Householder transformations and optimal linear combinations

Several theorems related to the Householder transformation and separability criteria are proven. Orthogonal transformations, topology, divergence, mathematical matrices, and group theory are discussed

Geometric Aspects of Ambrosetti-Prodi operators with Lipschitz nonlinearities

For Dirichlet boundary conditions on a bounded domain, what happens to the critical set of the Ambrosetti-Prodi operator if the nonlinearity is only a Lipschitz map? It turns out that many properties which hold in the smooth case are preserved, despite of the fact that the operator is not even differentiable at some points. In particular, a global Lyapunov-Schmidt decomposition of great convenience for numerical inversion is still available

Positron emission tomography in detection of metastatic leiomyosarcoma in a postoperative patient: a case report

In leiomyosarcoma (LMS) abnormal vaginal bleeding is the most common reported symptom in patients (56%), followed by pelvic mass (54%), and pain (22%). LMS is often hard to diagnosis on a uterine biopsy because it does not originate in the endometrium and may not invade into the cavity. Non-specific symptoms as well as difficulty in diagnosis being made by biopsy, means that many LMS tumors are often mistaken for fibroids preoperatively. To our knowledge this is the only reported case of FDG-PET being used in the postoperative evaluation of a patient with LMS and a suspicious lung mass. Our case shows there may be a place for PET scans in the post-op surveillance of LMS. This method would be ideally suited, considering the metastatic spread pattern of LMS

Increasing the capacity of the Tory II-C Side Support System

The Tory II-C lateral suspension has been designed for 4 g`s of lateral acceleration of the duct. Calculations and model tests indicate that this requirement has been met or exceeded. In order to have a more realistic model to test, Tory II-C springs are going to be fitted around the full scale core slice which was previously built up. Instrumented accelerations of this assembly should give the most direct demonstration that is possible of the response of the system to flight. This memorandum discusses, knowing the capabilities of the present system, the design changes necessary to suit different maximum accelerations by increasing the capacity of the Tory II-C side support system

Toolbox for analyzing finite two-state trajectories

In many experiments, the aim is to deduce an underlying multi-substate on-off kinetic scheme (KS) from the statistical properties of a two-state trajectory. However, the mapping of a KS into a two-state trajectory leads to the loss of information about the KS, and so, in many cases, more than one KS can be associated with the data. We recently showed that the optimal way to solve this problem is to use canonical forms of reduced dimensions (RD). RD forms are on-off networks with connections only between substates of different states, where the connections can have non-exponential waiting time probability density functions (WT-PDFs). In theory, only a single RD form can be associated with the data. To utilize RD forms in the analysis of the data, a RD form should be associated with the data. Here, we give a toolbox for building a RD form from a finite two-state trajectory. The methods in the toolbox are based on known statistical methods in data analysis, combined with statistical methods and numerical algorithms designed specifically for the current problem. Our toolbox is self-contained - it builds a mechanism based only on the information it extracts from the data, and its implementation on the data is fast (analyzing a 10^6 cycle trajectory from a thirty-parameter mechanism takes a couple of hours on a PC with a 2.66 GHz processor). The toolbox is automated and is freely available for academic research upon electronic request

Application of ERTS-1 imagery to state wide land information system in Minnesota

There are no author-identified significant results in this report

Some comments on Ian Rumfitt's bilateralism

Ian Rumfitt has proposed systems of bilateral logic for primitive speech acts of assertion and denial, with the purpose of `exploring the possibility of specifying the classically intended senses for the connectives in terms of their deductive use' (Rumfitt (2000): 810f). Rumfitt formalises two systems of bilateral logic and gives two arguments for their classical nature. I assess both arguments and conclude that only one system satisfies the meaning-theoretical requirements Rumfitt imposes in his arguments. I then formalise an intuitionist system of bilateral logic which also meets those requirements. Thus Rumfitt cannot claim that only classical bilateral rules of inference succeed in imparting a coherent sense onto the connectives. My system can be extended to classical logic by adding the intuitionistically unacceptable half of a structural rule Rumfitt uses to codify the relation between assertion and denial. Thus there is a clear sense in which, in the bilateral framework, the difference between classicism and intuitionism is not one of the rules of inference governing negation, but rather one of the relation between assertion and denial