Someone just viewed: Re: Someone just viewed: https://www.google.com/search?pws=0&gl=us&biw=1536&bih=754&tbm=isch&sa=1&ei=mlYdXOaMMcW_rQHr6Z_ABQ&q=FROM+OLGA+SHULMAN+LEDNICHENKO+TO+BIBI+NETANYAHU+-%3E+A+FOR+ALIYA+P+FOR+PAIN+&oq=FROM+OLGA+SHULMAN+LEDNICHENKO+TO+BIBI+NETANYAHU+-%3E+A+FOR+ALIYA+P+FOR+PAIN+&gs_l=img.3…6742.6742..7553…0.0..0.108.108.0j1……1….1..gws-wiz-img.0MxLKzGDWrA#imgdii=a4Gn44JxIHFvYM:&imgrc=nRHXEgPBbqEmYM:

https://www.google.com/search?pws=0&gl=us&biw=1536&bih=754&tbm=isch&sa=1&ei=mlYdXOaMMcW_rQHr6Z_ABQ&q=FROM+OLGA+SHULMAN+LEDNICHENKO+TO+BIBI+NETANYAHU+-%3E+A+FOR+ALIYA+P+FOR+PAIN+&oq=FROM+OLGA+SHULMAN+LEDNICHENKO+TO+BIBI+NETANYAHU+-%3E+A+FOR+ALIYA+P+FOR+PAIN+&gs_l=img.3…6742.6742..7553…0.0..0.108.108.0j1……1….1..gws-wiz-img.0MxLKzGDWrA#imgdii=mob2VkvWaLxOuM:&imgrc=gBQT5yA8f8TNCM:

Someone just viewed: Fwd: Someone just viewed: Fwd: Someone just viewed: HAPPY DIWALI TO EVEN TRUMP -> DON – DID JOE BIDEN SAY ” BIND LADEN IS DEAD BUT TRUMP IS ALIVE ? ” – MEANS IT COULD HAVE BEEN TRUMP TOWERS – SEE ATATCHED – REGARSD THE CLINTON FROM LUCKNOW

https://www.google.com/search?pws=0&gl=us&tbm=isch&q=HAPPY+DIWALI+TO+EVEN+TRUMP+-%3E+DON+-+DID+JOE+BIDEN+SAY+%22+BIND+LADEN+IS+DEAD+BUT+TRUMP+IS+ALIVE+?+%22+-+MEANS+IT+COULD+HAVE+BEEN+TRUMP+TOWERS+-+SEE+ATTACHED+-+REGARDS+THE+CLINTON+FROM+LUCKNOW&nfpr=1&sa=X&ved=0ahUKEwi9wNLG1PrgAhVFro8KHZqhANUQvgUIJigB&biw=1536&bih=754&dpr=1.25#imgrc=uerFm8sGA821uM:

Someone just viewed: Fwd: Someone just viewed: Fwd: Someone just viewed: Re: Someone just viewed: FROM OLGA SHULMAN LEDNICHENO TO BARACK AND MICHELLE OBAMA, WHAT PRICE GANDHI ITEM SONG?

https://www.google.com/search?q=:+FROM+OLGA+SHULMAN+LEDNICHENO+TO+BARACK+AND+MICHELLE+OBAMA,+WHAT+PRICE+GANDHI+ITEM+SONG%3F&pws=0&gl=us&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiMv8aC1PrgAhXOXCsKHcT9BR4Q_AUIDigB&biw=1536&bih=754#imgrc=_

Milwaukee!

I HAD TO GO FROM AUSTIN TO FON DU LAC, WISCONSIN.

IT WAS A LAY OVER IN MILWAUKEE..

WELL…

[youtube http://youtube.com/w/?v=GVzo9P3JQTI]

[youtube http://youtube.com/w/?v=HBuW3TmVe30]

HERE IS WHAT I CAN SAY ABOUT MILWAUKEE AND ITS IN WISCONSIN : USA ., WISCONSIN IS A STATE AND IN USA AND USA IS A CONTINENT :)

[1] I STAYED THERE IN HOTELS : MARIOTTT AND SOMETIMES IN SHERATON AND ONCE IT WAS ALL FULL BECAUS EOF THE BIG GAME – SO, WE STAYED AT A LOCAL HOTEL.. WE MENAING ALL OF THAM CONSULATNTS FROM SOMWHERE ELS EIN USA

[2] I AM AN EXTOVERT AND UNLIKE AMERICANS I TALK TO STARNGERS – MENAING, ITS MY BUSINESS NOT NONE OF YOUR BUSINESS TYPE OF GUY I AM .. U CAN ASK BUBBA – FOR EXPLANATION ..

[3] PEOPLE IN WISCONSIN, ARENT LIKE PEOPLE IN NEW YORK OR BERKELEY, WHICH IS ALSO WHERE I STAYED AT MARIIOTT FOR MONTHS AND I USED TO LIVE IN CALFIRNONIA ALSO.

