Elementary proofs concerning results about functions on the n-sphere

Subordination Results on Subclasses Concerning Sakaguchi Functions

Elementary Proofs of Some Results on Representations of P-groups

A result of Roquette 3] states that if D is an absolutely irreducible representation of a p-group G over the eld of complex numbers, then D can be realized in K((g) j g 2 G), where is the character of D and K = Q or K = Q(i) according to whether p 6 = 2 or p = 2. Based on Baum and Clausen's 1] algorithm for computing the irreducible representations of supersolvable groups, we give an elementary...

Elementary Proofs on Optimal Stopping

Abstract Elementary proofs of classical theorems on pricing perpetual call and put options in the standard Black-Scholes model are given. The method presented does not rely on stochastic calculus and is also applied to give prices and optimal stopping rules for perpetual call options when the stock is driven by a Lévy process with no positive jumps, and for perpetual put options for stocks driv...

Elementary Proofs of Various Facts about 3-cores

Using elementary means, we derive an explicit formula for a3(n), the number of 3-core partitions of n, in terms of the prime factorization of 3n + 1. Based on this result, we are able to prove several infinite families of arithmetic results involving a3(n), one of which specializes to the recent result of Baruah and Berndt which states that, for all n ≥ 0, a3(4n + 1)= a3(n). 2000 Mathematics su...

Elementary Proofs of Identities for Schur Functions and Plane Partitions

By a plane partition, we mean a finite set, P , of lattice points with positive integer coefficients, {(i, j, k)} ⊆ N, with the property that if (r, s, t) ∈ P and 1 ≤ i ≤ r, 1 ≤ j ≤ s, 1 ≤ k ≤ t, then (i, j, k) must also be in P . A plane partition is symmetric if (i, j, k) ∈ P if and only if (j, i, k) ∈ P . The height of stack (i, j) is the largest value of k for which there exists a point (i,...