Dec 10, 2013
Nov 17, 2013
EMIS ELibM: Mathematical Collections and Conference Proceedings
http://www.emis.de/proceedings/index.html
- 8th International Conference Words 2011
Prague, Czech Republic, 12-16th September 2011 - Workshop on Finsler Geometry and Its Applications
Debrecen, Hungary, 24–29 May 2009 - Geometry, Integrability and Quantization VIII
Varna, Bulgaria: June 9–14, 2006. - The 26th Winter School Geometry and Physics
Srni, Czech Republic, 14–21 January 2006 - Contemporary geometry and Related Topics
Neda Bokan, Mirjana Djorić, Anatoly T. Fomenko, Zoran Rakić, Bernd Wegner, Julius Wess (eds.), Belgrade, Serbia and Montenegro 26 June–2 July 2005 - The 29th International Conference of the International Group for the Psychology of Mathematics Education
Helen Chick and Jill L. Vincent (eds.), Melbourne, Australia 10–15 July 2005 - Geometry, Integrability and Quantization VII
Varna, Bulgaria: June 2–10, 2005. - The 28th International Conference of the International Group for the Psychology of Mathematics Education
Marit Johnsen Høines and Anne Berit Fuglestad (eds.), Bergen, Norway 14–18 July, 2004 - New Developments in Electronic Publishing
Hans Becker, Kari Stange, Bernd Wegner (eds). Stockholm, Sweden: 25–27 June, 2004 - Geometry, Integrability and Quantization VI
Varna, Bulgaria: June 3–10, 2004. - Geometry, Integrability and Quantization V
Varna, Bulgaria: June 5–12, 2003. - Geometry, Integrability and Quantization IV
Varna, Bulgaria: June 6–15, 2002. - Mathematical Knowledge Management (MKM'2001)
Schloss Hagenberg, Austria: September 24–26, 2001 - Workshop on Special Geometric Structures in String Theory
Dmitri V. Alekseevsky, Vicente Cortés, Chandrashekar Devchand and Antoine Van Proeyen (eds.). Bonn, Germany: 8–11 Sep 2001 - Margarita mathematica en memoria de José Javier (Chicho) Guadalupe Hernández
Luis Español and Juan L. Varona (eds.), Logroño, Spain: 2001 - Geometry, Integrability and Quantization III
Varna, Bulgaria: September 1–10, 2001. - TOPOSYM 2001
Prague, Chech Republic: August 19–25, 2001 - Geometry, Integrability and Quantization II
Varna, Bulgaria: June 7–15, 2000. - AMS Special Session on Nonabsolute Integration
Pat Muldowney and Erik Talvila (eds.). Toronto, Canada: 23–24 Sep 2000 - ALGORITMY 2000
Podbanske, Slovakia: September 10–15, 2000 - Geometry & Applications
Novosibirsk, Russia: March 13–16, 2000 - Steps in Differential Geometry
Debrecen, Hungary: July 25–30, 2000 - Geometry, Integrability and Quantization I
Varna, Bulgaria: September 1–10, 1999. - Summer School on Differential Geometry
Coimbra, Portugal: September 3–7, 1999 - International Congress of Mathematicians (ICM 1998)
Berlin, Germany: August 18–27, 1998 - Second Meeting on Quaternionic Structures in Mathematics and Physics
Roma, Italy: September 6–10, 1999 - Meeting on Quaternionic Structures in Mathematics and Physics
Trieste, Italy: September 5–9, 1994 - The International Conference on Secondary Calculus and Cohomological Physics
Moscow, Russia: August 24–August 31, 1997 - 1st International Meeting on Geometry and Topology
Braga, Portugal: September 11–13, 1997 - 9th International Conference on Domain Decomposition Methods
Ullensvang, Norway: June 3–8, 1996 - XIV C.E.D.Y.A. / IV C.M.A.
