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For trace class operators A, B B1(H) (H a complex, separable Hilbert space), the product formula for Fredholm determinants holds in the familiar form detH((IH − A)(IH − B)) = detH(IH − A)detH(IH − B). When trace class operators are replaced by Hilbert–Schmidt operators A, B B2(H) and the Fredholm determinant detH(IH − A), A B1(H), by the 2nd regularized Fredholm determinant detH,2(IH − A) = detH((IH − A) exp(A)), A B2(H), the product formula must be replaced by detH,2((IH − A)(IH − B)) = detH,2(IH − A)detH,2(IH − B) × exp(− trH(AB)). The product formula for the case of higher regularized Fredholm determinants detH,k(IH−A), A Bk(H), k N, k 2, does not seem to be easily accessible and hence this note aims at filling this gap in the literature.

http://archive.org/details/parameterplanede1094512801

In this solid text Michael Oberg presents his version of American Indian history. From the start he works to avoid presenting just another encyclopedic narrative likely to leave readers "awash in a sea of facts and data disconnected from any coherent narrative." To this end he focuses on how eleven Indigenous communities dealt with the European invasions of North America. His list includes groups as disparate as the Chumash and Pueblo peoples in the West, the Potawatomis and Dakota Sioux in the North, the Crows, Kiowas, and Caddos in the Plains, and Eastern peoples such as the Mohegans, Powhatans, Cherokees, and Senecas. With this approach he illustrates the variety of these Indian nations' experiences in dealing with the changes wrought by contact with the invading powers.

The dissertation complicates the familiar narrative about the coming of the Civil War in American national history by exploring how several Native American groups participated in the conflicts of Kansas Territory.The creation of Kansas in the lands reserved for removed tribes brought fervent local negotiation over land and treaty rights between Indians and whites. Most Indians were forced to select new options and allegiances by the impositions of white settlers' agendas and federal initiatives. Rather than hapless victims of settler manipulation, members of several reservation communities on the Kansas-Missouri border, among a total of twenty-six tribes, vied for political and legal control in ways that shaped and salvaged the legal survival and identities of these tribal nations.The dissertation examines how two members of the Wyandot community negotiated their identities around divergent American discourses of race and ethnicity, how the Christian Moravian Indian community contested the terms of their own future collective place and identity, how the New York Indians vied for treaty rights in competition with settlers' claims groups, and how the Delaware Indians responded to legal violations by whites. The multi-faceted conflicts left many Indians to choose sides between competing white political partisans and between a future of U.S. citizenship or separate tribal collectivity. Over these chapters, Indians negotiate their own individual or group identities by the maintenance or expansion of particular discourses of difference. The choices and discourses related to Indian collectivity were, in part, colonial legacies that informed tribal nationalism and identity later in time.The importance of territorial Kansas is not simply a battle between white partisans over the fate of slavery and democratic government, but also a critical struggle between Indians and whites that re-defined racial and ethnic identities and collective rights of Native peoples during the Civi

This work will explore the interconnections between political power and the various forms of corruption endemic in Denver in the late 19th century placing municipal corruption and election fraud into the larger political, economic, social and cultural framework. Municipal political corruption in Denver operated through a series of relationships tying together, the city police, political factions, utility and industrial leaders, con men, gamblers, protection rackets and the election of U.S. Senators. This work will explore not only the operational ties, but also how these ties served all parties, and the discourse used to rationalize the behavior and distribute blame. The dates for this study are bracketed by two significant events: a mayoral election and trial in 1889-1890, and the City Hall War in the spring of 1894. Each of these events represents a point when a rupture in the tight net of political control sparked a battle for hegemony with a concomitant turn to corruption and election fraud on the part of competing political factions. The level of municipal corruption in Denver was not necessarily unusual; however, the extent of the documentation enables a detailed analysis. Denver newspapers blamed the corruption on an unspecified "gang" and a shadowy "machine." The editors railed against the scourge of con men, and simultaneously used the ubiquitous fraud as a metaphor for trickery and corruption of all kinds. This detailed analysis reveals a more complex series of events through which a cabal of business and industry leaders seized control of both the city and the state government, giving them the political power to wage what has been called a war against labor.

