Several conjectured and proven generalizations of the Brouwer Fixed Point Theorem are examined, the plane fixed point problem in particular. The difficulties in proving this important conjecture are discussed. It is shown that it is true when strong additional assumptions are made. Canonical examples are produced which demonstrate the differences between this result and other generalized fixed point theorems.

Several conjectured and proven generalizations of the Brouwer Fixed Point Theorem are examined, the plane fixed point problem in particular. The difficulties in proving this important conjecture are discussed. It is shown that it is true when strong additional assumptions are made. Canonical examples are produced which demonstrate the differences between this result and other generalized fixed point theorems.

Binocular eye-gaze tracking can be used to estimate the point-of-gaze (POG) of a subject in real-world three-dimensional (3D) space using the vergence of the eyes. In this thesis, a novel non-contact, model-based technique for 3D POG estimation is presented. The non-contact system allows people to select real-world objects in 3D physical space using their eyes, without the need for head-mounted equipment. Using a model-based POG estimation algorithm allows for free head motion and a single stage of calibration. The users were free to naturally move and reorient their heads while operating the system, within an allowable headspace of 3.2 x 9.2 x 14 cm. A rela tively high precision, as measured by the standard deviation of the 3D POG estimates, was measured to be 0.26 cm and was achieved with the use of high speed sampling and digital filtering techniques. When observing points in a 3D volume, large head and eye rotations are far more common than when observing a 2D screen. A novel corneal reflection pattern matching algorithm is presented for increasing image feature tracking reliability in the presence of large eye rotations. It is shown that an average accuracy of 3.93 cm was achieved over seven different subjects and a workspace volume of 30 x 23 x 25 cm (width x height x depth). An example application is presented illustrating the use of the 3D POG as a human computer interface in a 3D game of Tic-Tac-Toe on a 3 x 3 x 3 volumetric display.

Floating point numbers are used in many applications that  would be well suited to a higher parallelism than that offered in a CPU. In  these cases, an FPGA, with its ability to handle multiple calculations  simultaneously, could be the solution. Unfortunately, floating point  operations which are implemented in an FPGA is often resource intensive,  which means that many developers avoid floating point solutions in FPGAs or  using FPGAs for floating point applications. Here the potential to get less expensive floating point operations by using ahigher radix for the floating point numbers and using and expand the existingDSP block in the FPGA is investigated. One of the goals is that the FPGAshould be usable for both the users that have floating point in their designsand those who do not. In order to motivate hard floating point blocks in theFPGA, these must not consume too much of the limited resources. This work shows that the floating point addition will become smaller withthe use of the higher radix, while the multiplication becomes smaller by usingthe hardware of the DSP block. When both operations are examined at the sametime, it turns out that it is possible to get a reduced area, compared toseparate floating point units, by utilizing both the DSP block and higherradix for the floating point numbers.

This essays purpose is to accentuate the meaning of the knowledge of the design elements color, form and texture in the hair design education. Both the Bauhaus school and Pivot Point education campaign close knowledge in color, form and texture. In my study of the literature I compared the Bauhaus school with Pivot Point International Inc, study material for hair design education. From the similarities in this material I develop a project in color, form and texture. This was a teaching test for students in the hair design education at the upper secondary. My conclusion is that you, already in this first semester, can see which students who have the design interest and touch. In my discussion I have, with inspiration from The Bauhaus school and Pivot Point education, some suggests for the future in hair design education in the upper secondary.

The ABR point-to-multipoint connection is now playing a more important role. Many consolidation algorithms have been proposed to solve the consolidation noise problems and the slow transient response problem. But few timeout algorithms are proposed to handle the ¡§non-responsive¡¨ branches problems for the multicast connections. We proposed a timeout algorithm which can handle the ¡§non-responsive¡¨ branches problems and with a lower implementation complexity. Simulation results also show that the proposed timeout algorithm can efficiently handle the ¡§non-responsive¡¨ branches and can use the available bandwidth within a small period of time.

