The covering number of M24M_{24}

A finite cover $\mathcal{C}$ of a group $G$ is a finite collection of proper subgroups of $G$ such that $G$ is equal to the union of all of the members of $\mathcal{C}$. Such a cover is called {\em minimal} if it has the smallest cardinality among all finite covers of $G$. The covering number of $G$, denoted by $\sigma(G)$, is the number of subgroups in a minimal cover of $G$. In this paper the covering number of the Mathieu group $M_{24}$ is shown to be 3336

Some perpendicular arrays for arbitrarily large t

AbstractWe show that perpendicular arrays exist for arbitrarily large t and with λ = 1. In particular, if d devides (t+1) then there is a PA1(t, t+1, t+(f(t+1)d)). If υ ≡ 1 or 2 (mod 3) then there is a PAλ(3, 4, υ) for any λ. If 3 divides λ then there is a PAλ(3, 4, υ) for any v. If n⩾2 there is a PA1(4, 5, 2n+1). Using recursive constructions we exhibit several infinite families of perpendicular arrays with t⩾3 and relatively small λ. We finally discuss methods of constructing perpendicular arrays based on automorphism groups. These methods allow the construction of PA's with (k−t)>1

A Public Key Cryptosystem Based on Non-abelian Finite Groups

Abstract We present a new approach to designing public-key cryptosystems, based on covers and logarithmic signatures of nonabelian finite groups. Initially, we describe a generic version of the system for a large class of groups. We then propose a class of 2-groups and argue heuristically about the system's security. The system is scalable, and the proposed underlying group, represented as a matrix group, affords significant space and time efficiency

An Entzia-dominated marsh-type agglutinated foraminiferal assemblage from a salt marsh in Tubli Bay, Bahrain

A salt-marsh assemblage of agglutinated foraminifera was recovered from a salt marsh on the east side of Tubli Bay in eastern Bahrain. This locality is one of the last remaining patches of salt marsh on the east coast of Tubli Bay. The salt marsh is covered by a single marsh plant species, Arthrocnemum macrostachyum. Samples were collected from beneath the Arthrocnemum canopy in two transects beginning at the maximum landward extent of halophytic plants in the high marsh and extending to a tidal channel at the seaward side of the low marsh. A distinct elevation-related zonation in foraminifera is observed from the high marsh to the low marsh. The trochamminids Entzia macrescens and Trochammina inflata are characteristic of the high marsh, whereas Ammonia, Elphidium, Peneroplis and smaller miliolids become common in the middle part of the marsh transect. The tidal channel at the lower limit of the marsh contains an assemblage dominated by Ammonia, Elphidium, adult specimens of Pen-eroplis, and smaller miliolids, with Clavulina and Agglutinella as the only agglutinated taxa. Living specimens of Entzia and Trochammina were observed during the winter 2019–2020 sampling season, whereas samples collect-ed in Autumn 2019 contained only dead specimens. One new species, ?Sigmoilina canisdementis sp. nov., is de-scribed herein. This is the first report of a live Entzia-dominated salt marshassemblage in the Arabian Gulf region

Computing a Lattice Basis Revisited

International audienc

‘Albania: €1’ or the story of ‘big policies, small outcomes’: how Albania constructs and engages its diaspora

Since the fall of the communist regime in the early 1990s, Albania has experienced one of the most significant emigrations in the world as a share of its population. By 2010 almost half of its resident population was estimated to be living abroad – primarily in neighbouring Greece and Italy, but also in the UK and North America. This chapter discusses the emergence and establishment of the Albanian diaspora, its temporal and geographical diversity, and not least its involvement with Albania itself. Albania’s policymaking and key institutions are considered, with a focus on matters of citizenship; voting rights; the debate on migration and development; and not least the complex ways in which kin-state minority policies – related to ethnic Albanians living in Kosovo, Montenegro, southern Serbia, Macedonia and Greece – are interwoven with Albania’s emigration policies

Simple method for enhancing the performance of lossy plus lossless image compression schemes

Lossy plus lossless techniques for image compression split an image into a low-bit-rate lossy representation and a residual that represents the difference between this low-rate lossy image and the original. Conventional schemes encode the lossy image and its lossless residual in an independent manner. We show that making use of the lossy image to encode the residual can lead to significant savings in bit rate. Further, the complexity increase to attain these savings is minimal. The savings are achieved by capturing the inherent structure of the image in the form of a noncausal prediction model that we call a prediction tree. This prediction model is then used to transmit the lossless residual. Simulation results show that a reduction of 0.5 to 1.0 bit/pixel can be achieved in bit rates compared to the conventional approach of independently encoding the residual