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FAQs
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How do you register a trademark, such as company name?
One question I am often asked regarding trademarks whenever I discuss IP law with a group of young budding students, entrepreneurs or startup companies is “How to register a trademark in India?”. There are several articles and blogs that explains how to register a trademark in India in one way or the other but I hope that this post will be comprehensive enough to answer most of them.A trademark is anyword (PEPSI, COCO COLA, PEPSODENT),name (RAYMOND VEIL, CHRISTIAN LOUBOUTIN),surname (TATA, BATA, BAJAJ),signature (LOUIS PHILIPPE),letters (BMW, IBM, HDFC),numeral (555, 501),symbol (MERCEDES BENZ THREE POINTED STAR, ADDIDAS PYRAMID),device (AMUL GIRL, PILLSBURY BOY),color scheme (PIZZA HUT, DOMINOS),packaging (CADBURY’S),shape of goods (COCO COLA BOTTLE)or any combination thereof that identifies and distinguishes the source of the goods of one party from those of others.When the mark is used in respect of services then the mark is also commonly referred to as Service Mark. Ex: DHL, HILTON, INFOSYS are service marks. However, since the distinction between goods and services are not always clear, the term trademark is often used to include service marks as well.What is classification of goods and services or classes?When you file an application for registration of a trademark you need to mention the list of goods/services for which you intend to use your trademark. India follows an international system of classification called the “Nice Classification” according to which the goods and services are categorized into 45 classes, with goods covered in classes 1 to 35 and services covered under classes 36 to 45.If the trademark is AMUL the goods for which it is used are “cheeses” and the class will be “29″. Likewise if the trademark is EXPEDIA the services for which it is used are “Online reservations and information regarding travel etc” and the class will be 39.If you do not know which class or classes your goods or services fall in, please use the Classification search tool euroclass or the list of goods/services as published by the Indian trademark office.Search the records of the Indian Trademark Office – Online!Prevention is better than cure. Before you file an application for or consider using your trademark, search the records of the Indian trademark office to check if someone has already chosen the same or a similar trademark. You will have to search the exact class of goods and services for which you will be using your trademark. If you see any similar trademarks already on the records of the trademark office, it should raise a red flag! You will now have to carefully analyze each and every trademark and take a call on going forward with the same mark or possibly changing your trademark so that you don’t infringe another’s trademark rights.Search using Google.One of the best things that happened in this century– Punch in your trademark at Google and viola! Magic! Merely because a trademark is not filed for registration with the trademark office, does not mean it is available for you to take. In a common law country like India, usage of a trademark gets importance over filing an application/obtaining registration for a trademark. Search using Google and see if anyone is using the trademark you want to adopt. If you see a similar mark do a bit of research to see how much they have used their mark, period of usage, goods or services for which is it used, has the mark gained any reputation etc. More importantly, compare the marks yourself and decide whether your trademark will infringe the rights of the other person. Your few minutes of research will save you from the risk of choosing deceptively similar marks, resulting in lengthy oppositions and infringement action costing time and money. a. File an application with the trademark office.Congratulations! You have cleared the first two hurdles. Give yourself a pat on the back for discovering that you are going to have exclusive rights on your trademark, and proceed with filing a trademark application. You can either file a paper application with the Indian Trademark Office (TMO) or file an application online at http://ipindia.nic.in. You will require a digital signature and an Axis/SBI bank account for filing the application online. The official fee is INR.3500 (approx USD 70) per mark/class.If you are a foreign entity who wants to protect your trademark in India, consider claiming priority.India is a member to the Paris Convention and signatory to the TRIPS agreement. Hence an application can be filed in India claiming priority from the application filed in a foreign country, provided the foreign application was filed not earlier than 6 months from the date of filing the application in India.Required information:a. Name of the person/organization that will own the rights to the trademark (applicant);b. Address of the applicant;c. Nature of business of the applicant; (Ex:Manufacturers, Merchants, Traders, Service Providers)d. Trademark;e. Class;f. Specification of goods or services;g. Date of first use of your mark in India;h.When priority is claimed:(i) Priority date;(ii) Priority application number;Priority Country.Required documents:a. Application form in duplicate;b. Representation sheet in duplicate;c. When priority is claimed:(i) Certified copy of the priority application.d. Official fee by way of cheque/demand draft or cash.Trademark Offices and their Jurisdiction:There are five trademark offices in India and in which office your application is to be filed depends on your registered office address. If you do not have an address in India then the trademark office is decided on the basis of the address of your legal counsel.The jurisdiction of each trademark office is as follows:Mumbai – State of Maharashtra, Madhya Pradesh and GoaNew Delhi – State of Jammu & Kashmir, Punjab, Haryana, Uttar Pradesh, Himachal Pradesh, Union Territory