A Survey on Fixed Divisors

In this article, we compile the work done by various mathematicians on the topic of the fixed divisor of a polynomial. This article explains most of the results concisely and is intended to be an exhaustive survey. We present the results on fixed divisors in various algebraic settings as well as the applications of fixed divisors to various algebraic and number theoretic problems. The work is presented in an orderly fashion so as to start from the simplest case of $\Z,$ progressively leading up to the case of Dedekind domains. We also ask a few open questions according to their context, which may give impetus to the reader to work further in this direction. We describe various bounds for fixed divisors as well as the connection of fixed divisors with different notions in the ring of integer-valued polynomials. Finally, we suggest how the generalization of the ring of integer-valued polynomials in the case of the ring of $n \times n$ matrices over $\Z$ (or Dedekind domain) could lead to the generalization of fixed divisors in that setting.Comment: Accepted for publication in Confluentes Mathematic

Branched chain aldehydes: production and breakdown pathways and relevance for flavour in foods

Branched aldehydes, such as 2-methyl propanal and 2- and 3-methyl butanal, are important flavour compounds in many food products, both fermented and non-fermented (heat-treated) products. The production and degradation of these aldehydes from amino acids is described and reviewed extensively in literature. This paper reviews aspects influencing the formation of these aldehydes at the level of metabolic conversions, microbial and food composition. Special emphasis was on 3-methyl butanal and its presence in various food products. Knowledge gained about the generation pathways of these flavour compounds is essential for being able to control the formation of desired levels of these aldehydes

GEM Operation in Negative Ion Drift Gas Mixtures

The first operation of GEM gas gain elements in negative ion gas mixtures is reported. Gains up to several thousand were obtained from single-stage GEMs in carbon disulfide vapor at low pressure, and in mixtures of carbon disulfide with Argon and Helium, some near 1 bar total pressure.Comment: 7 pages, 3 figure

Mud peeling and horizontal crack formation in drying clays

Mud peeling is a common phenomenon whereby horizontal cracks propagate parallel to the surface of a drying clay. Differential stresses then cause the layer of clay above the crack to curl up to form a mud peel. By treating the clay as a poroelastic solid, we analyse the peeling phenomenon and show that it is caused by the gradient in tensile stress at the surface of the clay, analogously to the spalling of thermoelastic materials. For a constant water evaporation rate at the clay surface we derive equations for the depth of peeling and the time of peeling as functions of the evaporation rate. Our model predicts a simple relationship between the radius of curvature of a mud peel and the depth of peeling. The model predictions are in agreement with the available experimental data available

Clay fine fissuring monitoring using miniature geo-electrical resistivity arrays

Abstract This article describes a miniaturised electrical imaging (resistivity tomography) technique to map the cracking pattern of a clay model. The clay used was taken from a scaled flood embankment built to study the fine fissuring due to desiccation and breaching process in flooding conditions. The potential of using a miniature array of electrodes to follow the evolution of the vertical cracks and number them during the drying process was explored. The imaging technique generated two-dimensional contoured plots of the resistivity distribution within the model before and at different stages of the desiccation process. The change in resistivity associated with the widening of the cracks were monitored as a function of time. Experiments were also carried out using a selected conductive gel to slow down the transport process into the cracks to improve the scanning capabilities of the equipment. The main vertical clay fissuring network was obtained after inversion of the experimental resistivity measurements and validated by direct observations