In [Leh], Emma Lehmer constructed a parametric family of units in real quintic fields of prime conductor p = t + 5t + 15t + 25t+ 25, as translates of Gaussian periods. Later, Schoof and Washington [SW] showed that these units were fundamental units. In this note, we observe that Lehmer’s family comes from the covering of modular curves X1(25) −→ X0(25). This gives a conceptual explanation for t...

A straightforward approach to provide protection against packet losses due to network outages with a longest duration of T time units is to duplicate the original packets and send each copy separated in time by at least T time units. This approach is commonly referred to as "time-shifted redundancy", "temporal redundancy", or simply "delayed duplication". This document defines an attribute to i...

This paper argues that immunological memory is in the same class of associative memories as Kanerva’s Sparse Distributed Memory, Albus’s Cerebellar Model Arithmetic Computer, and Marr’s Theory of the Cerebellar Cortex. This class of memories derives its associative and robust nature from a sparse sampling of a huge input space by recognition units (B and T cells in the immune system) and a dist...

We propose a transformed estimator for the slope coefficients of panel models with interactive effects. The estimation method does not require prior knowledge dimension factor structure. It is consistent and asymptotically normally distributed under fairly general conditions when N fixed T→∞ or T N→∞, both are large NT→a≠0<∞. Moreover, because transformation equivalent to aggregating cross-sect...

Abstract The aim of the present study is to explore strategies in enumerating units three dimensional (3D) arrays. We analyse enumeration students grade 3 (ages 8 9) situations cubical and spherical representations 3D By exploring students’ these two situations, we find that difficulties arrays can be traced units-locating, with consequence applying double triple counting. Our results also indi...

The objective of this work in progress is to endogenise the firm sector in the classic Diamond Dybvig setup. This should better able us to understand how shocks are transmitted within sectors. 1 The basic setup and the players • Consider an economy with three periods, t = 0, 1, 2. • There exists a single divisible consumption good in each period. • There are three types of agents: depositors, f...

We consider a k-out-of-n system with repair under T -policy. Life time of each component is exponentially distributed with parameter λ. Server is called to the system after the elapse of T time units since his departure after completion of repair of all failed units in the previous cycle or until accumulation of n−k failed units, whichever occurs first. Service time is assumed to be exponential...

An auditory-perception inspired singing voice separation algorithm for monaural music recordings is proposed in this paper. Under the framework of computational auditory scene analysis (CASA), the music recordings are first transformed into auditory spectrograms. After extracting the spectral-temporal modulation contents of the timefrequency (T-F) units through a two-stage auditory model, we de...