Proof without Words is the central theme for the first issue of At Right Angles for 2015 (Issue IV-1). Quite a challenge even for those accustomed to crisp and succinct arguments. Check out the collection of visual proofs we have assembled for the March issue. We also feature an interesting way to calculate square roots and cube roots. ‘Paradoxes’ links language and math and this is followed by a thought provoking article on ‘Generalization and Specialization’. With this issue we begin a new series called ‘Low Floor High Ceiling Tasks’. Mark Kleiner has reviewed ‘Love and Math’ Regular features continue and the pullout continues the two part series on geometry. The link to the soft copy is http://teachersofindia.org/en/periodicals/right-angles-march-2015 . .
We have now crossed 1500 regular readers who receive the magazine -apart from the many who download soft copies. If you are not so already and would like to be on our subscriber’s list and receive the hard copy regularly please do mail your postal address to AtRightAngles@apu.edu.in Please note that the mailing of hard copies is restricted to India.Our discussion group on FaceBook sees some interesting problems being posted. To join, go to https://www.facebook.com/groups/829467740417717/ and "Join". You need a Facebook account and would have to sign in. You can also search for "AtRiUM: At Right Angles, Us and Math" in Facebook.
RMS Workshop on
Morse Functions and Handle-body Decomposition of Manifolds
May 12 – 13, 2015
Apply from HERE.
Please fill the form linked HERE to convey your opinion.
Meeting on 19th January 2015
10 a.m. Declaring open the building by cutting the ribbon and lighting of the Kuthu Vilakku.
Meeting at the auditorium
Welcome Address: Dr.R. Balakrishnan, Founder-Secretry of RMS
Presidential Address: Dr. Ravi Kulkarni, President of RMS. Full Text.
Address by Dr.V. Krishnamurthy, President, National College Council.
Dr. P. Bhattacharyya, Former Vice-Chancellor, Tezpur University
Shri S. Raghunathan, Secretary, National College Council
Dr.K. Anbarasu, Principal, National College
Dr. T.E.S. Raghavan, Professor of Mathematics, University of Chicago, Illinois, USA.
Dr.E. Sampathkumar, Founder-Academic Secretary of RMS
Vote of Thanks: Dr. K. Srinivas, Secretary, RMS.
Lecture/Film by Dr.K. Srinivasa Rao on Srinivasa Ramanujan
Zentralblatt has published a nice review of Lecture Notes Series Vol. 18 that captured the essence of ICCTA-93 that was held at IIT, Mumbai during Dec. 5-24, 1993.
Click HERE to read.
JRMS is now included in the Thompson Reuters SCIENCE CITATION INDEX EXPANDED 2014.
The list is maintained in alphabetical order. Online the listing of JRMS can be found here (it is the last entry on this page as on 31-Oct-2014):
A PDF copy of the Citation Index is available for download from HERE.
The association EU-MATHS-IN (promoted by the EMS and ECMI) has launched a new service: a website for advertising jobs for mathematicians in companies or institutions working on industrial contracts.
The scope of this website is to advertise jobs in industrial mathematics and related fields.
Jobs announcements can be found or deposited at the address:
Dear Friends of the Ramanujan Math Society,
You may know that RMS was founded in 1985. In the last 29 years, it has reached a high status in the mathematical community in India, and it is considered as a premier Society promoting higher mathematics in India.
The "Journal of the Ramanujan Math Society", which also started in 1985, has reached international standards, and is considered a flagship mathematics journal coming from India.
In 2005 RMS started "The Lecture Notes series of the Ramanujan Math Society". It has published 20 volumes and Collected Works of three eminent mathematicians of the 20th century from India: Prof.s S. S. Pillai, S. Minakshisundaram, and Hans Raj Gupta.
In the last 29 years, RMS has regularly conducted Annual Conferences, and some international conferences, in which many distinguished mathematicians from within India, and abroad, have participated, including some Fields Medalists, and men and women of similar distinction.
From last year, it has started some Regional Programmes, including "Undergraduate Teachers Enrichment Programmes" (UGTE's), and for High School teachers, programmes jointly with Aziz Premji University (APU-RMS Programmes). From July 1, 2013 to May 31, 2014, RMS conducted 13 UGTEs and 4 APU-RMS Programmes.
