The Erdős discrepancy problem asks, "Does there exist a sequence t = {t_i}_{1≤i<∞} with each t_i ∈ {-1,1} and a constant c such that |∑_{1≤i≤n} t_{id}| ≤ c for all n,c ∈ ℕ = {1,2,3,...}?" The discrepancy of t equals sup_{n≥1} |∑_{1≤i≤n} t_{id}|. Erdős conjectured in 1957 that no such sequence exists. We examine versions of this problem with fixed values for c and where the values of d are restricted to particular subsets of ℕ. By examining a wide variety of different subsets, we hope to learn more about the original problem. When the values of d are restricted to the set {1,2,4,8,...}, we show that there are exactly two infinite {-1,1} sequences with discrepancy bounded by 1 and an uncountable number of in nite {-1,1} sequences with discrepancy bounded by 2. We also show that the number of {-1,1} sequences of length n with discrepancy bounded by 1 is 2^{s2(n)} where s2(n) is the number of 1s in the binary representation of n. When the values of d are restricted to the set {1,b,b^2,b^3,...} for b > 2, we show there are an uncountable number of infinite sequences with discrepancy bounded by 1. We also give a recurrence for the number of sequences of length n with discrepancy bounded by 1. When the values of d are restricted to the set {1,3,5,7,..} we conjecture that there are exactly 4 in finite sequences with discrepancy bounded by 1 and give some experimental evidence for this conjecture. We give descriptions of the lexicographically least sequences with D-discrepancy c for certain values of D and c as fixed points of morphisms followed by codings. These descriptions demonstrate that these automatic sequences. We introduce the notion of discrepancy-1 maximality and prove that {1,2,4,8,...} and {1,3,5,7,...} are discrepancy-1 maximal while {1,b,b^2,...} is not for b > 2. We conclude with some open questions and directions for future work.

Steam has been widely used as the source of heating in commercial buildings and industries throughout the twentieth century. Even though contemporary designers have moved to hot water as the primary choice for heating, a large number of facilities still use steam for heating. Medical campuses with on-site steam generation and extensive distribution systems often serve a number of buildings designed prior to the mid-1980s. The steam is typically used for preheat as its high thermal content helps in heating the air faster and prevents coils from freezing in locations with extreme weather conditions during winter. The present work provides a comprehensive description of the various types of steam heating systems, steam coils, and valves to facilitate the engineer's understanding of these steam systems. A large percentage of the steam coils used in buildings are provided with medium pressure steam. Veterans Integrated Service Network and Army Medical Command Medical Facilities are examples which use medium pressure steam for heating. The current design manual for these medical facilities recommends steam at 30psig be provided to these coils. In certain cases although the steam heating coil is designed for a 5psig steam pressure, it is observed that higher pressure steam is supplied at the coil. A higher steam pressure may lead to excessive heating, system inefficiency due to increased heat loss, simultaneous heating and cooling, and increased maintenance cost. Field experiments were conducted to evaluate the effect of lowering steam pressure on the system performance. A 16% reduction in temperature rise across the coil was found when the steam pressure in the coil was reduced from 15psig to 5psig. The rise in temperature with lower pressure steam was sufficient to prevent coil freeze-up even in the most severe weather conditions. Additional benefits of reduced steam pressure are reduced flash steam losses (flash steam is vapor or secondary steam formed when hot condensate from the coil is discharged into a lower pressure area, i.e., the condensate return line) and radiation losses, increased flow of air through the coil thereby reducing air stratification and reduced energy losses in the event of actuator failure. The work also involved evaluating the existing control strategies for the steam heating system. New control strategies were developed and tested to address the short comings of existing sequences. Improved temperature control and occupant comfort; elimination of valve hunting and reduced energy consumption were benefits realized by implementing these measures.

L-Lactate dehydrogenases (LDH) are ¡§house keeping¡¨ enzymes. The LDH isozymes are known to be a very stable, slow-evolving and suitable to be a model to elucidate the phylogenetic relationships among various species. The cDNA sequences of LDH-A4 (muscle) and LDH-B4 (heart) from green iguana (Iguana iguana) were determined. The results of isozyme electrophoresis demonstrated that there are two isoforms of Iguana iguana LDH-B isozyme and called LDH-B and LDH-b. The protein structures of LDH-B and LDH-b monomer were constructed, and these two proteins have the same structure except the 5 different amino acids. The phylogenetic relationships between green iguana and other vertebrates, whose LDH cDNA sequences published previously, were analyzed by phylogenetic tree construction methods Mega2 program as well as Phylip program. These results on the relationships among lizards indicate that Iguana iguana is closer to Sceloporus woodi than to Sceloporus undulates. The divergent times between Iguana iguana and Sceloporus woodi, Iguana iguana and Sceloporus undulatus were estimated about 98 and 188 million years, respectively. The sequences of mitochondrial DNA(12S, 16S and ND1) among these three lizards were also analyzed, and the results were consistent with the traditional phylogenetics that species in the same genus were closer. The unexpected relationship that different genus of Iguana iguana and Sceloporus woodi is closer than that within same genus of Sceloporus woodi and Sceloporus undulates by analyzing among vertebrates LDH isozymes remained to be further confirmed.

