2010 – ÖSYS Öğrenci Seçme ve Yerleştirme Sistemi

Birinci Aşama : Yüseköğretime Geçiş Sınavı (YGS)

Sınav Tarihi : Nisan ayının ilk yarısında

Testler ve Soru Sayıları

l Türkçe testi : 40 soru

l Temel Matematik Testi : 40 Soru

l Sosyal Bilimler Testi : 40 Soru

l Fen Bilimleri Testi : 40 Soru

TOPLAM : 160 Soru

Sınav Süresi : 160 dakika

Testlerin Niteliği : Ortak müfredata dayalı testler

2009-ÖSS’deki ilk 4 test ile aynı niteliklere sahip

Soru Kitapçığı : Tek Soru Kitapçığı

Cevap Kağıdı : Tek Cevap Kağıdı

Birinci Aşama (YGS) Puan Türleri

Testlerin Ağırlıkları (% olarak)

Puan Türü Türkçe Tem. Mat. Sos. Bil. Fen Bil.

YGS-1 20 40 10 30

YGS-2 20 30 10 40

YGS-3 40 20 30 10

YGS-4 30 20 40 10

YGS-5 37 33 20 10

YGS-6 33 37 10 20

YGS Puanları Değer Aralıkları: Her puan türündeki puanlar, en küçüğü 100

en büyüğü 500 olan puanlar olarak hesaplanacaktır.

Birinci Aşama (YGS) Taban Puanları ve Sağlayacağı Haklar:

1) Taban puan-1^*

Önlisans programları ile açıköğretim programlarını tercih etme hakkı.

2) Taban Puan-2^*

İkinci aşama sınavlara katılma hakkı.

3) Taban Puan-3^*

Birinci aşama puanlarıyla da öğrenci alan lisans programlarını tercih etme

hakkı (2009-ÖSYS’de SAY-1, SÖZ-1 veya EA-1 puanlarıyla girilen programlar)

*) YÖK Genel Kurulunda Taban Puanların daha sonra belirlenmesi kararı alınmıştır.

Taban puanlar en geç 2010 ÖSYS Kılavuzunda açıklanacaktır.

İkinci Aşama : Lisans Yerleştirme Sınavları (LYS)

Sınav Tarihi : Haziran ayının ikinci yarısında

(bir ya da iki hafta sonunda)

Sınavlar, Testler ve Soru Sayıları

1. Matematik Sınavı

l Matematik testi : 50 Soru, 75 dakika

l Geometri testi : 30 Soru, 45 dakika

TOPLAM : 80 Soru, 120 dakika

Notlar:

1) Matematik ve Geometri testleri için ayrı Soru Kitapçıkları kullanılacaktır.

2) Cevap Kağıdı iki test için ortak olacaktır.

3) Geometri testindeki sorularının 8 tanesi Analitik Geometri sorusu olacaktır.

2. Fen Bilimleri Sınavı

l Fizik testi : 30 Soru, 45 dakika

l Kimya testi : 30 Soru, 45 dakika

l Biyoloji testi : 30 Soru, 4 dakika

TOPLAM : 90 Soru, 135 dakika

Notlar:

1) Fizik, Kimya ve Biyoloji testleri için ayrı Soru Kitapçıkları kullanılacaktır.

2) Cevap Kağıdı üç test için ortak olacaktır.

3. Edebiyat, Coğrafya Sınavı

l Türk Dili ve Edebiyatı testi : 56 Soru, 85 dakika

l Coğrafya-1 testi : 24 Soru, 35 dakika

TOPLAM : 80 Soru, 120 dakika

Notlar:

1) Türk Dili ve Edebiyatı testi ile Coğrafa-1 testi için ayrı Soru Kitapçıkları

kullanılacaktır.

2) Cevap Kağıdı iki test için ortak olacaktır.

4. Sosyal Bilimler Sınavı

l Tarih testi testi : 44 Soru, 65 dakika

l Coğrafya-2 testi : 16 Soru, 25 dakika

l Felsefe Grubu testi : 30 Soru, 45 dakika

TOPLAM : 90 Soru, 135 dakika

Notlar:

1) Tarih, Coğrafya-2 ve Felsefe Grubu testleri için ayrı Soru Kitapçıkları

kullanılacaktır.

2) Cevap Kağıdı üç test için ortak olacaktır.

3) Felsefe Grubu testinde 10 Psikoloji, 10 Sosyoloji, 10 da Mantık sorusu yer

alacaktır.

5. Yabancı Dil Sınavı

l Yabancı Dil testi : 80 Soru, 120 dakika

Notlar:

1) Yabancı Dil testi İngilizce, Almanca ve Fransızca dillerinde hazırlanacaktır.

2) Yabancı Dil testi için tek Soru Kitapçığı ve tek Cevap Kağıdı kullanılacaktır.

