Pattern Avoidance in Task-Precedence Posets

We have extended classical pattern avoidance to a new structure: multiple task-precedence posets whose Hasse diagrams have three levels, which we will call diamonds. The vertices of each diamond are assigned labels which are compatible with the poset. A corresponding permutation is formed by reading these labels by increasing levels, and then from left to right. We used Sage to form enumerative conjectures for the associated permutations avoiding collections of patterns of length three, which we then proved. We have discovered a bijection between diamonds avoiding 132 and certain generalized Dyck paths. We have also found the generating function for descents, and therefore the number of avoiders, in these permutations for the majority of collections of patterns of length three. An interesting application of this work (and the motivating example) can be found when task-precedence posets represent warehouse package fulfillment by robots, in which case avoidance of both 231 and 321 ensures we never stack two heavier packages on top of a lighter package.Comment: 17 page

Diamonds and their mineral inclusions from the Sloan diatremes of the Colorado-Wyoming State Line kimberlite district, North America

Bibliography: v. 1, pages 157-171.The Sloan diamonds were investigated for their physical characteristics, inclusion mineralogy and composition, and carbon isotope composition. The relationships between these features are described and interpreted with respect to diamond genesis. The physical characteristics investigated include crystal state, crystal regularity, primary morphology, resorption morphology, primary and secondary sizejmass, colour, surface features and inclusion content. Significant relationships between these characteristics were found. The proportion of an individual crystal, lost during resorption, decreases with increasing diamond size. Larger crystals and diamonds displaying brown colours appear to have been more susceptible to breakage relative to smaller crystals and diamonds of other colours, respectively. Brown colours were more common on smaller diamonds relative to larger stones and, further, were more common on single crystal forms relative to twinned/aggregate crystals. Variation in diamond physical characteristics between the various kimberlite phases in the Sloan 1 & 2 complex has been documented. The Sloan 2 phase is characterized by larger and less resorbed diamonds relative to those in other kimberlite phases in the diatreme. In addition, corrosion sculpture is much more common on Sloan 2 diamonds

INCREASING DOMESTIC CONSUMPTION OF SOUTH AFRICAN WINES: IDENTIFYING THE KEY MARKET SEGMENTS OF THE “BLACK DIAMONDS”

Although South Africans are not predominantly wine drinkers, the industry is looking for ways to develop the local market to balance exports. The black middle class, increasingly referred to as the Black Diamonds are the most powerful marketing trend in the last 10 years as they have emerged as the strongest buying influence in the economy and making inroads in understanding this market presents a good opportunity. The study asserts that the key factors influencing the South African consumers’ behavior are age, gender, income, race and wine drinking history. The study also asserts that not only are the black middle class are different from the white middle class but within the Black Diamonds different segments exist. The industry should particularly focus on marketing to the women and the “Start me up” age group in the group as there is limited consumer knowledge about wines, but a high willingness to experiment. The study also suggests various new brand communication platforms that can be explored to reach this market as well as co-opetition between industry stakeholders.Black Diamonds, wine consumer behavior, alcoholic beverages, Agribusiness, Demand and Price Analysis,

