung before he interrupts with their social structure. NO HOPE TO CHANGE FOR THE BLACK: DAVID CARROLL
- Deelovelly 4 hours ago
That man is soooo fine. MGK yummy.
- Rico Brinson 4 hours ago
So happy and proud to see Dr/Brother Umar shut these haters down once again!!!!
- megan Camacho 4 hours ago
Char is madd af lmmfao
- N O M F U N D O 4 hours ago
- JJ C 4 hours ago
When he said brother Kanye I started laughing 🤦🏽♂
- RAY RAY 4 hours ago
Hurry up and get Tht mf off the street
- Chasemonie.ramboLilrobert 4 hours ago
I swear Dr. Umar is our Malcolm X!!!


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During the CISSP® training you're given deeper knowledge and background information regarding information security with sufficient room for discussion of your questions, all for a good preparation for passing the exam.
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Question about Kyocera FS-1028MFP
Why is the screen in lock mode on error cf248,it will not allow me to exit the screen or clear any thing out or even go into settings Kyocera 1028mfp
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U.S. law firms White & Case and Latham & Watkins are among the law firms advising Saudi state oil giant Aramco on its massive initial public offering, according to a prospectus released on Saturday by the company.
New York-based White & Case is advising Aramco, the world's largest oil producer, on matters related to foreign investors and laws, while the Riyadh-based Law Office of Megren M. Al-Shaalan is counseling the company on domestic matters, according to the prospectus.
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EA expects to sell 5-6 million copies of Anthem by March 30
EA CFO says the company expects Anthem to sell 5-6 million units by the end of March
EA has been providing a bunch of new details about its various games in development, riding off of the uber-success of its just-released Apex Legends. The company has also provided some sales estimates of BioWare's upcoming game; Anthem.
EA CFO Blake Jorgensen said that EA is aiming for 5-6 million units to be sold by the end of March, and given that Anthem launches on February 15 this gives the company just 6 weeks to hit that lofty goal. Jorgensen said that the recent success of the Anthem demo gives them confidence that the game will be a success (to the tune of 5-6 million units) during its important few weeks post-launch.
Anthem will also make even more money for EA from microtransactions, something the company refers to as "live services". We will see how Anthem sales go when it launches in just over a week from now, and through to the end of March.
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Opuszczasz polską wersję strony.
Na stronie anglojęzycznej nie będziesz mieć możliwości kontynuacji zakupów.
Czy chcesz przejść na wersję anglojęzyczną?
Beginning from 2019.01.01 PWM Edition is not going to process any orders placed in internet shop by individual customers from countries other than Poland. Please find your local distributor on the list, or order our sheet music through the Hal Leonard online shop: http://www.musicshopeurope.com http://www.halleonard.com
for Viola and Piano
- Publisher: PWM Edition
Cat. no. 838
Wojciech Gawroński's Sonata, Op. 22 for viola and piano, probably composed at the very end of the nineteenth century, is by any standards worthy of attention. It is of crucial historical significance, as the first known Polish chamber work to use viola. Admittedly, in his Trio in G minor, Op. 8, completed probably in the spring of 1829, Fryderyk Chopin considered the question, after one performance, of possibly 'using viola instead of violin', but it is Gawroński's Sonata that is currently regarded as the first cyclical work for viola in the Polish musical literature. The only earlier work is Henryk Wieniawski's Rêverie, dating from the times when the composer himself occasionally played viola in a string quartet (1859).
The Sonata opens with a dignified polonaise theme, which, together with the intertwining quick triplet second theme, forms the basis for the quite distinct sonata allegro form. The second movement, a gloomy, solemn funeral march in ABA1 form, is followed by a third movement ripe with humour, but mixed with a touch of reflection, in a quite elaborate sonata-rondo form.
Compared to the quite abundant, albeit little known, British and German literature for viola and piano from the turn of the twentieth century (e.g. York Bowen, Arnold Bax, Robert Fuchs, Friedrich Kiel), this work is an extremely interesting, if rather forgotten, example.
Bogusława Hubisz-Sielska
translated by John Comber
- Series:
- Language of edition: eng, pol
- Number of pages: 42+16
- Cover: softcover
- No. of edition: 2
- Published: 2019
- Type: solo part (instrumental) + accompaniment
- Size: N4 vertical (235x305 mm)
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Recently Downloaded: Paper ID: ART2020859, Total 103 Articles Downloaded Today
Neuroprotective Activity of Saussrealappa (Clarke) on Experimental Animal Model
S. Parveen, B. Benjamin Samuel, S. Sunil Kumar
Abstract: Neuroprotection refers to the strategies and relative mechanism able to defused the central nervous system against the neuronal injury. Depression is whole body illness which involves not only mood or emotion but also the physical body and thought process. There are two types of mental depression namely unipolar depression in which mood swings is common (about 75% of cases). The second type is bipolar depression (about 25% of cases) sometimes also called as endogenous depression. Many theories proposed to explain the mechanism of ageing at the molecular level the oxidative stress or free radical hypothesis has received wide support at the biochemical level oxidation. Neurodegeneration is a process involved in both neuropath logical conditions and brain ageing although the brain accounts for less than 2% of the body weight it consumes about 20% of the oxygen available through respiration. Many flavonoids extracted from nature plants have been reported to exert antidepressant like effect in animal studies. Saussurea lappa (Compositae) is cultivated as a medicinal plant in the Himalayas. Costi Amari radix or costus root was an important item of Roman trade with India, and is believed to have been the dried root of Saussurea lappa have reviewed extensively the medicinal importance. The animals treated with Saussurea lappa extract produced dose dependent activity against neurological deficit, anti-depressant activity and Nootropic activity. Anxiolytic effect was not produced by the extract.
Keywords: Nootropic activity, bipolar depression, oxidative stress, Anxiolytic activity.
Country: India, Subject Area: Pharmaceutical Science
Pages: 2170 - 2173
Edition: Volume 8 Issue 5, May 2019
How to Cite this Article?
S. Parveen, B. Benjamin Samuel, S. Sunil Kumar, "Neuroprotective Activity of Saussrealappa (Clarke) on Experimental Animal Model", International Journal of Science and Research (IJSR), https://www.ijsr.net/archive/v8i5/show_abstract.php?id=ART20198355, Volume 8 Issue 5, May 2019, 2170 - 2173
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