The current membership of RMS is over 1000, and includes most Bhatanagar awardees, Swarnajayanti Fellows, and other mathematicians of similar distinction, young and older, from India.
Despite such stature in the mathematical world, RMS is still an organisation with meager resources. It has reached its academic stature mainly through the generosity of some of its rich friends with a large heart, who generously support its each major activity fulfilling an urgent timely need.
Otherwise, after 29 years, RMS does not have even its own office, and has a very small paid staff. The whole work is done by a few dedicated individuals, who often pay partially for expenses from their own pockets. For example, for over two decades,a member has given 8 rooms in his house, which are used as an "RMS-office".
Because of paucity of funds, it cannot take any large-scale activities on its own, like the Regional Programmes mentioned above, which will greatly benefit the mathematics community in India, the faculty and the students.
Occasionally, RMS gets funds from the national funding agencies, like NBHM, DST etc, and also contributions from a few rich organisations and individuals.
But potentially it can also generate funds from many people who see the merits, and value of the work of RMS. Both are valuable in their own ways. But the second type of contributions also involve many minds, and fosters noble feelings of an active, participating, community.
Just consider how typically a temple, a church, a masjid, or a gurudwara gets built! Please consider RMS as a temple of mathematics, which is worth building for the advancement
of mathematics suitable for the 21st century India!!
You can help RMS by becoming a Life Member, a Donor, a Benefactor, or a Patron, and recommending your friends to become one. You can
also help RMS by not only reading good mathematics from our publications, but also buying some of our publications, or recommending them to the libraries of your institutions. There are also Institutional Memberships suitable for individual Colleges and Universities, affording some advantages for students at the respective College or University.
The Executive Committee (EC) has decided to give 20% discount on all the volumes of the RMS Lecture Notes Series, and 25% discount for the whole set.
We love mathematics, and many of us earn our living through mathematics. It was never possible to make a lot of money by becoming a mathematics teacher!
But still the society deeply respects our profession, and these days, at least allows us to earn a decent living! So we may leave some part in our last wills for RMS.
You can also set up an endowment in the name of a distinguished mathematician, a teacher and/or a researcher. Each year we shall honor him/her in a suitable national or regional meeting.
This type of help will help RMS to build its corpus.
In addition, the EC of RMS has identified four "RMS-Projects".
You can make ear-marked contributions to these projects, and hold the EC responsible to complete these projects in a time-bound way. This is a good way to encourage specific activities from an organisation, and is a check on organisation's tendency to control and hoard the funds it receives.
The projects are:
1) Building Fund:
For a long time, RMS has thought about buying some land and building an office-building.
Some people have already made some contributions. Currently, it has about Rs 1.2 lakhs in this Fund.
The expected expenses are between Rs 1.5 crores to Rs 2 crores.
2) Regional Programmes:
These programmes are briefly mentioned above. For more details, please visit our web-site:
www.ramanujanmathsociety.org. Click on the item 3 of the bulletin board there.
This will be a recurrent expense, about Rs 20 lakhs per year.
3) Support of Publications:
Each year, we are regularly bringing out 4 issues of JRMS, and 3 or 4 volumes of
Lecture Notes Series, and Collected Works. We wish to bring about more Collected Works. It takes about 2 years
of some very intense work to bring about a single volume of Collected Works. A timely donation
from a US-based Foundation was useful in bringing out the Collected Works of S.S. Pillai.
This is a recurrent expense, about Rs 10 lakhs per year.
4) Joint Meeting with AMS in Dec 2016:
RMS and the Indian Math Society (IMS) have come together, and are going to have a
major meeting jointly with the American Math society in Dec 2016. This will be like a mini-ICM
for RMS and IMS members!
We have appealed to other math societies to join us, and we wish to make it truly a meeting of the mathematical communities in India and US.
AMS expects 150 participants from the US and 600 from India.
The estimated expense will be about Rs 1 to 1.5 crores.
We appeal to the mathematical community to help RMS by your contributions small or large, so that together we can develop mathematics in India by raising the standards of teaching and encouraging high-level research. In our opinion, the two aspects, namely, teaching and research in mathematics, are two sides of the same coin. They are at the root of not only scientific and technological development, but they are also measures of general cultural awareness of the society.