[4] PEOEPLE, IN GENERAL LIKED ONE WORD CALELD BILL CLINTON – A LOT.. EVEN THE CONSERVATVES DID – AND ALSO, THEY DONT NECESSARILY HAVE WHATS CALELD NEW YORK VALUES, ME MEANS BUBBA, OCCASSIA AND WHATS HER NAME ILHAN OMAR AND WHAT THAT OTHER ONE – YEAH THAT MUSLIM GIRL WHO DOESNT LIKE JEWS .. WHATS HER NAME – I FORGOT – SO, U KNOW , I LEARNT THAT ALL POLITICIS IS LOKAL.. AND THEY DONT AT LEST IN WISCONSIN – { THEY HAVE BIG PLATTERS, AND LOTS OF CHHEESE } YEAH SO I WAS SAYING THAT THEY DONT ECESSARILY KNOW MUCH ON SUSHI OR POTATO KANISH – WHICH BTW IS JEWSIH OR MATZO BALL – WHICH IS ALSO JEWISH – OR SAY SATEE – WHCH IS INDONESIAN OR – LAMB VINDALOO WHICH IS I GUESS VIETNAMESE – OR LIKE MOROCCAN ARUGUULA CHICKEN OR STUFF LIKE SAKE – WHICH IS WARM AND JAPANESE AND YEAH MISO SOUP – AND NAVRATAN KORMA – AND SAMBAR IDLI, AND DAL ROTI – AND FOEI GRASS – WHCH WOULD BE FRENCH OR SAY LIKE BARGETTE – OR U KNOW THEY MAY KNOW MERLOT, BUT – THINGS LIKE – UTTAPAM – AND MASALA AND ONION DOSA – ETC – BTW, HW AMANY OF YOU CONTESTANTS, KNOW UTTAPAM AND MASALA DOSA AND SAMBAR IDLI – OTHER THAN KAMALA HARRIS ? – LIKE HOW MANY ? –

ME MEANS – THERE IS A TENDENCY IN DEMOCRATCI PARTY TO LOOK DOWN UPON THOSE WHO ARE WELL LOKAL – THSOE WHO DONT KNOW THAT WHITE BREAD AND SLICE BREAD ARENTTHE ONLY BREADS, BECAUSE THERE IS ROTI , NAAN AND BAGETTE – I HAVE A MESSAGE FOR U – HOW MANY OF U KNOW UTTAPUM, VADA PAU, PAV BHAJI, FOEI GRASS, , MASALA DOSA, IDLI SAMBAR – AND SO ON ?

DID U GET THE POINT ?

OH AND ALSO STUFF LIKE TENNIS – AND STUFF – ISNT REALLY FASHIONABLE IN WISCONSIN , YA KNOW.. I MEAN U MAY LIKE MARTINA NAVRATIVOLA, BECAUSE HATS COMMON BETWEEN NAVRATILOVA AND ELEN DE GENERE IS THAT BOTH ARE LESBIAN – BUT HOW MANY OF U – ACTUALLY HAVE PLAYED TENNIS – ?

IF U WANT TO REPERESNET THE WHOLE USA – NOT JUST THE COASTS – THEN U CANT JUST BE HAPPY THAT U WENT TO MARDI GRASS ON A SPRING BREAK WONCE UPON A AS A SCHOOL –

I MEAN THATS HWAT I THINK..

From: Tom Perez <democraticparty>
Date: Mon, Mar 11, 2019 at 10:59 PM
Subject: Milwaukee!
To: ajay mishra <ajayinsead03>

The 2020 Convention is where we’ll officially nominate our candidate for president, and it’ll serve as the launchpad for our eventual nominee’s fight to defeat Trump.

DemocratsJoin us.
pixel.gif?r=0d67c51161261f3e1259a49b59026ee5642d6a86

The DNC just announced some exciting 2020 news today, and I wanted to be sure you heard it:

The 2020 Democratic National Convention will be held in Milwaukee, Wisconsin!

Milwaukee has a dynamic story to tell — this choice elevates the importance of the heartland and a diverse community working together. After a decade of Republican attacks on working people, labor unions, and communities of color, Democrats saw some of our biggest and most historic gains last year in Wisconsin with the election of Governor Tony Evers and Lieutenant Governor Mandela Barnes. The city of Milwaukee and the state of Wisconsin, under new leadership, represent a stronger and more successful Democratic Party.

Selecting a convention city is an important step in our road to 2020, and let me tell you, Ajay, I couldn’t be more excited. The Democratic National Convention is where our party will officially nominate our candidate for president of the United States, and it’ll serve as the launchpad for our eventual nominee’s fight to defeat Donald Trump and win the White House in 2020.

Will you donate $10 to the DNC’s One-Term President Fund to help ensure our party has the resources necessary to defeat Donald Trump and the GOP’s fundraising machine in 2020? Winning the White House and seats in all 50 states in 2020 won’t be possible without a strong and well-resourced Democratic Party.

If you’ve saved your payment information with ActBlue Express, your donation will go through immediately.

EXPRESS DONATE: $10
EXPRESS DONATE: $25
EXPRESS DONATE: $50
EXPRESS DONATE: $100
EXPRESS DONATE: $200
Or donate another amount.

The DNC launched our One-Term President Fund last month because the stakes in this race for the White House have never been higher. Trump’s campaign has already raised over $130,000,000 — a staggering and unprecedented amount for a sitting president. They’ve been spending aggressively on digital and TV ads to grow and energize their base. It’s clear that the Trump campaign is taking this race seriously, which is why Democrats don’t have an ounce of time to spare.

Our party’s nominee will inherit the organizing infrastructure, technology, and resources of the DNC, so support from committed Democrats like you will have a direct impact on our nominee’s chances of winning in 2020.

The Democratic Party is the only official party organization tasked with winning the White House in 2020 and seats nationwide, which is why your support for our party today is mission-critical. Waiting until the general election begins to kick our efforts into high gear will be too late, so there’s never been a more important time to support the Democratic Party with a contribution.

Chip in $10 — or any amount you can afford — to join the Democratic Party’s powerful movement to take on Trump and Republicans in 2020. This critical work can’t happen without the support of grassroots Democrats like you.