Abstract¡G Athyrioid ferns¡]Athyrioideae, Dryopteridaceae¡^consist of about 700 species with a distribution range from tropical to temperate zone in the world. In Taiwan, the subfamily includes 50 species commonly found from lowland to around 3000 meters in elevation. Phylogenetic relationships and the generic circumscription of athyrioid genera are confused and controversial. In this study, trnL-trnF spacer, which is a nucleotide sequence between genes in the chloroplast, was used to analyze and infer the phylogenetic relationships and evolutionary status of 35 species. Phylogenetic trees produced by neighbor-joining and maximum-parsimony methods are similar in topology. Athyrium and Cornopteris form a clade, and this indicates Cornopteris is more closely related to Athyrium than to Diplazium. Anisogonium nests within Diplazium clade, and it implies these two genera congeneric. Anisocampium is distinct from Athyrium sensu stricto and forms a clade with Athyrium nipponicum. Deparia clade includes Athyriopsis, Lunathyrium, Dryoathyrium, Dictyodroma, Diplazium subsinuatum and Matteuccia. These four clades may be seen as the core part of athyrioid ferns. Woodsia and Thelypteridaceae cluster next to these four clades. Cystopteris and Gymnocarpium occupy a position between Thelypteridaceae and Dryopteridaceae. Rhachidosorus is neither closely related to Athyrium nor Diplazium. Hypodematium is distantly related to athyrioid ferns and forms a clade with Dryopteridaceae. Therefore, Hypodematium may be isolated from athyrioid ferns. Based on the evidences mentioned above, athyrioid ferns are suggested to be closely related to Thelypteriaceae, and are probably members of Woodsiaceae¡]including Thelypteridaceae¡^instead of Dryopteridaceae. In addition, Cystopteris and Gymnocarpium are the most basal lineage of Woodsiaceae sensu lato. The core group of athyrioid ferns probably better treated as a monophyletic tribe or subfamily of Woodsiaceae at current stage.

Various approaches have been proposed for finding the longest common subsequence (LCS) of two sequences. The time complexities of these algorithms are usually $O(n^2)$ in the worst case, where $n$ is the length of input sequences. However, these algorithms would become infeasible when the input length, $n$, is very long. Recently, the $k$-LCS $(k ≥ 2)$ problem has become more attractive. Some algorithms have been proposed for solving the problem, but the execution time required for solving the $k$-LCS problem is still too long to be practical. In this thesis, we propose a genetic algorithm for solving the $k$-LCS problem with time complexity $O(Gpk(n + |P_j|))$, which $G$ is the number of generations, $p$ is the number of template patterns, $k$ is the number of input sequences, $n$ and $|P_j|$ are the length of input sequences and the length of template patterns, respectively. As our experimental results show, when $k$ is 20 and $n$ is 1000, the performance ratio ($|CS|/|LCS|$) of our algorithm is greater than 0.8, where $|CS|$ denotes the length of the solution we find, and $|LCS|$ represents the length of the real (optimal) LCS. Comparing the performance ratios with Expansion Algorithm and BNMAS Algorithm, our algorithm is much better than them when the number of input sequences varies from 2 to 20 and the length of the input sequences varies from 100 to 2000.

Thesis (Ph. D.)--University of Washington, 2001. / Vita. Includes bibliographical references (p. 120-124).

Thesis (Ph. D.)--University of Texas at Austin, 2001. / Vita. Includes bibliographical references. Available also from UMI/Dissertation Abstracts International.

Thesis (M.S.)--West Virginia University, 2002. / Title from document title page. Document formatted into pages; contains iii, 19 p. Includes abstract. Includes bibliographical references (p. 17-19).

For many applications, such as cryptography and digital communications, binary sequences with certain specific properties are required. These include a balance of 0's and 1's in a period, ideal runs frequencies, good auto- and cross-correlation spectra, and high linear complexity. Perfect Linear Complexity Profile sequences (PLCPs) have the linear complexity of all subsequences (starting with the first bit) equal to half the length of the subsequence (this is the expected value for a random sequence). We investigate the density - proportion of ones - of finite length PLCPs, both in general and for specific examples. We gain results on the average, maximal and minimal densities, as well as their limits as the length tends to infinity. We also study whether the PLCP property is preserved under various decimations. PLCPs are characterised by a simple linear recurrence modulo 2. We look at similar "nearly" perfect profiles and characterise sequences with these profiles in terms of similar recurrences. Also sequences with a PLCP up to a point and then constant complexity are characterised in terms of the convergents in the continued fraction expansion of the generating function of PLCPs, and we look briefly at their corresponding periods. Sequences with bounded jumps in their linear complexity are discussed and a method of generating them is suggested. The interleaving of shifts of a sequence with out-of-phase auto-correlation equal to -1 and balance, in a specific order, seems to be a fundamental method of generating longer sequences with this auto-correlation property. It is shown that two pairs of families of these sequences, derived in different ways, are in fact equivalent. The analysis highlights the general method mentioned above, and so provides examples of families of sequences with 2-valued auto-correlation by changing the ingredients in the interleaving pattern. We also look at the cross-correlation of sequences with this interleaved structure.

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