İkinci Aşama (LYS) Puan Türleri

1. MF Grubu Puan Türleri (SAY-2 yerine kullanılacak)

Testlerin Ağırlıkları (% olarak)

P. Türü Türkçe Tem.Mat. Sos.Bil. Fen Bil. Mat. Geo. Fiz. Kim. Biyo.

MF-1 11 16 5 8 26 13 10 6 5

MF-2 11 11 5 13 16 7 13 12 12

MF-3 11 11 7 11 13 5 13 14 15

MF-4 11 14 6 9 22 11 13 9 5

MF-1 puan türü Matematik Ağırlıklı Temel Bilim Programları için,

MF-2 puan türü Fen Ağırlıkı Temel Bilim programları için,

MF-3 puan türü Sağlık Bilimleri programları için,

MF-4 puan türü ise Mühendislik ve Teknik Programlar için öngörülmüştür.

2. TM Grubu Puan Türleri (EA-2 yerine kullanılacak )

Testlerin Ağırlıkları (% olarak)

P. Türü Türkçe Tem.Mat. Sos.Bil. Fen Bil. Mat. Geo. TD ve Edb. Coğ-1

TM-1 14 16 5 5 25 10 18 7

TM-2 14 14 7 5 22 8 22 8

TM-3 15 10 10 5 18 7 25 10

TM-1 puan türü az da olsa Matematik ağırlıklıdır.

TM-3 puan türü az da olsa Türkçe-Edebiyat ağırlıklıdır.

TM-2 puan türünde Matematik ile Türkçe-Edebiyat eşit ağırlıklıdır.

3. TS Grubu Puan Türleri (SÖZ-2 yerine kullanılacak )

Testlerin Ağırlıkları (% olarak)

P. Türü Türkçe Tem.Mat. Sos.Bil. Fen Bil. TD ve Edb. Coğ-1 Tar. Coğ-2 Fel.Gr

TS-1 13 10 12 5 15 8 15 7 15

TS-2 18 6 11 5 25 5 15 5 10

TS-1 puan türü sosyal programlar için,

TS-2 puan türü dil (Türkçe, edebiyat) ve tarih programları için öngörülmüştür.

4. Yabancı Dil Grubu Puan Türleri

Testlerin Ağırlıkları (% olarak)

P. Türü Türkçe Tem.Mat. Sos.Bil. Fen Bil. Yab. Dil

DİL-1 15 6 9 5 65

DİL-2 25 7 13 5 50

DİL-1 puan türü İngilizce, Almanca ve Fransızca Yabancı Dil Programları için,

DİL-2 puan türü diğer Dil Programları için öngörülmüştür.

2009-ÖSYS Puan Türlerinin 2010 ÖSYS’deki karşılıkları

1. Önlisans ve Açıköğretim Programları

2009-ÖSYS 2010-ÖSYS

SAY-1 YGS-1 veya YGS-2

SÖZ-1 YGS-3 veya YGS-4

EA-1 YGS-5 veya YGS-6

2. Lisans Programları (Meslek Lisesi çıkışlı adayların ek puanla girdikleri hariç)

2009-ÖSYS 2010-ÖSYS

SAY-2 MF-1, MF-2, MF-3 veya MF-4

SÖZ-2 TS-1 veya TS-2

EA-2 TM-1, TM-2 veya TM-3

DİL DİL-2 veya DİL-2

3. Lisans Programları (Meslek Lisesi çıkışlı adayların ek puanla girdikleri)

2009-ÖSYS 2010-ÖSYS

SAY-1 Birinci Puan Türü : MF-1, MF-2, MF-3 veya MF-4

İkinci Puan Türü : YGS-1 veya YGS-2

SÖZ-1 Birinci Puan Türü : TS-1 veya TS-2

İkinci Puan Türü : YGS-3 veya YGS-4

EA-1 Birinci Puan Türü : TM-1, TM-2 veya TM-3

İkinci Puan Türü : YGS-5 veya YGS-6

İki puan türü bulunan programlara yerleştirmede, iki puandan büyük olanı

kullanılacaktır.

Ortaöğretim Başarı Puanı (OBP) ve

Ağırlıklı Ortaöğretim Başarı Puanı (AOBP) Değer Aralıkları

OBP ve AOBP mevcut hesaplama yöntemine göre hesaplanacak,

ancak değer aralığı 50 – 100 yerine 100 – 500 olacaktır.

Yerleştirme Puanlarının Hesaplanması

1) Yerleştirme puanları hesaplanırken, Ağırlıklı Ortaöğretim Başarı Puanı (AOBP)

0,15 ile çarpılarak sınav puanlarına (YGS ve LYS puanları) eklenecektir.

