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- Andrén, Lina J., 1980-
(författare)
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On Latin squares and avoidable arrays
- 2010
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis consists of the four papers listed below and a survey of the research area. I Lina J. Andrén: Avoiding (m, m, m)-arrays of order n = 2k II Lina J. Andrén: Avoidability of random arrays III Lina J. Andr´en: Avoidability by Latin squares of arrays with even order IV Lina J. Andrén, Carl Johan Casselgren and Lars-Daniel Öhman: Avoiding arrays of odd order by Latin squares Papers I, III and IV are all concerned with a conjecture by Häggkvist saying that there is a constant c such that for any positive integer n, if m ≤ cn, then for every n × n array A of subsets of {1, . . . , n} such that no cell contains a set of size greater than m, and none of the elements 1, . . . , n belongs to more than m of the sets in any row or any column of A, there is a Latin square L on the symbols 1, . . . , n such that there is no cell in L that contains a symbol that belongs to the set in the corresponding cell of A. Such a Latin square is said to avoid A. In Paper I, the conjecture is proved in the special case of order n = 2k . Paper III improves on the techniques of Paper I, expanding the proof to cover all arrays of even order. Finally, in Paper IV, similar methods are used together with a recoloring theorem to prove the conjecture for all orders. Paper II considers another aspect of the problem by asking to what extent way a deterministic result concerning the existence of Latin squares that avoid certain arrays can be used when the sets in the array are assigned randomly.
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| 2. |
- Pei, Zhichao, 1965-
(författare)
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Carbohydrate Synthesis and Study of Carbohydrate-Lectin Interactions Using QCM Biosensors and Microarray Technologies
- 2006
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Interactions between carbohydrates and proteins are increasingly being recognized as crucial in many biological processes, such as cellular adhesion and communication. In order to investigate the interactions of carbohydrates and proteins, the development of efficient analytic technologies, as well as novel strategies for the synthesis of carbohydrates, have to be explored. To date, several methods have been exploited to analyze interactions of carbohydrates and proteins, for example, biosensors, nuclear magnetic resonance (NMR); enzyme-linked immunosorbent assays (ELISA), X-ray crystallography and array technologies. This thesis describes the development of novel strategies for the synthesis of carbohydrates, as well as new efficient strategies to Quartz Crystal Microbalance- (QCM-) biosensors and carbohydrate microarrays technologies. These methodologies have been used to probe carbohydrate-lectin-interactions for a range of plant and animal lectins.
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