The donation may be sent in the form of Multi City Cheque/DD/International Cheque drawn in favour of `Ramanujan Mathematical Society' payable at any bank in Chennai-India and may be sent to
Prof. K. Srinivas
The Institute of Mathematical Sciences,
C.I.T. Campus, Taramani (PO)
The donations can also be made in the form of Wire Transfer. For details kindly write to Prof. K. Srinivas (srinivas.kotyadaATgmail.com)
For an earmarked donation or setting up of an endowment,
please write a detailed letter, stating the purpose of a donation or an endowment.
Ravi S. Kulkarni,
The RMS bye-laws were formulated in 1985. Since then, there were some amendments, which were noted in the minutes of the meetings of the Executive Committee (EC) in the last 29 years. But the new Presidents and the ECs, did not have a written record of what these amendments were.
You may recall a major controversy in 2010-2013 was about an item which was minuted in the minutes, but not entered in the printed version of the bye-laws.
I requested Prof. Balakrishnan to prepare the amendments of the bye-laws including those listed in the past minutes. Fortunately, he was the one who had formulated the 1985 bye-laws. He did a splendid and very careful job. Prof. Sampathkumar, Srinivas, Kumaresan, and I have gone through some preliminary drafts.
The EC discussed the last-but-one draft on 22nd June, 2014, and made some minor changes. We distributed the final draft at the General Body (GB) meeting on 24th June 2014, and asked the members to send their comments to the President by 31st July, 2014.
For the benefit of those who could not attend the GB-meeting, we are posting them on the web-site.
After a discussion of the issues which the members may raise, the EC hopes to issue a new, printed, amended, version of the bye-laws,
by the end of August 31, 2014.
BYE-LAW AMENDMENTS 2014
(PROPOSED 30.6.2014 VERSION)
1) Name of the Society:
The name of the Society shall be
‘RAMANUJAN MATHEMATICAL SOCIETY’
2) Address of the Society:
The address of the Registered Office of the Society is Department of Mathematics,
National College, Tiruchirappalli 620001.
3) Date of formation of the Society:
The Society shall be deemed to have been Formed on July 1, 1985.
4) Registrar of the District in whose Jurisdiction the office is situated:
The Registered Office of the Society is located in the jurisdiction of the Registrar of Societies,
Tiruchirappalli Registration District, Tamil Nadu.
5) Business hours of the Office:
The office of the Society shall have its business
hours between 2 p.m. and 4 p.m. on all the working days.
The objective of the Society shall be to promote advanced study and research in mathematics,
and mathematics education, its allied subjects and their applications.
7) Activities of the Society:
Towards its objectives, the Society shall
i) Publish one or more journals, bring out lecture notes series etc.,
conforming to international standards encompassing all branches of mathematics.
ii) Convene annual conferences inviting all of its members and
conduct general body meetings for planning the Society’s activities for the future.
iii) Organize regional, national, and international, seminars, symposia etc., on special topics.
8) Name of the person authorized to sue or to be sued:
The Secretary of the Society shall be authorized to sue or to be sued on behalf of the Society.
9) Name of the person empowered:
The President of the Society is empowered to give to give directions in regard to the business of the Society.
10) Enrolment of Members:
i) All persons who accept the objectives of the Society shall be eligible
for membership in the Society. Such persons could become Life Members, Donors,
Benefactor Members or Patrons. Institutions can become Institutional Members.
Each member in the above
fourcategories is eligible to view on line all past issues
of the Journal of the Ramanujan Mathematical Society prior to five years
from the current date. The other periodical that is currently being published by
the Society, namely, The Mathematics Newsletter, can be viewed and downloaded
free by all members of the Society. This facility is available to Institutional Members as well.
In addition, each Institutional Member can nominate two first year P.G. math students
(second year undergraduate students in case the institution does not have a
post-graduate program) as members of the Society for two consecutive years
from the year of becoming an institutional member. Every such student member
shall have the same privilege of a regular member of the Society for a period
of two years but without voting rights.
Each person applying for membership in the Society shall submit an
online application for membership indicating a proposer and a person for
seconding it-the last two persons being members of the Society.
ii) Membership Fees:
Category of Membership, For applicants who normally reside in India (in RS.), For applicants who reside outside India (in U.S. $)
1. Life Member 2,500 100
2 Donor 5,000 200
4. Patron 15,000 500 (effective from 2014)
5. Institutional Members 20,000 700
iii) Payment of Fees:
All members shall pay their fees online or by multicity cheques or by cash to the Treasurer of the Society.
