 # Mathematics

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Entries on Mathematics Acc 101 ( Basic Accounting i)

ASSIGNMENT

0.0 (0 reviews) Glow Like Moon With the Lady With Focus

0.0 (0 reviews)  Representation Theory of the Symmetric Group Sn

Casting a look on the treatise, starting with group and it was defined as a nonempty set G closed under the binary operation ∗ such that the some axioms are satisfied. Types of group, the symmetric group Sn, transposition, cycle type of G, definition of representation theory of a group G which is a homomorphism ρ : G → GL(V) for some vector space V. i.e for all g,h ∈ G we have GL(V) ρ(g ∗h) = ρ(g)∗ρ(h), historical remark of representation theory and some examples were also discussed in this chapter. In chapter two, Matrix representation was discussed as a map such that ρ(gh) = ρ(g) ρ(h). ρ : G→GLn(C) Irreducible representations were also discussed with their definitions. Theequivalency of any two representations (ρ,V ) and (σ,U) of the same group G was also defined in this chapter. Chapter three of this project deals with conjugacy classes in the symmetric group Sn and it was defined as two elements g and g∈ G are called conjugate if there exists h ∈ G such that g= hgh−1, also the conjugacy class of g ∈ G was said to be {hgh−1|h ∈ G}, where G is the union of different conjugacy classes. Similarly in this chapter , we said that an inner product < u,v > is ρ-invariant if for all h ∈ G we have < u,v >=< ρ(h)u,ρ(h)v > for all u,v ∈ V. Also in this chapter, the definition of character of a representation, central function, group algebra of G, faithful representation, direct product of representations, canonical inner product were also provided. Some theorems, lemma and propositions were stated and proved.

5.0 (1 reviews)  Substrate Effect on Crystallinity Development in Thin Film Nanocrystalline Silion

Thin film nanocrystalline silicon is an attractive material for thin film photovoltaic application. It is known to suffer less degradation than amorphous silicon.

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