Vic, Spain: September 18–22, 1995 - Nonlinear Analysis, Function Spaces and Applications Vol. 6
Prague, Czech Republic: May 31–June 5, 1998 - Nonlinear Analysis, Function Spaces and Applications Vol. 5
Prague, Czech Republic: May 23–28, 1994 - Function Spaces, Differential Operators and Nonlinear Analysis
Paseky na Jizerou, Czech Republic: September 3–9, 1995 - Surgery and Geometric Topology
Josai University, Sakado, Japan: September 17–20, 1996 - 3rd International Conference on Approximation and Optimization in the Caribbean
Puebla, Mexico: October 8–13, 1995 - 7th International Conference on Differential Geometry and Its Applications
Brno, Czech Republic: August 10–14, 1998 - 6th International Conference on Differential Geometry and Its Applications
Brno, Czech Republic: August 28–September 1, 1995 - 5th International Conference on Differential Geometry and Its Applications
Opava, Czechoslovakia: August 24–28, 1992
Nov 16, 2013
Differential Geometry: A beginner's journey.
A good summary:
http://www.math.uga.edu/~shifrin/ShifrinDiffGeo.pdf
Focusing on surface:
http://en.wikipedia.org/wiki/Differential_geometry_of_surfaces?action=render
Applications of Differential Geometries:
Helping to solve other unsolved maths problem:
http://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics
http://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics
Possible applications of differential geometry concepts:
Elementary Geometry
- Center of an arc determined with straightedge and compass.
- Surface areas: Circle, trapezoid, triangle, sphere, frustum, cylinder, cone...
- Power of a point with respect to a circle.
- Euler's line goes through the orthocenter, the centroid and the circumcenter.
- Euler's circle is tangent to the incircle and the excircles (Feuerbach, 1822).
- Barycentric coordinates & trilinears examplify homogeneous coordinates.
- Elliptic arc: Length of the arc of an ellipse between two points.
- Perimeter of an ellipse. Exact formulas and simple ones.
- Circumference of an ellipse: Unabridged discussion.
- Surface of an ellipse.
- Volume of an ellipsoid (either a spheroid or a scalene ellipsoid).
- Surface area of a spheroid (oblate or prolate ellipsoid of revolution).
- Quadratic equations in the plane describe ellipses, parabolas, or hyperbolas.
- Centroid of a circular segment. Find it with Guldin's (Pappus) theorem.
- Parabolic arc of given extremities with a prescribed apex between them.
- Focal point of a parabola. y = x 2 / 4f (where f is the focal distance).
- Parabolic telescope: The path from infinity to focus is constant.
- Make a cube go through a hole in a smaller cube.
- Octagon: The relation between side and diameter.
- Constructible regular polygons and constructible angles (Gauss).
- Areas of regular polygons of unit side: General formula & special cases.
- For a regular polygon of given perimeter, the more sides the larger the area.
- Curves of constant width: Reuleaux Triangle and generalizations.
- Irregular curves of constant width. With or without any circular arcs.
- Solids of constant width. The three-dimensional case.
- Constant width in higher dimensions.
- Fourth dimension. Difficult to visualize, but easy to consider.
- Volume of a hypersphere and hyper-surface area, in any dimensionality.
- Hexahedra. The cube is not the only polyhedron with 6 faces.
- Descartes-Euler Formula: F-E+V=2 but restrictions apply.
Topology:
- Metric spaces: The motivation behind more general topological spaces.
- Abstract topological spaces are defined by calling some subsets open.
- Closed sets are sets (of a topological space) whose complements are open.
- Subspace F of E: Its open sets are the intersections with F of open sets of E.
- Separation axioms: Flavors of topological spaces, according to Trennung.
- Compactness of a topological space: Any open cover has a finite subcover.
- Real-valued continuous functions on compact sets attain their extremes.
- Borel sets. Tribes form the topological foundation for measure theory.
- Locally compact sets contain a compact neighborhood of every point.
