Algebraic reflexivity of isometry groups and automorphism groups of some operator structures

We establish the algebraic re exivity of three isometry groups of operator structures: The group of all surjective isometries on the unitary group, the group of all surjective isometries on the set of all positive invertible operators equipped with the Thompson metric, and the group of all surjective isometries on the general linear group of B(H), the operator algebra over a complex infinite dimensional separable Hilbert space H. We show that those isometry groups coincide with certain groups of automorphisms of corresponding structures and hence we also obtain the re exivity of some automorphism groups

Leveraging Software-Defined Radio for a Scalable Wide-band Wireless Channel Measurement System

Wireless channel characterization is important for determining both the requirements for a wireless system and its resulting reliability. Wireless systems are becoming ever more pervasive and thus are expected to operate in increasingly more cluttered environments. While these devices may be fixed in location, the channel is still far from ideal due to multipath. Under such conditions, it is desirable to have a means of taking wireless channel measurements in a low-cost and distributed manner, which is not always possible using typical channel measurement equipment. This thesis leverages a software-defined radio (SDR) platform to perform wideband wireless channel measurements. Specifically, the system can measure the scalar frequency response of a wireless channel in a distributed manner and provides measurements with an average mean-squared error of 0.018 % σ and a median error not exceeding 0.631 dB when compared to measurements taken with a vector network analyzer. This accuracy holds true in a highly multipath environment, with a measurement range of ~40 dB. The system is also capable of scaling to multiple wireless links which will be measured simultaneously (up to three links are demonstrated). After validating the measurement system, a measurement campaign is undertook using the system in a highly multipath environment to demonstrate a possible application of the system

Extension of some theorems of complex functional analysis to linear spaces over the quaternions and Cayley numbers

In this work certain aspects of Functional Analysis are considered in the setting of linear spaces over the division rings of the real Quaternions and the real Cayley algebra. The basic structure of Banach spaces over these division rings and the rings of bounded operators on these spaces is developed. Examples of finite and infinite dimensional spaces over these division rings are given. Questions concerning linear functionals, the Hahn-Banach Theorem and Reflexivity are considered. The Stone-Weierstrass Theorem is proven for functions with values in a real Cayley Dickson algebra of dimension n. The concepts of inner product spaces and Hilbert spaces over the Quaternions and the Cayley algebra are developed. An extensive study of Hilbert spaces over the Quaternions is carried out. In the case of Hilbert spaces over the Quaternions, the Riesz-Representation Theorem and the Jordan-von Neumann Theorem are proven. In addition, spectral theorems for both self-adjoint and normal operators are proven for finite dimensional Hilbert spaces. These results are extended to infinite dimensional spaces for the cases of compact self-adjoint operators and compact normal operators. The spectrum of an arbitrary bounded Hermitian operator on a Hilbert space over the Quaternions is shown to be non-void. A generalization of the Fourier Transform for functions in L[1 over Q](-infinity, infinity) and L[2 over Q]( ](-infinity, infinity) is given. The Plancherel Theorem is proven for functions in L[2 over Q](-infinity, infinity). Finally, the Jordan-von Neumann theorem is proven for a Hilbert space over the Cayley algebra --Abstract, pages ii-iii

Isometric properties of elementary operators

AbstractWe consider the elementary operator L, acting on the Hilbert–Schmidt Class C2(H), given by L(T)=ATB, with A and B bounded operators on H. We establish necessary and sufficient conditions on A and B for L to be a 2-isometry or a 3-isometry. We derive sufficient conditions for L to be an n-isometry. We also give several illustrative examples involving the weighted shift operator on l2 and the multiplication operator on the Dirichlet space

Migraines During Pregnancy Linked to Stroke and Vascular Diseases: US Population-Based Case-Control Study

Objective To examine the association between migraine and cardiovascular diseases during pregnancy. Design US population based case-control study. Setting Nationwide inpatient sample, from the Healthcare Cost and Utilization Project of the Agency for Healthcare Research and Quality. Population 18 345 538 pregnancy related discharges from 2000 to 2003. Main outcome measures Diagnosis of migraine, as identified by ICD-9 codes 346.0 and 346.1. Stroke and other vascular diseases were identified by using standard ICD-9 codes. Results From the hospital discharges with a pregnancy discharge code, 33 956 migraine codes were identified: 185 per 100 000 deliveries. Diagnoses that were jointly associated with migraine codes during pregnancy (excluding pre-eclampsia) were stroke (odds ratio 15.05, 95% confidence interval 8.26 to 27.4), myocardial infarction/heart disease (2.11, 1.76 to 2.54), pulmonary embolus/venous thromboembolism (3.23, 2.06 to 7.07), and hypertension (8.61, 6.43 to 11.54), as well as preeclampsia/gestational hypertension (2.29, 2.13 to 2.46), smoking (2.85, 2.53 to 3.21), and diabetes (1.96, 1.64 to 2.35). However, migraine was not associated with several non-vascular diagnoses (pneumonia, transfusions, postpartum infection or haemorrhage). Conclusions In this large, population based sample of pregnant women admitted to hospital, a strong relation existed between active peripartum migraine and vascular diagnoses during pregnancy. Because these data do not allow determination of which came first, migraine or the vascular condition, prospective studies of pregnant women are needed to explore this association further

Turtle Lake irrigation and wildlife area

Presented at Water for agriculture and wildlife and the environment: win-win opportunities: proceedings from the USCID wetlands seminar on June 27-29, 1996 in Bismarck, North Dakota.Includes bibliographical referencesThe Turtle Lake Irrigation Area (TLIA) is located in near the town of Turtle Lake in central North Dakota. The TLIA is adjacent to the McClusky Canal, a project feature of the Garrison Diversion Unit (GDU), which transports Missouri River water into the area. The GDU Reformulation Act of 1986 authorized the development of 13,700 acres (5,500 hectares) of irrigation in the TLIA. The conceptual plan presented in this paper is the first step in a process to develop a water delivery project, which places equal emphasis on wildlife, irrigation and economic development in the Turtle Lake area of North Dakota. The planning process and the conceptual plan emphasize sharing of wildlife and agricultural benefits on the same parcels of land, avoidance of environmental impacts, development of wildlife and agriculture enhancement features, and onsite mitigation. The process and concepts are unique relative to normal project-planning efforts and project features. The plan is the result of a cooperative effort by local landowners, with assistance from an interagency planning team, comprised of federal, state and local agencies to envision a multipurpose water development project. The project has not been developed as of 1996; however, planning and implementation efforts are proceeding