Y-YGS = YGS + (0,15 x AOBP)

Y-LYS-MF = LYS-MF + (0,15 x AOBP)

Y-LYS-TM = LYS-MF + (0,15 x AOBP)

Y-LYS-TS = LYS-TS + (0,15 x AOBP)

Y-LYS-DİL = LYS-DİL + (0,15 x AOBP)

LYS, YGS ve AOBP puanları en büyük değeri 500 olduğu için, yerleştirme

puanının en büyük değeri:

500 + (0,15 x 500) = 575 olacaktır

2) Meslek lisesi ve öğretmen lisesi çıkışlı adaylar kendi alanlarındaki lisans

programlarına yerleştirilirken yerleştirme puanlarına eklenecek ek puan

(0,06 x AOBP) olarak hesaplanacaktır.

Ek puanın en büyük değeri 500 x 0,06 = 30 olacaktır.

3) Bir önceki yıl bir yükseköğretim programına merkezi sistemle yerleştirilen

veya ön kayıtla kaydolan adayların yerleştirme puanları hesaplanırken 0,15

ve 0,06 katsayılarının yarısı alınacaktır (0,15 yerine 0,075; 0,06 yerine de 0,03)

Twin Prime Proof Proffered

By Eric W. Weisstein

Author's note:
After this news story was written, a serious error was found in Arenstorf's proof. In particular, Lemma 8 was found to be incorrect. As a result, the paper has been retracted and the twin prime conjecture remains fully open.
June 9, 2004--A recent preprint by Vanderbilt University mathematician R. F. Arenstorf appears to come close to settling the long-standing question of the infinitude of twin primes. Twin primes are pairs of prime numbers such that the larger member of the pair is exactly 2 greater than the smaller, i.e., primes p and q such that q - p = 2. Explicitly, the first few twin primes are (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), and (41, 43).

The properties and the distribution of twin primes (so named by P. Stäckel, 1892-1919) are active areas of mathematical research. While the distribution of twin primes has remained elusive, mathematician V. Brun proved in 1919 that the sum of the reciprocals of the members of each twin prime pair

converges to a definite number even if the sum contains an infinite number a terms, a result known as Brun's theorem. The number B, known as Brun's constant, is difficult to compute, but is known to be approximately equal to 1.902160583104. (Amusingly, it was T. Nicely's 1995 high-precision computation of Brun's constant that first revealed a serious hardware bug in Intel's Pentium microprocessor.) Since the sum of the reciprocals of all the primes diverges (which represents a strengthening of Euclid's second theorem on the infinitude of the primes that was first proved by Euler in 1737), Brun's theorem shows that the twin primes are sparsely distributed among the primes.

The twin prime conjecture states that there are an infinite number of twin primes. While Hardy and Wright (1979) note that "the evidence, when examined in detail, appears to justify the conjecture," and Shanks (1993) states even more strongly, "the evidence is overwhelming." Hardy and Wright also note that the proof or disproof of conjectures of this type "is at present beyond the resources of mathematics."

In fact, no proof of the twin primes conjecture had been constructed despite the efforts of dozens of mathematicians over almost a century. In contrast, a recent preprint has apparently succeeded in showing the existence of prime arithmetic progressions of any length k, a related and also long-outstanding problem (MathWorld headline news story, April 12, 2004).

In a May 26 preprint, however, R. F. Arenstorf published a proposed proof of the twin prime conjecture in a stronger form due to Hardy and Littlewood (1923). The proof uses methods from classical analytic number theory, including the properties of the Riemann zeta function, ideas from the proof of the prime number theorem, and a so-called Tauberian theorem by Wiener and Ikehara from 1931, the last of which leads almost immediately to Arenstorf's main result.

While Arenstorf's approach looks promising, an error in one particular step of the proof (specifically, Lemma 8 on page 35; a lemma is short theorem used in proving a larger theorem) has recently been pointed out by French mathematician G. Tenenbaum of the Institut Élie Cartan in Nancy (Tenenbaum 2004). While mathematicians remain hopeful that any holes in the proof can be corrected, Tenenbaum opines that this particular error may have serious consequences for the integrity of the overall proof. Additional analysis by other mathematicians over the coming weeks and months will establish whether, like the originally flawed proof of Fermat's last theorem, the twin prime result can also be corrected, thus finally settling this long-open problem, or if it requires additional insight and tools before it can finally be cracked.

References

Arenstorf, R. F. "There Are Infinitely Many Prime Twins." Preprint. 26 May 2004.
http://arXiv.org/abs/math.NT/0405509

Brun, V. "La serie 1/5 + 1/7 + 1/11 + 1/13 + 1/17 + 1/19 + 1/29 + 1/31 + 1/41 + 1/43 + 1/59 + 1/61 + ..., les dénominateurs sont nombres premiers jumeaux est convergente où finie." Bull. Sci. Math. 43, 124-128, 1919.

Guy, R. K. "Gaps between Primes. Twin Primes." §A8 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 19-23, 1994.

Hardy, G. H. and Littlewood, J. E. "Some Problems of 'Partitio Numerorum.' III. On the Expression of a Number as a Sum of Primes." Acta Math. 44, 1-70, 1923.

Hardy, G. H. and Wright, E. M. An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, p. 5, 1979.

Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, pp. 30 and 219, 1993.

Tenenbaum, G. "Re: Arenstorf's paper on the Twin Prime Conjecture." NMBRTHRY@listserv.nodak.edu} mailing list. 8 Jun 2004.
http://listserv.nodak.edu/scripts/wa.exe?A2=ind0406&L=nmbrthry&F=&S=&P=1119

The Mathematics of Tsunamis

By Eric W. Weisstein and Michael Trott

January 14, 2005--The recent tragic events following the December 2004 magnitude 9.0 earthquake in the Indian Ocean have reminded us of the need for scientific understanding and modeling of complicated physical phenomena in order to prevent unnecessary loss of life from natural disasters (cf. Post and Vatta 2005).

While the full-scale physics and modeling of tsunamis are difficult problems requiring the use of supercomputers and complicated custom software, a number of approximations can be made that render the problem of tsunami propagation tractable for a computer of modest power running off-the-shelf software such as Wolfram Research's Mathematica.

The simplest theory of water waves that reasonably approximates the behavior of real ocean waves is the system of coupled partial differential equations known as the shallow water wave equations (Pelinovsky et al. 2001, Layton 2002), reproduced above. Here, u and v are the horizontal velocity components of the water surface, x and y are the spatial coordinates of the wave, t is elapsed time, g is the acceleration due to gravity, and h is the height of the wave above the ocean floor topography b.

Part of the physics of tsunamis encompasses the phenomenon of "breaking," or flipping over, as waves near a coastline. However, as the top interface of the water touches only the layer of air above it, it is essentially free. This means the differential equations must be solved in the context of a so-called free boundary value problem, which in general are notoriously difficult to handle and require complicated and difficult computations (Guyenne and Grilli 2003). In addition, as a tsunami propagates over long distances, so-called Coriolis acceleration terms must be included to account for the fact that the frame of reference with respect to which the wave is propagating (i.e., the Earth) is rotating.

Zahibo et al. (2003) have carried out such full-blown calculations. But because the shallow water wave equations are difficult to solve, these equations are sometimes simplified in a number of ways, including by linearizing them. The linearized version takes the velocity of water particles to be (u, v) = , i.e., the gradient of a scalar potential. Even this linearized version has highly nontrivial boundary conditions that are difficult to treat correctly. Taking various asymptotic limits of Euler's equations of inviscid motion results in a host of integrable and nearly integrable equations such as the Korteweg-de Vries equation, Camassa-Holm equation, nonlinear Schrödinger equation, and so on (Rahman 1995, Johnson 2003). Unfortunately, while these equations have exact (integrable) solutions, they also diverge from the true behavior described by the full equations for any but very short time scales (Johnson 2003). Full solution of the shallow water wave equations is therefore needed in order to gain any realistic picture of tsunami propagation.

Visualization of a tsunami computed by Mathematica by numerically solving the shallow water wave equations. Initial conditions are a Gaussian displacement, and the bottom geometry is taken to be flat in the deep ocean, approaching the shoreline like a cosine function, and radially symmetric.

To create the tsunami visualization shown above, we used Mathematica's NDSolve command to solve the shallow water wave equations for an initial Gaussian water displacement. The ocean floor is assumed to be deep and of constant depth in the middle, while smoothly sloping towards the shore like a cosine function. In the animation above, we can clearly see a number of real physical effects, including (1) local propagation of the tsunami, (2) a small offset of the ocean level inside the radial wavefront (an effect only present in even-dimensional systems; in this case, 2-dimensional), and (3) a steepening of the wavefront as it nears the shore. The animation is halted as the wave nears the shore because the shallow wave equations cease providing an accurate description of the wave's propagation as the depth becomes comparable to the wavelength.

Much more complicated simulations performed with custom software and actual coastlines can be seen on the website of the National Oceanic and Atmospheric Administration. Readers interested in the code used to generate this animation may download the corresponding Mathematica notebook. Solving the equations takes less than a minute on a moderately fast desktop computer.

References

Guyenne, P. and Grilli, S. T. "Computations of Three-Dimensional Overturning Waves in Shallow Water: Dynamics and Kinematics." Proc. 13th Int. Offshore and Polar Eng. Conf., Honolulu, Hawaii, USA, May 25-30, 2003. International Society of the Offshore and Polar Engineers, 2003.

Johnson, R. S. "The Classical Problem of Water Waves: A Reservoir of Integrable and Nearly-Integrable Equations." J. Nonl. Math. Phys. 10, Suppl. 1, 72-92, 2003. http://www2.math.uic.edu/~bona/papers/boussineq-paper.pdf

Layton, A. T. and van de Panne, M. "A Numerically Efficient and Stable Algorithm for Animating Water Waves." Visual Comput. 18, 41-53, 2002.