Thank you for stepping up today, Ajay. Let’s do this!

Tom

Tom Perez
Chair
Democratic National Committee

P.S. I’m excited to announce that the 2020 Democratic National Convention will be held in Milwaukee, Wisconsin. Our party has so much work to do in order to prepare to take back the White House, restore the guard rails of our democracy, and make government work for American families. That’s why I hope you’ll donate $10 to our One-Term President Fund to help Democrats win the White House and seats nationwide in 2020.

If you no longer wish to receive emails from the DNC, submit this form to unsubscribe.

If you’d only like to receive our most important messages, sign up to receive less email or opt in to our SMS program by signing up to receive text messages.

This email was sent to ajayinsead03. If this isn’t your preferred email address, update your contact information. If you’re ready to elect Democrats in all 50 states, make a contribution today. This organization is powered by you, and we’d love to hear your ideas. Just reply to this email to send any comments, criticisms, or feedback. Our community management team reads every message from supporters like you. Thanks for supporting our party!

Contributions or gifts to the Democratic National Committee are not tax deductible. Paid for by the Democratic National Committee, www.Democrats.org, and not authorized by any candidate or candidate’s committee.

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Someone just viewed: FROM AJAY MISHRA AND YONI NETANYAHU TO BARACK OBAMA I KNOW IT’S HARD TO BELIEVE BUT PEOPLE LIKE US WHO ARE PURE HAVE NOTHING TO HIDE, FOR OLGA WE SAY FUCK EVEN HANUMAN WHO THE FUCK MOHAMMAD

https://www.google.com/search?q=FROM+AJAY+MISHRA+AND+YONI+NETANYAHU+TO+BARACK+OBAMA+I+KNOW+IT%27S+HARD+TO+BELIEVE+BUT+PEOPLE+LIKE+US+WHO+ARE+PURE+HAVE+NOTHING+TO+HIDE,+FOR+OLGA+WE+SAY+FUCK+EVEN+HANUMAN+WHO+THE+FUCK+MOHAMMAD&pws=0&gl=us&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjs3o__zfrgAhUX448KHT6MCk4Q_AUIDigB&biw=1536&bih=754

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https://www.google.com/search?q=FROM+AJAY+MISHRA+AND+YONI+NETANYAHU+TO+BARACK+OBAMA+I+KNOW+IT%27S+HARD+TO+BELIEVE+BUT+PEOPLE+LIKE+US+WHO+ARE+PURE+HAVE+NOTHING+TO+HIDE,+FOR+OLGA+WE+SAY+FUCK+EVEN+HANUMAN+WHO+THE+FUCK+MOHAMMAD&pws=0&gl=us&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjs3o__zfrgAhUX448KHT6MCk4Q_AUIDigB&biw=1536&bih=754#imgrc=tmKz7zWWRSh0MM:

Someone just viewed: WEL.. YEAH – AJAY IS WRONG ABOUT EVERYTHING – WEHN IN DOUBT ASK MY MOM AND DAA AND FOR THAT MATTER ANYONE ELSE – REGARDS 324368521

https://www.google.com/search?q=WEL..+YEAH+-+AJAY+IS+WRONG+ABOUT+EVERYTHING+-+WHEN+IN+DOUBT+ASK+MY+MOM+AND+DAA+AND+FOR+THAT+MATTER+ANYONE+ELSE+-+REGARDS+324368521&pws=0&gl=us&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiW46u7y_rgAhXaYH0KHWzuC0MQ_AUIDigB&biw=1536&bih=754&dpr=1.25#imgdii=OYxRIHh53aHMdM:&imgrc=W9eM8Pp4rgiCVM:

Someone just viewed: 643361467 WHERE IS THAT GAUSSIAN PRIME NUMBER FROM AUSTIN RIGHT NOW

https://www.google.com/search?q=643361467+WHERE+IS+THAT+GAUSSIAN+PRIME+NUMBER+FROM+AUSTIN+RIGHT+NOW&pws=0&gl=us&source=lnms&tbm=isch&sa=X&ved=0ahUKEwi0x92Oy_rgAhW34XMBHSgGCMIQ_AUIDigB&biw=1536&bih=754#imgrc=_

From: Streak <notifications>
Date: Mon, Mar 11, 2019 at 10:15 PM
Subject: Someone just viewed: 643361467 WHERE IS THAT GAUSSIAN PRIME NUMBER FROM AUSTIN RIGHT NOW
To: <ajayinsead03>


Someone just viewed your email with the subject: 643361467 WHERE IS THAT GAUSSIAN PRIME NUMBER FROM AUSTIN RIGHT NOW
Details
People on thread: YONI NETANYAHU OLGA BLOG POST BY EMAIL
Device: Android Tablet
Location: chittagong, b

eyJlbWFpbF9pZCI6IlJNX3lBUUVBQVdsdHBYZTBPZFpxX0NweThUbEZtQT09In0=

Someone just viewed: Re: FROM OLGA – LESSONS IN ENGLISH AND WHAT NOT DTO DO, IN MATHS AND FRENCH -> HONEY -> IS IT CALLED DOB PLUS A PRIME NUMBER = 1987 ?