of Delhi and ChandigarhKolkatta – State of Arunachal Pradesh, Assam, Bihar, Orissa, West Bengal, Manipur, Mizoram, Meghalaya, Sikkim , Tripura and Union Territory of Nagaland, Andamar & Nicobar Island.Ahmedabad – State of Gujarat and Rajasthan and Union Territory of Damman, Diu, Dadra and Nagar HaveliChennai – State of Andhra Pradesh, Kerala, Tamil Nadu, Karnataka and Union Territory of Pondicherry and Lakshadweep Island.Once the application is filed the trademark office issues a filing receipt and one copy of the representation sheet stamped with the application number and the filing date as proof of filing the application. You can thereafter see the status of your trademark application online using the application number.b. Examination of your trademark application.In approximately seven to nine months the trademark office will send you the examination report either citing the objections consisting of absolute or relative grounds or both, or, in the absence of any objections allowing the application to be published in the upcoming trademarks journal for a third party to raise objections to the registration. The time to respond to the examination report is 30 days from the receipt of the same and this deadline cannot be extended. So it is important that you file a response with the trademark office within the deadline of 30 days.The objections under absolute grounds are that– your trademark is not distinctive; i.e.: your trademark is not capable of distinguishing the goods and or services of one person from those of others.– your trademark is descriptive or devoid of any distinctive character; i.e.: your trademark directly refers to the goods or services for which the protection is sought. Ex: Trademark FAIRBEAUTY filed for cosmetics under class 03 cannot be registered.– your trademark is a generic term or is customary to trade; Ex: APPLE for fruits, SOFTWARE for software services cannot be registered.The objections under absolute grounds can be over come by stating that your trademark has acquired distinctiveness by extensive usage over a period of time and that the public in general, identifies your product or service by your trademark and that the public identifies only you in relation to your trademark and no one else. Documentary evidence is required to be filed in support of your claim along with your response.The objections under relative grounds are: the existence of similar trademarks on the records of the trademark office.The objections under relative grounds can be over come by stating that your trademark is different from the other cited marks in the examination report.In what ways your trademark is different from the others needs to be explained in detail. Submission of documentary evidence of extensive usage of your trademark will also help you to strengthen your case.c. Hearing before the examiner.In about six months from filing your response to the examination report, the trademark office will either allow the application to be published in the upcoming trademarks journal for a third party to raise objections to the registration or fix a hearing by sending you a hearing notice with a date and time to meet the examiner and explain why your trademark should be allowed to proceed towards registration. This opportunity should be exploited to explain to the examiner, the evidences filed at the time of responding to the examination report in detail and to submit additional evidence. Subsequently the examiner will pass an order either allowing or refusing registration of your application. If it is a refusal, you can appeal against the order of the examiner before the Intellectual Property Appellate Board (IPAB) with 15 days of such refusal.d. Publication of the application in the trademarks journal.Within two to three weeks from the date of the examiner’s order to publish the trademark, the trademark application is published in the trademarks journal. You can download the trademark journal and check if your mark has been advertised. After the expiry of four months from the date of publication of the trademarks journal in which your mark was published, check the status of your trademark application online and if there are no objections to your trademark by way of oppositions filed by any other person, write a follow up letter to the trademark office requesting registration of your trademark and issuance of your trademark registration certificate.In the event of any person raising an objection to your trademark application by way of an opposition, the trademark office will notify you of the objection along with the copy of the notice of opposition as filed by the other party. Opposition proceedings are complicated and we suggest that you consult your legal counsel.e. Registration of your trademark and issuance of the registration certificate.If no objections are received by way of oppositions to your trademark application within this four month period, the trademark office will grant registration to your trademark and issue the registration certificate. Once you receive the registration certificate peruse the contents of the certificate to ensure that there is no discrepancy in the data and in case of any, bring it to the attention of the examiner and have it rectified.f. Renewal of your trademark registration.Every trademark registration is valid for a period of ten years from the date of filing the application. An application for renewal of a trademark registration can be made six months prior to the expiry of the registration. The renewal fee is INR 5000 (approx USD 100) per mark/class. A trademark can be renewed every ten years and thereby protected indefinitely.With an economy of a billion people, you should consider applying for a trademark registration at the nascent stage of your business to avoid time consuming and expensive litigation to protect your rights.Raja Selvam - rselvam@selvamandselvam.in
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How difficult is it to immigrate to Singapore, become a citizen & own a property?