National Oceanic and Atmospheric Administration. "NOAA Home Page: Tsunamis." http://www.noaa.gov/tsunamis.html

National Oceanic and Atmospheric Administration. "Tsunami: Indonesia 12-2004." http://www.noaanews.noaa.gov/video/tsunami-indonesia12-2004.qt

Pelinovsky, E.; Talipova, T.; Kurkin, A.; and Kharif, C. "Nonlinear Mechanism of Tsunami Wave Generation by Atmospheric Disturbances." Natural Hazard and Earth Sci. 1, 243-250, 2001.

Post, D. E. and Votta, L. G. Physics Today 58, 35, January 2005. http://www.aip.org/pt/vol-58/iss-1/contents.html

Rahman, M. Water Waves: Relating Modern Theory to Advanced Engineering Practice. Oxford, Enlgand: Clarendon Press, p. 306, 1995.

Zahibo, N.; Pelinovsky, E.; Yalciner, A. C.; Kurkin, A.; Koselkov, A.; and Zaitsev, A. "The 1867 Virgin Island Tsunami." Natural Hazard and Earth Sci. 3, 367-376, 2003.

47th Known Mersenne Prime Apparently Discovered

By Eric W. Weisstein

June 7, 2009--Less than a year after the 45th and 46th known Mersenne primes were discovered, Great Internet Mersenne Prime Search (GIMPS) project organizer George Woltman is reporting in a June 7 email to the GIMPS mailing list that a new Mersenne number has been flagged as prime and reported to the project's server. If verified, this would be the 47th Mersenne prime discovered. A verification run on the number has been started, and more details will be made available when confirmation of the discovery has been completed. The prime was apparently discovered in April, but was not noticed due to a configuration problem with the server that prevented a notification email being sent to the search organizers.

[Postscript: The prime has now been officially verified and announced to be M_42643801, which has 12837064 decimal digits, making it the 46th known Mersenne prime ranked by size, and hence only the second largest. It was found by Norwegian GIMPS participant Odd Magnar Strindmo.]

Mersenne numbers are numbers of the form M_n = 2ⁿ - 1, giving the first few as 1, 3, 7, 15, 31, 63, 127, .... Interestingly, the definition of these numbers therefore means that the nth Mersenne number is simply a string of n 1s when represented in binary. For example, M₇ = 2⁷ - 1 = 127 = 1111111₂ is a Mersenne number. In fact, since 127 is also prime, 127 is also a Mersenne prime.

The study of such numbers has a long and interesting history, and the search for Mersenne numbers that are prime has been a computationally challenging exercise requiring the world's fastest computers. Mersenne primes are intimately connected with so-called perfect numbers, which were extensively studied by the ancient Greeks, including by Euclid. A complete list of indices n of the previously known Mersenne primes is given in the table below (as well as by sequence A000043 in Neil Sloane's On-Line Encyclopedia of Integer Sequences). The last of these has a whopping 12,978,189 decimal digits. However, note that the region between the 39th and 40th known Mersenne primes has not been completely searched, so it is not known if M_20,996,011 is actually the 40th Mersenne prime.

The following table summarizes all known Mersenne primes.

