Bounds of some real (complex) solution of a finite system of polynomial equations with rational coefficients

We discuss two conjectures. (I) For each x_1,...,x_n \in R (C) there exist y_1,...,y_n \in R (C) such that \forall i \in {1,...,n} |y_i| \leq 2^{2^{n-2}} \forall i \in {1,...,n} (x_i=1 \Rightarrow y_i=1) \forall i,j,k \in {1,...,n} (x_i+x_j=x_k \Rightarrow y_i+y_j=y_k) \forall i,j,k \in {1,...,n} (x_i \cdot x_j=x_k \Rightarrow y_i \cdot y_j=y_k) (II) Let G be an additive subgroup of C. Then for each x_1,...,x_n \in G there exist y_1,...,y_n \in G \cap Q such that \forall i \in {1,...,n} |y_i| \leq 2^{n-1} \forall i \in {1,...,n} (x_i=1 \Rightarrow y_i=1) \forall i,j,k \in {1,...,n} (x_i+x_j=x_k \Rightarrow y_i+y_j=y_k)Comment: LaTeX2e, 28 pages, a shortened and revised version will appear in Mathematical Logic Quarterly 56 (2010), no.2, under the title ``Two conjectures on the arithmetic in R and C'

EFRC Bulletin 77

EFRC's regular newletter covering policy, agricutlural research, policy and advisory wor

A framework for documenting and analyzing life-cycle costs using a simple network based representation

The introduction of high reliability systems combined with new ways of operating complex systems, particularly in aircraft design and operation has received much attention in recent years. Some systems are now being introduced into service, however, justifying such systems on a financial basis is difficult and may act to limit the rate of introduction on new products. Conventional life cycle costing based on a hierarchical cost breakdown structure is poor at recording and analysing the cost implications of introducing new technologies that have effects that span more than one phase in the life cycle. There is a risk that too much emphasis is put on ‘faith’ that a candidate technology will reduce cost because the cost analysis methods lack descriptive and analytical power. We describe an approach to representing the costs associated with introducing new technologies and evaluating their total cost. Our aim was to facilitate the comparison of different technological choices in new product development, with a particular interest in how the perceived benefits of enhanced reliability systems can be shown in a way that is inclusive, objective and easy to understand

Cosmic D-Strings and Vortons in Supergravity

Recent developments in string inspired models of inflation suggest that D-strings are formed at the end of inflation. Within the supergravity model of D-strings there are 2(n-1) chiral fermion zero modes for a D-string of winding n. Using the bounds on the relic vorton density, we show that D-strings with winding number n>1 are more strongly constrained than cosmic strings arising in cosmological phase transitions. The D-string tension of such vortons, if they survive until the present, has to satisfy 8\pi G_N \mu \lesssim p 10^{-26} where p is the intercommutation probability. Similarly, D-strings coupled with spectator fermions carry currents and also need to respect the above bound. D-strings with n=1 do not carry currents and evade the bound. We discuss the coupling of D-strings to supersymmetry breaking. When a single U(1) gauge group is present, we show that there is an incompatibility between spontaneous supersymmetry breaking and cosmic D-strings. We propose an alternative mechanism for supersymmetry breaking, which includes an additional U(1), and might alleviate the problem. We conjecture what effect this would have on the fermion zero modes.Comment: 11 page

Levels or Differences in Meat Demand Specification

We estimated a wholesale demand system for beef, pork, lamb, chicken, and turkey using quarterly U.S. data and a dynamic, CBS system (Keller and Van Driel). The CBS system is a differential system, which means that it might be more appropriately applied in those situations where the data have unit roots. If there are unit roots, differencing the data can improve the properties of the estimates. If the data do not have unit roots, differencing the data might harm the properties of the estimates. We tested the specification of the model's error terms using state-space techniques. State-space units allow one to deal with roots on the unit circle without filtering the data (See Durbin and Koopman). The demand system has only four independent error terms. The state-space model we used could have decomposed these four independent error terms into four errors with unit roots and four with 0 roots. Adding state-space features to the model greatly improved its performance as measured by the likelihood ratio statistics. The estimates imply that the raw demand data have two unit roots and three 0 roots. Our mixed approach improves the properties of the estimates.Demand and Price Analysis,

The Racist Impact of Redistributive Public Policies: Handout versus Hand-Up

Federal government policies, while benefitting some urban areas, have historically been detrimental to African-American people. Years of welfare and housing policies have placed central city residents, especially African-Americans, at a disadvantage which they have not overcome. Policies that once denied benefits to Black people, such as public welfare and federally-insured mortgages, morphed into stigmatized policies which, when available to Blacks, became obstacles to their advancement. These same policies enabled the majority White population to do what they were initially designed to do – provide a toehold during a period of temporary economic decline after which personal advancement was possible. The effects of public welfare and housing policies may help to explain the vast differences in the economic status of Blacks as compared to Whites reported in recent research. The current wage Black-White gap is wide, but more telling is the enormous wealth gap between the two groups historically and currently. The Black-White wage gap increased between 2000 and 2018 while the Black-White wealth gap was the same in 2016 as it was in 1962. This paper explores how changes in the objectives, design, implementation of welfare and housing assistance have contributed to the wealth disparity and accumulation of assets. Intentionally antiracist policies are needed to counter the racist impacts of past and present policies

Maximality and Applications of Subword-Closed Languages

Characterizing languages D that are maximal with the property that D* ⊆ S⊗ is an important problem in formal language theory with applications to coding theory and DNA codewords. Given a finite set of words of a fixed length S, the constraint, we consider its subword closure, S⊗, the set of words whose subwords of that fixed length are all in the constraint. We investigate these maximal languages and present characterizations for them. These characterizations use strongly connected components of deterministic finite automata and lead to polynomial time algorithms for generating such languages. We prove that the subword closure S⊗ is strictly locally testable. Finally, we discuss applications to coding theory and encoding arbitrary blocks of information on DNA strands. This leads to very important applications in DNA codewords designed to obtain bond-free languages, which have been experimentally confirmed