Very easy! I did itGet hired by Singapore company - search for the job: MyCareersFutureIf a Company will decide to hire you, they will process application for Employment pass themselves - you will need just to sign form.If nobody will hire you - register your own company and hire yourself. (That’s what I did 14 years ago)Company registration is here-> Portal HomeBy April 15 of the next year go to - IRAS website and file your taxes (don’t forget to pay them too)After getting your First notice of assessment (tax) go to Immigration & Checkpoints Authority of Singapore and apply for Permanent Resident status (completely online application now)Once you become PR get two more year of working and paying tax and go to Immigration & Checkpoints Authority of Singapore site to apply for citizenshipEvery year about 20000 people actually receive singapore citizenship.I did it myself (started process in 2004 got my passport in 2011 - it took that Long because I also build company, get married in 2006, got kids in 2007 and 2009)And I have lowest chances (1.5%) due to my Caucasian race - Chinese, Malays and Indians have much bigger quota)Just ask me for helpProperty ownership is simple once you have citizenship - just search and buy www.propertyguru.com.sg/singapore
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What is it like to be the only Deaf person in a hearing family?
I am completely qualified to answer this. I am the only deaf person in the entire family tree of mine. From my parents point of view, it was scary and confusing for them, not because of the disability but because they didn't know how to guide me or how to bring me up. But luckily, they received tons of supports and so they somehow found the right persons to connect and help me be the person I am today. They know I am also human, and never actually treated me differently. Maybe that's the reason I never knew I was different in the early stages of my life. After repeatedly contact with the outside world, only I did come to know that we weren't the same as others. I infact, believed that all of us, normal hearing and deaf people used to talk with lips movement like I just did. When we all were kids, my cousins and other friends of mine used to whisper stuffs into my ears, like everyone does. I used to feel puzzled that what are they saying, I used to let it off. I thought it's nothing. Later only I realised its people were talking about something. That time I made sure to let people know to talk face to face and not to whisper into my ears, as it would have been of no use. Basically it's both a rewarding experience as well as a learning experience for me. It's then I realised that I do have parents and family as supports, but I can't expect them to find all the answers for me as they are also learning it along with me. I had to learn to find those by myself. They (my parents and my close family) have tried their best to make my life easier, by talking in English to me, and conversing to me with the help of social medias like WhatsApp, messaging. They even try to ensure if subtitles are happening for the particular movie we plan to watch in theatre. My aunts (like my parent's sisters, or their brother's wife) try their best to converse with me in English, and they keep lamenting for not having learnt proper English. I try my best to convince them that's it's alright, I really appreciate their efforts. It's actually my family who has been really supportive in this journey of mine. I do thank god for having received an amazing family. My parents let me know beforehand, that I would definitely have to do hardwork, but I always left it aside. Now though I know the value of hardwork. I used to believe that if I weren't deaf, my life would be easier. But then I realised, life being easier isn't full of sunshine, it tends to get boring after a while. Came to the conclusion that life should be a mixture of Hardwork and relaxation too. Every single and small achievements of mine are recorded in my family mind. Few Hindi words spoken is a delight for them. Or if I achieve something related to hearing stuff, they express their happiness. They know it's not taken for granted. Couple of things happened after I joined this family. ->Made English language a part of daily conversations, not just Hindi. ->Let everyone know that I am actually normal, and made me comfortable in the atmosphere. ->Taught me to live comfortably and manage in this world.->Taught that impossible is just a word. ->Even my younger brother looks up to me, I don't think he knows that I actually have a disability. ->Learnt that I am a good human being. ->Learnt that family and close friends will stand by you, for anything. ->Oh yeah, how could I forget the overprotective shell I am in, created by my parents. Basically it's an amazing journey for me.
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How is S. Ramanujan looked at by the international fraternity of mathematicians?