[youtube http://youtube.com/w/?v=5zvjXY7mJ9o]

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[youtube http://youtube.com/w/?v=VvHvNwWSh5Y]

[youtube http://youtube.com/w/?v=P0p5r_ibGT4]

https://www.google.com/search?q=FROM+OLGA+-+LESSONS+IN+ENGLISH+AND+WHAT+NOT+TO+DO,+IN+MATHS+AND+FRENCH+-%3E+HONEY+-%3E+IS+IT+CALLED+DOB+PLUS+A+PRIME+NUMBER+%3D+1987+%3F&pws=0&gl=us&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjlp6rfx_rgAhUJWCsKHQiIDvEQ_AUIDigB&biw=1536&bih=754&dpr=1.25#imgdii=9HDKJepPfr6rpM:&imgrc=gOaXavjSP3zRIM:

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From: Streak <notifications>
Date: Mon, Mar 11, 2019 at 10:15 PM
Subject: Someone just viewed: Re: FROM OLGA – LESSONS IN ENGLISH AND WHAT NOT DTO DO, IN MATHS AND FRENCH -> HONEY -> IS IT CALLED DOB PLUS A PRIME NUMBER = 1987 ?
To: <ajayinsead03>


Someone just viewed your email with the subject: Re: FROM OLGA – LESSONS IN ENGLISH AND WHAT NOT DTO DO, IN MATHS AND FRENCH -> HONEY -> IS IT CALLED DOB PLUS A PRIME NUMBER = 1987 ?
Details
People on thread: YONI NETANYAHU OLGA BLOG POST BY EMAIL
Device: Android Tablet
Location: chittagong, b

eyJlbWFpbF9pZCI6IlJNX3lBUUVBQVdsdHBYYmRGTTh3MnJXclV4bloydz09In0=

Someone just viewed: 324368521 WITH THE GAUSSIAN PRIME FROM LUCKNOW OR AUSTIN OR ? – gOOGLE SAYS 6 RESULTS

https://www.google.com/search?q=324368521+WITH+THE+GAUSSIAN+PRIME+FROM+LUCKNOW+OR+AUSTIN+OR+%3F&pws=0&gl=us&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiayJj-xvrgAhXHXysKHQDEBhoQ_AUIDigB&biw=1536&bih=754#imgdii=1KcCB-Ip10DiyM:&imgrc=wrldBnz9GDf6dM:

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https://www.google.com/search?q=324368521+WITH+THE+GAUSSIAN+PRIME+FROM+LUCKNOW+OR+AUSTIN+OR+%3F&pws=0&gl=us&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiayJj-xvrgAhXHXysKHQDEBhoQ_AUIDigB&biw=1536&bih=754#imgrc=_

From: Streak <notifications>
Date: Mon, Mar 11, 2019 at 10:15 PM
Subject: Someone just viewed: 324368521 WITH THE GAUSSIAN PRIME FROM LUCKNOW OR AUSTIN OR ? – gOOGLE SAYS 6 RESULTS
To: <ajayinsead03>


Someone just viewed your email with the subject: 324368521 WITH THE GAUSSIAN PRIME FROM LUCKNOW OR AUSTIN OR ? – gOOGLE SAYS 6 RESULTS
Details
People on thread: YONI NETANYAHU OLGA BLOG POST BY EMAIL
Device: Android Tablet
Location: chittagong, b

eyJlbWFpbF9pZCI6IlJNX3lBUUVBQVdsdHBXc3ZHYUZuQmdaUkVYUnVXdz09In0=

Someone just viewed: IS THIS TIGER BEING DISPLAYED IN THE GUASSIAN PRIME OF MINE ? TELL ME INDIANS AND SHIT

OH CHITTAGONG,

HEY HELLO

SO THOSE WHO DOT KNOW HERE IS CHITTAGONG

[youtube http://youtube.com/w/?v=_4hAaEMHIyY]

BTW, YOU TUBE CO FOUNDER ONEOF THEM IS BANGLADESHI GUY, ANOTHER IS CHINESE AND 3RD PARTNER WAS AMEICN, AND THEN GOOGLE BOUGHT IT

THERE IS ALSO A MOVIE CALED CHITTAGONG SEE BELOW

[youtube http://youtube.com/w/?v=8C7sOtAgpns]

https://www.google.com/search?q=FROM+OLGA+LEDNICHENKO+IS+THIS+TIGER+BEING+DISPLAYED+IN+THE+GAUSSIAN+PRIME+OF+MINE+%3F+TELL+ME+INDIANS+AND+SHIT&pws=0&gl=us&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiF28voxfrgAhUCXCsKHZryBdoQ_AUIDigB&biw=1536&bih=754#imgdii=ekp_gB6eyYLT1M:&imgrc=NwmvxtkbBE1EmM:

From: Streak <notifications>
Date: Mon, Mar 11, 2019 at 10:15 PM
Subject: Someone just viewed: IS THIS TIGER BEING DISPLAYED IN THE GUASSIAN PRIME OF MINE ? TELL ME INDIANS AND SHIT
To: <ajayinsead03>


Someone just viewed your email with the subject: IS THIS TIGER BEING DISPLAYED IN THE GUASSIAN PRIME OF MINE ? TELL ME INDIANS AND SHIT
Details
People on thread: YONI NETANYAHU OLGA BLOG POST BY EMAIL
Device: Android Tablet
Location: chittagong, b

eyJlbWFpbF9pZCI6IlJNX3lBUUVBQVdsdHBXcG5iWGotUU0wWUFPRklmQT09In0=

643361467 324368521 18 ALAHIRI STREET ERODE

[youtube http://youtube.com/w/?v=49ZHZWE7INU]

