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In this paper we determine the homology and the cohomology groups of two properly discontinuous groups of isometries of the hyperbolic plane having non-compact orbit spaces and the fundamental group of a graph of groups with a finite vertex groups and no trivial edges by extending Lyndon's partial free resolution for finitely presented groups. For the first two groups, we obtain partial extensions and the corresponding homology. We also compute the corresponding cohomology groups for one of these groups. Finally we obtain homology and cohomology in all dimensions for the last of the above mentioned groups by constructing a full resolution for this group.

In a previous paper [1] we constructed a free resolution for a class of groups which include Fuchsian groups with compact orbit spaces [2, 3], infinite polyhedral groups, plane crystallographic groups p2, p3, p4 and p6 and Dyck's groups [4], and used this resolution for computation of the integral homology and cohomology of these groups. Lyndon [5] determined the cohomology of groups with a single defining relation. The plane crystallographic groups p1 and pg and Artin's braid group B3 are among these groups. In this paper we have constructed free resolutions for certain classes of groups–resolutions which are particularly suitable for direct computation of the homology and the cohomology of these groups for any coefficient module. These classes of groups include the plane crystallographic groups pm, cm and pgg. We have computed the integral homology and cohomology from each of the free resolutions obtained.

In this paper the authors obtained a method of constructing free resolutions of Z for finitely presented groups directly from their presentations by extending Lyndon's 3-term partial resolution to a full-length resolution. Authors resolutions and the method of their construction are such that free generators of the modules and the boundary homomorphisms are directly and explicitly obtained by solving of linear equations over the corresponding integral group rings, and hence these are immediately applicable for computing homology and cohomology of the groups for arbitrary coefficient modules. Authors have also described a general situation where their method is valid. The method has been used for a number of classes of group including Fuchsian groups, a few Euclidean crystallographic groups, NEC groups, the fundamental groups of a few interesting manifolds, groups of isometries of the hyperbolic plane and a few nilpotent groups of class 2.

This report gives a detailed assessment of several key technical issues that needs resolution for the existing structural materials with emphasis on application in liquid metal reactors (LMRs), in particular, sodium cooled fast reactors. The work is a combined effort between Argonne National Laboratory (ANL) and Oak Ridge National Laboratory (ORNL) with ANL as the technical lead, as part of Advanced Structural Materials Program for the Advanced Fuel Cycle Initiative (AFCI) Reactor Campaign. The report is the second deliverable in FY09 (M2505050201) under the work package "Advanced Materials Code Qualification".The overall objective of the Advanced Materials Code Qualification project is to evaluate the key technical requirements for the qualification of currently available and future advanced materials for application in sodium reactor systems and the resolution of issues that the U.S. Nuclear Regulatory Commission (NRC) has raised in the past on structural materials in support of the design and licensing of the LMR. Advanced materials are a critical element in the development of sodium reactor technologies. Enhanced materials performance not only improves safety margins and provides design flexibility, but also is essential for the economics of future advanced sodium reactors. Qualification and licensing of advanced materials are prominent needs for developing and implementing advanced sodium reactor technologies. However, the development of sufficient database and qualification of these materials for application in LMRs require considerable amount of time and resources. In the meantime, the currently available materials will be used in the early development of fast reactors.Nuclear structural component designs in the U.S. comply with the ASME Boiler and Pressure Vessel Code Section III (Rules for Construction of Nuclear Facility Components) and the NRC grants licensing. As the LMR will operate at higher temperatures than the current light water reactors (LWRs), the design of elevated-temperature components must comply with ASME Section III Subsection NH (Class 1 Components in Elevated Temperature Service). Assessment of materials performance issues and high temperature design methodology issues pertinent to the LMR were presented in an earlier report (Natesan et al. 2008). In a subsequent report ), we addressed the needs in high temperature methodologies for design of various high temperature components in sodium cooled fast reactor.The present report addresses several key technical issues for the currently available structural materials such as Type 304 and 316 austenitic stainless steels and ferritic steels such as 2.25Cr-1Mo and modified 9Cr-1Mo. The 60-year design life for the LMR presents a significant challenge to the development of database, extrapolation/prediction of long-term performance, and high temperature structural design methodology. The current Subsection NH is applicable to the design life only up to 34 years. No experimental data contain test durations of 525,000 hours, and it is impractical...