Thanks a lot for asking such a beautiful question.I honestly confess that my knowledge regarding others’ view especially other mathematicians’s view about Ramanujan is much limited, but what I know , I would tell you.Mathematicians agreed almost unanimously on the point that it was not possible for someone to imagine those results of Ramanujan without solving / proving.I think the best view most of the mathematicians adopt at this point is of Ramanujan’s colleague and intimate friend, Hardy.Well, once G. H. Hardy rated his contemporary mathematicians based on pure talent.Hardy rated himself a score of 25 out of 100,J.E. Littlewood 30, David Hilbert 80 andRamanujan 100 !Hardy also said that Ramanujan’s solutions were "arrived at by a process of mingled argument, intuition, and induction, of which he was entirely unable to give any coherent account”These words of Hardy himself speak volumes of Ramanujan:“I have to form myself, as I have never really formed before and try to help you to form, some of the reasoned estimate of the most romantic figure in the recent history of mathematics, a man whose career seems full of paradoxes and contradictions, who defies all cannons by which we are accustomed to judge one another and about whom all of us will probably agree in one judgement only, that he was in some sense a very great mathematician.”Some mathematician point out that the educational lapse Ramnanujan had, made some negative impacts in his findings among which some are absolutely wrong for the naked eye. Of course, I agree but anway,The words I saw in the book, The man who knew infinity speak thus:Ramanujan’s prodigy could be comprehended only as Sheer intuitive brilliance. And that coupled to long, hard hours on his slate made up for most of his educational lapse.This ‘poor and solitary Hindu pitting his brains against the accumulated wisdom of Europe’ as Hardy called him, had rediscovered a century of mathematics and made new discoveries that would captivate mathematicians for next century.S.Chandrasekhar, Indian Astrophysicist, Nobel laureate 1983, told thus:“I think it is fair to say that almost all the mathematicians who signNowed distinction during the three or four decades following Ramanujan were directly or indirectly inspired by his example.Even those who do not know about Ramanujan’s work are bound to be fascinated by his life.”“The fact that Ramanujan’s early years were spent in a scientifically sterile atmosphere, that his life in India was not without hardships that under circumstances that appeared to most Indians as nothing short of miraculous. He had gone to Cambridge, supported by eminent mathematicians, and had returned to India with very assurance that he would be considered, in time as one of the most original mathematicians of the century.Bertrand arthur william russell, British philosopher & mathematician, Nobel laureate and almost contemporary to Ramanujan, stated thus:“I found Hardy and Littlewood in a state of wild excitement because they believe, they have discovered a second Newton, a Hindu Clerk in Madras… He wrote to Hardy telling of some results he has got, which Hardy thinks quite wonderful.”Regarding what mathematicians think now about Ramanujan, I cannot give an exact answer because, I haven’t gone after it.Anyway, after Ono and his colleagues proved that the mock theta functions were correct, they are now used in calculating the entropy of Black holes, and well, that actually is a sign that many many mathematicians around the world are in search of finding out proofs to state Ramanujan’s theories. The precise reason for all these search is because they know that He Is Right! Not absolutely but still He is right upto a certain extent and the mathematical world is yet to comprehend it in its fullness.But well, I can only quote a contemporary English Mathematician to state that they have a high regard towards Ramanujan:“Srinivasa Ramanujan was a mathematician so great that his name transcends jealousies, the one superlatively great mathematician whom India has produced in the last thousand years.”He continued thus: “His leaps of intuition confound mathematicians even today, a century after his death. His papers are still plumbed for their secrets. His theorems are being applied in areas- polymer chemistry, computers, astrophysics, molecular physics, even (it has been recently suggested) cancer – scarcely imaginable during his lifetime. And always the nagging question: What might have been, had he been discovered a few years earlier, or lived a few years longer?”I don’t know whether I have in anyway answered your question dear Friend Ashish.But Anyway thanks a lot for asking it and I hope someone else would give an even better answer.
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Why do healthcare facilities (labs) panic when you ask for your medical records?