A Nitrogen and Carbon Stable Isotope Study of some Western Australian Diamonds

The carbon and nitrogen stable isotope ratios, nitrogen content and aggregation state have been measured in diamonds from Australian magmatic and alluvial sources and from a Chinese placer deposit. There are no consistent relationships between any of these properties, and there are no consistent relationships with diamond shape or colour. Both individual diamonds and diamond sources are shown to be heterogeneous and have a range of ẟ13C and ẟ15N values. The widest range in Western Australian magmatic diamonds occurs in Ellendale 9 samples which have -22.1‰ ≤ ẟ13C ≤ 0.0‰ and -9.3‰ ≤ ẟ15N ≤ -9.9‰. Diamonds from placer deposits have a wider range of ẟ15N and ẟ13C values however (-14.8‰ ≤ ẟ13C ≤ +1.9‰ & -28.4‰ ≤ ẟ15N ≤+9.7‰ in Northern Queensland samples). This may be due to placers representing multiple primary sources. A relationship between diamond paragenesis and ẟ13C value is shown. Eclogitic diamonds worldwide have a mean ẟ13C value of -8.6 ± 5.8‰ and range from ẟ13C = -34.5‰ to +1.5‰. In contrast, peridotitic paragenesis diamonds have a mean ẟ13C value of -5.4 ± 2.6‰, and their range in ẟ13C values is from -23.5‰ to +0. 1‰. ẟ15N data from diamonds of known provenance are scarce, but there are no significant differences between eclogitic and lherzolitic diamonds from Western Australia. Eclogitic diamonds have a mean ẟ15N value of 4.9‰ ±4.6‰ whereas lherzolitic diamonds have a mean ẟ15N value of 4.1‰ ±4.9‰. These parageneses have different mean ẟ15N values when compared to the mean ẟ15N value of samples thought to be of the harzburgitic paragenesis. It is provisionally suggested that carbon and nitrogen stable isotope ratios may discriminate eclogitic, lherzolitic and harzburgitic paragenesis samples. Three Argyle diamonds and a single Ellendale diamond are zoned in ẟ13C and ẟ15N values, nitrogen content and aggregation state. Models for these zonation profiles are consistent with diamond formation by fractional crystallization, and fractionation factors of α ≤ 1.001 for carbon and α = 1.004 for nitrogen during diamond growth are suggested. These samples are also zoned in age and in the most extreme case a difference of 1.2 Ga between the core and rim of a diamond 5 mm in diameter is found. All available diamond ẟ15N data are combined and it is concluded that ẟ15N = 0‰ ± 6‰ is a characteristic of the sub-continental lithospheric upper mantle. Heterogeneities within this are however evident when ẟ13C and ẟ15N covariations are considered. It is suggested that the subduction of oceanic sediment, carbonates and peridotite into the mantle, combined with isotope fractionation processes are responsible for the stable isotope characteristics of the diamond source region. A possible trend of increasing ẟ15N value in diamonds as their age decreases is noted, and it is speculated that this may be a result of a kinetic fractionation during mantle degassing and atmosphere formation

Intrinsic Carrier Parameters and Optical Carrier Injection Method in High-Purity Diamonds

Diamond attracts increasing attentions as a semiconductor, since high-purity synthesized diamonds have become commercially available in these decades. For appropriate design of any devices, the basic carrier transport parameters should be known. However, it has been difficult to determine carrier parameters in diamond, because the controlled doping and Ohmic contact formation have been hard to achieve. In this chapter, a modern experimental method to measure basic carrier parameters, such as the effective mass, scattering times, and mobility of intrinsic diamonds, is introduced. The method, i.e., nanosecond time-resolved cyclotron resonance (TRCR), is applicable to optically injected carriers in intrinsic diamonds without wire connection. Following the key technique of optical carrier injection, detailed analysis methods for the cyclotron resonance spectra are introduced. The extracted basic parameters of diamond are summarized in comparison to those of silicon and germanium in the same group-IV semiconductor family. This is worthy for triggering further ideas in application-oriented researches using widespread materials

Transport through a strongly coupled graphene quantum dot in perpendicular magnetic field

We present transport measurements on a strongly coupled graphene quantum dot in a perpendicular magnetic field. The device consists of an etched single-layer graphene flake with two narrow constrictions separating a 140 nm diameter island from source and drain graphene contacts. Lateral graphene gates are used to electrostatically tune the device. Measurements of Coulomb resonances, including constriction resonances and Coulomb diamonds prove the functionality of the graphene quantum dot with a charging energy of around 4.5 meV. We show the evolution of Coulomb resonances as a function of perpendicular magnetic field, which provides indications of the formation of the graphene specific 0th Landau level. Finally, we demonstrate that the complex pattern superimposing the quantum dot energy spectra is due to the formation of additional localized states with increasing magnetic field.Comment: 6 pages, 4 figure

Clouded Diamonds: Without Binding Arbitration and More Sophisticated Dispute Resolution Mechanisms, the Kimberley Process Will Ultimately Fail in Ending Conflicts Fueled by Blood Diamonds

In 2003, under an initiative of the United Nations (U.N.), various nations of the world gave life to the Kimberley Process Certification Scheme (KPCS)-a method by which consumers of all levels could know the origin of their diamonds-with the Scheme only certifying those harvested from legal, government-run mines. The Scheme\u27s drafters believed that, if given the choice, consumers would choose to buy diamonds mined legally, with profits flowing to legitimate sources of power. However, the KPCS as it stands is voluntary and lacks the teeth needed to deter its violators. The KPCS lacks a binding arbitration agreement and needs a more articulate and sophisticated method of resolving disputes and violations among its signatory countries. This article will offer suggestions for increasing the efficiency of the KPCS