Quasiclassical and Quantum Systems of Angular Momentum. Part II. Quantum Mechanics on Lie Groups and Methods of Group Algebras

In Part I of this series we presented the general ideas of applying group-algebraic methods for describing quantum systems. The treatment was there very "ascetic" in that only the structure of a locally compact topological group was used. Below we explicitly make use of the Lie group structure. Basing on differential geometry enables one to introduce explicitly representation of important physical quantities and formulate the general ideas of quasiclassical representation and classical analogy

Multiport VNA Measurements

This article presents some of the most recent multiport VNA measurement methodologies used to characterize these highspeed digital networks for signal integrity. There will be a discussion of the trends and measurement challenges of high-speed digital systems, followed by a presentation of the multiport VNA measurement system details, calibration, and measurement techniques, as well as some examples of interconnect device measurements. The intent here is to present some general concepts and trends for multiport VNA measurements as applied to computer system board-level interconnect structures, and not to promote any particular brand or produc

On the Hyperbolicity of Lorenz Renormalization

We consider infinitely renormalizable Lorenz maps with real critical exponent $\alpha>1$ and combinatorial type which is monotone and satisfies a long return condition. For these combinatorial types we prove the existence of periodic points of the renormalization operator, and that each map in the limit set of renormalization has an associated unstable manifold. An unstable manifold defines a family of Lorenz maps and we prove that each infinitely renormalizable combinatorial type (satisfying the above conditions) has a unique representative within such a family. We also prove that each infinitely renormalizable map has no wandering intervals and that the closure of the forward orbits of its critical values is a Cantor attractor of measure zero.Comment: 63 pages; 10 figure

Streaming Tree Transducers

Theory of tree transducers provides a foundation for understanding expressiveness and complexity of analysis problems for specification languages for transforming hierarchically structured data such as XML documents. We introduce streaming tree transducers as an analyzable, executable, and expressive model for transforming unranked ordered trees in a single pass. Given a linear encoding of the input tree, the transducer makes a single left-to-right pass through the input, and computes the output in linear time using a finite-state control, a visibly pushdown stack, and a finite number of variables that store output chunks that can be combined using the operations of string-concatenation and tree-insertion. We prove that the expressiveness of the model coincides with transductions definable using monadic second-order logic (MSO). Existing models of tree transducers either cannot implement all MSO-definable transformations, or require regular look ahead that prohibits single-pass implementation. We show a variety of analysis problems such as type-checking and checking functional equivalence are solvable for our model.Comment: 40 page

Development and operation of a pixel segmented liquid-filled linear array for radiotherapy quality assurance

A liquid isooctane (C$_{8}$H$_{18}$) filled ionization linear array for radiotherapy quality assurance has been designed, built and tested. The detector consists of 128 pixels, each of them with an area of 1.7 mm $\times$ 1.7 mm and a gap of 0.5 mm. The small pixel size makes the detector ideal for high gradient beam profiles like those present in Intensity Modulated Radiation Therapy (IMRT) and radiosurgery. As read-out electronics we use the X-Ray Data Acquisition System (XDAS) with the Xchip developed by the CCLRC. Studies concerning the collection efficiency dependence on the polarization voltage and on the dose rate have been made in order to optimize the device operation. In the first tests we have studied dose rate and energy dependences, and signal reproducibility. Dose rate dependence was found lower than 2.5 % up to 5 Gy min$^{-1}$, and energy dependence lower than 2.1 % up to 20 cm depth in solid water. Output factors and penumbras for several rectangular fields have been measured with the linear array and were compared with the results obtained with a 0.125 cm$^{3}$ air ionization chamber and radiographic film, respectively. Finally, we have acquired profiles for an IMRT field and for a virtual wedge. These profiles have also been compared with radiographic film measurements. All the comparisons show a good correspondence. Signal reproducibility was within a 2% during the test period (around three months). The device has proved its capability to verify on-line therapy beams with good spatial resolution and signal to noise ratio.Comment: 16 pages, 12 figures Submitted to Phys. Med. Bio