This report presents both the most essential known results and new results in the theory of partially ordered groups and rings. This report deals with partially ordered groups and rings in an algebraic aspect because it is more important than partially ordered, fully ordered and lattice-ordered semigroup theory.

No description available.

Thesis (Ph. D.)--Lehigh University, 2004. / Includes vita. Includes bibliographical references (leaves 73-74).

Thesis--University of Michigan. / "Reprinted from American journal of mathematics, vol. LXX, no. 3, July, 1948."

No description available.

It may be said of certain pairs of elements of a set that one element precedes the other. If the collection of all such pairs of elements in a given set exhibits certain properties, the set and the collection of pairs is said to constitute a partially ordered set. The purpose of this paper is to explore some of the properties of partially ordered sets.

Gives the basic definitions and theorems of similar partially ordered sets; studies finite partially ordered sets, including the problem of combinatorial analysis; and includes the ideas of complete, dense, and continuous partially ordered sets, including proofs.

Thesis (Ph.D.)--University of Nebraska-Lincoln, 2008. / Title from title screen (site viewed Dec. 15, 2008). PDF text: vi, 93 p. ; 616 K. UMI publication number: AAT 3333017. Includes bibliographical references. Also available in microfilm and microfiche formats.

Scour is the leading cause of bridge failure in the United States. It is the result of the erosive action of flowing water excavating and carrying away material from the beds and/or banks of streams. To ensure public safety and minimize potential bridge damage caused by scour, a countermeasure is incorporated at a stream or bridge crossing system to monitor, control, inhibit, change, delay, or minimize stream and bridge stability problems, including scour. Countermeasures can be installed at the time of construction for new bridges or can be retrofitted to existing bridges when stability issues arise. Riprap is the most commonly used countermeasure for scour protection. It is the most understood, studied and documented of all the countermeasures. In addition to basic, loose riprap, partially grouted riprap (PGR) is also an option when selecting a countermeasure. PGR is relatively new in the United States, but has been used widely in Europe to prevent scour or erosion of the bed, banks, shoreline, and at piers and abutments. PGR construction involves placement of specifically sized riprap on top of granular filters or geotextile filter and/or a combination of both filters. A high slump Portland cement based grout is used to interlock the riprap by partially filling one-third to one-half of the total void space of the original riprap. Grouting is done in the dry or in the wet by hose or by automated mechanical means. Turbidity and pH level are the main problems when using grouting. Currently in Pennsylvania, the selection of appropriate countermeasures and the design for bridge foundation protection against scour have in general been restricted in their applications to mainly dumped riprap, which can be displaced after each flood. Similar to Hydraulic Engineering Circular No. 23 (HEC 23), Abboud et al. (1) developed a set of matrices that are used as guidelines for scour countermeasure selection for the State of Pennsylvania. Abboud et al. (1) also developed design guidelines for the recommended scour countermeasures. Partially grouted riprap was considered by Abboud et al. (1) as vital countermeasure to control scour at Pennsylvania bridge abutments and piers. Based on guidance developed by Federal Waterway Engineering and Research Institute (BAW) in Germany, HEC 23 Design Guidelines 12 "Partially Grouted Riprap at Bridge Piers" provided general requirements for grouting materials and standard European testing for grout quality and consistency. Hence, there is a critical need to develop guidelines to select grout design mix that minimize the environmental impact and to utilize current US standards to control the grout design mix for the construction in the dry and in the wet. An experimental research study was established in this research program to develop general requirements for grouting materials for partially grouting riprap "in the wet" and "in the dry" that can be used in the scour countermeasure construction of partially grouted riprap at scour critical bridges in the state of Pennsylvania. The research program intended to utilize current US standards to evaluate grout quality and consistency. In this experimental research, a number of grout quality control tests were conducted and a correlation between the European Flow Table Test and ASTM C 1611"Standard Test Method for Slump of Self-Consolidating Concrete" was established. Recommendations for grout mix design for construction in the wet and in the dry is presented with general guidance of grouting materials for the design guidelines of partially grouted riprap for piers and abutment. / Civil Engineering

No description available.