In this paper, we study a generalization of z-ideals in the ring C(X) of continuous real valued functions on a completely regular Hausdorff space X. The notion of a weak ideal and naturally a weak z-ideal and a prime weak ideal are introduced and it turns out that they behave such as z-ideals in C(X).

Introduction: The Viking and Mars Pathfinder landing sites and a wide variety of rocky locations on the Earth show size-frequency distributions that follow an exponential when expressed in cumulative fractional area covered by rocks of a given diameter or larger versus diameter plots. Mars lander rock distributions have been fit by an equation of the form: Fk(D) = k exp [-q(k) D], where Fk(D) i...

As pointed out in the introduction to this book, shales contain the lion’s share of earth history that is recorded in sedimentary rocks. Understanding their deposition is key to the reconstruction of past oceans, landscapes, climates, and climatic cycles. Yet, whereas students of sandstones and carbonates have been able to learn a great deal about the deposition of these rocks from studying bed...

Non-statistical weak measurements yield weak values that are outside the range of eigenvalues and are not rare, suggesting that weak values are a property of every preand-post-selected ensemble. They also extend the applicability and valid regime of weak values.

The oldest rocks which have been found so far (on the Earth) date to about 3.8 to 3.9 billion years ago (by several radiometric dating methods). Some of these rocks are sedimentary, and include minerals which are themselves as old as 4.1 to 4.2 billion years. Rocks of this age are relatively rare, however rocks that are at least 3.5 billion years in age have been found on North America, Greenla...

O'Neil et al. (Reports, 26 September 2008, p. 1828) presented neodymium-142 data for rocks from northern Quebec, Canada, and suggested that these rocks may represent the oldest preserved crustal section on Earth. We argue that the age of the rocks is based on a spurious correlation between rocks that are probably not co-genetic and negative (142)Nd anomalies that may be the result of an analyti...

In this paper, we present a tiling method for generating piles of rocks without any computationally demanding physically-based simulation. Previous techniques rely on a periodic tiling of rocks and generate unrealistic repetitive patterns. In contrast, our approach relies on a modified corner cube algorithm to generate a set of aperiodic tiles. We generalize the construction method so that the ...

Archean rocks may provide a record of early Earth environments. However, such rocks have often been metamorphosed by high pressure and temperature, which can overprint the signatures of their original formation. Here, we show that the early Archean banded rocks from Isua, Akilia, and Innersuartuut, Greenland, are enriched in heavy iron isotopes by 0.1 to 0.5 per mil per atomic mass unit relativ...

a r t i c l e i n f o Recent high-resolution GPS and seismological data reveal that tectonic faults exhibit complex, multi-mode slip behavior including earthquakes, creep events, slow and silent earthquakes, low-frequency events and earthquake afterslip. The physical processes responsible for this range of behavior and the mechanisms that dictate fault slip rate or rupture propagation velocity ...