For many years, archaeologists have relied on Munsell Soil Color Charts (MSCC) as tools for standardizing the recording of soil and sediment colors in the field and artifacts such as pottery in the lab. Users have identified multiple potential sources of discrepancy in results, such as differences in inter-operator perception, light source, or moisture content of samples. In recent years, researchers have developed inexpensive digital methods for color identification, but these typically cannot be done in real time. Now, a field-ready digital color-matching instrument is marketed to archaeologists as a replacement for MSCC, but the accuracy and overall suitability of this device for archaeological research has not been demonstrated. Through three separate field and laboratory trials, we found systematic mismatches in the results obtained via device, including variable accuracy against standardized MSCC chips, which should represent ideal samples. At the same time, the instrument was consistent in its readings. This leads us to question whether using the “subjective” human eye or the “objective” digital eye is preferable for data recording of color. We discuss how project goals and limitations should be considered when deciding which color-recording method to employ in field and laboratory settings, and we identify optimal procedures.

Johnson's cavity model relating indenter geometry and deformation resulting from elastic-plastic indentations is appropriate for a wide variety of materials. In the case of nanoindentations in single crystal BCC metals, limitations are reached when creep is not fully accounted for. Both the standard Berkovich and cube corner geometries show that the ratio of plastic zone radius to contact radius increases with the duration of time at the peak load. Indenter tip geometry is shown to play an important role in this phenomenon. Length scale phenomena, such as the indentation size effect, are also subject to various interpretations. The traditional definition of hardness does not produce similar trends with indentation length scale between the blunt Berkovich geometry and the sharper cube corner tip. However, the ratio of plastic zone radius to contact radius proves to be a tip geometry independent method of assessing the plasticity of these metals.

Throughout ℤp and ℚp will, respectively, denote the ring of p-adic integers and the field of p-adic numbers (for p prime). We denote by [Copf]p the completion of the algebraic closure of ℚp with respect to the p-adic metric. Let vp denote the p-adic valuation of [Copf]p normalised so that vp(p)=1. Put []p={ω∈[Copf]p[mid ]ωpn=1 for some n[ges ]0} so that []p is the union of cyclic (multiplicative) groups Cpn of order pn (for n[ges ]0).

Let UD(ℤp) denote the [Copf]p-algebra of all uniformly differentiable functions f[ratio ]ℤp→[Copf]p under pointwise addition and convolution multiplication *, where for f, g∈UD(ℤp) and z∈ℤp we have

formula here

the summation being restricted to i, j with vp(i+j−z)[ges ]n.

This situation is a starting point for p-adic Fourier analysis on ℤp, the analogy with the classical (complex) theory being substantially complicated by the absence of a p-adic valued Haar measure on ℤp (see [5, 6] for further details).

In this paper, we establish the generalized discriminant theorem governing uniqueness of symmetric polynomials in n variables of least total degree dn, k which vanish when any k + 1 of the variables are equal.