Statistical power of epidemiological studies of low dose levels of ionizing radiation and cancer

The purpose of this research is to inspect the statistical power of studies that investigate the effects of low dose ionizing radiation on the incidence of/mortality from cancer. I use a procedure proposed in a similar study to handle a problem regarding the incidence of childhood leukemia from background ionizing radiation. I study this procedure critically and make some adjustments to make its performance better. I also propose some substitute methods to the methods proposed in the aforementioned reference in order to calculate the power. In addition, I propose other methods not used in the study mentioned above. I evaluate the efficiency of my proposed approaches using simulated data. The improved method can be applied to the National Dose Registry of Canada (NDR) to produce the power curves. The outcomes then can be used to propose the most suitable study design. Some of the previous epidemiological studies based on NDR can also be evaluated in terms of power

Hyperreflexivity of the bounded n-cocycle spaces of Banach algebras

The concept of hyperreflexivity has previously been defined for subspaces of $B(X,Y)$, where $X$ and $Y$ are Banach spaces. We extend this concept to the subspaces of $B^n(X,Y)$, the space of bounded $n$-linear maps from $X\times\cdots\times X=X^{(n)}$ into $Y$, for any $n\in \mathbb{N}$. If $A$ is a Banach algebra and $X$ a Banach $A$-bimodule, we obtain sufficient conditions under which \Zc^n(A,X), the space of all bounded $n$-cocycles from $A$ into $X$, is hyperreflexive. To do so, we define two notions related to a Banach algebra: The strong property (\B) and bounded local units (b.l.u). We show that there are sufficiently many Banach algebras which have both properties. We will prove that all C$^*$-algebras and group algebras have the strong property (\B). We also prove that finite CSL algebras and finite nest algebras have this property. We further show that for an arbitrary Banach algebra $A$ and each $n\geq 2$, $M_n(A)$ has the strong property (\B) whenever it is equipped with a Banach algebra norm. In particular, this implies that all Banach algebras are embedded into a Banach algebra with the strong property (\B). With regard to bounded local units, we show that all $C^*$-algebras and many group algebras have b.l.u. We investigate the hereditary properties of both notions to construct more example of Banach algebras with these properties. We apply our approach and show that the bounded $n$-cocycle spaces related to Banach algebras with the strong property (\B) and b.l.u. are hyperreflexive provided that the space of the corresponding $n+1$-coboundaries are closed. This includes nuclear C$^*$-algebras, many group algebras, matrix spaces of certain Banach algebras and finite CSL and nest algebras. We finish the thesis with introducing {\it the hyperreflexivity constant}. We make our results more precise with finding an upper bound for the hyperreflexivity constant of the bounded $n$-cocycle spaces

On the Fourier algebra of certain hypergroups

We consider certain classes of hypergroups and address some problems regarding their Fourier algebras, including zero product preserving maps, local derivations and weak amenability. The key tool in our approach is to show that the Fourier algebra of such hypergroups has the so called property (): This property has already been shown to be very effective in solving problems related to zero product preserving maps and local derivations provided that some other conditions are satisfied. Some examples of groups and hypergroups, the Fourier algebras of which have the property () satisfying all those conditions are given. Our examples are the class of almost abelian groups and double coset hypergroups of Gelfand pairs. We also prove that if H is the double coset hypergroup of a Gelfand pair, then A(H) is weakly amenable. We provide some results on the direct product of commutative (regular) Fourier hypergroups. Mathematics Subject Classification (2010): Primary: 47B48; Secondary: 43A30