Solving the Dirichlet problem constructively

The Dirichlet problem is of central importance in both applied and abstract potential theory. We prove the (perhaps surprising) result that the existence of solutions in the general case is an essentially nonconstructive proposition: there is no algorithm which will actually compute solutions for arbitrary domains and boundary conditions. A corollary of our results is the nonexistence of constructive solutions to the NavierStokes equations of fluid flow. But not all the news is bad: we provide reasonable conditions, omitted in the classical theory but easily satisfied, which ensure the computability of solutions

A new look at low-energy nuclear reaction (LENR) research: a response to Shanahan

In his criticisms of the review article on LENR by Krivit and Marwan, Shanahan has raised a number of issues in the areas of calorimetry, heat after death, elemental transmutation, energetic particle detection using CR-39, and the temporal correlation between heat and helium-4. These issues are addressed by the researchers who conducted the original work that was discussed in the Krivit-Marwan (K&M) review paper

Excess of power during electrochemical loading : materials, electrochemical conditions and techniques

"Notes on The ENEA-University of Missouri NRL-SRI International Research Activities." ENEA, University of Missouri, NRL and SRI are cooperating within the frame of an International Program. The research field is on Metal Hydrogen Systems for Energy Applications and is oriented to develop nanostructured materials to be used into electrochemical devices and to study the Fleischmann and Pons Effect. Progress in material science and improvement in controlling the effect is presented

Constraints on energetic particles in the Fleischmann-Pons experiment

In recent Fleischmann–Pons experiments carried out by different groups, a thermal signal is seen indicative of excess energy production of a magnitude much greater than can be accounted for by chemistry. Correlated with the excess heat appears to be 4He, with the associated energy near 24 MeV per helium atom. In nuclear reactions, the energy produced is expressed through the kinetic energy of the products; hence, it would be natural to assume that some of the reaction energy ends up as kinetic energy of the 4He nucleus. Depending on the energy that the helium nucleus is born with, it will result in radiation (such as neutrons or x-rays) that can be seen outside of the cell. We have computed estimates of the expected neutron and x-ray emission as a function of helium energy and compared the results with upper limits taken from experiments. Experimental results with upper limits of neutron emission between 0.008 and 0.8 n/J are found to correspond to upper limits in alpha energy between 6.2 and 20.2 keV

Optics and Quantum Electronics

Contains table of contents on Section 3 and reports on nineteen research projects.Defense Advanced Research Projects Agency Grant F49620-96-0126Joint Services Electronics Program Grant DAAH04-95-1-0038National Science Foundation Grant ECS 94-23737U.S. Air Force - Office of Scientific Research Contract F49620-95-1-0221U.S. Navy - Office of Naval Research Grant N00014-95-1-0715Defense Advanced Research Projects Agency/National Center for Integrated Photonics TechnologyMultidisciplinary Research InitiativeU.S. Air Force - Office of Scientific ResearchNational Science Foundation/MRSECU.S. Navy - Office of Naval Research (MFEL) Contract N00014-91-J-1956National Institutes of Health Grant R01-EY11289U.S. Navy - Office of Naval Research (MFEL) Contract N00014-94-0717Defense Advanced Research Projects Agency Contract N66001-96-C-863

Optics and Quantum Electronics

Contains table of contents for Section 3 and reports on eighteen research projects.Defense Advanced Research Projects Agency/MIT Lincoln Laboratory Contract MDA972-92-J-1038Joint Services Electronics Program Grant DAAH04-95-1-0038National Science Foundation Grant ECS 94-23737U.S. Air Force - Office of Scientific Research Contract F49620-95-1-0221U.S. Navy - Office of Naval Research Grant N00014-95-1-0715MIT Center for Material Science and EngineeringNational Center for Integrated Photonics Technology Contract DMR 94-00334National Center for Integrated Photonics TechnologyU.S. Navy - Office of Naval Research (MFEL) Contract N00014-94-1-0717National Institutes of Health Grant 9-R01-EY11289MIT Lincoln Laboratory Contract BX-5098Electric Power Research Institute Contract RP3170-25ENEC

Constructive Methods in Mathematics

The point of using constructive methods in mathematics is to explicitly exhibit any object or algorithm that the mathematician claims exists; so constructive proof provides, in principle, a mechanical method. Loosely speaking, one replaces the absolute notion of truth in mathematics, with (algorithmic) provability

Real Analysis in Paraconsistent Logic

This paper begins an analysis of the real line using an inconsistency- tolerant (paraconsistent) logic. We show that basic field and compactness properties hold, by way of novel proofs that make no use of consistency- reliant inferences; some techniques from constructive analysis are used instead. While no inconsistencies are found in the algebraic operations on the real number field, prospects for other non-trivializing contradictions are left open

Deformations with smallest weighted Lp average distortion and Nitsche type phenomena

The existence and uniqueness properties for extremal mappings with smallest weighted Lp distortion between annuli and the related Grotzsch type problems are discussed. An interesting critical phase type phenomena is observed. When p < 1, apart from the identity map, minimizers never exist. When p = 1 we observe Nitsche type phenomena; minimisers exist within a range of conformal moduli determined by properties of the weight function and not otherwise. When p > 1 minimisers always exist. Interpreting the weight function as a density or "thickness profi le" leads to interesting models for the deformation of highly elastic bodies and tearing type phenomena