- General properties of sequences characterize topological properties.
- Continuous functions let the inverse image of any open set be open.
- Restrictions remain continuous. Continuous extensions may be impossible.
- The product topology makes projections continuous on a cartesian product.
- Tychonoff's Theorem: Any product of compact spaces is compact.
- Connected sets can't be split by open sets. The empty set is connected.
- Path-connected sets are a special case of connected sets.
- Homeomorphic sets. An homeomorphism is a bicontinuous function.
- Arc-connected spaces are path-connected. The converse need not be true.
- Homotopy: A progessive transformation of a function into another.
- The fundamental group: The homotopy classes of all loops through a point.
- Homology and Cohomology. Poincaré duality.
- Descartes-Euler Formula: F-E+V = 2, but restrictions apply.
- Euler Characteristic: c (chi) extended beyond its traditional definition...
- Winding number of a continuous planar curve about an outside point.
- The dog on a leash theorem.
- A topological proof of the fundamental theorem of algebra.
- Fixed-point theorems by Brouwer, Shauder and Tychonoff.
- Turning number of a planar curve with a well-defined oriented tangent.
- Real projective plane and Boy's surface.
- Hadwiger's additive continuous functions of d-dimensional rigid bodies.
- Eversion of the sphere. An homotopy can turn a sphere inside out.
- Classification of surfaces: "Zero Irrelevancy Proof" (ZIP) by J.H. Conway.
- Braid groups: Strands, braids and pure braids.
Completeness:
- Complete metric space: A space in which all Cauchy sequences converge.
- Flawed alternatives to completeness.
- Banach spaces are complete normed vector spaces.
- Fréchet spaces are generalized Banach spaces.
Fractal Geometry:
- Fractional exponents were first conceived by Nicole d'Oresme (c. 1360).
- The von Koch curve (and snowflake): Dimension of self-similar objects.
- Hausdorff dimension is revealed by a covering with balls of radius < e.
- The Julia set and the Fatou set of an analytic function are complementary.
- The Mandelbrot set was so named by Adrien Douady & John H. Hubbard.
Angles and Solid Angles:
- Planar angles (from one direction to another) are signed quantities.
- Bearing: Unless otherwise specified, this is the angle west of north.
- Solid angles are to spherical patches what planar angles are to circular arcs.
- Circular measures: Angles and solid angles aren't quite dimensionless...
- Solid angle formed by a trihedron : Van Oosterom & Strackee (1983).
- Solid angle subtended by a rhombus. Apex of a right rhombic pyramid.
- Formulas for solid angles subtended by patches with simple shapes.
- Right ascension and declination. Precession of celestial coordinates (a,d).
Curvature and Torsion:
- Curvature of a planar curve: Variation of inclination with distance dj/ds.
- Curvature and torsion of a three-dimensional curve.
- Distinct curvatures and geodesic torsion of a curve drawn on a surface.
- The two fundamental quadratic forms at a point of a parametrized surface.
- Lines of curvature: Their normal curvature is extremal at every point.
- Geodesic lines. Least length is achieved with zero geodesic curvature.
- Meusnier's theorem: Tangent lines have the same normal curvature.
- Gaussian curvature of a surface. The Gauss-Bonnet theorem.
- Parallel-transport of a vector around a loop. Holonomic angle of a loop.
- Total curvature of a curve. The Fary-Milnor theorem for knotted curves.
- Linearly independent components of the Riemann curvature tensor.
Planar Curves:
- Cartesian equation of a straight line: passing through two given points.
- Confocal Conics: Ellipses and hyperbolae sharing the same pair of foci.
- Spiral of Archimedes: Paper on a roll, or groove on a vinyl record.
- Hyperbolic spiral: The inverse of the Archimedean spiral.
- Catenary: The shape of a thin chain under its own weight.
- Witch of Agnesi. How the versiera (Agnesi's cubic) got a weird name.