[youtube http://youtube.com/w/?v=VYygrKm-J_Q]

https://www.google.com/search?pws=0&gl=us&biw=1536&bih=754&tbm=isch&sa=1&ei=vIyGXLGBOoWmwgO7ib_wAw&q=643361467+324368521++18+ALAHIRI++STREET+ERODE&oq=643361467+324368521++18+ALAHIRI++STREET+ERODE&gs_l=img.3…65178.68906..69464…0.0..0.157.1574.0j11……1….1..gws-wiz-img.oskf4-qnpeM#imgdii=bf49xYsT56Q9jM:&imgrc=-KqJaZ7QSvek5M:

We all have a choice to make in this moment

From: Kamala Harris <info>
Date: Mon, Mar 11, 2019 at 10:01 PM
Subject: We all have a choice to make in this moment
To: <LEDNICHENKOOLGA>

In a little over two weeks, we will close the books on the first FEC filing deadline of our campaign. Once we release our fundraising numbers, our opponents — both those running in the Democratic primary and Trump’s team — will dissect our report to get a sense of how strong our campaign is.

I will be honest: at the end of this email, I am going to ask you to make a contribution to power our campaign for president. I want you to know why it’s so important, and what difference your contribution will make.

The money we raise can’t capture the powerful conversations about the future of our country I’ve had with people on the campaign trail. And fundraising can’t measure the passion of our grassroots activists and volunteers who are fired up and ready to get to work — to do more — to win this campaign.

But our fundraising does have direct impacts on the choices our campaign makes right now. It helps us make big investments in our organization that will grow our movement. And it helps us respond to dishonest attacks.

Our campaign finance system is stacked against everyday people — corporations and dark-money groups are able to spend as much as they want to sway our democracy. Let’s be clear: this is wrong — but it is what we are up against.

But from day one, I made a commitment to you: our campaign will reject all contributions from corporate PACs and federal lobbyists — instead, putting our campaign in the hands of the people.

We are already facing attacks from Donald Trump’s allies — including the NRA — and it will only get tougher from here. There will be nasty attacks and millions spent against us to stop our campaign. But I’ve been taking on tough fights my entire life. I’m not afraid of them. Especially knowing I have you in my corner.

So here is where I ask you: can you step up today with a contribution to power our campaign for president?

If you’ve saved your payment information with ActBlue Express, your donation will go through immediately:

Chip in $10 now
Chip in $25 now
Chip in $50 now
Chip in $100 now
Chip in $250 now
Another Amount

At the end of March when we close out our first quarterly FEC report, I know we will be proud to share the growing number of grassroots contributors who are pitching in what they can to our campaign, whether it’s $5, $10, or $50. I hope your name will be there, too.

Thank you for all that you’ve done — and will do — to power our movement.

For The People,

— Kamala Harris

PAID FOR BY KAMALA HARRIS FOR THE PEOPLE

This email was sent to LEDNICHENKOOLGA. You received this message because you are subscribed to Senator Kamala Harris’ mailing list.
You can adjust your email preferences here, or unsubscribe from receiving further emails here.

Ramanujan’s birthplace on 18 Alahiri Street, Erode ::Ramanujan (literally, “younger brother of Rama”, a Hindu de ity12:12) was born on 22 December 1887 into a Tamil Brahmin Iyengar family in Erode, Madras Presidency (now Tamil Nadu ), at the residence of his maternal grandparents.12:11 His father, K. Srinivasa Iyengar, originally from Thanjavur dis trict, worked as a clerk in a sari shop.12:17–18 His mother, Komalatammal, was a housewife and also sang at a local temple.13 They lived in a small traditional home on Sarangapani Sannidhi Street in the town of Kumbakonam.14 The fam ily home is now a museum. When Ramanujan was a year and a half old, his mother gave birth to a son, Sadagopan, who died less than three months later. In December 1889, Ramanujan contracted smallpox, though he recovered, unlike 4,000 others who would die in a bad year in the Thanjavur district around this time. He moved with his mother to her parents’ house i n Kanchipuram, near Madras (now Chennai). His

  1. A certain street has between 50 and 500 houses in a row, numbered 1, 2, 3, 4, … consecutively. There is a certain house on the street such that the sum of all the house numbers to the left side of it is equal to the sum of all the house numbers to its right. Find the number of this house.

The story behind this problem is as follows. A friend of Ramanujan, P. C. Mahalanobis, who was also a student at Cambridge and who later became an eminent statistician, read about this problem while visiting Ramanujan. Ramanujan was in the kitchen, cooking. Mahalanobis solved the problem, and then turned to Ramanujan and said, “Here’s a problem for you.” “What problem? Tell me,” said Ramanujan, still stirring vegetables. Mahalanobis read the problem. Ramanujan immediately said, “Take down the solution.” He then dictated a continuous fraction that expressed all the infinite solutions to the problem if you ignore the constraint of 50 to 500 houses. So as a bonus problem, can you emulate Ramanujan and find a formula that generates this general solution?

As usual, Quanta readers responded magnificently to this puzzle, obtaining the correct answer (house number 204, on a street with 288 houses) using a variety of methods. With simple algebra, it is easy to obtain the equation 2h2 = n(n + 1), where h is the house number, and n is the total number of houses. This is an equation with an infinite number of integer solutions (the general name for an equation requiring integer solutions is Diophantine equation). We now have to find integer solutions with n in the range 50 to 500, which can be done by using a brute-force search using a spreadsheet, or by computer programming, as several readers did. Another approach is to start small — it is quite easy to find solutions to the above equation for small numbers such as h = 1, n = 1 followed by h = 6, n = 8. From this you can find a simple recurrence relation between h and n, or between successive h’s or n’s, using standard techniques for recurrences, as Greg Egan did. This yields all the infinite solutions recursively. Amazingly, Tom Nichols was able to derive a closed-form solution using the time-honored technique of playing with the numerical solutions. Congratulations, Tom! The young Ramanujan would have approved!