All membership fees are payable before March 31st of each year to
become eligible members from the succeeding July 1st.
A member desiring to go from one category to a higher category may pay only the difference
(higher category minus the category the member is in) fees.
Henceforth, the term for Life-memberships, Donors, Benefactors, Patrons, and Institutional Members will be for 10 years.
After 8 years starting from June 2014, the then EC will consider appropriate modification in the fee-structure, which will come into affect starting from June 2024.
11) Voting rights of members:
Every member of the Society in the four categories, namely, Life Member, Donor, Benefactor,
and Patron shall have the privilege of casting his or her vote in the elections conducted by the Society.
12) Management of the Society:
The affairs of the Society shall be managed by an Executive Committee (EC) consisting
of a President, a Vice-President, a Secretary, an Academic Secretary, a Treasurer,
the Editors-in-Chief of all the different publications of the Society, three other members,
living Founder Members. The Managing Editors of different publications will be members
of the EC without voting rights.
The Executive Committee shall have powers to
i) Admit new members to the Society.
ii) Frame such bye-laws as are consistent with the promotion of the
welfare of the Society and get them passed by the General Body.
iii) Appoint assistants and secretaries wherever necessary.
iv) Sanction amounts for the ordinary working expenses of the Society and also for the publications of the Society.
v) Prepare the annual budget and present it at the General Body Meeting of the Society.
vi) Sanction local chapters of the Society on such terms as appear suitable in each case, and to revoke such action.
vii) Appoint chartered accountants to audit the accounts of the Society.
ix) Accept endowments, donations, fees and charges to the Society.
x) Nominate the members of the Editorial Boards of the Publications of the Society
xi) To expel any member who is working against the interest of the Society.
xii) To recommend Fellows of the Ramanujan Mathematical Society (FRMS).
xiii) Generally deal with all matters pertaining to the management of the Society.
xiv) For reaching these objectives, each year the EC may spend about 10% of its corpus of the previous year
a) procuring new equipment (about 2%),
b) payments for RMS meetings (about 2%) ,
c) payments for RMS-related travel of the EC-members ( about 2%),
d) payments for office maintenance and salaries for office staff (about 4%).
The functions of the Members of the Executive Committee:
The President will have both academic and administrative duties. He shall preside over the meetings
of the Executive Committee and the General Body of the Society.
He has the right to offer the
first plenary talk in the
Annual Conference, on a subject of his choice.
He shall take the initiative to generate funds
for the Society by welcoming sponsors and donors, build rapport with other national
and international math societies to promote mathematical interest in our country and
interact with governmental agencies for strengthening the mathematical base
among our students and faculties.
The Vice-President shall discharge the functions of the President at the Executive Committee
and General Body meetings of the Society in the absence of the President.
He will assist the President in the academic functions and administration of the Society by working with him in tandem.
The Secretary will assist the President in carrying out all administrative work concerning the Society.
In particular he will maintain the Society's registration, 80 G tax-exempt status, and FCRA status for foreign donations.
The Academic Secretary will assist the President in carrying out all the academic functions of the Society.
The Treasurer will be in charge of the collection of membership fees and other funds, and maintenance of
the accounts and expenditure relating to the societies.
The three members will assist the President, Vice President, Secretary, and Academic Secretary at least in one of the
three activities listed in section 7, or in any administrative activity.
All members of the EC will try to attend the RMS Meetings as much as possible, and try to procure the expenses incurred in
carrying out their duties, from outside sources.
They should normally reside in India.
All members of the EC will be mathematicians of academic repute in research and teaching,
and with administrative experience in educational institutions.
13) Constitution of the Executive Committee (EC)
The EC will be elected by the electoral college consisting of Life Members, Donors, Benefactors,
and Patrons of the Society. The members of the EC shall hold office for a period
of three years from April 1st of the year of their election.
In case a member of the EC other than the President resigns his position
before the expiry of his term, the President shall nominate an RMS member in consultation with the EC,
to discharge the functions of the member
who had resigned till the expiry of the term of office of the EC.
In the event of the President resigning his post, the Vice-President shall discharge the duties of the President.
