Dihedral Group, 4-Torsion on an Elliptic Curve, and a Peculiar Eigenform Modulo 4

We work out a non-trivial example of lifting a so-called weak eigenform to a true, characteristic 0 eigenform. The weak eigenform is closely related to Ramanujan's tau function whereas the characteristic 0 eigenform is attached to an elliptic curve defined over ${\mathbb Q}$. We produce the lift by showing that the coefficients of the initial, weak eigenform (almost all) occur as traces of Frobenii in the Galois representation on the 4-torsion of the elliptic curve. The example is remarkable as the initial form is known not to be liftable to any characteristic 0 eigenform of level 1. We use this example as illustrating certain questions that have arisen lately in the theory of modular forms modulo prime powers. We give a brief survey of those questions

Filtrations of dc-weak eigenforms

The notions of strong, weak and dc-weak eigenforms mod $p^n$ was introduced and studied by Chen, Kiming and Wiese. In this work, we prove that there can be no uniform weight bound (that is, depending only on $p$, $n$) on dc-weak eigenforms mod $p^n$ of fixed level when $n \geq 2$. This is in contrast with the result of Kiming, Rustom and Wiese which establishes a uniform weight bound on strong eigenforms mod $p^n$. As a step towards studying weights bounds for weak eigenforms mod $p^n$, we provide a criterion which allows us to detect whether a given dc-weak eigenform mod $p^n$ is weak.Comment: 26 pages. This is a revised version with several corrections. The statement of the main result is now more precis

Yes, we need a central bank

The financial system of a country comprises entities engaged in transactions involving financial instruments in money, capital, and foreign exchange markets. This sector has strong linkages with other sectors of the economy like external, fiscal and real sectors. The apex financial institution in every country is its Central Bank and the State Bank of Pakistan functions as our Central Bank. Section 9A. 1. of the State Bank of Pakistan Act 1956 shoulders the function of securing the soundness of the financial system explicitly upon the Central Board of Directors of the Bank. Traditionally, it has been considered ideal to place banking supervision under the umbrella of Central Bank because this function is key to the conduct of monetary policy and financial stability oversight. Financial sector reforms and restructuring process started in the early 1990s. Objectives of reforms were to create a level playing field for financial institutions and markets for instilling competition, strengthening their governance and supervision, and adopting a market-based indirect system of monetary, exchange and credit management for better allocation of financial resources. Reforms covered seven important areas: financial liberalisation, institutional strengthening, domestic debt management, monetary management, banking law, foreign exchange, and capital market.Central bank

Optimizing Service Differentiation Scheme with Sized-based Queue Management in DiffServ Networks

In this paper we introduced Modified Sized-based Queue Management as a dropping scheme that aims to fairly prioritize and allocate more service to VoIP traffic over bulk data like FTP as the former one usually has small packet size with less impact to the network congestion. In the same time, we want to guarantee that this prioritization is fair enough for both traffic types. On the other hand we study the total link delay over the congestive link with the attempt to alleviate this congestion as much as possible at the by function of early congestion notification. Our M-SQM scheme has been evaluated with NS2 experiments to measure the packets received from both and total link-delay for different traffic. The performance evaluation results of M-SQM have been validated and graphically compared with the performance of other three legacy AQMs (RED, RIO, and PI). It is depicted that our M-SQM outperformed these AQMs in providing QoS level of service differentiation.Comment: 10 pages, 9 figures, 1 table, Submitted to Journal of Telecommunication

Scalability and robustness of a market-based network resource allocation system

In this paper, we consider issues related to scalability and robustness in designing a market-based multi-agent system that allocates bandwidth in a communications network. Specifically, an empirical evaluation is carried out to assess the system performance under a variety of design configurations in order to provide an insight into network deployment issues. This extends our previous work in which we developed an application that makes use of market-based software agents that compete in decentralised marketplaces to buy and sell bandwidth resources. Our new results show that given a light to moderate network traffic load, partitioning the network into a few regions, each with a separate market server, gives a higher call success rate than by using a single market. Moreover, a trade-off in the number of regions was also noted between the average call success rate and the number of messages received per market server. Finally, given the possibility of market failures, we observe that the average call success rates increase with an increasing number of markets until a maximum is reached

On acoustic cavitation of slightly subcritical bubbles

The classical Blake threshold indicates the onset of quasistatic evolution leading to cavitation for gas bubbles in liquids. When the mean pressure in the liquid is reduced to a value below the vapor pressure, the Blake analysis identifies a critical radius which separates quasistatically stable bubbles from those which would cavitate. In this work, we analyze the cavitation threshold for radially symmetric bubbles whose radii are slightly less than the Blake critical radius, in the presence of time-periodic acoustic pressure fields. A distinguished limit equation is derived that predicts the threshold for cavitation for a wide range of liquid viscosities and forcing frequencies. This equation also yields frequency-amplitude response curves. Moreover, for fixed liquid viscosity, our study identifies the frequency that yields the minimal forcing amplitude sufficient to initiate cavitation. Numerical simulations of the full Rayleigh-Plesset equation confirm the accuracy of these predictions. Finally, the implications of these findings for acoustic pressure fields that consist of two frequencies will be discussed.Comment: 14 pages, Presented at APS/DFD conference in Philadelphia 199