The first step to finding the solution without using trial-and-error methods is to recognize that the equation we obtained above can be expressed as a Pell equation of the form nx2 + 1 = y2, as described below. There are two well-known ways to solve these kinds of equations. The first, which doesn’t use continued fractions, is a method based on work done by the Indian mathematician Brahmagupta a thousand years before Pell, and transformed into a general method called the chakravala, or cyclic, method by Bhaskara II in the 12th century. The second method is based on continued fractions, the complete theory of which was perfected by Lagrange in the 18th century.

This brings us back to the bonus question. What is the continued fraction that Ramanujan came up with? Just by inspecting our equation, we can see that the ratio n:h will approach 2–√ as n and h increase indefinitely. The continued fraction for 2–√ is [1; 2, 2, 2, 2, …]. As Greg Egan described, this does yield the solutions, but not elegantly — you have to perform different operations on the odd and even convergents, and the solutions are not in order. A better approach derives the Pell equation and is described by Christopher Long:

Let there be n houses and let m be the excluded house, then the sum of 1 + … + (m – 1) must equal 1/2 of the sum of (1 + … + n) – m. This gives m(m – 1)/2 = n(n + 1)/4 – m/2 or 2m^2 = n(n + 1). Now complete the square on the right and we have 2m^2 + 1/4 = (n + 1/2)^2; finally, multiply by 4 to get (2n + 1)^2 – 8m^2 = 1. This is equivalent to solving the Pell equation x^2 – 8*y^2 = 1, as x must be odd. Solutions for x, ycan be generated from the continued fraction for sqrt(8) = [2; 1, 4, 1, 4, …].

This is definitely a better continued fraction for this problem. The convergents are 2, 3, 14/5, 17/6, 82/29, 99/35, 478/169, 577/204, … The denominators of every even-numbered convergent give the house numbers in succession, and their numerators (n) give the number of houses as (n – 1)/2.

This is good, but is there a better answer that Ramanujan might have come up with? It hasn’t been recorded, and I can’t look into his mind, but there is a more elegant answer. To see it, notice that the ratio 2n + 1 to h in this problem starts out at 3 and must decrease every time in succession — it must get monotonically closer to 8–√ as n and h increase. The convergents of the above continued fraction, on the other hand, oscillate from one side of the limit value to the other, which is why its odd-numbered convergents have to be discarded. How can we correct this? Well, there is a noncanonical form of the continued fraction for 8–√ that does do that: [3; –6, 6, –6, 6, –6, 6, …]. The convergents of this continued fraction are precisely successive solutions to the problem: 3, 17/6, 99/35, 577/204, etc. Here is how the continued fraction looks when written out in full in elegant, albeit slightly nonstandard, form:

3−16−16−16−16−1⋱

From this continued fraction, it is easy to derive the recurrence hn+1 = 6hn – hn-1, which was described by Tom Nichols and Michael, and the corresponding recurrence for n, posted by Sudhir Kumar. From standard continued fraction theory we can easily derive the quadratic equation mentioned by Michael, x2 = 6x – 1. The theory also gives an elegant closed-form solution ((3+8–√)k) that you can write down directly, just by inspecting the continued fraction. If you carry out this expansion, and gather and add all the like terms, the multiplier of the radical gives h, the house number, and the integer part gives the number 2n + 1, where n is the number of houses. If we want to separate the two, we can obtain the following closed forms from this:

2n+1=(3+8√)k+(3−8√)k2

and

h=(3+8√)k–(3−8√)k28√

The latter is a simpler version of the same closed form obtained by Tom Nichols.

Thank you, everyone, for the great comments. I feel compelled to award two Quanta T-shirts this time: one to Tom Nichols for his discovery of the closed form, and the other to Christopher Long for his solution of the Pell equation. If this column has stimulated your interest in continued fractions, there is an excellent tutorial online.

FROM AJAY MISHRA AND OLGA SHULMAN LEDNCHENKO TO OBAMA AND CLINTONS AND NETANYAHU AND PUTIN AND TO BUBBA -> DATES AND NUMBERS DID HAPPENS, HAPPENED AND WILL OR MAY HAPPENES – ALL OF THEM DATES AND NUMBERS IN OLGA OBAMA CLINTON MISHRA NETANYAHU RUSSHIAN AND INDIAN DATES AND NUMBERS

[youtube http://youtube.com/w/?v=orawG7vt68o]

[youtube http://youtube.com/w/?v=WIOtnn6meWA]

[youtube http://youtube.com/w/?v=x2hngvTsOkg]

DID ME SAY SOMETHING BIBI?