This slender volume lays out the story of the creation, evolution, and demise of the mid-nineteenth- century region known as "Indian Country." An amorphous and frequently changing area located in the Plains, one might posit that it existed more on paper than on the ground. The author traces four legal actions underlying the creation of such a region: the Royal Proclamation of 1763, the 1803 Louisiana Purchase, the 1830 Indian Removal Act, and the 1834 Indian Trade and Intercourse Act. The latter guaranteed the tribes' rights to their land beyond the Mississippi forever. As Unrau's analysis demonstrates, the contrast between American ideas for and actions toward the area proved fatal to hopes for the success of an Indian Country. Several early chapters focus on changing ideas about the region's land quality and potential resources. The discussion demonstrates clearly how the early negative assessments of the Plains by Zebulon Pike and Stephen Long faded quickly during the 1820s as Santa Fe traders and others crossed the region repeatedly. By the 1830s tribal immigrants from the East and pioneer farmers who squatted along the eastern edges of Indian Country all spoke highly of rich farm lands there. As a result, shortly after the 1834 Trade and Intercourse Act passed, Missouri politicians succeeded in extending that state's northwestern corner west to the Missouri River through the Platte Purchase. Only one step in the dismemberment of the Indian Country, it illustrated the inability or unwillingness of the federal government to protect the tribes from being overrun and dispossessed by speculators. The 1854 passage of the Kansas-Nebraska Act opened much of the eastern Plains to settlement, resulting in the dispossession of the Indians still there.

This dissertation examines tribal-state relations in Alabama and Louisiana during the 1970s and 1980s. These relationships were the outcomes of the Southern Indian Movement, which emerged just as regional and national racial politics began shifting and southern states started to recognize Indian populations through the development of Indian Affairs Commissions. Through these state agencies, Indian groups forged strong networks with local, state, and national agencies while advocating for cultural preservation and revitalization, economic development, and the implementation of community services. Commissions also brought formerly isolated groups, each with different goals and needs, together for the first time, creating an assortment of alliances and divisions. These unique relationships between tribes and states additionally served state interests by giving legislators the opportunity to wage public relations campaigns, to make racialized critiques of the Black Civil Rights Movement, to emphasize the South's indigenous identity, and to assert states' rights by assuming federal responsibilities.

This book is yet another result of the Lewis and Clark mania that has swept across much of the West and through the scholarly publishing community with interests in that region. It approaches the topic from an unexplored angle by looking at what members of the expedition did after their 1806 return to St. Louis. To do so, Larry Morris tries to focus on what he describes as "fascinating events" rather than merely giving the reader a string of mini-biographies. This approach allows him to range widely in time and place as he follows events in people's lives. At the same time it prevents him from offering any thesis or central theme that might hold the disparate stories together beyond the repeated overlapping of the veterans' experiences. By examining the lives of thirty-three people, many of whom were quite ordinary, Morris faces several challenges. One of them is balance. Some of the participants, Lewis and Clark or Sacagawea, for example, have received plenty of attention in numerous books and articles, as has York, William Clark's slave. Others disappeared almost as soon as they completed their epic journey, and sources for them are thin or even non-existent. Related to this issue is Morris's definition of what constituted a "fascinating" event in the lives of his subjects. Such experiences as murder, suicide, escape from or death at the hands of Indians all qualify. Certainly those involved in the Missouri River trade or trapping in the Northern Rockies faced repeated danger there. Another problem is how much attention to give events and issues previously examined by earlier scholars. Morris's longest chapter, for example, narrates events surrounding the October 1809 death of Meriwether Lewis which have already received ample scrutiny. A further instance occurs in the discussion of Sacagawea's death, which includes conflicting theories about this event, though settling on the generally accepted 1812 date as the correct one. At times stories not clearly related to

