Let X be a Banach space and Y be a closed subspace of X. Given a bounded linear functional f on Y , the Hahn-Banach theorem guarantees that there exists a linear extension ˜ f 2 X of f which preserves the norm of f. But it does not state that such ˜ f is unique or not. If every f in Y does have a unique norm preserving extension ˜ f in X , we say that Y has the unique extension property, or, following P. R. Phelps, the property U in X. A. E. Taylor [17] and S. R. Foguel [7] had shown that every subspace Y of X has the unique norm-preserving extension property in X if and only if the dual space X is strictly convex. As known in [11], X is smooth if X is strictly convex. The converse does not hold in general unless X is reflexive. In this thesis, we show that if a subspace Y of a Banach space X has the unique extension property then the norm of Y is outward smooth in X. The converse holds when Y is reflexive. Note that our conditions are local, i.e., they depend on Y only, but not on X. Several related results are also derived. Our work extends and unifies recent results in literature.

Protecting privacy of individuals is critical for forensic genetics. In a kinship/identity testing, related DNA profiles between user's query and the DNA database need to be extracted. However, unrelated profiles cannot be revealed to each other. The challenge is today's DNA database usually contains millions of DNA profiles, which is too big to perform privacy-preserving query with current cryptosystem directly. In this thesis, we propose a scalable system to support privacy-preserving query in DNA Database. A two-phase strategy is designed: the first is a Short Tandem Repeat index tree for quick fetching candidate profiles from disk. It groups loci of DNA profiles by matching probability, so as to reduce I/O cost required to find a particular profile. The second is an Elliptic Curve Cryptosystem based privacy-preserving matching engine, which performs match between candidates and user's sample. In particular, a privacy-preserving DNA profile matching algorithm is designed, which achieves O(n) computing time and communication cost. Experimental results show that our system performs well at query latency, query hit rate, and communication cost. For a database of one billion profiles, it takes 80 seconds to return results to the user.

This thesis investigates, develops and implements algorithms for shape- preserving curve and surface design that aim to reflect the shape characteristics of the underlying geometry by achieving a visually pleasing interpolant to a set of data points in one or two dimensions. All considered algorithms are local and useful in computer graphics applications. The thesis begins with an introduction to existing methods which attempt to solve the shape-preserving 1 curve interpolation problem using C cubic and quadratic splines. Next, a new generalized slope estimation method involving a parameter t, which is used to control the size of the estimated slope and, in turn, produces a more visually pleasing shape of the resulting curve, is proposed. Based on this slope generation formula, new automatic and interactive algorithms for constructing 1 shape-preserving curves from C quadratic and cubic splines are developed and demonstrated on a number of data sets. The results of these numerical experiments are also presented. Finally, a method suggested by Roulier which 1 generates C surfaces interpolating arbitrary sets of convex data on rectangular grids is considered in detail and modified to achieve more visually pleasing surfaces. Some numerical examples are given to demonstrate the performance of the method.

The texture of processed berry fruits changes both during processing and subsequent storage. A study was made of these changes in processed strawberries, raspberries, blackberries, and blue- berries, spin-cooked and stored at 100°F. for 28 days in tin and glass containers. Four samples, from each of the two replications of the above, four berries,were analyzed immediately after processing and after 3, 7, 14, and 28 days of storage at 100°F. Physical measurement of texture was obtained by the use of Maryland Shear-press. The work diagrams thus obtained were studied in detail. These samples, after being subjected to the Shear-press, were analyzed for percent A.I.S. and total pectin. The results indicated the following: 1. There was no significant difference in the texture, percent A.I.S. and total pectin, between berries processed and stored in tin and glass containers over a period of 28 days at 100°F, 2. Highest correlation was obtained between texture as measured by partial work and total pectin in case of strawberries and blueberries and between maximum force and percent A.I.S. in raspberries and blackberries. 3. Maryland Shear-press gave characteristic work diagrams for each of the four berries, which were consistent throughout. 4. A linear relationship was obtained between sample size and texture as measured by the total work. / Graduation date: 1963

Ten, twenty, and thirty percent of dextrose were used in place of sucrose to preserve the Maraschino-type cherries because of the expectation that the smaller sized molecules would enter the cherry tissue more readily and thus increase the weight and volume of the fruit. Other samples, sucrose and percent dextrose replacement, were tested with the pH of the syrup controlled at 3.0. Both cold and hot processes were used, and samples were tested every two days during the concentrating period for drained weight of the cherries; volume of the cherries; pH, inversion, and degree Brix of the syrup. The commercial product, with the trade name "glucose", was also tested in another series of samples. Owing to its insolubility at low temperatures only the hot process was used. The results show that dextrose increases the weight of cherries in the cold process, whereas the difference in weight gain is not as noticeable in the hot process. "Glucose" gives approximately the same results as does dextrose. High inversion of the syrup of a sample does not indicate a comparable weight gain in the cherries because the monosaccharides are concentrated in the fruit tissue. By controlling the pH of the syrup at 3.0 no advantage in increasing the weight of the cherries is gained. / Graduation date: 1940

Graduation date: 1948

Graduation date: 1948

Graduation date: 1954

Graduation date: 1958

Thesis (Ph. D.)--University of Wisconsin--Madison, 1983. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 93-96).