- Folium of Descartes.
- Lemniscate of Bernoulli: A quartic curve shaped like the infinity symbol.
- Along a Cassini oval, the product of the distances to the two foci is constant.
- Limaçons of Pascal: The cardioid (unit epicycloid) is a special case.
- On a Cartesian oval, the weighted average distance to two poles is constant.
- The envelope of a family of curves is everywhere tangent to one of them.
- The evolute of a curve is the locus of its centers of curvature.
- Involute of a curve: Trajectory of a point of a line rolling on that curve.
- Parallel curves share their normals, along which their distance is constant.
- The nephroid (or two-cusped epicycloid ) is a catacaustic of a circle.
- Freeth's nephroid: A special strophoid of a circle.
- Bézier curves are algebraic splines. The cubic type is the most popular.
- Piecewise circular curves: The traditional way to specify curved forms.
- Intrinsic equation [curvature as a function of arc length] may have spikes.
- The quadratrix (trisectrix) of Hippias squares the circle and trisects angles.
- The parabola is constructible with straightedge and compass.
- Mohr-Mascheroni constructions use the compass alone (no straightedge).
http://demonstrations.wolfram.com/siteindex.html
Nov 13, 2013
Nov 9, 2013
A generalization of a number pattern from base 10 to base 16, and base 20, and base 32
First looking at the decimals number patterns:
12*9+3 : 111
123*9+4 : 1111
1234*9+5 : 11111
12345*9+6 : 111111
123456*9+7 : 1111111
1234567*9+8 : 11111111
12345678*9+9 : 111111111
123456789*9+10 : 1111111111
And the python generator for this:
def get_first(p1, mynum):
p2 = p1 + str(mynum)
n2 = int(p2) * 9 + (mynum+1)
print "%s*9+%d : %d"%(p2,mynum+1, n2)
get_first(p2, mynum+1)
get_first("1", 2)
Can it be generalize to base 16?
Yes:
12*15+0x3 : 0x111
123*15+0x4 : 0x1111
1234*15+0x5 : 0x11111
12345*15+0x6 : 0x111111
123456*15+0x7 : 0x1111111
1234567*15+0x8 : 0x11111111
12345678*15+0x9 : 0x111111111L
123456789*15+0xa : 0x1111111111L
123456789a*15+0xb : 0x11111111111L
123456789ab*15+0xc : 0x111111111111L
123456789abc*15+0xd : 0x1111111111111L
123456789abcd*15+0xe : 0x11111111111111L
123456789abcde*15+0xf : 0x111111111111111L
123456789abcdef*15+0x10 : 0x1111111111111111L
And the program is:
def pattern_base16(p1, mynum):
p2 = p1 + hex(int(str(mynum)))[2:]
n2 = int(p2,16) * 15 + (mynum+1)
print "%s*15+%s : %s"%(p2,hex(mynum+1), hex(n2))
pattern_base16(p2, mynum+1)
pattern_base16("1", 2)
And for base 20:
12*19+3 : 111
123*19+4 : 1111
1234*19+5 : 11111
12345*19+6 : 111111
123456*19+7 : 1111111
1234567*19+8 : 11111111
12345678*19+9 : 111111111
123456789*19+a : 1111111111
123456789a*19+b : 11111111111
123456789ab*19+c : 111111111111
123456789abc*19+d : 1111111111111
123456789abcd*19+e : 11111111111111
123456789abcde*19+f : 111111111111111
123456789abcdef*19+g : 1111111111111111
123456789abcdefg*19+h : 11111111111111111
123456789abcdefgh*19+i : 111111111111111111
123456789abcdefghi*19+j : 1111111111111111111
123456789abcdefghij*19+10 : 11111111111111111111
and the program is:
from baseconv import BaseConverter
def base10_to_20(nos):
base20 = BaseConverter('0123456789abcdefghij')