Hoping to avoid violent incidents and possible warfare along its frontiers, the fledgling United States government established in 1796 a system for dealing with depredation claims. It provided the machinery through which both Indians and pioneers could apply for indemnity for losses incurred as a result of their dealings with each other. Despite such benign goals, the machinery seldom operated as envisioned. The claims process, too slow to prevent recurring violence, was so fraud-ridden that even honest claimants had to run a gauntlet of suspicious officials to have their cases considered. As a result, Larry Skogen states, throughout its entire 124 year history the process did little more than "clog the machinery of the federal government." He uses this discussion of depredation claims to illustrate the nineteenth-century shift in American tort law from strict liability and sovereign immunity to negligence and the right of private citizens to sue the federal government. This book, then, combines the study of federal policy with that of shifting currents in the national legal system. Beginning with early treaties, some written before the Constitution, the United States promised to punish pioneers who committed crimes against Indians and demanded that tribes surrender their people who committed similar acts against whites. Gradually that effort evolved into a formal claims system. Working through the War Department, and after 1849 through the Interior Department, Indian Office personnel gathered evidence, took claims papers, and sent their findings on to Washington. There the evidence rarely persuaded officials to offer damages. Except for some 1834 claims paid to people in Missouri and Georgia, the system frustrated everyone. Finally, in 1891 Congress gave jurisdiction over Indian depredation claims to the United States Court of Claims where it remained until 1920 when the system shut down. Based on monumental amounts of archival research, Skogen's narrative follows

Euthanasia is a subject that is fraught with legal, medical and religious overtones. It is a highly charged emotional subject on which the majority of the American public appear to have a definite opinion. Yet, these opinions are not formed in a vacuum and are usually to be found based upon an individual's personal experiences and upbringing; the experiences of friends, acquaintances, or co-workers; and the views and comments heard, seen and read through America's mass media. By studying one specialized form of communication, the popular American magazine between 1896 and 1976, a clearer understanding emerges of the roots of today's euthanasia controversy. The magazines surveyed suggested that the euthanasia argument shifted its emphasis at mid century from the right to choose and its attendant corollaries to the right to die with its corresponding issues. Underlying this shift is the subliminal acknowledgment that America, through an unwritten contract with techno-medicine, has exchanged its self-determination for the promises of biological restructuring and prolongation of human life. Such a contract denies individual freedom to determine the importance of one's quality of life versus quantity of life. Americans since 1976 have been searching for ways to recapture their self-determination in the end-of-life decision making process.

In the past decade biography as a field within American history has made a strong comeback, and Robert M. Utley's study of the Hunkpapa Lakota (Sioux) leader Sitting Bull is an excellent contribution to the field. Writing the life story of an Indian leader who died more than one hundred years ago is difficult at best. For example, even the birth date of the subject is open to question. Nevertheless, the author has written a thorough, balanced, and informed book. In it Sitting Bull emerges as a rational person living within his culture, having recognizable goals, and experiencing both success and failure. Utley's narrative rests solidly on what is known or can be reconstructed about nineteenth-century Hunkpapa society.

This project develops a set of multi-layered perceptron neural networks to serve as performance baselines for the classification of the material condition of a representative helicopter intermediate gearbox by advanced neural network models currently under development. The first half of a collection of machinery condition sensor data recording induced faults in a TH-1L helicopter intermediate gearbox is used to develop candidate network configurations and the second half of the data collection to test the candidate networks. The data is derived from three accelerometer sensor channels. The network with the lowest average machinery condition classification error is chosen as the baseline network for that sensor channel and described in "C" computer program code. The error in gearbox machinery condition classification for these networks ranges from 2.2% for the sensor channel five network to 7.9% for the channel 5+6+7 combined network.

In New Spain, the professionalization of medicine followed the same pattern as in Europe and was prompted by similar intellectual and political factors. As with their European colleagues, the local medical elite of the late eighteenth century was greatly influenced by the Enlightenment, working tirelessly to advance medical science and improve the quality of treatment available to the public. Scientific developments in Europe influenced practitioners in New Spain through local and imported publications as well as through the arrival of a large number of European practitioners. While the Enlightenment played an important role from the scientific and medical points of view, international politics proved crucial to the development of surgery and its rapid rise to a professional level. The intense rivalry among nations prompted Spain to reorganize its armies and consequently, to turn its attention to military surgery. In Mexico, the establishment of formal surgical education and the reorganization of the armies resulted in the arrival of foreign practitioners and the creation of a two tiered system based on nationality. Of equal importance for the initial stages of professionalization was the rapid erosion of traditional social values in the late colonial period. As reflected by the increasing laxity in the enforcement of the limpieza de sangre requirements, race and ancestry as a measure of status were beginning to give way to personal merit. The medical professional gives a unique opportunity to analyze the fascinating world of late colonial Mexico. The hierarchical organization of the profession reflects contemporary society and offers a glance at daily life from the point of view of various socio-economic levels while the relations among its members mirror the complicated relations among the different segments of society. The growing criollo nationalism becomes patent in the attitude of some practitioners, an echo of future and more profound antagonism. From an inte