#		digits	year	discoverer (reference)	value
1	2	1	antiquity		3
2	3	1	antiquity		7
3	5	2	antiquity		31
4	7	3	antiquity		127
5	13	4	1461	Reguis (1536), Cataldi (1603)	8191
6	17	6	1588	Cataldi (1603)	131071
7	19	6	1588	Cataldi (1603)	524287
8	31	10	1750	Euler (1772)	2147483647
9	61	19	1883	Pervouchine (1883), Seelhoff (1886)	2305843009213693951
10	89	27	1911	Powers (1911)	618970019642690137449562111
11	107	33	1913	Powers (1914)	162259276829213363391578010288127
12	127	39	1876	Lucas (1876)	170141183460469231731687303715884105727
13	521	157	Jan. 30, 1952	Robinson (1954)	68647976601306097149...12574028291115057151
14	607	183	Jan. 30, 1952	Robinson (1954)	53113799281676709868...70835393219031728127
15	1279	386	Jun. 25, 1952	Robinson (1954)	10407932194664399081...20710555703168729087
16	2203	664	Oct. 7, 1952	Robinson (1954)	14759799152141802350...50419497686697771007
17	2281	687	Oct. 9, 1952	Robinson (1954)	44608755718375842957...64133172418132836351
18	3217	969	Sep. 8, 1957	Riesel	25911708601320262777...46160677362909315071
19	4253	1281	Nov. 3, 1961	Hurwitz	19079700752443907380...76034687815350484991
20	4423	1332	Nov. 3, 1961	Hurwitz	28554254222827961390...10231057902608580607
21	9689	2917	May 11, 1963	Gillies (1964)	47822027880546120295...18992696826225754111
22	9941	2993	May 16, 1963	Gillies (1964)	34608828249085121524...19426224883789463551
23	11213	3376	Jun. 2, 1963	Gillies (1964)	28141120136973731333...67391476087696392191
24	19937	6002	Mar. 4, 1971	Tuckerman (1971)	43154247973881626480...36741539030968041471
25	21701	6533	Oct. 30, 1978	Noll and Nickel (1980)	44867916611904333479...57410828353511882751
26	23209	6987	Feb. 9, 1979	Noll (Noll and Nickel 1980)	40287411577898877818...36743355523779264511
27	44497	13395	Apr. 8, 1979	Nelson and Slowinski	85450982430363380319...44867686961011228671
28	86243	25962	Sep. 25, 1982	Slowinski	53692799550275632152...99857021709433438207
29	110503	33265	Jan. 28, 1988	Colquitt and Welsh (1991)	52192831334175505976...69951621083465515007
30	132049	39751	Sep. 20, 1983	Slowinski	51274027626932072381...52138578455730061311
31	216091	65050	Sep. 6, 1985	Slowinski	74609310306466134368...91336204103815528447
32	756839	227832	Feb. 19, 1992	Slowinski and Gage	17413590682008709732...02603793328544677887
33	859433	258716	Jan. 10, 1994	Slowinski and Gage	12949812560420764966...02414267243500142591
34	1257787	378632	Sep. 3, 1996	Slowinski and Gage	41224577362142867472...31257188976089366527
35	1398269	420921	Nov. 12, 1996	Joel Armengaud/GIMPS	81471756441257307514...85532025868451315711
36	2976221	895832	Aug. 24, 1997	Gordon Spence/GIMPS	62334007624857864988...76506256743729201151
37	3021377	909526	Jan. 27, 1998	Roland Clarkson/GIMPS	12741168303009336743...25422631973024694271
38	6972593	2098960	Jun. 1, 1999	Nayan Hajratwala/GIMPS	43707574412708137883...35366526142924193791
39	13466917	4053946	Nov. 14, 2001	Michael Cameron/GIMPS	92494773800670132224...30073855470256259071
40	20996011	6320430	Nov. 17, 2003	Michael Shafer/GIMPS	12597689545033010502...94714065762855682047
41?	24036583	7235733	May 15, 2004	Josh Findley/GIMPS	29941042940415717208...67436921882733969407
42?	25964951	7816230	Feb. 18, 2005	Martin Nowak/GIMPS	12216463006127794810...98933257280577077247
43?	30402457	9152052	Dec. 15, 2005	Curtis Cooper and Steven Boone/GIMPS	31541647561884608093...11134297411652943871
44?	32582657	9808358	Sep. 4, 2006	Curtis Cooper and Steven Boone/GIMPS	12457502601536945540...11752880154053967871
45?	37156667	11185272	Sep. 6, 2008	Hans-Michael Elvenich/GIMPS	20225440689097733553...21340265022308220927
46?	42643801	12837064	Jun. 12, 2009	Odd Magnar Strindmo/GIMPS	16987351645274162247...84101954765562314751
47?	43112609	12978189	Aug. 23, 2008	Edson Smith/GIMPS	31647026933025592314...80022181166697152511

The 13 largest known Mersenne primes (including the latest candidate) have all been discovered by GIMPS, which is a distributed computing project being undertaken by an international collaboration of volunteers. Thus far, GIMPS participants have tested and double-checked all exponents n below 18,000,949, while all exponents below 26,181,803 have been tested at least once. The candidate prime has yet to be verified by independent software running on different hardware. If confirmed, GIMPS will make an official press release that will reveal the number and the name of the lucky discoverer.

References

Caldwell, C. K. "The Largest Known Primes."
http://www.utm.edu/research/primes/largest.html

GIMPS: The Great Internet Mersenne Prime Search. "47th Known Mersenne Prime Found!"
http://www.mersenne.org

GIMPS: The Great Internet Mersenne Prime Search Status.
http://www.mersenne.org/status.htm

Woltman, G. "New Mersenne Prime?" Message to The Great Internet Mersenne Prime Search List. Jun. 4, 2009.
http://www.mail-archive.com/prime@hogranch.com/msg02351.html

Woltman, G. "New Mersenne Prime?" Message to The Great Internet Mersenne Prime Search List. Jun. 7, 2009.
http://www.mail-archive.com/prime@hogranch.com/msg02362.html

Woltman, G. "It's Official - 47th Mersenne Prime Found" Message to The Great Internet Mersenne Prime Search List. Jun. 12, 2009.
http://www.mail-archive.com/prime@hogranch.com/msg02379.html

Math Model Accurately Mimics Cell Division In Carbon-cycling Bacterium

Scientists from the Department of Biological Sciences and the Virginia Bioinformatics Institute (VBI) at Virginia Tech have developed a quantitative, mathematical model of DNA replication and cell division for the bacterium Caulobacter crescentus. C. crescentus, an alpha-proteobacterium that inhabits freshwater, seawater and soils, is an ideal organism for genetic and computational biology studies due to the wealth of molecular information that has been accumulated by researchers. It also plays a key role in global carbon cycling in its natural environment.

