Representations of Hopf Ore extensions of group algebras and pointed Hopf algebras of rank one

In this paper, we study the representation theory of Hopf-Ore extensions of group algebras and pointed Hopf algebras of rank one over an arbitrary field $k$. Let H=kG(\chi, a,\d) be a Hopf-Ore extension of $kG$ and $H'$ a rank one quotient Hopf algebra of $H$, where $k$ is a field, $G$ is a group, $a$ is a central element of $G$ and $\chi$ is a $k$-valued character for $G$ with $\chi(a)\neq 1$. We first show that the simple weight modules over $H$ and $H'$ are finite dimensional. Then we describe the structures of all simple weight modules over $H$ and $H'$, and classify them. We also consider the decomposition of the tensor product of two simple weight modules over $H'$ into the direct sum of indecomposable modules. Furthermore, we describe the structures of finite dimensional indecomposable weight modules over $H$ and $H'$, and classify them. Finally, when $\chi(a)$ is a primitive $n$-th root of unity for some $n>2$, we determine all finite dimensional indecomposable projective objects in the category of weight modules over $H'$.Comment: arXiv admin note: substantial text overlap with arXiv:1206.394

A Life Cycle Assessment on Various Alternative Liquid Fuel Options in Western Australia

This thesis assesses the life cycle energy, water and carbon footprints of several biofuels production processed, considering (a) biomass from phase farm with trees; (b) biodiesel from waste cooking oil with utilising the by-product (crude glycerol); and ( c) bioslurry from biochar bio-oil and crude glycerol

Multi-dimensional volume rendering for PC- based medical simulation

Ph.DDOCTOR OF PHILOSOPH

Phase-Adjusted Estimation of the COVID-19 Outbreak in South Korea Under Multi-Source Data and Adjustment Measures: A Modelling Study

Based on the reported data from February 16, 2020 to March 9, 2020 in South Korea including confirmed cases, death cases and recovery cases, the control reproduction number was estimated respectively at different control measure phases using Markov chain Monte Carlo method and presented using the resulting posterior mean and 95% credible interval (CrI). At the early phase from February 16 to February 24, we estimate the basic reproduction number R0 of COVID-19 to be 4.79(95% CrI 4.38 - 5.2). The estimated control reproduction number dropped rapidly to Rc ≈ 0.32(95% CrI 0.19 - 0.47) at the second phase from February 25 to March 2 because of the voluntary lockdown measures. At the third phase from March 3 to March 9, we estimate Rc to be 0.27 (95% CrI 0.14 - 0.42). We predict that the final size of the COVID-19 outbreak in South Korea is 9661 (95% CrI 8660 - 11100) and the whole epidemic will be over by late April. It is found that reducing contact rate and enhancing the testing speed will have the impact on the peak value and the peak time

The physical origin of the periodic activity for FRB 20180916B

Fast radio bursts (FRBs) are transient radio signals with millisecond-duration, large dispersion measure (DM) and extremely high brightness temperature. Among them, FRB 20180916B has been found to have a 16-day periodic activity. However, the physical origin of the periodicity is still a mystery. Here, we utilize the comprehensive observational data to diagnose the periodic models. We find that the ultra-long rotation model is the most probable one for the periodic activity. However, this model cannot reproduce the observed rotation measure (RM) variations. We propose a self-consistent model, i.e., a massive binary containing a slowly rotational neutron star and a massive star with large mass loss, which can naturally accommodate the wealth of observational features for FRB 20180916B. In this model, the RM variation is periodic, which can be tested by future observations.Comment: 12 pages, 8 figure