Having constructed a plantation economy in the Yazoo Mississippi Delta, white Delta planters struggled to retain control of African-American labor after the start of the Civil War. In their effort, the planters manipulated the Freedmen's Bureau; passed the Black Code; sought out foreign labor; and condoned extralegal intimidation. The Civil War disrupted the plantation economy of the Yazoo Delta, prompting the planters to pursue innovative means to preserve the status quo. To achieve this end, they fought with the Confederate government for control of the militia, attempting to stabilize an economy rocked by military incursions, deserters, and outbreaks of lawlessness. Emancipation, the ultimate disruption to the plantation, precipitated a struggle between these former masters and African-Americans seeking to find the meaning of their freedom. The United States government also attempted to restructure the plantation economy of the Delta after the Civil War, but planters often manipulated federal authority to their advantage. Charged with protecting the interests of the freedmen, the Freedmen's Bureau, for example, frequently accommodated the labor needs of Delta planters, even transporting labor to the plantations when necessary. Similarly, Union military commanders frequently supported the planters in their attempt to control black labor. Delta planters, however, wished themselves entirely free of outside governance. Thus, in 1865, they helped formulate the Black Code, seeking to limit the labor options of the freedmen. When Congress negated this code, the planters sought foreign laborers to force African-Americans into economic desperation. Under congressional patronage, moderate Republicans, led by Delta planter James L. Alcorn, attempted to build a party led by white men and supported by African-American votes. When this moderate "Alcorn Republican" system failed in 1873, the planters aligned themselves with the "straight out" Democratic party, rather than suppo

By the time the United States acquired most of the Great plains through the Louisiana Purchase, many Indians of the upper Missouri River valley had encountered French, British, and Anglo-American fur traders in their homeland. Most Native Americans in that region seem to have welcomed the manufactured goods these intruders brought, but at the same time some objected to the whites' disruption of earlier trade patterns. Nearly all of the Missouri Valley tribes appear to have disliked some aspects of the fur and hide trade, and many violent incidents occurred. As a village dwelling tribe located along the Missouri River in South Dakota, the Arikara Indians could not avoid participation in the existing trade activities or the violence that seemed to grow out of them. Although limited in numbers and hemmed in by often hostile neighboring tribes, these people proved difficult partners for European, American, and Indian traders of the early nineteenth century. Between the 1790s and the smallpox epidemic of 1837 the Arikaras launched sporadic raids and attacks against other Indians as well as white traders who passed their villages. In doing so they were little different from their Sioux or Pawnee neighbors. Nevertheless, because of their actions traders and government officials considered them to be unpredictable and often dangerous. This view became so widespread that nearly every historical discussion of the early Missouri Valley and Rocky Mountain fur trade comments on Arikara hostility. In fact, most modern. historians merely echo early nineteenth-century criticism of the Arikaras as capricious and "savage" people, basing this characterization on the fur trade accounts from that era. Such an interpretation tends to obscure a better understanding of Arikara actions and motivations. Certainly the tribe was uncooperative and, at times, dangerous to the traders. Yet the basis for negative comments about the villagers often grew from other causes. As Lewis .Saum has pointed

Differential energy loss (Mev/mg/sq cm) and range (mg/sq cm) data were calculated for low and medium energy protons and alpha particles in the following eight explosives: RDX (cyclotrimeth ylene trinitramine), HMX (cyclotetramethylene tetranitramine), TNT (2,4,6-trinitrotoluene), PETN (pentaerythritol tetranitrate), tetryl (2,4,6-trinitrophenyl methyl nitramine), lead styphnate, mercury fulminate, and lead azide. The well-known Bethe theory was followed in establishing the proton ranges. Experimental proton differential energy loss data and theoret ical computations were used to establish atomic stopping number versus energy curves for the elements hydrogen, carbon, nitrogen, oxygen, and lead between 20 Kev and 25 Mev. From these curves, molecular stopping numbers were calcu lated. The alpha-particle ranges were obtained from the established proton ranges.