Development of Diplocarpon rosae in leaves of roses differing in their susceptibility

Imperial Users onl

An uncountable union of line segments with null two-dimensional measure

In this paper we construct an uncountable union of line segments $T$ which has full intersection with the sets $(\{ 0\} \times [0, 1]) \cup (\{ 1\} \times [0, 1])\subset\mathbb{R}^2$ but has null two-dimensional measure. Further results are proved on the decay rate of $\mu (T)$ if the line segments comprising $T$ are replaced with increasingly fine approximations by parallelograms

Globalization in the twenty-first century in quest of a new paradigm

The historical significance of the tragedy on September 11 in 2001 may well be compared to the tragedy of June 28 in 1914 - the assassination in Sarajevo. Both tragedies closed two symbolic chapters of world history, i.e. that of the nineteenth century liberalism [1815-1914) and that of twentieth century nee-liberalism (1991- 200 l). The view that September l l , 200 l opened a new chapter in global histo­ry has found full confirmation in the poll of 275 opinion leaders conducted by the International Herald Tribune and the Pew Research Centre for People and Press. The phenomenon of global terrorism should be interpreted as a consequence of two failings in the last decade of the twentieth century. The first failing was the absence of a grand strategic vision for ordering the global stage after the col­lapse of the Soviet Empire. The second failing of the last decade of the twentieth century was the almost total disappearance of concern for the tragic plight of societies around the globe that led to polarization between rich and poor

Absorption phenomena in quantum walks

The quantum walk is a unitary analogue to the discrete random walk, and its properties have been increasingly studied since the turn of the millennium. In comparison with the classical random walk, the quantum walk exhibits linear spreading and initial condition dependent asymmetries. As noted early on in the conjecture and subsequent calculation of absorption probabilities in the one dimensional Hadamard walk, the interaction of the quantum walk with an absorbing boundary is fundamentally divergent from classical case. Here, we will survey absorption probabilities for a more general collection of one dimensional quantum walks and extend the method to consider d-dimensional walks in the presence of d-1 dimensional absorbing walls. However, these results are concerned only with local behavior at the boundary in the form of absorption probabilities. The main results of this thesis are concerned with the global behavior of finite quantum walks, which can be described by linear spreading in the short term, modal phenomena in the mid term, and stable distributions in the exceedingly long term. These theorems will be rigorously proved in the one-dimensional case and extrapolated to higher dimensional quantum walks. To this end we introduce QWSim, a new and robust computational engine for displaying finite two dimensional quantum walks