<p>In this thesis a new method for the option pricing will be introduced with the help of the Mellin transforms. Firstly, the Mellin transform techniques for options on a single underlying stock is presented.After that basket options will be considered. Finally, an improvement of existing numerical results applied to Mellin transforms for 1-basket and 2-basket American Put Option will be discussed concisely. Our approach does not require either variable transformations or solving diffusion equations.</p> / thesis

In this thesis a new method for the option pricing will be introduced with the help of the Mellin transforms. Firstly, the Mellin transform techniques for options on a single underlying stock is presented.After that basket options will be considered. Finally, an improvement of existing numerical results applied to Mellin transforms for 1-basket and 2-basket American Put Option will be discussed concisely. Our approach does not require either variable transformations or solving diffusion equations. / thesis

Student Number : 9708525G - PhD thesis - School of Mathematics - Faculty of Science / Sequences of numbers have important applications in the field of Computer Science. As a result they have become increasingly regarded in Mathematics, since analysis can be instrumental in investigating algorithms. Three concepts are discussed in this thesis, all of which are concerned with ‘words’ or ‘sequences’ of natural numbers where repeated letters are allowed: • The number of distinct values in a sequence with geometric distri- bution In Part I, a sample which is geometrically distributed is considered, with the objective of counting how many different letters occur at least once in the sample. It is concluded that the number of distinct letters grows like log n as n → ∞. This is then generalised to the question of how many letters occur at least b times in a word. • The position of the maximum (and/or minimum) in a sequence with geometric distribution Part II involves many variations on the central theme which addresses the question: “What is the probability that the maximum in a geometrically distributed sample occurs in the first d letters of a word of length n?” (assuming d ≤ n). Initially, d is considered fixed, but in later chapters d is allowed to grow with n. It is found that for 1 ≤ d = o(n), the results are the same as when d is fixed. • The average depth of a key in a binary search tree formed from a sequence with repeated entries Lastly, in Part III, random sequences are examined where repeated letters are allowed. First, the average left-going depth of the first one is found, and later the right-going path to the first r if the alphabet is {1, . . . , r} is examined. The final chapter uses a merge (or ‘shuffle’) operator to obtain the average depth of an arbitrary node, which can be expressed in terms of the left-going and right-going depths.

This thesis explores one possible method of preventing helicopter crashes caused by brownout using the noise generated by the helicopter rotor as an altimeter. The hypothesis under consideration is that the helicopter's height, velocity, and obstacle locations with respect to the helicopter, can be determined by comparing incident and reflected rotor noise signals, provided adequate bandwidth and signal to noise ratio. Heights can be determined by measuring the cepstrum of the reflected helicopter noise. The velocity can be determined by measuring small amounts of Doppler distortion using the Mellin-Scale Transform. Height and velocity detection algorithms are developed, optimized for this application, and tested using a microphone array. The algorithms and array are tested using a hemianechoic chamber and outside in Georgia Tech's Burger Bowl. Height and obstacle detection are determined to be feasible with the existing array. Velocity detection and surface mapping are not successfully accomplished.

<p dir="ltr">We present first order asymptotic estimates for the divisor function problem, the set of lists (restricted number of divisors) problem, and a generalization of the overpartition problem. In particular, we prove Kotesovec's conjecture for A294363 from the OEIS and also extend his conjecture to a full asymptotic treatment by providing an estimate in terms of elementary functions for the EGF coefficients directly rather than the log of the coefficients. We also provide asymptotic estimates for generalizations of the set of lists and overpartition problem, while making comparisons to any existing Kotesovec conjectures. We perform the asymptotic analysis via Mellin transforms, residue analysis, and the saddle point method. These families of generating functions have potential application to families of randomly generated partitions in which ordered subsets of a partition that exceed a certain fixed size may be one of two different objects and to overpartitions with potential heading labels.</p>