A Hopf Algebra from Preprojective Modules

Let $Q$ be a finite type quiver i.e. ADE Dynkin quiver. Denote by $\Lambda$ its preprojective algebra. It is known that there are finitely many indecomposable $\Lambda$-modules if and only if $Q$ is of type $A_1,A_2,A_3,A_4$. In this paper, extending Lusztig's construction of $U\frak{n}_+$, we study an algebra generated by these indecomposable submodules. It turns out that it forms the universal enveloping algebra of some nilpotent Lie algebra inside the function algebra on Lusztig's nilpotent scheme. The defining relations of the corresponding nilpotent Lie algebra for type $A_1, A_2,A_3,A_4$ are given here.Comment: 11 pages, 2 figure

Design and development of an automated metered dose inhaler (MDI) for asthmatic patient

To date, infant with illness associated with the pulmonary airway is treated by a doctor using a spacer device with metered dose inhaler (MDI) to allow the infant to breathe in the medication known as salbutamol. Current asthma spacer does not provide systematic way of monitoring and displaying the percentage value of the propellant. Furthermore, user non-compliance is found to contribute towards longer recovery rate. Therefore, this product is designed and developed capable of detecting the propellant level inhaled by the infant by using a MQ-6 gas sensor and monitoring its percentage value. The display of available puffs of MDI canister and the battery indicator for the system are also included in the device. The automated actuation MDI was required a push button to press the MDI canister where this project utilised Arduino Nano as the microcontroller to control the system operation and all the reading values will be displayed on the OLED. RGB LED is also used to visualise the propellant level. The obtained results of the detection of propellant in voltage from the MQ-6 gas sensors were analysed in MATLAB to make comparison through the obtained results. Without propellant, voltage recorded is 0.640±0.024V whereas high concentration of propellant displayed voltage of 1.126±0.020V. The mean standard error rate of propellant detection is 5.584%. The first design of the actuation device and interface monitoring display of automated MDI were recorded the highest percentage which is 75% and 80%. The concentration of propellant depends on the ambient temperature due to the MQ-6 gas sensor required minimum working temperature between 20oC to 22oC. The mean weight of the MDI canister for each puff is 6.257mg and the standard deviation is 3.629mg. Due to experiment conducted, the speed and pressure of pressing MDI canister causes variability in the released of salbutamol and propellant. Observation proved that ambient temperature and propellant released amount also influenced the final reading from the automated actuation MDI

The Very Bright and Nearby GRB 130427A: The Extra Hard Spectral Component and Implications for Very High-energy Gamma-ray Observations of Gamma-ray Bursts

The extended high-energy gamma-ray (>100 MeV) emission occurring after the prompt gamma-ray bursts (GRBs) is usually characterized by a single power-law spectrum, which has been explained as the afterglow synchrotron radiation. We report on the Fermi Large Area Telescope (LAT) observations of the >100 MeV emission from the very bright and nearby GRB 130427A, up to ~100 GeV. By performing time-resolved spectral fits of GRB 130427A, we found a strong evidence of an extra hard spectral component above a few GeV that exists in the extended high-energy emission of this GRB. This extra spectral component may represent the first clear evidence of the long sought-after afterglow inverse Compton emission. Prospects for observations at the very high-energy gamma-rays, i.e., above 100 GeV, are described.Comment: 6 pages, 2 figures, presented at the 4th High Energy Phenomena in Relativistic Outflows (HEPRO IV) meeting held in Heidelberg, July 23-26, 2013; to be published in IJMPC

Families and states: citizenship and demography in the Greco-Roman world

This paper investigates the interrelationship between states and families. At different levels of organization, both play a large role in shaping the context in which individuals live their lives. Yet when it comes to understanding key demographic events in the ancient Mediterranean world – birth, marriage, migration, family structures, and death – they are hardly brought together. In this paper, I argue that Greek and Roman demographic patterns were tightly connected with their own specific political-institutional frameworks that developed over the course of (city-)state formation processes. This interaction was shaped in particular by the emergence of diverging notions of citizenship in the Greek and the Roman world, which went hand in hand with the installment of disparate incentives and disincentives to certain demographic behaviors. Differing citizenship criteria, in other words, invoked different demographic behaviors. A ‘political demography’ perspective, therefore, helps us understand how and why Greek and Roman individuals selected their marriage candidates on different criteria, and sheds light on divergences in their respective emphases on extended family ties.