Nearly all of MR-imaging in use today is based on a k-space approach making use of the fact, that a linear spatial encoding field – i.e. a gradient – leads to a linear variation of the Larmor frequency of spins. Localization is then achieved by Fourier transformation of the acquired time domain signal into the frequency domain, which directly corresponds to the spatial domain. Consequently two-...

ACKNOWLEDGEMENTS My thesis advisor Dr. Naci Inci's unlimited tolerance and respectful interest has always been a strong intensive while doing this project. I would like to thank Dr. Canan Baysal who has always believed in my success at Sabanci University. Mehmet Bozkurt's discipline and eruditeness has always enlightened my academic career. Lastly, of course, my family and Güneş Avcı were alway...

Warp and weft spacing and its coefficient of variation affect the physical properties of fabrics such as fabric hand, frictional and mechanical properties. In this paper the weft and warp spacing and its coefficient of variation for plain weave is calculated using Fourier transforms. Different methods have been used in this work including autocorrelation function. First, two dimensional power s...

Warp and weft spacing and its coefficient of variation affect the physical properties of fabrics such as fabric hand, frictional and mechanical properties. In this paper the weft and warp spacing and its coefficient of variation for plain weave is calculated using Fourier transforms. Different methods have been used in this work including autocorrelation function. First, two dimensional power s...

In our last work, we formulate a Fourier transformation on the infinitedimensional space of functionals. Here we first calculate the Fourier transformation of infinite-dimensional Gaussian distribution exp ( −πξ ∞ −∞ α 2(t)dt ) for ξ ∈ C with Re(ξ) > 0, α ∈ L2(R), using our formulated Feynman path integral. Secondly we develop the Poisson summation formula for the space of functionals, and defi...

The purpose is to formulate a Fourier transformation for the space of functionals, as an infinitesimal meaning. We extend R to ( ∗R) under the base of nonstandard methods for the construction. The domain of a functional is the set of all internal functions from a ∗-finite lattice to a ∗-finite lattice with a double meaning. Considering a ∗-finite lattice with a double meaning, we find how to tr...