If the offices of both the President and the Vice-President fall vacant, the EC shall elect an RMS
member to act as President till a new president gets duly elected.
14) The election of the EC:
i) For the election of the EC, the following procedure shall be adopted: The Secretary shall call for nominations for the various positions in the new EC, which is to take charge on the 1st April of any particular year, during the month of December of the previous year.
Only those nominations, which are supported in writing by not less than two different members (excluding the nominee) shall be considered as valid. The EC shall also prepare suitable nominations for the various posts. In case an election is necessitated, it shall be by secret ballot and in such a case, the ballot papers indicating valid nominations being sent by post around 1st of February. There shall be a period of at least 45 days between the date of calling of nominations and the date of receipt of nominations as also between the date of dispatch of ballot papers to the members and the date of receipt of ballot papers from members. A simple majority shall determine the result of the election in each case, and in case of a tie, the final election shall be determined by mutual consent between the contestants failing which the outcome shall be determined by lot.
ii) The election shall be conducted by a Returning Officer nominated by the EC.
iii) The quorum for an EC meeting shall be four. All the members of the EC are eligible to vote and the President of the meeting shall have a casting vote.
iv) The EC shall meet at least once in a year. A notice of at least 15 days time shall
be given for each such meeting. However, decisions could be taken by circulation in
case there is no immediate possibility of convening a meeting of the EC.
v) Any member of the EC is eligible to seek election to any position in the EC at the expiry of his current term of office.
15) Policy towards accepting Donations, and Endowments:
Each donation by cheque may be ear-marked for a mathematical activity of RMS, or it may be for the corpus
Each donation by cheque, along with any interest generated thereof, if ear-marked, will be used in 10 years
from the date of its acceptance, for the specified activity.
Each Endowment will be accepted for a period of 10 years. The donations received for creating an endowment,
and any interest generated thereof, will be used in 10 years.
The Secretary of the Society shall maintain a list of donors per year, which will be exhibited on the web-site.
16) Filing of Returns to the Registrar of Societies:
The Secretary of the Society shall file any statement required to be filed
under the Tamil Nadu Societies Registration Act before the appropriate authorities.
17) Audit of Accounts of the Society:
The EC shall publish every year not later than the month of June duly
audited statement of accounts pertaining to the previous year ending on
18) Supply of copies of bye-laws and audited statements to members:
The bye-laws and audited statement of accounts shall be
to all of members
of the Society.
19) Imposition of fine on any breach of the provisions of the bye-laws by any member:
The EC shall have the right to impose fines on any member of the Society for any breach
of the provisions of the bye-laws of the Society.
20) Investment of the funds of the Society:
The funds of the Society shall be invested in fixed deposits and savings bank accounts in
one or more nationalized banks to be operated jointly by the Secretary and Treasurer of the Society.
21) Application of funds:
The funds of the Society shall not be used for any purpose other than those that support the objectives of the Society.
22) Annual General Body Meeting:
There shall be a meeting of the general body of the Society before 31st July of every year
consisting of the life members, donors, benefactors, and patrons. This meeting will be a
part of the annual conference of the Society and take place on the second day of the conference.
The agenda for this meeting shall be sent 21 days in advance and it will include, inter alia,
i) Adoption of the minutes of the previous General Body Meeting,
ii) EC’s report on the current and future activities of the Society,
iii) Auditor’s report including audited statement of accounts for the previous year ending March 31st,
iv) Budget for the succeeding year.
WITHIN 30 DAYS OF THE ANNUAL GENERAL BODY MEETING, THE SECRETARY SHALL
FILE THE FOLLOWING DOCUMENTS WITH THE REGISTRAR OF SOCIETIES:
a) A certificate to the effect that the Society functioned normally and as per the bye-laws of the Society during the previous year.
b) Minutes of the EC Meeting and the General Body Meeting.
c)Signed copy of the Audited Statement of Accounts (in original)
d) List of members of the Society in Form VI
e) List of inclusions/deletions in Form VII.
Members desirous of bringing in any specific matter for discussion at the General Body Meeting
shall give details of the same to the Secretary of the Society at least one month in advance to the date of the meeting.
The quorum for the general body meeting shall be 30.
Members could also request the EC to call for an extra-ordinary meeting of the
General Body provided at least one half of the total number of members as on date
of requisition agree on such a call. The EC shall then arrange for such an
extra-ordinary meeting within a period of one month from the date of requisition.