The researchers work will appear in the August 14 edition of PLoS Computational Biology. The article is by Genetics, Bioinformatics, and Computational Biology graduate student Shenghua Li, research scientist Paul Brazhnik, Professor and Director of VBI's Cyberinfrastructure Group Bruno Sobral, and University Distinguished Professor of Biological Sciences John Tyson.

The mathematical model described in the paper allows researchers to study and analyze the systems-level dynamics of the Caulobacter cell cycle, test hypotheses and suggest crucial new experiments. "By careful examination of the large amount of experimental information available about the genes, proteins and biochemical reactions involved in regulating the cell division of C. crescentus, we have developed a good understanding of the mechanism of cell division in this organism and a realistic, quantitative mathematical model of the molecular machinery that oversees Caulobacter's cell division cycle," said John Tyson.

Caulobacter normally undergoes a cell cycle that produces two different types of offspring: a motile "swarmer cell" with a flagellum, a slender thread-like structure that allows the bacterium to swim, and an immobile "sessile stalked cell" that lacks a flagellum. The two cell types undergo different development programs but share the same core molecular regulatory system that controls whether the cell commits to a new round of DNA synthesis and to the cell division process. This regulatory core comprises three key proteins – DnaA, GcrA, and CtrA – that act as control points or master switches for DNA replication and cell division. The new math model allows scientists to investigate how these proteins vary with time and their link to physiological events in both stalked and swarmer cells.

"Cells have some similarities to computers in the sense that they engage in information processing", said Tyson. "However, prokaryotic cells like Caulobacter have been somewhat neglected as information systems in studies by scientists. While computers are precise, digital processors, cells are analog systems that operate for the most part in sloppy, watery environments. Conveying instructions for DNA replication and cell division has profound consequences for a cell and needs to be done with considerable accuracy and precision and that's one of the reasons why we want to be able to model the process." Tyson added: "We have been able to establish a wiring diagram that maps the essential regulatory steps for DNA replication and cell division in Caulobacter in a way that is similar to how you would define a computer process. The model provides a rigorous account of the consequences of our hypotheses, which can be compared to experimental observations to test the model."

With the model in place, the researchers confirmed that it correctly represents the sequence of physiological events that take place during cell division. They were able to show in simulations that the model accurately describes how the different proteins change in quantity during the cell division cycle. Taking this one step further, they were also able to simulate the impact of specific known mutations on cell function.

Mutant cells provide valuable information about how individual components of the cell cycle control system affect the features (phenotype) of cells. Commented Tyson: "Our model allows you to perform quantitative predictions for novel mutants. We have performed simulations of some novel mutants that to our knowledge have not been described in the scientific literature. For example, the math model predicts that if the master regulator CtrA cannot be properly phosphorylated, which is a key step in the activation of CtrA, then the cell replicates its DNA but cannot divide. It will grow very long and eventually die. Specific predictions like this can test the reliability of the model. A validated model can then be used to design new experiments by in silico simulations."

The researchers have built a math model that allows for the study of how the protein components change with time. Future versions of the model will also take into account the spatial localization of the proteins. Said Bruno Sobral: "Caulobacter crescentus is a member of the alpha-proteobacteria, a group of diverse organisms whose members have successfully adopted different lifestyle and energy-yielding strategies over the course of evolution. Caulobacter was also recently detected as a human pathogen, which makes its study directly relevant to human health. Since many genes and mechanisms discovered in Caulobacter are evolutionarily conserved among the alpha-proteobacteria our computational model of cell replication may be applicable to other family members, in particular the causative agents of brucellosis in cattle and Rocky Mountain spotted fever in humans."

www.sciencedaily.com

World Record In Packing Puzzle Set In Tetrahedra Jam: Better Understanding Of Matter Itself?

ScienceDaily (Aug. 15, 2009) — Finding the best way to pack the greatest quantity of a specifically shaped object into a confined space may sound simple, yet it consistently has led to deep mathematical concepts and practical applications, such as improved computer security codes.

When mathematicians solved a famed sphere-packing problem in 2005, one that first had been posed by renowned mathematician and astronomer Johannes Kepler in 1611, it made worldwide headlines.

Now, two Princeton University researchers have made a major advance in addressing a twist in the packing problem, jamming more tetrahedra -- solid figures with four triangular faces -- and other polyhedral solid objects than ever before into a space. The work could result in better ways to store data on compact discs as well as a better understanding of matter itself.

In the cover story of the Aug. 13 issue of Nature, Salvatore Torquato, a professor in the Department of Chemistry and the Princeton Institute for the Science and Technology of Materials, and Yang Jiao, a graduate student in the Department of Mechanical and Aerospace Engineering, report that they have bested the world record, set last year by Elizabeth Chen, a graduate student at the University of Michigan.

Using computer simulations, Torquato and Jiao were able to fill a volume to 78.2 percent of capacity with tetrahedra. Chen, before them, had filled 77.8 percent of the space. The previous world record was set in 2006 by Torquato and John Conway, a Princeton professor of mathematics. They succeeded in filling the space to 72 percent of capacity.