F*ck I am going to get sued.Shoot, I don't have the staff to deal with this right now.Shoot, I haven't dealt with this for ages. What was the protocol again for giving patients access to their files?They most likely are not trying to hide anything from you. More likely they are afraid that you are planning to sue them out of business over something relatively minor that may or may not have much significance and which may not have been directly in their control. This may not be the case here but due to cultural changes suing is becoming more common, as has losing cases even when you have not done anything wrong, so the fear of lawsuit and the consequences of just being sued is a real concern.Most practices and labs don't tend to have spare staff floating around to accommodate requests like this so having sufficient staff to provide the core service of testing people while providing you copy of your files (which may not all be neatly stored together) by manually photocopying pages and pages check details on every page is another concern.And finally, there likely is a protocol on how to deal with this. This protocol is likely not on fresh memory as requests like these may not be very common. Does the request need to be on a specific form? How do I confirm the patient's id? How much should the patient be charged? Within how may days do we need to produce the records? How many days do we allow for the patient to pick them up before destroying them? Many questions you need to try to remember an answer to while the patient is judging your facial expressions.From my experience labs very rarely interact with patients directly and access to lab results is usually through the records held at your doctors office. Labs do 'just' the labour of sampling and testing, the results are between you and your doctor. You wouldn’t turn up to the apple factory after purchasing an iphone online and expect to pick it up.
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Is Ramanujan overrated as a mathematician?
No never, i think he is underrated to some extent!Roughly speaking, for these things,Ramanujan’s name is seen everywhere around the world, even if some might disagree.•Magic Square•Brocard – Ramanujan Diophatine equation•Dougall – Ramanujan identity•Hardy – Ramanujan number•Landau – Ramanujan constant•Ramanujan’s congruences•Ramanujan – Nagell equation•Ramanujan – Peterssen conjecture•Ramanujan – Skolem’s theorem•Ramanujan – Soldner constant•Ramanujan summation•Ramanujan theta function•Ramanujan graph•Ramanujan’s tau function•Ramanujan’s ternary quadratic form•Ramanujan’s prime•Ramanujan’s costant•Ramanujan’s sum•Rogers – Ramanujan’s identityNow, let us see a quote of an English Mathematician“Srinivasa Ramanujan was a mathematician so great that his name transcends jealousies, the one superlatively great mathematician whom India has produced in the last thousand years.”He continued thus: “His leaps of intuition confound mathematicians even today, a century after his death. His papers are still plumbed for their secrets. His theorems are being applied in areas- polymer chemistry, computers, astrophysics, molecular physics, even (it has been recently suggested) cancer – scarcely imaginable during his lifetime. And always the nagging question: What might have been, had he been discovered a few years earlier, or lived a few years longer?”I think you must know the various contributions of this great man.A few words regarding the 1729, Ramanujan NumberHardy arrived in a cab numbered 1729He commented that the number was uninteresting or dull.Instantly Ramanujan claimed that it was the smallest natural number which can be written as sum of cubes in 2 ways1729 = sum of cubes of 12 and 1/ sum of cubes of 10 and 9.Actually only this much is available in the popular version of the story.But Ramanujan had worked extensively on this number and made some simple reuslts along with other startling contributions.1729 = 7 x 13 x 19 product of primes in A.P1729 divisible by its sum of digits.1729 = 19 x 911729 is a sandwich number or HARSHAD number."Ramanujan was using 1729 and elliptic curves to develop formulas for a K3 surface," Ono says. "Mathematicians today still struggle to manipulate and calculate with K3 surfaces. So it comes as a major surprise that Ramanujan had this intuition all along."Ono had worked with K3 surfaces before and he also realized that Ramanujan had found a K3 surface, long before they were officially identified and named by mathematician André Weil during the 1950s.Just as K2 is an extraordinarily difficult mountain to climb, the process of generalizing elliptic curves to find a K3 surface is considered an exceedingly difficult math problem.And in Ramanujan’s writing he was relying on this number 1729 in order to arrive at some combination of numbers which could prove that Fermat’s last conjecture could be counter exampled.there are some popular misconceptions regarding ramanujan:Ramanujan recorded the bulk of his results in four notebooks of loose leaf paper (About 4000 theorems)These results written up without any derivations.Since paper was very expensive, He would do most of his work (derivations) on SLATE and transfer just the results to paper.Hence the perception that he was unable to prove his results and simply thought up the final result directly is NOT CORRECTProfessor Bruce C.Berndt of University of Illinois, who worked on Ramanujan note books, stated that “Over the last 40 years, nearly all of Ramanujan’s theorems have been proven right”.Also Mathematicians