On Atkin-Swinnerton-Dyer congruence relations

In this paper we exhibit a noncongruence subgroup \G whose space of weight 3 cusp forms S_3(\G) admits a basis satisfying the Atkin-Swinnerton-Dyer congruence relations with two weight 3 newforms for certain congruence subgroups. This gives a modularity interpretation of the motive attached to S_3(\G) by A. Scholl and also verifies the Atkin-Swinnerton-Dyer congruence conjecture for this space.Comment: 25 page

Java/XML-based Trading Information Processing System for produce wholesale market

The purpose of this project is to investigate the use of the emerging XML technologies to improve online Business to Business (B2B) supply chain processes

Relocation and high-rise living : a study of Singapore's public housing

Public housing in Singapore is one of the most significant development programmes in the state. It has been centrally planned and implemented by the Government not only to tackle housing problems and rebuild the decaying inner city areas, but also to restructure Singapore society in terms of the visions of the power elite.This study attempts to examine the social and political implications of relocation and public housing in Singapore, and to analyse the difficulties faced by and the impact of relocation on individuals and families from the various constrasting groups of relocatees, with an emphasis on problems of economic hardship, adaptation to high-rise living, and neighbourliness in the public housing estates.To achieve this task, three types of material have been used, viz. official data, empirical material from previous studies, and empirical data and information collected during fieldwork. The fieldwork comprises a sample survey of 1,200 households and an in-depth study of 27 relocated families.The thesis consists of three parts. The first part reviews the literature on relocation and public housing and the conceptual framework employed in their study. The second part examines the policies underlying and the salient social and political aspects of relocation and public housing in Singapore. The final part analyses the data and information obtained from the sample survey and the in-depth study.The findings of the present study show that while the Singapore Government has made some impressive quantitative achievements of its public housing programme, some of its original objectives may never be fully achieved. Two of the eight hypotheses deduced from the assumptions and observations of the previous studies are refuted by data obtained from the present study. Five of them are however supported, and one is inconclusive. Some sensitive issues relating to public housing in Singapore, which have significant social and political effects and yet are usually avoided by most researchers, are also analysed and discussed in the light of their policy implications

Hierarchical Macroporous Polymers: Synthesis and Characterisation

This thesis describes the production of two types of hierarchical macroporous polymers using the emulsion templating technique. The first are those with a hierarchy of macroporous, defined as the efficient packing of pores with multi-modal pore size distributions. The second are macroporous polymers containing a hierarchical particulate network, defined by an interconnected particle network within the polymer matrix. In the first section of the thesis, macroporous hierarchy was achieved using 3 different methods. In the first method, the properties of surfactant stabilised high internal phase emulsion (HIPE) were optimised by varying selected emulsification parameters such as the surfactant concentration and stirring rate. The Finite Element Method (FEM) was subsequently used to qualitatively compare and validate the effect of pore hierarchy on the Young’s modulus of macroporous polymers. It was believed that the hierarchical arrangement of macropores facilitated the load transfer during compression, which improved its mechanical properties. The second method involved the use of a mixed surfactant and particle emulsifier system to prepare w/o HIPEs. The mixture of surfactants and particles in the emulsion produced synergistic effects which resulted in a hierarchical macroporous arrangement after polymerisation. The hierarchical porous materials prepared using this method showed high gas permeabilities while maintaining high crush strengths and Young’s moduli compared to ‘conventional’ poly(merised)HIPEs. The improvement in mechanical strength despite the high interconnectivity was attributed to the efficient packing of macropores in a hierarchical configuration. The third approach was to mechanically-froth viscous air in w/o emulsion templates. A bio-based monomer, acrylated epoxidised soyabean oil (AESO) was chosen as a component of the continuous phase of the emulsion for its high viscosity and ability to trap air bubbles during mechanical frothing. Medium Internal Phase Emulsions (MIPEs) containing varying concentrations of AESO were mechanically frothed to incorporate air bubbles, prior to polymerisation. This was found to generate a multi-modal distribution of droplets and air bubbles which polymerised into hierarchical foams with high porosities of up to 81%. In the second section of the thesis, a hierarchical particulate network within the polymer matrix of a porous material was produced using Pickering HIPEs stabilised by varying the concentrations of thermally reduced graphene oxide (rGO) flakes. Macroporous nanocomposites containing 0.006 vol.% of rGO had a conductivity of 1.2 10-5 Sm-1, demonstrating the presence of an interconnected, conducting rGO network within the polymer matrix. The rGO-network created an additional level of hierarchy in these macroporous materials which also improved the overall mechanical properties (viscoelastic properties, Young’s modulus and crush strength).Open Acces

On Atkin and Swinnerton-Dyer Congruence Relations (2)

In this paper we give an example of a noncongruence subgroup whose three-dimensional space of cusp forms of weight 3 has the following properties. For each of the four residue classes of odd primes modulo 8 there is a basis whose Fourier coefficients at infinity satisfy a three-term Atkin and Swinnerton-Dyer congruence relation, which is the $p$-adic analogue of the three-term recursion satisfied by the coefficients of classical Hecke eigen forms. We also show that there is an automorphic $L$-function over $\mathbb Q$ whose local factors agree with those of the $l$-adic Scholl representations attached to the space of noncongruence cusp forms.Comment: Last version, to appear on Math Annale

Symbolic dynamical model of average queue size of random early detection algorithm

In this paper, a symbolic dynamical model of the average queue size of the random early detection (RED) algorithm is proposed. The conditions on both the system parameters and the initial conditions that the average queue size of the RED algorithm would converge to a fixed point are derived. These results are useful for network engineers to design both the system parameters and the initial conditions so that internet networks would achieve a good performance

Invariant set of weight of perceptron trained by perceptron training algorithm

In this paper, an invariant set of the weight of the perceptron trained by the perceptron training algorithm is defined and characterized. The dynamic range of the steady state values of the weight of the perceptron can be evaluated via finding the dynamic range of the weight of the perceptron inside the largest invariant set. Also, the necessary and sufficient condition for the forward dynamics of the weight of the perceptron to be injective as well as the condition for the invariant set of the weight of the perceptron to be attractive is derived

Fourier coefficients of noncongruence cuspforms

Given a finite index subgroup of SL2(ℤ) with modular curve defined over ℚ, under the assumption that the space of weight k (≥2) cuspforms is one-dimensional, we show that a form in this space with Fourier coefficients in ℚ has bounded denominators if and only if it is a congruence modular form. © 2012 London Mathematical Society