return base20.encode(nos)
def base20_to_10(mystring):
base20 = BaseConverter('0123456789abcdefghij')
return int(base20.decode(mystring))
def pattern_base20(p1, mynum):
p2 = p1 + base10_to_20(mynum)
#print "p2=%s"%p2
n2 = base20_to_10(p2) * 19 + (mynum+1)
print "%s*19+%s : %s"%(p2, base10_to_20(mynum+1), base10_to_20(n2))
pattern_base20(p2, mynum+1)
pattern_base20("1", 2)
And for base 32:
12*31+3 : 111
123*31+4 : 1111
1234*31+5 : 11111
12345*31+6 : 111111
123456*31+7 : 1111111
1234567*31+8 : 11111111
12345678*31+9 : 111111111
123456789*31+a : 1111111111
123456789a*31+b : 11111111111
123456789ab*31+c : 111111111111
123456789abc*31+d : 1111111111111
123456789abcd*31+e : 11111111111111
123456789abcde*31+f : 111111111111111
123456789abcdef*31+g : 1111111111111111
123456789abcdefg*31+h : 11111111111111111
123456789abcdefgh*31+i : 111111111111111111
123456789abcdefghi*31+j : 1111111111111111111
123456789abcdefghij*31+k : 11111111111111111111
123456789abcdefghijk*31+l : 111111111111111111111
123456789abcdefghijkl*31+m : 1111111111111111111111
123456789abcdefghijklm*31+n : 11111111111111111111111
123456789abcdefghijklmn*31+p : 111111111111111111111111
123456789abcdefghijklmnp*31+q : 1111111111111111111111111
123456789abcdefghijklmnpq*31+r : 11111111111111111111111111
123456789abcdefghijklmnpqr*31+s : 111111111111111111111111111
123456789abcdefghijklmnpqrs*31+t : 1111111111111111111111111111
123456789abcdefghijklmnpqrst*31+u : 11111111111111111111111111111
123456789abcdefghijklmnpqrstu*31+v : 111111111111111111111111111111
123456789abcdefghijklmnpqrstuv*31+w : 1111111111111111111111111111111
123456789abcdefghijklmnpqrstuvw*31+10 : 11111111111111111111111111111111
And the program is:
from baseconv import BaseConverter
def base10_to_32(nos):
base32 = BaseConverter('0123456789abcdefghijklmnpqrstuvw')
return base32.encode(nos)
def base32_to_10(mystring):
base32 = BaseConverter('0123456789abcdefghijklmnpqrstuvw')
return int(base32.decode(mystring))
def pattern_base32(p1, mynum):
p2 = p1 + base10_to_32(mynum)
#print "p2=%s"%p2
n2 = base32_to_10(p2) * 31 + (mynum+1)
print "%s*31+%s : %s"%(p2, base10_to_32(mynum+1), base10_to_32(n2))
pattern_base32(p2, mynum+1)
The BaseConverter python module is downloaded following the two articles below:
http://stackoverflow.com/questions/2267362/convert-integer-to-a-string-in-a-given-numeric-base-in-python
https://bitbucket.org/semente/baseconv
Oct 12, 2013
Aug 18, 2013
Aug 17, 2013
Project Euler Problem Nos 43
Original problem posted at:
http://projecteuler.net/problem=43
This is my solution to problem 43:
Output from the python script:
[('160', '603', '035', '357', '572', '728', '289'), ('460', '603', '035', '357', '572', '728', '289'), ('106', '063', '635', '357', '572', '728', '289'), ('406', '063', '635', '357', '572', '728', '289'), ('130', '309', '095', '952', '528', '286', '867'), ('430', '309', '095', '952', '528', '286', '867')]
Or after rearranging the digits according to the rules in problem 43:
4160357289
1460357289
4106357289
1406357289
4130952867
1430952867
These are the six numbers that satisfy all the properties and will add up to the answer.
