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Yayın A new theory of complex rays(Oxford Univ Press, 2004-12) Hasanoğlu, ElmanA new approach to the theory of complex rays is presented. It is shown that the three-dimensional Minkowski space, the variant of the well known four-dimensional space-time Minkowski space of the special theory of relativity, is more appropriate for describing both real and complex rays than the usual Euclidean space. It turns out that in this space complex rays, as real ones, may have quite definite directions and magnitudes. This allows us to understand the geometrical meaning of the complex magnitudes such as complex distances and complex angles, intensively discussed over the last several decades. From this point of view a new interpretation of the Gaussian beams and reflection laws is presented.Yayın The statistics of energy states of a Hookean model for proteins(TÜBİTAK, 2000) Erzan, Ayşe; Tüzel, ErkanA generic model of a random polypeptide chain, with discrete torsional degrees of freedom and Hookean springs connecting pairs of hydrophobia residues, reproduces the energy probability distribution of real proteins over a very large range of energies. We show that this system with harmonic interactions, under dissipative dynamics driven by random noise, leads to a distribution of energy states obeying a modified one-dimensional Ornstein-Uhlenbeck process with reflecting boundary conditions, and giving rise to distributions of the Wigner or inverse Gaussian form. A continuum approximation leads to a path integral formulation of the problem.












