On the alleged simplicity of impure proof

Roughly, a proof of a theorem, is “pure” if it draws only on what is “close” or “intrinsic” to that theorem. Mathematicians employ a variety of terms to identify pure proofs, saying that a pure proof is one that avoids what is “extrinsic,” “extraneous,” “distant,” “remote,” “alien,” or “foreign” to the problem or theorem under investigation. In the background of these attributions is the view that there is a distance measure (or a variety of such measures) between mathematical statements and proofs. Mathematicians have paid little attention to specifying such distance measures precisely because in practice certain methods of proof have seemed self- evidently impure by design: think for instance of analytic geometry and analytic number theory. By contrast, mathematicians have paid considerable attention to whether such impurities are a good thing or to be avoided, and some have claimed that they are valuable because generally impure proofs are simpler than pure proofs. This article is an investigation of this claim, formulated more precisely by proof- theoretic means. After assembling evidence from proof theory that may be thought to support this claim, we will argue that on the contrary this evidence does not support the claim

Exploring and Monitoring of Methane Hydrate Deposits

Relatively recently, in the last 20 years, it was discovered that methane hydrate (MH) deposits are globally distributed in the permafrost and oceans. Before 1965 when first deposits were discovered in nature, it was believed that MH can occur only in laboratory conditions or in vast parts of the Universe. Presently it is presumed that this solid crystalline compounds in which CH4 molecules occupies the water ice lattices (nominal chemical formula of MH is C4H62O23) can serve as an energy source favorably to the all of the world remaining conventional hydrocarbon sources. The worldwide estimates of MH deposits range from 2x1014 m3 to 3.053x1018 cubic meters. This uncertainty partly results from our limitations in geological understanding of the MH deposits, which is due to the relatively bad quality of data obtained by presently available seismic and electromagnetic techniques. Moreover, MH deposits can become vulnerable to climate changes, which were already occurring in geological past whit tremendous consequences for the global life on Earth. Thus, further development of advanced techniques is needed to enhance our abilities to better characterize, quantify and monitor the MH deposits. In the work presented 14 MeV neutrons and associated alpha particle imaging (API) where used to quantify the amount of MH in the sample. Samples were prepared from sea sediment, quartz sand and MH simulant. MH simulant with chemical formula C4H46O23 was made from sucrose (25 % by mass) and water. MH quantity was measured by measuring the carbon content in the sample [1-8]

The role of 14 MeV neutrons in light element nucleosynthesis

The 14 MeV neutron induced nuclear reactions which might contribute to better understanding of so-called “cosmological lithium problem” have been discussed. The BBN theory predicted 7Li overestimated value could be lowered by 2n induced reactions on Li-isotopes and/or 7Be destruction via resonance in d+7Be→9B process. Proposals for 6Li+2n and 7Li+2n reactions cross section evaluations and measurements are discussed in some details. We discuss also a preliminary measurements of n-n coincidences from the 10B(n,2n)9B reaction with two neutron detectors placed outside the cone of 14 MeV tagged neutron beam. From the time-of-flight measurements and known geometry we deduce the neutron energies and calculate the 9B missing mass spectrum

The role of 14 MeV neutrons in light element nucleosynthesis

The 14 MeV neutron induced nuclear reactions which might contribute to better understanding of so-called “cosmological lithium problem” have been discussed. The BBN theory predicted 7Li overestimated value could be lowered by 2n induced reactions on Li-isotopes and/or 7Be destruction via resonance in d+7Be→9B process. Proposals for 6Li+2n and 7Li+2n reactions cross section evaluations and measurements are discussed in some details. We discuss also a preliminary measurements of n-n coincidences from the 10B(n,2n)9B reaction with two neutron detectors placed outside the cone of 14 MeV tagged neutron beam. From the time-of-flight measurements and known geometry we deduce the neutron energies and calculate the 9B missing mass spectrum

Exploring and Monitoring of Methane Hydrate Deposits

Relatively recently, in the last 20 years, it was discovered that methane hydrate (MH) deposits are globally distributed in the permafrost and oceans. Before 1965 when first deposits were discovered in nature, it was believed that MH can occur only in laboratory conditions or in vast parts of the Universe. Presently it is presumed that this solid crystalline compounds in which CH4 molecules occupies the water ice lattices (nominal chemical formula of MH is C4H62O23) can serve as an energy source favorably to the all of the world remaining conventional hydrocarbon sources. The worldwide estimates of MH deposits range from 2x1014 m3 to 3.053x1018 cubic meters. This uncertainty partly results from our limitations in geological understanding of the MH deposits, which is due to the relatively bad quality of data obtained by presently available seismic and electromagnetic techniques. Moreover, MH deposits can become vulnerable to climate changes, which were already occurring in geological past whit tremendous consequences for the global life on Earth. Thus, further development of advanced techniques is needed to enhance our abilities to better characterize, quantify and monitor the MH deposits. In the work presented 14 MeV neutrons and associated alpha particle imaging (API) where used to quantify the amount of MH in the sample. Samples were prepared from sea sediment, quartz sand and MH simulant. MH simulant with chemical formula C4H46O23 was made from sucrose (25 % by mass) and water. MH quantity was measured by measuring the carbon content in the sample [1-8]

Red mud characterization using atomic and nuclear analytical techniques

Red mud is a toxic waste left as a byproduct in aluminum production Bayer process. Since it contains significant concentrations of other chemical elements interesting for industry, including Rare Earths Elements (REEs), it is also potential secondary ore source. Recent events in some countries have shown that red mud presents a serious environmental hazard if not properly stored. The subject of our study is evaluation of the red mud elemental composition, especially yttrium, scandium, gallium and REEs, from an ex-aluminum plant in Obrovac, Croatia, left from the processing of bauxite mined during late 70's and early 80's at the eastern Adriatic coast and stored in open concrete basins for more than 30 years since then. © 2012 IEEE

Evaluation of elemental composition of sediments from the Adriatic Sea by using EDXRF technique.

723 sediment samples collected along the eastern Adriatic coast have been analyzed using Energy Dispersive X-Ray Fluorescence. Factor Analysis and GIS have been used for the evaluation of the resulting data base containing information on K, Ca, Ti, Cr, Mn, Fe, Ni, Cu, Zn, Ga, As, Br, Rb, Sr, Y, and Pb concentration levels in order to find spatial relationships in distribution of measured elements. This study can be used to identify background values and to evaluate sediment quality standards

Analysis of carbon soil content by using tagged neutron activation

Here we describe a prototype for non-destructive, in-situ, accurate and cost-effectively measurement procedure of carbon in soil based on neutron activation analysis using 14 MeV tagged neutron beam. This technology can be used for carbon baseline assessment on regional scale and for monitoring of its surface and depth storage due to the changes in agricultural practices undertaken in order to mitigate global climate change. © 2012 SPIE