http://projecteuler.net/problem=43
This is my solution to problem 43:
#!/usr/bin/python
### problem 43
import string
def get_divisible_set(n):
myset=[]
for i in range(2,999):
if (i%n==0):
myset.append(str(i).zfill(3))
###myset.append(str.format("%03d", i))
###n = '4'
###>>> print n.zfill(3)
###>>> '004'
return myset
def check_adjoining_item(a, b):
if ((a[1]==b[0])and(a[2]==b[1])):
return 1
else:
return 0
def get_adjoining_set(seta, setb):
myset=[]
#### assuming setb is the smaller set....
mylenb=len(setb)
mylena=len(seta)
for i in range(mylenb):
for j in range(mylena):
###print seta[j], setb[i]
mysettmp=set(seta[j])
mysettmp=mysettmp.union(set(setb[i]))
if (check_adjoining_item(seta[j], setb[i])==1) and (len(mysettmp)==4):
myset.append((seta[j],setb[i]))
return myset
myset17=get_divisible_set(17)
myset13=get_divisible_set(13)
myset11=get_divisible_set(11)
myset=get_adjoining_set(myset13, myset17)
nextset=[]
for i in range(len(myset)):
#print myset[i]
(a,b)=myset[i]
tmp=[]
mysettmp=set()
tmp.append(a)
tmpset=get_adjoining_set(myset11, tmp)
if len(tmpset)>0:
for j in range(len(tmpset)):
(c,d)=tmpset[j]
mysettmp=set(d)
mysettmp=mysettmp.union(set(c))
mysettmp=mysettmp.union(set(a))
mysettmp=mysettmp.union(set(b))
if len(mysettmp)==5:
nextset.append((c,a,b))
print "aaaa"
print nextset
myset7=get_divisible_set(7)
nextset1=[]
for i in range(len(nextset)):
(a,b,c)=nextset[i]
tmp=[]
mysettmp=set()
tmp.append(a)
tmpset=get_adjoining_set(myset7, tmp)
if len(tmpset)>0:
for j in range(len(tmpset)):
(d,e)=tmpset[j]
mysettmp=set(e)
mysettmp=mysettmp.union(set(d))
mysettmp=mysettmp.union(set(a))
mysettmp=mysettmp.union(set(b))
mysettmp=mysettmp.union(set(c))
if len(mysettmp)==6:
nextset1.append((d,e,b,c))
print "bbb"
print nextset1
myset5=get_divisible_set(5)
nextset2=[]
for i in range(len(nextset1)):
(a,b,c,d)=nextset1[i]
tmp=[]
mysettmp=set()
tmp.append(a)
tmpset=get_adjoining_set(myset5, tmp)
if len(tmpset)>0:
for j in range(len(tmpset)):
(e,f)=tmpset[j]
mysettmp=set(f)
mysettmp=mysettmp.union(set(e))
mysettmp=mysettmp.union(set(a))
mysettmp=mysettmp.union(set(b))
mysettmp=mysettmp.union(set(c))
mysettmp=mysettmp.union(set(d))
if len(mysettmp)==7:
nextset2.append((e,a,b,c,d))
print "bbb"
print nextset2
myset3=get_divisible_set(3)
nextset3=[]
for i in range(len(nextset2)):
(a,b,c,d,e)=nextset2[i]
tmp=[]
mysettmp=set()
tmp.append(a)
tmpset=get_adjoining_set(myset3, tmp)
if len(tmpset)>0:
for j in range(len(tmpset)):
(f,g)=tmpset[j]
mysettmp=set(g)
mysettmp=mysettmp.union(set(f))
mysettmp=mysettmp.union(set(a))
mysettmp=mysettmp.union(set(b))
mysettmp=mysettmp.union(set(c))
mysettmp=mysettmp.union(set(d))
mysettmp=mysettmp.union(set(e))
if len(mysettmp)==8:
nextset3.append((f,a,b,c,d,e))
myset2=get_divisible_set(2)
nextset4=[]
for i in range(len(nextset3)):
(a,b,c,d,e,f)=nextset3[i]
tmp=[]
mysettmp=set()
tmp.append(a)
tmpset=get_adjoining_set(myset2, tmp)
if len(tmpset)>0:
for j in range(len(tmpset)):
(g,h)=tmpset[j]
mysettmp=set(h)
mysettmp=mysettmp.union(set(g))
mysettmp=mysettmp.union(set(a))
mysettmp=mysettmp.union(set(b))
mysettmp=mysettmp.union(set(c))
mysettmp=mysettmp.union(set(d))
mysettmp=mysettmp.union(set(e))
mysettmp=mysettmp.union(set(f))
if len(mysettmp)==9:
nextset4.append((g,a,b,c,d,e,f))
print "final ans"
print nextset4
Output from the python script:
[('160', '603', '035', '357', '572', '728', '289'), ('460', '603', '035', '357', '572', '728', '289'), ('106', '063', '635', '357', '572', '728', '289'), ('406', '063', '635', '357', '572', '728', '289'), ('130', '309', '095', '952', '528', '286', '867'), ('430', '309', '095', '952', '528', '286', '867')]
Or after rearranging the digits according to the rules in problem 43:
4160357289
1460357289
4106357289
1406357289
4130952867
1430952867
These are the six numbers that satisfy all the properties and will add up to the answer.
Aug 13, 2013
Physics World Cup Problems & Solutions (II)
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[PDF]pdf 1 - IYPT Archive
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[PDF]ranking after pf4 - IYPT
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[PDF]The Regulations of the International - IYPT
Jul 30, 2011 - The Regulations of the International. Young Physicists' Tournament. I. International Young Physicists' Tournament. The International Young ... -
[PDF]2 - IYPT Bratislava 2006
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[PDF]Overview for Round: 1
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[PDF]Download - IYPT
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[PDF]Odborná komisia - IYPT
International Organizing Committee. Young Physicists' Tournament. EC meeting. Minutes. November 10th – 11th 2012, Taipei, Taiwan. Present: Alan Allinson ... -
[PDF]Overview for Round: 3
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[PDF]IOC meeting Minutes - IYPT
International Organizing Committee. Young Physicists' Tournament. IOC meeting. Minutes. July 30th 2011, Safavi Hotel, Esfahan, Iran. Agenda. The agenda ... -
[PDF]Round: 3 - IYPT
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[PDF]IYPT 2012
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[PDF]Problems for IYPT 2011
Problems for IYPT 2011. 1. Adhesive tape. Determine the force necessary to remove a piece of adhesive tape from a horizontal surface. Investigate the influence ... -
[PDF]Scoring Guidelines - IYPT
Revised after IOC feedback and approved by EC on 2011-11-03. A report should include: • a presentation of the appropriate concepts, theories and principles of ... -
[PDF]Odborná komisia - IYPT
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[PDF]Tournament Annual IOC meeting, Alpenhotel Goessing ... - IYPT
Jul 17, 2010 - International Organizing Committee. Young Physicists' Tournament. Annual IOC meeting, Alpenhotel Goessing, Austria. Minutes. July 16th ... -
[PDF]Problem submission form IYPT 2013
Apr 30, 2012 - International Organizing Committee. Young Physicists' Tournament. Problem submission form IYPT 2013. Country. Author's name e-mail. -
[PDF]η - IYPT Archive
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[PDF]Round: 3, Room: Room A
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[PDF]Overview for Round: 5
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[PDF]Round: 1, Room: Room D
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[PDF]Overview for Round: 2
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[PDF]f - iypt solutions
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[PDF]Round: 2 - IYPT
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[PDF]Round: 2 - IYPT
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[PDF]Dynamic Bubbles - IYPT
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[PDF]l - IYPT Archive
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[PDF]x - iypt solutions
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