Olympiad combinatorics

... Calculate the standard potential for the cathode half reaction if the standard reduction potential for the anode half reaction is 0.83 V and fG (H2O(l)) is -237 kJ·mol-1 4 3rd IChO Theoretical ... =  as v = at K E = 2(Eo + E =   - (Eo + 1546  ) - (Eo +  )= -  + 8167 )) = 0.0 1435  (HD) = 4 3rd IChO Theoretical Problems, Official English Version Name: Code: · = · = 1.1154 10 =...

Ngày tải lên: 29/06/2013, 19:58

Ngày tải lên: 18/07/2013, 01:26

Ngày tải lên: 24/01/2014, 00:20

... introduce 2n−1 f (k) < n f (n) ≤ 1/n2 g(n) = k=n Then g(n) − g(n + 1) = f (n) − f (2n) − f (2n + 1) = (f (2n) + f (2n + 1))3 − f (2n) − f (2n + 1) = (f (2n) + f (2n + 1)) f (2n) f (2n + 1) = ... |M \ A| + |F \ A| + |A| = 2( n − l) + l = 2n − l But the degree of any vertex of G is 2k and thus we get 2k ≤ 2n − l, that is, l ≤ 2n − 2k Finally, 2k − n < l ≤ 2n − 2k implies that k < 3n This ... f...

Ngày tải lên: 07/03/2014, 07:20

Ngày tải lên: 07/03/2014, 19:20

Ngày tải lên: 07/03/2014, 19:20

... Questions of Hanoi Open Mathematical Olympiad 1.1 Hanoi Open Mathematical Olympiad 2006 1.1.1 Junior Section, Sunday, April 2006 1.1.2 Senior Section, Sunday, April 2006 1.2 Hanoi Open Mathematical ... = abcd be the 4-digit prime number Prove that the equation ax3 + bx2 + cx + d = has no rational roots 10 1.3 Hanoi Open Mathematical Olympiad 2008 1.3 Hanoi Op...

Ngày tải lên: 07/03/2014, 19:20

... k(k + 2) 1 − k k+2 for any positive integer k, so 1 1 1 + + + + + 15 35 63 99 14 3 1 1 1 + + + + + = × 3 × 5 × 7 × 9 × 11 11 × 13 1 1 1 = − + − + ··· + − 3 11 13 1 = × 1 = 13 13 Example 10 If ab ... 3x 5x − (1 + 3x) 15 − 2x + 16 − 2x =1 = = , 1 15 15 15 10 − 6x x 14 x − (10 − 6x) 10 − 13 x x 2x − − = − = , 2 14 14 x− it follows that 16 − 2x 10 − 13...

Ngày tải lên: 11/03/2014, 16:55

... 231–264 Minimal surfaces from circle patterns: Geometry from combinatorics By Alexander I Bobenko∗ , Tim Hoffmann∗∗ , and Boris A Springborn∗∗* Introduction The theory of polyhedral surfaces ... such a Gauss map MINIMAL SURFACES FROM CIRCLE PATTERNS 233 This definition of discrete minimal surfaces leads to a construction method for discrete S-isothermic minimal...

Ngày tải lên: 15/03/2014, 09:20

... From Erdos to Kiev Probkms of Olympiad Caliber - ."lICE ~ "Uo" "",,1>1< 1",,,,,._ to play" (lit loot, mpl< fOf limll of L 10.• P"" " w"h to ,

Ngày tải lên: 15/03/2014, 15:55

... A Country: _ Student Code: _ IBO2010 KOREA THEORETICAL TEST Part A The 21st INTERNATIONAL BIOLOGY OLYMPIAD 11th – 18th July, 2010 Changwon, KOREA THEORETICAL TEST: PART A Time available: ... shows the experimental results Based on this experiment, find the most accurate explanation or expectation for the light control of flowering in this plant, A This plant flowers whenever the total ....

Ngày tải lên: 16/03/2014, 07:20

... IBO2010 KOREA THEORETICAL TEST Part B Country: Student Code: _ The 21st INTERNATIONAL BIOLOGY OLYMPIAD 11th – 18th July, 2010 Changwon, KOREA THEORETICAL TEST: PART B Time available: ... at this stage II With a mitogen treatment, such as an epidermal growth factor, an arrested cell at this stage proceeds to the next stage of the cell cycle III The cell cycle check point at this ... you...

Ngày tải lên: 16/03/2014, 07:20

... IBO -200 9 JAPAN THEORETICAL TEST Part A Student Code: _ 20th INTERNATIONAL BIOLOGY OLYMPIAD Tsukuba, JAPAN 12th – 19th July, 200 9 THEORETICAL TEST: PART A Time available: 120 minutes ... primary productivity (g/m2/year) Biomass (kg/m2) Tropical rainforest 2200 45 I 200 0 15 II 1200 30 III 900 Boreal forest 800 20 Choose from A to F in the table below the most appropriate combinat...

Ngày tải lên: 16/03/2014, 07:20

... Annals of Mathematics, 164 (2006), 603–648 Combinatorics of random processes and sections of convex bodies By M Rudelson and R Vershynin* Abstract We find a sharp ... cardinality of the set A COMBINATORICS OF RANDOM PROCESSES 617 Separating tree This and the next step are versions of corresponding steps of [MV 03], where they were written in terms of fun...

Ngày tải lên: 22/03/2014, 20:20