agreed unanimously on the point that it was not possible for someone to imagine those results without solving / proving.Well, once G. H. Hardy rated his contemporary mathematicians based on pure talent.Hardy rated himself a score of 25 out of 100,J.E. Littlewood 30, David Hilbert 80 andRamanujan 100 !Hardy also said that Ramanujan’s solutions were "arrived at by a process of mingled argument, intuition, and induction, of which he was entirely unable to give any coherent account”Let me tell something about the Hardwork of Ramanujan:Once P.C. Mahalanobis, the founder of Indian Statistical Institute visited Ramanujan while in Cambridge and said to him: “ Ramanju, these English Mathematicians say that you are a Genius, A real incomparable Genius.Immediately, showing his thickly black elbow Ramanujan replied, dear friend, everything owes to this elbow.Shocked by the answer, P.C. Asked: How Can it be so?????Ramanujan replied with a smile: “During my childhood days, while using a slate for calculations, repeated erasing used to leave remnants of chalk in it, then I stopped using duster for rubbing.”“This meant that every few minutes I had to rub my slate using my elbow, it means I owe everything to this elbow.”If you want to go through the life of Srinivasa Ramanujan in its fullness, I humbly refer to you my guide, the book which opened my eyes towards realizing the pearl of Indian Mathematics, and that is:“The man who knew infinity: A life of the Genius Ramanujan”It was written by Robert Kanigel.In that book Kanigel claims some very amazing facts about Ramanujan.Sheer intuitive brilliance coupled to long, hard hours on his slate made up for most of his educational lapse.This ‘poor and solitary Hindu pitting his brains against the accumulated wisdom of Europe’ as Hardy called him, had rediscovered a century of mathematics and made new discoveries that would captivate mathematicians for next century.S.Chandrasekhar, Indian Astrophysicist, Nobel laureate 1983, told thus:“I think it is fair to say that almost all the mathematicians who signNowed distinction during the three or four decades following Ramanujan were directly or indirectly inspired by his example.Even those who do not know about Ramanujan’s work are bound to be fascinated by his life.”“The fact that Ramanujan’s early years were spent in a scientifically sterile atmosphere, that his life in India was not without hardships that under circumstances that appeared to most Indians as nothing short of miraculous. He had gone to Cambridge, supported by eminent mathematicians, and had returned to India with very assurance that he would be considered, in time as one of the most original mathematicians of the century.The words of Hardy himself speak volumes of Ramanujan:“I have to form myself, as I have never really formed before and try to help you to form, some of the reasoned estimate of the most romantic figure in the recent history of mathematics, a man whose career seems full of paradoxes and contradictions, who defies all cannons by which we are accustomed to judge one another andabout whom all of us will probably agree in one judgement only, that he was in some sense a very great mathematician.”Bertrand arthur william russell, British philosopher & mathematician, Nobel laureate and almost contemporary to Ramanujan, stated thus:“I found Hardy and Littlewood in a state of wild excitement because they believe, they have discovered a second Newton, a Hindu Clerk in Madras… He wrote to Hardy telling of some results he has got, which Hardy thinks quite wonderful.”The life of Ramanujan is actually a textbook from which many things could be conceived. Despite the hardship faced by Ramanujan, he rose to such a scientific standing and reputation no Indian has ever enjoyed.It should be enough for youngsters like us to comprehend that if we can work hard with indomitable determination, sheer perseverance and sincere commitment, we too can perhaps soar the way like Srinivasa Ramanujan.Talking about certain contributions of Ramanujan which shook me off my feet.As we all know we use the notation P(n) to represent the number of partitions of an integer n. Thus P(4) = 5, similarly, P(7) = 15.I don’t need to explain that If we were to start enumerating the partitions for larger numbers, even for small numbers such as 10 we start seeing that there is a combinatorial explosion! To illustrate this consider P(30) = 5604 and P(50) = 204226 and so on. (btw, partitions can be visualized by Young tableau!).A similar search was on for asymptotic formulae for the partition number P(n) and because of the combinatorial explosion an accurate formula was considered difficult. Ramanujan believed that he could come up with an accurate formula even though it was considered extremely hard, and he came close.One work of Ramanujan (done with G. H. Hardy) is his formula for the number of partitions of a positive integer n, the famous Hardy-Ramanujan Asymptotic Formula for the partition problem. The formula has been used in statistical physics and is also used (first by Niels Bohr) to calculate quantum partition functions of atomic nuclei.The formula he proposed gives a very close value to that of the true value, and it is a mouth-watering feat considering its very pattern less nature.I had written another answer in quora regarding how Ramanujan provided a rapidly converging series as the value of Pi. I will just copy and paste it here.For a long time, the series used for finding the value of Pi was given by the Leibniz-Gregory Series.