The fundamental group of a closed orientable surface of genus g is the quotient of the free group on the 2g generators a1,...,ag,b1,...,bg by the normal subgroup generated by the following product of g commutators: a1b1a1-1b1-1...agbgag-1bg-1.
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G = C/6 where C is the number in the class and G is the number in each group.
Definition of the Schuler period is: T = 2 pi X sq rt of R/G where R = radius of earth surface or 6372 km G = Gravity acceleration at the earth's surface or 9.81 m/s ^2 T= 5064 s or 84.4 min
1) You can add/subtract functions: f(x) +- g(x) = (f +- g)(x). 2) You can multiply/divide functions: f(x) */ g(x) = (f */ g)(x). 3) You can compose functions: f(x) . g(x) = (f(g(x))) = (f . g)(x). Let f(x) = 3x + 1 and g(x) = x2 Ex 1. (f + g)(x) = x2 + 3x + 1 Ex 2. (f * g)(x) = (3x + 1) * x2 = 3x3 + x2 Ex 3. (f(g(x))) = 3(x2) + 1 (Note that you replace all the x's in the function f(x) with the whole value of g(x).
The actual gravitational force at the surface of the Earth (about 9.81 m/sec/sec) will vary as the distance from the Earth's center varies, and also due to variations in the density of the rock layers under any given location. There are slight variations in the value of g about earth's surface. These variations result from the varying density of the geologic structures below each specific surface location
A Group is a finite or infinite set of elements with a well defined law of composition defined on its members.A Group G must satisfy the following propeties:Closure: If a and b are any two members in G then there is unique element c = ab which is a member of G.Associative Law: If a b abd c are any three elements of G, then (ab)c = a(bc).Identity: There is an element, i, in G such that ai = ia = a for all a in G. i is called the identity for G.Inverse: For every element, a, in G, there is an element in G denoted by a-1 such that aa-1 = a-1a = i.Note that G need not be commutative ie ab need not be ba.