Four proteins exhibiting different rates of denaturation or precipitation with increasing cooking temperature from 63 to 73°C for beef and 67 to 79°C for pork were selected for developing a ratio model and incorporating the results into a mathematical expression. Monoclonal antibodies (Mabs) against lactate dehydrogenase isozyme 5 (LDH-5), bovine serum albumin (BSA), porcine enolase, and bovine myoglobin were developed for use in a sandwich enzyme-linked immunosorbent assay (ELISA) to simultaneously investigate changes in protein concentration with incremental increases in temperature. Four groups of mice were immunized separately with commercially available or purified protein (LDH-5, BSA, enolase, or myoglobin). After reporting ample blood serum titers, spleen cells were harvested and fused with SP2 myeloma tumor cells using an electro fusion cell manipulator. Hybridoma containing wells were screened against their respective protein to isolate hybridomas secreting protein specific Mabs. Tissue culture flask produced Mabs were used initially in sandwich ELISA assay testing. Mabs were tested against ground beef and pork cooked to instantaneous endpoint temperatures (EPTs). A 6 g section removed from the geometric center of each sample was homogenized in phosphate buffer, centrifuged, and a 1 ml aliquot collected for analysis. Microtiter plates were coated with goat anti-mouse IgG antibody (2 mg/ml) to act as a capture antibody for the protein specific monoclonal antibody concentrated from cell culture supernatant. Serial diluted muscle (beef or pork) extract (10 ml) from each EPT was applied to a microtiter plate. A protein A/G purified polyclonal antibody (Pab) was applied, followed by a goat anti-rabbit IgG peroxidase conjugated antibody. Concentration was determined by comparison to a standard curve. After multiple cell fusions, 24, 29, 66, and 12 cell lines secreting protein specific Mabs against LDH-5, BSA, enolase, and myoglobin, respectively, were produced. Six Mabs against LDH-5 reported R2 values > 0.9 indicating high specificity and affinity for LDH-5. Sandwich ELISA assays development with Mabs against BSA, enolase, and myoglobin was not as successful. Mouse ascites produced Mabs against BSA, enolase, and myoglobin were also unsuccessful when used in a sandwich ELISA. However, preliminary data suggested a multiple antigen ratio model still remained a viable option.

In addition to the previous pipelined floating-point CORDIC design, three different architectures supporting both CORDIC rotation mode and vectoring mode are proposed in this thesis. Detailed analysis and comparison of these architectures are addressed in order to choose the best architecture with minimized area cost and computation latency given the required bit accuracy. Based on the comparison, we have chosen the best architecture and implemented an IEEE single precision floating-point CORDIC processor. The mathematical analysis of the computation errors is done to minimize the bit width of the composing arithmetic components during implementation. The comparison results of different architectures also serve as a general guideline for the design of floating-point sine/cosine units. Finally, we study the application of the floating-point CORDIC to 3D graphics acceleration.

Thesis (Ph. D.)--Johns Hopkins University, 1916. / Vita. "Reprinted from American journal of mathematics, vol. XL, no. 1, January, 1918."

Binocular eye-gaze tracking can be used to estimate the point-of-gaze (POG) of a subject in real-world three-dimensional (3D) space using the vergence of the eyes. In this thesis, a novel non-contact, model-based technique for 3D POG estimation is presented. The non-contact system allows people to select real-world objects in 3D physical space using their eyes, without the need for head-mounted equipment. Using a model-based POG estimation algorithm allows for free head motion and a single stage of calibration. The users were free to naturally move and reorient their heads while operating the system, within an allowable headspace of 3.2 x 9.2 x 14 cm. A rela tively high precision, as measured by the standard deviation of the 3D POG estimates, was measured to be 0.26 cm and was achieved with the use of high speed sampling and digital filtering techniques. When observing points in a 3D volume, large head and eye rotations are far more common than when observing a 2D screen. A novel corneal reflection pattern matching algorithm is presented for increasing image feature tracking reliability in the presence of large eye rotations. It is shown that an average accuracy of 3.93 cm was achieved over seven different subjects and a workspace volume of 30 x 23 x 25 cm (width x height x depth). An example application is presented illustrating the use of the 3D POG as a human computer interface in a 3D game of Tic-Tac-Toe on a 3 x 3 x 3 volumetric display.