π = (4/1) - (4/3) + (4/5) - (4/7) + (4/9) - (4/11) + (4/13) - (4/15) ...But in order to give the value of Pi correctly upto 5 decimal places, this series required around 500000 terms.Now, in the Indian tradition, another formula was given by Nilakantha, a mathematician of Kerala School of Mathematics who lived couple of centuries before Leibniz and the series converged much rapidly.π = 3 + 4/(2*3*4) - 4/(4*5*6) + 4/(6*7*8) - 4/(8*9*10) + 4/(10*11*12) - 4/(12*13*14) ...And in order to give the value of Pi upto 5 decimal places, this series required only 6 terms. And thats a great thing but which failed to catch the eye of westerners until the nineteenth century.Now, take into consideration all these and what Ramanujan did. Ramanujan simply penned down an infinite series, looking so horrendous, which would be equal to the reciprocal of Pi.And this is the most rapidly converging series ever given for the value of Pi and the algorithm based on this have actually been used in computers.Now the most beautiful factor. In order to have the value of Pi upto 6 decimal places the infinite series of Ramanujan needed only ONE SINGLE TERM.And you take the second term and there you have suddenly the value of Pi upto 11 terms in your hands.I think it speaks something Great, and Ramanujan was indeed Great!!!Ramanujan has done extensive works in finding out highly composite numbers, and he has written down a long list of similar numbers which had more factors than any of the previous number.The highest highly composite number listed by Ramanujan is 6746328388800Having 10080 factorsHe received his degree from the university (later named Ph.D) for his work of highly composite numbers.I would just say another thing which caught my eye and unleashed an array of thoughts.Ramanujan while sick and dying in India, mentioned some very peculiarly behaving functions which mimicked the original moldular functions.The mock theta functions remained a mystery for most part of the last century and only the Great Ono made inroads towards their reality.In fact, no one at the time understood what Ramanujan was talking about.It wasn’t until 2002, through the work of Sander Zwegers, that we had a description of the functions that Ramanujan was writing about in 1920,' Ono said.Ono and his colleagues drew on modern mathematical tools that had not been developed before Ramanujan’s death to prove this theory was correct.Ramanujan actually wrote those functions claiming that he saw it in a scroll in the hands of A Goddess.Anyway now they are used to calculate the entropy of Black Holes ( A concept which developed years after his death.)Ono’s team was stunned to find the function could be used today.'No one was talking about black holes back in the 1920s when Ramanujan first came up with mock modular forms, and yet, his work may unlock secrets about them,' Ono says.Ramanujan’s Intuition Stands OUT!I think, just for a fun I would show the Mock Theta FunctionsNow I think I shoudl mention atleast something about the impact of Ramanujan’s work on statistical physics.For example imagine studying the statistics of a gas made of electrons confined to 2D. You could do something complicated like model the exact positions and momenta of many of electrons along with the force between them. Or you can simplify by imagining that the electrons can only occupy positions on a discrete triangular lattice, and instead of a repulsive force you can make the simple approximation that two electrons aren't allowed to be next to each other.The result is the Hard hexagon model and some work of Ramanujan's appears when you try to model it. Even if it's not physically realistic, these models share characteristics with more realistic physical models and give useful insight.In fact a whole bunch of different identities related to Ramanujan's work can appear when you study these kinds of simple physical models, especially 2-dimensional models. Eg. Hard Hexagon ModelI think I will conclude with a simple assumption of Ramanujan, I think it deserves mention:The mock theta functions which we mentioned earlier looked unlike any known modular forms, but he stated that their outputs would be very similar to those of modular forms when computed for the roots of 1, such as the square root -1. Characteristically, Ramanujan offered neither proof nor explanation for this conclusion.It was only 10 years ago that mathematicians formally defined this other set of functions, now called mock modular forms. But still no one fathomed what Ramanujan meant by saying the two types of function produced similar outputs for roots of 1.Ono and his colleagues have exactly computed one of Ramanujan’s mock modular forms for values very close to -1. They discovered that the outputs rapidly balloon to vast, 100-digit negative numbers, while the corresponding modular form balloons in the positive direction.Ono’s team found that if you add the corresponding outputs together, the total approaches 4, a relatively small number. In other words, the difference in the value of the two functions, ignoring their signs, is tiny when computed for -1, just as Ramanujan said. Incredible Intuition !\I think I can say nothing more, but if at all someone asks me, I would say if I know!By the way, I have actally spoken nothing regarding the complex mathematical contributions of this great mathematician,even without that I think you are thrilled and that is why, even if the statement is wrong in itself.