Beyond making a new world record, Torquato and Jiao have devised an approach that involves placing pairs of tetrahedra face-to-face, forming a "kissing" pattern that, viewed from the outside of the container, looks strangely jumbled and irregular.

"We wanted to know this: What's the densest way to pack space?" said Torquato, who is also a senior faculty fellow at the Princeton Center for Theoretical Science. "It's a notoriously difficult problem to solve, and it involves complex objects that, at the time, we simply did not know how to handle."

Henry Cohn, a mathematician with Microsoft Research New England in Cambridge, Mass., said, "What's exciting about Torquato and Jiao's paper is that they give compelling evidence for what happens in more complicated cases than just spheres." The Princeton researchers, he said, employ solid figures as a "wonderful test case for understanding the effects of corners and edges on the packing problem."

Studying shapes and how they fit together is not just an academic exercise. The world is filled with such solids, whether they are spherical oranges or polyhedral grains of sand, and it often matters how they are organized. Real-life specks of matter resembling these solids arise at ultra-low temperatures when materials, especially complex molecular compounds, pass through various chemical phases. How atoms clump can determine their most fundamental properties.

"From a scientific perspective, to know about the packing problem is to know something about the low-temperature phases of matter itself," said Torquato, whose interests are interdisciplinary, spanning physics, applied and computational mathematics, chemistry, chemical engineering, materials science, and mechanical and aerospace engineering.

And the whole topic of the efficient packing of solids is a key part of the mathematics that lies behind the error-detecting and error-correcting codes that are widely used to store information on compact discs and to compress information for efficient transmission around the world.

Beyond solving the practical aspects of the packing problem, the work contributes insight to a field that has fascinated mathematicians and thinkers for thousands of years. The Greek philosopher Plato theorized that the classical elements -- earth, wind, fire and water -- were constructed from polyhedra. Models of them have been found among carved stone balls created by the late Neolithic people of Scotland.

The tetrahedron, which is part of the family of geometric objects known as the Platonic solids, must be packed in the face-to-face fashion for maximum effect. But, for significant mathematical reasons, all other members of the Platonic solids, the researchers found, must be packed as lattices to cram in the largest quantity, much the way a grocer stacks oranges in staggered rows, with successive layers nestled in the dimples formed by lower levels. Lattices have great regularity because they are composed of single units that repeat themselves in exactly the same way.

Mathematicians define the five shapes composing the Platonic solids as being convex polyhedra that are regular. For non-mathematicians, this simply means that these solids have many flat faces, which are plane figures, such as triangles, squares or pentagons. Being regular figures, all angles and faces' sides are equal. The group includes the tetrahedron (with four faces), the cube (six faces), the octahedron (eight faces), the dodecahedron (12 faces) and the icosahedron (20 faces).

There's a good reason why tetrahedra must be packed differently from other Platonic solids, according to the authors. Tetrahedra lack a quality known as central symmetry. To possess this quality, an object must have a center that will bisect any line drawn to connect any two points on separate planes on its surface. The researchers also found this trait absent in 12 out of 13 of an even more complex family of shapes known as the Archimedean solids.

The conclusions of the Princeton scientists are not at all obvious, and it took the development of a complex computer program and theoretical analysis to achieve their groundbreaking results. Previous computer simulations had taken virtual piles of polyhedra and stuffed them in a virtual box and allowed them to "grow."

The algorithm designed by Torquato and Jiao, called "an adaptive shrinking cell optimization technique," did it the other way. It placed virtual polyhedra of a fixed size in a "box" and caused the box to shrink and change shape.

There are tremendous advantages to controlling the size of the box instead of blowing up polyhedra, Torquato said. "When you 'grow' the particles, it's easy for them to get stuck, so you have to wiggle them around to improve the density," he said. "Such programs get bogged down easily; there are all kinds of subtleties. It's much easier and productive, we found, thinking about it in the opposite way."

Cohn, of Microsoft, called the results remarkable. It took four centuries, he noted, for mathematician Tom Hales to prove Kepler's conjecture that the best way to pack spheres is to stack them like cannonballs in a war memorial. Now, the Princeton researchers, he said, have thrown out a new challenge to the math world. "Their results could be considered a 21st Century analogue of Kepler's conjecture about spheres," Cohn said. "And, as with that conjecture, I'm sure their work will inspire many future advances."

Many researchers have pointed to various assemblies of densely packed objects and described them as optimal. The difference with this work, Torquato said, is that the algorithm and analysis developed by the Princeton team most probably shows, in the case of the centrally symmetric Platonic and Archimedean solids, "the best packings, period."

Their simulation results are also supported by theoretical arguments that the densest packings of these objects are likely to be their best lattice arrangements. "This is now a strong conjecture that people can try to prove," Torquato said.

www.sciencedaily.com