"The object of this paper is to present a detailed, illustrated discussion of a portion of the theory of bilinear forms as found in Volume 2 of Lectures in Abstract Algebra by Nathan Jacobson. This theory involves the fundamental properties of bilinear forms on finite dimensional vector spaces over arbitrary division rings and includes such things as a discussion of the relationship between matrices and bilinear forms as well as the definition of the transpose of a transformation relative to a pair of bilinear forms; a definition independent of the matrix representations of the forms"--Introduction. / Typescript. / "May, 1955." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: Nickolas Heerema, Professor Directing Paper. / Includes bibliographical references (leaf 30).

Inaug.-diss.--Breslau. / Lebenslauf.

No description available.

This thesis presents modeling of bilinear flow in tight gas wells and its behavior on single matrix block drainage. The objectives of this research are to: simulate a tight gas well using matrix block drainage under constant production pwf and with a constant production rate; be able to predict the behavior of matrix block drainage; study the effect of natural fracture(s) near a well; examine the matrix block drainage in a natural fracture network; and to validate a matrix block drainage model with a hydraulic fracture analytical solution. Two different production scenarios, constant pwf and constant rate, are assigned to a tight gas well in matrix block drainage. Matrix block drainage has two distinct permeabilities; a low permeability matrix serves as the tight gas reservoir with a high permeability streak surrounding the matrix. A well only produces from the high permeability fracture. Models were run with different sensitivity cases toward fracture half length, xf, and fracture permeability kf,. The fracture half-length reflects on a/b aspect ratio. The analytical solution for hydraulic fracture developed by Cinco-Ley and Guppy serves as the validation of matrix block drainage. Analysis on the flow regimes which occurred for different geometries and properties are provided. The log-log diagnostic plot of pseudo-pressure drop/gas rates and the log-log plot of dimensionless pressure derivatives and dimensionless reciprocal production rates are presented. Finally, an attempt to normalize the late time and early time of all geometries and properties is presented to obtain one analytical solution.

This thesis presents modeling of bilinear flow in tight gas wells and its behavior on single matrix block drainage. The objectives of this research are to: simulate a tight gas well using matrix block drainage under constant production pwf and with a constant production rate; be able to predict the behavior of matrix block drainage; study the effect of natural fracture(s) near a well; examine the matrix block drainage in a natural fracture network; and to validate a matrix block drainage model with a hydraulic fracture analytical solution. Two different production scenarios, constant pwf and constant rate, are assigned to a tight gas well in matrix block drainage. Matrix block drainage has two distinct permeabilities; a low permeability matrix serves as the tight gas reservoir with a high permeability streak surrounding the matrix. A well only produces from the high permeability fracture. Models were run with different sensitivity cases toward fracture half length, xf, and fracture permeability kf,. The fracture half-length reflects on a/b aspect ratio. The analytical solution for hydraulic fracture developed by Cinco-Ley and Guppy serves as the validation of matrix block drainage. Analysis on the flow regimes which occurred for different geometries and properties are provided. The log-log diagnostic plot of pseudo-pressure drop/gas rates and the log-log plot of dimensionless pressure derivatives and dimensionless reciprocal production rates are presented. Finally, an attempt to normalize the late time and early time of all geometries and properties is presented to obtain one analytical solution.

Thesis--Bonn. Extra t.p. with thesis statement inserted. / Includes bibliographical references (p. 45).

Thesis--Bonn. Extra t. p. with thesis statement inserted. / Bibliography: p. 45.

Thesis (Ph. D.)--University of Missouri-Columbia, 2005. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (May 23, 2006) Vita. Includes bibliographical references.

The thesis explores the new expansions of eigenvalues for -£Gu =£f£lu in S with the Dirichlet boundary condition u=0 on $partial S$ by two conforming elements: the linear element $P_1$ and the bilinear element $Q_1$, and three non-conforming elements: the rotated bilinear element (denoted $Q_1^{rot}$), the extension of $Q_1^{rot}$ (denoted $EQ_1^{rot}$) and Wilson's element. The expansions indicate that $P_1$, $Q_1$ and $Q_1^{rot}$ provide the upper bounds of the eigenvalues, and $EQ_1^{rot}$ and Wilson's elements provide the lower bounds of the eigenvalues. Comparing the five finite elements, the $Q_1^{rot}$ element is more accurate. By the extrapolation, the superconvergence $O(h^4)$ can be obtained where $h$ is the boundary length of uniform squares. Numerical experiment are carried to verify the theoretical analysis made. (°Ñ·Ó¹q¤lÀÉp.4)

Traditional transfer function of integrators have warping effect in high frequency, this isn¡¦t good for make filter circuit. In reference[3] they mention a new transfer function to improve this error, but we found that the design of the previous circuit doesn¡¦t conform to the new transfer function. In this thesis, a different structure of integrator is presented, it use the method of double sampling to realize the modified bilinear transfer function, in addition, we also add a grounded-gate amplifier to decrease the input impedance and dummy switch technique what can reduce the charge injection error, then we use the central circuit to make the second order bandpass filter. The proposed circuit employ Hspice to simulate and design the form of the circuit layout, then use TSMC 0.35£gm CMOS process to make chip. The sampling frequency is 10MHz, the central frequency is 1MHz, and the power consumption is 1.78mW.