“ Ramanujan is the greatest Mathematician of all time, at least I believe so.”The next question is rather difficult to answer at any point of time.Because we cannot compare two mathematicians as we do with others, just as those who pointed out in their answers earlier, it is impossible to do so, because of various reasons.Anyway, my concern regarding such a thing would be as simple as this:when you have a room with a number of superbly drawn paintings , each perfect in its own regard, you can enjoy it and you know everything has its own value and each being diverse in what it offers, has a unique contribution towards the beauty and perfection of that room. The moment we remove even one of those paintings out, let it be the most simple or the most complex, we are in a way disrupting the rhythm, and the room is no more perfect, there is a vacuum, and for someone who has enjoyed the beauty of that room immensely, no other painting can give the room back its original perfection. Likewise, history especially the history of mathematics has unfolded in such a way that all those great ones from Pythagoras have been uniquely contributing to make this science beautiful. So, we cannot take even out of them, rather we can just accept the beauty of their companionship in developing Mathematics as our favourite science.Anyway I would like to point one more thing. How Ramanujan is indispensable from that list. Well, it is simply because we see an extraordinary harmonious blending of Reason and Revelation in his works, two seemingly contradicting factors, Intelligence and Intuition! That makes him all the more Unique
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What shocked you today?
PEOPLES EXPECTATIONS FROM GIRLS IN ARRANGED MARRIAGES…So this incident took place recently.My Cousin Brother who is 23 years old, his family is looking for a girl for marriage.First let me tell you about their family. They are very big farmers with other bussiness also running. In short , they are rich and live in their village.So after looking few girls, they finalised a girl after meeting her, but what happened is that in that meeting , only the boy and his parents went but my Nani and other relatives didn't go as they were not available due to some reasons. They finalised the marriage but most of my relatives and Nani were still unaware of who the girl was but the Boy liked the girl. ( Both of them have studied in the same schools till 12th as she is also from a nearby village and he knows her quite well that's why he agreed )But the problem arose 2 days later ( i.e yesterday) when after doing the engagement everyone returned home , and my nani told everyone that she didn't like the girl, she said that she was not even asked once and all that emotional drama. Few of my relatives who attended the function also agreed with her. (All this is happening after the engagement)She didn't tell the reason for disapproval but most probably it would be looks or not very rich family.We couldn't attend it as we live far away so just saw the photos and in photos , the girl looks good with fair skin and average height that too in very simple clothes.So the question here is -Who is actually at fault? - Ofcourse my relatives as they didn't see the girl earlier and later complaining on the choice of the boy and his mother.And why do people expect very beautiful 'bahu' , when all she has to do are the household chores for her whole life. ( In this scenario)All these things have put my mother under pressure as she is in full support of the marriage as her point is that the boy liked the girl and that is the main aim of marriage. Now she is angry on 'her mother' as she started this by complaining about the girl.The thing which shocked me is - in arranged marriages , people expect the girl to be educated , beautiful and what not but all they let her do are kitchen work.They see marriages more as a social status and the more dowry the guys family gets , they get more respect from society.It's 21st century , where people are achieving great heights whereas others are worried about dowry and marriages.All this needs to change !!.Thank you....All suggestions are welcome.!..FOLLOW ME!!Edit : thanks for the 100+ upvotes. It means a lot to me and encourages me to write more.
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What is the most asked question on Quora (by the number of questions merged into it)?
As someone who writes mostly technology-related answers, I see the following question so much it makes me want to tear my hair out:“Can iCloud Activation Lock be Bypassed?”For those who don’t know, Apple devices that have an iCloud account active on them with Find My iPhone enabled will lock the device to that Apple ID even if it is restored to factory defaults. This is designed to prevent thievery, since stolen devices (typically iPhones) are useless without the Apple ID password they are locked with to unlock it. It is incredibly common for people to sell devices without removing the lock beforehand (likely because they don’t know it exists, or how to remove it) or because it is stolen. Either way, the lock cannot be bypassed without that password… but that doesn’t stop everyone and their mother from asking if it can be done as if the rules somehow don’t apply to them.Instead of viewing the answers on an existing question, or even asking new people to answer that existing question, they make a new one. Every. Single. Time. Quora is absolutely flooded with these questions, and I get A2A requests for them more than anything else.
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