Sharif Digital Repository

The application of biocatalysts in organic reactions refers to the use of enzymes, purified or crude, to increase the reaction rate. The usage of biocatalysts in organic reactions have many advantages, including biocompatibility, ease of separation, high yield, reusability without losing activity, high selectivity, and the use of water as the solvent. Furthermore, the carbon–carbon bond formation is one of the most important reactions in the synthesis of organic compounds, drugs, and biomolecules. Using enzymes in organic reactions can provide insightful information about the enzymes catalytic activities and paves the way for systematic investigation of their mechanisms. The enzymes... 

After discovery of exotic structures by John Milnor, mathematicains understood that the classification problem of differential structures up to diffeomorphims is fundamentaly different from classification up to homeomorphism and new invarients are required to study differential topology. One the most important breakthroughs in this area was Donaldson’s idea which obtains a differential topological invariant for 4-manifolds with gauge theoritic ideas known as Yang-Mills (which are non-Abelian generalizations of Maxwell’s theory). A decade after Donaldson’s revolutionary idea Edward Witten and Natan Seiberg presented a new gauge theory known as Sieberg-Witten theory. Later mathematicians... 

In this thesis, we studied the oscillation of neutrino flavors and the measurement of mixing parameters through the detection of cosmic neutrinos at neutrino telescopes. Most of the astrophysical explosions predict the emission of neutrino flux and kilometer-scale detectors are under construction for the observation of these neutrinos. Detection of astrophysical neutrinos opens a new window to understand the neutrino properties and also the properties of astrophysical sources.In this thesis first we review the phenomenology of neutrino flavor oscillation and characteristics of neutrino mass matrix. By introducing a new class of invariants (under general transformation of lepton fields bases)... 

Excitability is one of the most important characteristics of a neuron. In 1948, Hodgkin identified three different types of excitability of neurons. Excitability an all of its types can be observed in Hodgkin-Huxley model of neuronal dynamics (H-H model) as a four-dimensional system of differential equations and in at least two dimensional reductions of H-H type models. By applying the theory of dynamical systems (e.g. bifurcation theory), one can give a mathematical definition of excitability.Excitability of the neuron is equivalent to that the neuronal model is near a bifurcation through which the state of the system approaches to a stable limit cycle. In this thesis, a two-dimensional... 

Neutrino flavor oscillations are clear evidence of massive neutrinos. It has been for more than a decade that neutrino physics became one of active topics in the field of particle physics and various experiments started studying the flavor oscillation of neutrinos. Unfortunately, experiments studying the flavor oscillations are only sensitive to the mass square difference, and they are incapable of providing more information about the absolute mass scale of neutrinos. Additionally, sterile neutrinos having non-standard interactions are under vast investigations and studies. Determination of neutrino masses and their effective number is among the most challenging problems by which...