23) The EC shall permit such matters for discussion in the General Body as long
as they do not go against the objectives of the Society as mentioned in Items 6 and 7 above.
24) Exhibition of Society’s books:
The membership list will be on the website. Every member of the Society shall have access to the minute books
and the account books of the Society at the registered office of the Society during
its office hours free of cost.
25) Publications of the Society:
Each publication of the Society shall be managed by an Editorial Board consisting of
one or twoEditor
a Managing Editor and a team of editors, all to be approved by the EC. The members of the Editorial Boards
shall be active researchers in their respective fields and it shall be their aim that they maintain a
high standard of the journals/periodicals in conformity with the objectives of the Society.
It is expected that an Editorial Board will represent several areas of mathematics. Two Editors-in-Chief representing different areas may be appointed. Each member of the Editorial Board
will assist the Chief Editor in procuring good articles, sending them to referees, and reaching a decision about acceptance
or rejection of an article
.Each member of the Editorial Board may submit his own work for publication, but it must be duly
handled by another editor.
A Chief Editor should normally reside in India.
A Chief Editor shall hold the office for a period five years. All other members of the Editorial Board
shall hold office for a period three years.
A Managing Editor
shall keep all the records of submission of articles,
assignment of an editor to take care of a submitted article,
the correspondence with the referees, and the final decision regarding acceptance or rejection.
Any member of an Editorial Board is eligible for re-nomination.
26) Advisory Committee:
If a President so desires, he can nominate an Advisory Committee, in consultation with the EC, consisting of five or six members.
The members of the Advisory Committee shall assist the EC in its promotion of academic activities, generation of funds,
and administrative aspects such as the Society's registration, the 80 G tax-exempt status, and the FCRA status.
The period of office of the Advisory Committee shall be coterminous with that of the corresponding EC. Any member of the
Advisory Committee is eligible for re-nomination.
27) Amendments to the bye-laws:
Amendments to the bye-laws could be considered if they do not violate the basic objectives of the Society. An amendment may come from a group consisting one or more members. The EC, if it so desires, may bring in a revised version of the amendment. The amendments by the members as also the revised versions as brought out by the EC will be placed before the General Body at its annual meeting and the decision will be taken by voting, if necessary. The President shall also have the voting right, and in case of a tie, the amendment, as moved by the EC, shall be declared to have been carried.
If the group of members is not satisfied with the outcome on their amendment , they may, if they could muster a strength of at least 50 members seek an opinion poll on their amendment by post/email soliciting a clear cut approval of their amendment.
The EC shall complete this opinion poll within a period of 90 days from the date of receipt of the amendment. The EC, on its part, could also go in for a similar opinion poll by post/email. In case of a tie, the President shall exercise his casting vote.
28) Dissolution of the Society:
This Society is a non-profit organization. In case of dissolution, it shall be handed over to a Society with similar objectives as decided by its General Body.
The original signatories to this Memorandum of Association who had set their hand in pursuance of Sec 7 (2) of Tamil Nadu Societies Registration Act 27 of 1975 were:
Dr. G. Sankaranarayanan, Professor of Mathematics, Annamalai University, Annamalainagar 608002.
Dr. S.R. K. Sangameswara Rao, Professor of Applied Mathemtics, Andhra University, Waltair 530003.
Dr.R. Balakrishnan, Professor of Mathematics, National College, Tiruchirappalli 620001.
Dr. E. sampathkumar, Professor of Mathematics, Karnatak University, Dharwad.
Dr. N. Jayasankaran, Professor of Mathematics, St. Joseph’s College, Tiruchirappalli 620002.
Dr. K.S. Padmanabhan, Professor of Mathematics, Ramanujan Institute of Advanced Study in Mathematics, Madras 600005.
Dr. Rajeswari Thiyagarajan, Professor of Mathematics, Bishop Heber College, Tiruchirappalli 620 017.
Dr. P.N. Ramachandran, Professor of Mathematics, Pushpam College, Poondi, Thanjavur Dt., Tamil Nadu.
Dr. N. Ramabhadran, Professor of Mathematics, Bharathidasan University, Tiruchirappalii 620023.
These major bye-law amendments were made by a team headed by Prof. R. Balakrishnan in June 2014.
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