A representation of the natural numbers by means of cycle-numbers, with consequences in number theory

In this paper we give rules for creating a number triangle T in a manner analogous to that for producing Pascal's arithmetic triangle; but all of its elements belong to {0, 1}, and cycling of its rows is involved in the creation. The method of construction of any one row of T from its preceding rows will be defined, and that, together with starting and boundary conditions, will suffice to define the whole triangle, by sequential continuation. We shall use this triangle in order to define the so-called cycle-numbers, which can be mapped to the natural numbers. T will be called the 'cyclenumber triangle'. First we shall give some theorems about relationships between the cyclenumbers and the natural numbers, and discuss the cycling of patterns within the triangle's rows and diagonals. We then begin a study of figures (i.e. (0,1)- patterns, found on lines, triangles and squares, etc.) within T. In particular, we shall seek relationships which tell us something about the prime numbers. For our later studies, we turn the triangle onto its side and work with a doubly-infinite matrix C. We shall find that a great deal of cycling of figures occurs within T and C, and we exploit this fact whenever we can. The phenomenon of cycling patterns leads us to muse upon a 'music of the integers', indeed a 'symphony of the integers', being played out on the cycle-number triangle or on C. Like Pythagoras and his 'music of the spheres', we may well be the only persons capable of hearing it!

FEEDER CATTLE PRICE DIFFERENTIALS IN GEORGIA TELEAUCTIONS

Three Georgia feeder cattle teleauction markets were analyzed from 1977 to 1988 to estimate the impacts of cattle characteristics and market conditions on prices. Cattle characteristic price impacts were similar to those in previous studies. The impact of feeder cattle futures price on teleauction price was positive but varied across markets. Optimal lot size ranged from 143 to 276 head. In one market, 14 lots were necessary to generate positive price impacts. Additional buyers were estimated to have a $.30/cwt per buyer impact on price.Demand and Price Analysis,

The Economics of a Centralized Judiciary: Uniformity, Forum Shopping and the Federal Circuit

In 1982, the US Congress established the Court of Appeals for the Federal Circuit (CAFC) as the sole appellate court for patent cases. Ostensibly, this court was created to eliminate inconsistencies in the application and interpretation of patent law across federal courts, and thereby mitigate the incentives of patentees and alleged infringers to "forum shop" for a preferred venue. We perform the first econometric study of the extent of non-uniformity and forum shopping in the pre-CAFC era and of the CAFC's impact on these phenomena. We find that in patentee-plaintiff cases the pre-CAFC era was indeed characterized by significant non-uniformity in patent validity rates across circuits and by forum shopping on the basis of validity rates. We find weak evidence that the CAFC has increased uniformity of validity rates and strong evidence that forum shopping on the basis of validity rates ceased several years prior to the CAFC's establishment. In patentee-defendant cases, we find that validity rates are lower on average, but do not find either significant non-uniformity of validity rates across circuits or significant forum shopping.

PRODUCT DIFFERENTIATION PROTECTION: DEVELOPING A STRATEGY FOR MULTIPLE PRODUCERS OF REGIONAL SPECIALTY CROPS

Specialty crops grown by multiple producers are often viewed by consumers as differentiated products that command a price premium. Since price premiums are dependent upon differentiation of an item from generic counterparts, specialty crops must have distinctive identities that cannot be copied or mimicked by others. Trademarks are normally employed to differentiate and protect products, but the limitation of trademarks to products from a single source means that differentiation of specialty crops grown by multiple producers may involve difficulties in precluding free riders from adopting the same name. Through a case study of Georgia's Vidalia Onions and an examination of producer price data, this article explores the problem of the protection of product differentiation of regional specialty crops grown by multiple producers.Agribusiness,

Ionized Gas Kinematics at High Resolution IV: Star Formation and a Rotating Core in the Medusa (NGC 4194)

NGC 4194 is a post-merger starburst known as The Medusa for its striking tidal features. We present here a detailed study of the structure and kinematics of ionized gas in the central 0.65 kpc of the Medusa. The data include radio continuum maps with resolution up to 0.18\arcsec (35 pc) and a $12.8\mu$m [NeII] data cube with spectral resolution $\sim4$\kms: the first {\it high resolution, extinction-free} observations of this remarkable object. The ionized gas has the kinematic signature of a core in solid-body rotation. The starburst has formed a complex of bright compact \HII~regions, probably excited by deeply embedded super star clusters, but none of these sources is a convincing candidate for a galactic nucleus. The nuclei of the merger partners that created the Medusa have not yet been identified.Comment: to appear in Ap

A New Taxonomy of Thin Markets

The traditional conception of a thin market based on transactions volume remains relevant in many agricultural markets but does not adequately frame emerging thin market issues. As non-price means of pricing goods becomes more common, some cash commodity markets have become residual markets. In some of these markets, not only the volume of transactions but also the representativeness of transactions to those on the related contract market is an important issue. This paper develops a concept of thin markets that accounts for this dimension of market thinness and proposes a research agenda related to this topic.Marketing,

Augmented Sustainability Measures for Scotland

We estimate and compare two empirical measures of the weak sustainability of an economy for the first time: the change in augmented green net national product (GNNP), and the interest on augmented genuine savings (GS). Yearly calculations are given for each measure for Scotland during 1992-99. Augmentation means including, using projections to 2020, changed production possibilities enabled by exogenous technical progress or changing oil prices. The change in augmented GNNP and interest on augmented GS are both always positive, showing no sustainability problem for Scotland then, according to the assumptions underlying our weak sustainability calculations. However, the former greatly exceeds the latter, a mismatch which poses an unresolved problem with the theory. Resolving it may require respecifying the utility functions used in mainstream growth theory.sustainability, Scotland, genuine savings, green NNP, augmentation

The Impacts of Market Structure and Contracts on Agricultural Markets

Experimental markets were used to isolate the effects of market structure and contract design on market outcomes. Preliminary results suggest that market structure drives outcomes, and not necessarily contract design. Future research will replicate experiments and add dimensions of market information.Political Economy,

Augmented Sustainability Measures for Scotland

We estimate and compare two empirical measures of the weak sustainability of an economy for the first time: the change in augmented green net national product (GNNP), and the interest on augmented genuine savings (GS). Yearly calculations are given for each measure for Scotland during 1992-99. Augmentation means including, using projections to 2020, production possibilities enabled by exogenous technical progress or changing terms of trade. In passing, we clarify the treatment of environmental expenditures in green accounting. The change in augmented GNNP and interest on augmented GS are both always positive, showing no sustainability problem for Scotland; but the former greatly exceeds the latter, showing an unresolved problem with the theorysustainability, Scotland, genuine savings, green NNP, augmentation