Linear spaces with many small lines

AbstractIn this paper some of the work in linear spaces in which most of the lines have few points is surveyed. This includes existence results, blocking sets and embeddings. Also, it is shown that any linear space of order v can be embedded in a linear space of order about 13v in which there are no lines of size 2

2-perfect m-cycle systems

AbstractThe spectrum for 2-perfect m-cycle systems of Kn has been considered by several authors in the case when m⩽7. In this paper we essentially solve the problem for 2-perfect m-cycle systems of Kn in the case where m is prime and 2m+1 is a prime power. In particular we settle the problem for m = 11 and 13 except for two or one possible exceptions respectively. The problem for m = 9 is also considered

An n to 2n embedding of incomplete idempotent latin squares for small values of n

AbstractIn 1983, necessary and sufficient conditions were obtained for an incomplete idempotent latin square of order n to be embedded in an idempotent latin square of order 2n, providing n>16. In this paper we consider the case where n⩽16

The spectrum for 2-perfect 6-cycle systems

AbstractRecently, the spectrum problem for 2-perfectm-cycle systems has been studied by several authors. In this paper we find the spectrum for 2-perfect 6-cycle systems with two possible exceptions. The connection between these systems and quasigroups satisfying some 2 variable identities is discussed

Existence of perfect Mendelsohn designs with k=5 and λ>1

AbstractLet υ, k, and λ be positive integers. A (υ, k, λ)-Mendelsohn design (briefly (υ, k, λ)-MD) is a pair (X, B) where X is a υ-set (of points) and B is a collection of cyclically ordered k-subsets of X (called blocks) such that every ordered pair of points of X are consecutive in exactly λ blocks of B. A set of k distinct elements {a1, a2,…, ak} is said to be cyclically ordered by a1<a2<⋯<ak<a1 and the pair ai, ai+t is said to be t-apart in cyclic k-tuple (a1, a2,…, ak) where i+t is taken modulo k. It for all t=1,2,…, k-1, every ordered pair of points of X is t-apart in exactly λ blocks of B, then the (υ, k, λ)-MD is called a perfect design and is denoted briefly by (υ, k, λ)-PMD. In this paper, we shall be concerned mainly with the case where k=5 and λ>1. It will be shown that the necessary condition for the existence of a (υ, 5, λ)-PMD, namely, λv(υ-1)≡0 (mod 5), is also sufficient for λ>1 with the possible exception of pairs (υ, λ) where λ=5 and υ=18 and 28

A multi-instrument approach to determining the source‐region extent of EEP-driving EMIC Waves

Recent years have seen debate regarding the ability of electromagnetic ion cyclotron (EMIC) waves to drive EEP (energetic electron precipitation) into the Earth's atmosphere. Questions still remain regarding the energies and rates at which these waves are able to interact with electrons. Many studies have attempted to characterize these interactions using simulations; however, these are limited by a lack of precise information regarding the spatial scale size of EMIC activity regions. In this study we examine a fortuitous simultaneous observation of EMIC wave activity by the RBSP‐B and Arase satellites in conjunction with ground‐based observations of EEP by a subionospheric VLF network. We describe a simple method for determining the longitudinal extent of the EMIC source region based on these observations, calculating a width of 0.75 hr MLT and a drift rate of 0.67 MLT/hr. We describe how this may be applied to other similar EMIC wave events

Anthropogenic Space Weather

Anthropogenic effects on the space environment started in the late 19th century and reached their peak in the 1960s when high-altitude nuclear explosions were carried out by the USA and the Soviet Union. These explosions created artificial radiation belts near Earth that resulted in major damages to several satellites. Another, unexpected impact of the high-altitude nuclear tests was the electromagnetic pulse (EMP) that can have devastating effects over a large geographic area (as large as the continental United States). Other anthropogenic impacts on the space environment include chemical release ex- periments, high-frequency wave heating of the ionosphere and the interaction of VLF waves with the radiation belts. This paper reviews the fundamental physical process behind these phenomena and discusses the observations of their impacts.Comment: 71 pages, 35 figure