[youtube http://youtube.com/w/?v=GwDd1js-lUM]

[youtube http://youtube.com/w/?v=Rh2YaZM2v5E]

[youtube http://youtube.com/w/?v=tuzsC0SBueQ]

[youtube http://youtube.com/w/?v=9oVXGCDfTW4]

[youtube http://youtube.com/w/?v=jsWsvM2CQ0w]

[youtube http://youtube.com/w/?v=zoxBjP7RCqQ]

[youtube http://youtube.com/w/?v=daCZMIrRFNc]

[youtube http://youtube.com/w/?v=BawiJgeL-84]

https://www.google.com/search?q=FROM+AJAY+MISHRA+AND+OLGA+SHULMAN+LEDNCHENKO+TO+OBAMA+AND+CLINTONS+AND+NETANYAHU+AND+PUTIN+AND+TO+BUBBA+-%3E+DATES+AND+NUMBERS+DID+HAPPENS,+HAPPENED+AND+WILL+OR+MAY+HAPPENES+-+ALL+OF+THEM+DATES+AND+NUMBERS+IN+OLGA+OBAMA+CLINTON+MISHRA+NETANYAHU+RUSSHIAN+AND+INDIAN+DATES+AND+NUMBERS&pws=0&gl=us&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiz96D2tPrgAhUBuI8KHaXtDoQQ_AUIDygC&biw=1536&bih=754&dpr=1.25#imgrc=_

DID ME SAY SOMETHING BARACK ? NO OLGA IS NOT RICH BARACK.. OK.. IT TAKES MONEY TO OPEN UP YOUR MIND AND BE FEARLESS

.

SO SUNDAR – WHATS THE RUSSHIANA AND HOPE ARKANSAS NUMBERS – ?

.

[youtube http://youtube.com/w/?v=QpIYFqgG64Q]

BUBBA -> THIS HAS ALL NUMBERS MINUS THE BRITISH NUMBERS AND HOPE ARKANSAS AND U KNOW RUSSHIAN NUMBERS – BUT EVERYTHING ELSE, IT IS HAS ENOUGH OF, SOMETHINGS HSOULD BE LEFT FOR MYSTERY – HILALRY JI – AM I WRONG?

BTW CHELSEA -> SO, I GUESS MATHS IS SOMETIMES USEFUL – NOT JUST PHYSCIS AND INROGANIC CHEMSITRY :)

Someone just viewed: Fwd: 💳 Become a card-carrying Democrat in 2019, ajay 💳

OH HELLO WISCONSIN

HEY PAUL RYAN .. U KNOW I USED TO FLY TO WISCONSIN , EVERY WEEK – MONDAY THRU FRIDAY OR MON THRU THURSDAY IN  FON DO LAC WISCONSIN I WAS .. FOR LIKE 7 OR 8. 5 MONTHS ..

U KNOW PAUL RYAN : I MUST SAY I WAS MORE IMPRESSED BY YOU, THAN I WAS WITH ROMNEY EVER – BECAUSE U BELIEVE IN THINGS THAT U BELIEVE IN WHERTEHR I DISAGREE OR NOT, IS A MATER OF OPINIONS VALEUS, AD BELIEFS,

BUT POLITICS AND OBAMA VERSUS ROMNEY ASIDE, I RESPET U – AND YEAH OWULD LOVE TO BE FT AND IN SHAPE LIKE U ARE – WELL.. U KNOW I WAS BURUCE LEE – , BUT OCOURSE BRUCE LEE WAS SHHOT AND THE USA NATION OF YOURS MADE ME SIDENTERAY –

BUT ALL THAT ASIDE, I GOTTTA SAY A FEW THINGS TO U PAUL

[A] PAUL KRUGMAN DOESNT HATE U – HE WJUST DISLIKES VON MISSES AND HAYEK, NOT BECAUSE HE DISLIEKS THEM BUT BECAUSE HE LIKES JEYNES

[B] TRUMP MADARCHOD, ISNT AN AMERICAN MODEL OF A CITIZEN – AND I THINK U KNOW THAT BY NOW

[C] IF U EVER HAVE TO U KNOW GET AN ALTERNATIVE OPINION MAYBE GOD FORBID FROM THE DEMOCATS, TRY PRESIDENT CLINTON – U MAY BE SURPRISED BUT ME AND BUBBA – DONT HATE OR EVEN DISLIKE THE GOP – IN FACT SOME OF THE GP WE LIKE.. SAME FOR HILLARY JI BTW

NOW, ONE THING – I HAVE TO SAY TO U IS THAT WHEN IT WAS OBAMA VERSUS ROMNEY, DID U NOTICE ENEVR SAID ANY BAD WORS TOWARD U ? – POINT ONE – INSTANCE – IF U CAN – OK – THEN WHAT THE FUCK IS DONALDN DOING IN YOUR GP AND TO YOUR GOP AND SAYING ABOUT NOT JUST U BUT ALSO OTHER IN THE GOP

AND

NOT TO RUN SALT ON YOUR WOUNDS – BUT THE TRUTH AND THE FACT IS THAT – NEITEHR DID THE TARRIFS NOR DID THE TAX UTS – REDUCE THE DEFICIT – BOTH THE TARDE AND THE BUDEHGTE/FISCAL DEFCIIT ARE HIGHER NOT LOWER – AND WHILE I AM AT IT – WHATS TRUMP’S PAKISTAN AND HINDUKUSH POLICY MAY IKNOW ? AND ALSO – IN LBYA – THERE WAS MRONING AFTER AND BARACK ADMITTED THAT WAS A MISTAKE – AND SYRIA DIDNT TURN OUT WELL, BUT – LAST ME HEARD THAT YOUR PRESDIENT THE DONALD – IS MULING SOME STUFF IN BOTH SYRIA AND AFGHAN – CAN U SEPLL IT OUT WHAT WTHAT WAS ?

THANKS

AND HAVE A NICE DAY

NOT THAT I LIKE ANY AMERICAN SPORTS ABUT I YEAH GOT TICKERS TO THE GREEN BAY PACKERS, I TOOK A CHICK WITH ME TO THE GAME

U KNOW I M FROM AUSTIN TEXAS BUT IEVEN IN THIS GAME – PACKERS VERSYS COWBOYS, I DIDNT AUTOMATICALLY CHOSOE BASED ON IDENTITY AND POLITICIS LIKE YALL DO
I JUST SAY LET THE BEST TEAM WIN

BTW IMMIGRANTS ARE NOT THAT ETHNOCENTRIC AS U KNOW WHO

[youtube http://youtube.com/w/?v=HBuW3TmVe30]

From: Streak <notifications>
Date: Mon, Mar 11, 2019 at 8:38 PM
Subject: Someone just viewed: Fwd: 💳 Become a card-carrying Democrat in 2019, ajay 💳
To: <ajayinsead03>


Someone just viewed your email with the subject: Fwd: 💳 Become a card-carrying Democrat in 2019, ajay 💳
Details
People on thread: YONI NETANYAHU OLGA BLOG POST BY EMAIL
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Someone just viewed: Re: FROM OLGA SHULMAN LEDNICHENKO TO CLINTONS AND OBAMA SO, VIVEKANAND AND CHCAGO AND TWIN TOEERS AND AND THAT DATES AND JULY 4 AND YONI NETANYAHU AND YONI DIED IN URDU PROGRAMMES WHO?

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..

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.

https://www.google.com/search?q=FROM+OLGA+SHULMAN+LEDNICHENKO+TO+CLINTONS+AND+OBAMA+SO,+VIVEKANANDA+AND+CHICAGO+AND+TWIN+TOWERS+AND+AND+THAT+DATES+AND+JULY+4+AND+YONI+NETANYAHU+AND+YONI+DIED+IN+URDU+PROGRAMMES+WHO%3F&pws=0&gl=us&source=lnms&tbm=isch&sa=X&ved=0ahUKEwijyruErfrgAhVYFHIKHSM3AmYQ_AUIDigB&biw=1536&bih=754#imgdii=h92CKeqKMNfeqM:&imgrc=0PntDgzaGbsplM:

action required INSEAD : help us defend our Giving Day Title!

From: Mike Davis, MBA 10J, President of NAA of USA <insead.usa>
Date: Mon, Mar 11, 2019 at 7:55 PM
Subject: [action required] INSEAD : help us defend our Giving Day Title!
To: <ajayinsead03>

3 easy steps, literally 2 minutes to action on all 3. :)

INSEAD National Alumni Association of USA
Register Now
Become a NAA Member Today
INSEAD National Alumni Association of USA
Beautiful people of INSEAD USA,

Giving Day is upon us, and we have a title to defend!

As you know, we placed #1 in participation last year, however, we have a bullseye on our backs from the other NAAs! Insert Eye of the Tiger theme. 😉

This year, we have a few Bonus opportunities!

  • Bonus #1 – you can get 3 TIMES the credit for team USA if you click on "Give Regularly" and select 3 installments to be billed in the future!
  • Bonus #2 This year, we have some USA Alumni who have kindly offered matching funds! What does this mean? It means, EXTRA CREDIT! Pledges of $500+ might be eligible for matching!

Want to go for the trifecta? Here’s how:

  1. Click on this link to give and select $250 (or greater)
  2. Select "Give Regularly"
  3. Ask 5 of your friends to give – heck, even simpler, forward this email to 5 of your friends.

But wait, there’s more:

  • Bonus #3 – if as an NAA, we double the participation from last year, I will double my giving day pledge.

Say it with me, WE GOT THIS. We will place #1 again this year!

Giving Day ends tomorrow, so please do this today :)

Thank you for taking the time to read this email.

Much love,
–MPD

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Someone just viewed: Re: Someone just viewed: Fwd: Someone just viewed: “Dead” and “Dying” redirect here. For the coloring process, see Dyeing. For other uses, see Dead (disambiguation) and Death (disambiguation).

https://www.google.com/search?q=Srinivasa+Ramanujan+FRS+(/%CB%88%CA%83ri%CB%90ni%CB%8Cv%C9%91%CB%90s%C9%99+r%C9%91%CB%90%CB%88m%C9%91%CB%90n%CA%8Ad%CA%92%C9%99n/%3B%5B1%5D+About+this+soundlisten+(help%C2%B7info)%3B+22+December+1887+%E2%80%93+26+April+1920)%5B2%5D+was+an+Indian+mathematician+who+lived+during+the+British+Rule+in+India.+Though+he+had+almost+no+formal+training+in+pure+mathematics,+he+made+substantial+contributions+to+mathematical+analysis,+number+theory,+infinite+series,+and+continued+fractions,+including+solutions+to+mathematical+problems+considered+to+be+unsolvable.+Ramanujan+initially+developed+his+own+mathematical+research+in+isolation:+%22He+tried+to+interest+the+leading+professional+mathematicians+in+his+work,+but+failed+for+the+most+part.+What+he+had+to+show+them+was+too+novel,+too+unfamiliar,+and+additionally+presented+in+unusual+ways%3B+they+could+not+be+bothered%22.%5B3%5D+Seeking+mathematicians+who+could+better+understand+his+work,+in+1913+he+began+a+postal+partnership+with+the+English+mathematician+G.+H.+Hardy+at+the+University+of+Cambridge,+England.+Recogniz&pws=0&gl=us&source=lnms&tbm=isch&sa=X&ved=0ahUKEwieorS-5_ngAhWTUn0KHRQdC98Q_AUIDygC&biw=1536&bih=754#imgdii=0fWSd90jkEMP4M:&imgrc=EqvNuqy5gKHyCM: