1,220 research outputs found
Complex and Hypercomplex Discrete Fourier Transforms Based on Matrix Exponential Form of Euler's Formula
We show that the discrete complex, and numerous hypercomplex, Fourier
transforms defined and used so far by a number of researchers can be unified
into a single framework based on a matrix exponential version of Euler's
formula , and a matrix root of -1
isomorphic to the imaginary root . The transforms thus defined can be
computed using standard matrix multiplications and additions with no
hypercomplex code, the complex or hypercomplex algebra being represented by the
form of the matrix root of -1, so that the matrix multiplications are
equivalent to multiplications in the appropriate algebra. We present examples
from the complex, quaternion and biquaternion algebras, and from Clifford
algebras Cl1,1 and Cl2,0. The significance of this result is both in the
theoretical unification, and also in the scope it affords for insight into the
structure of the various transforms, since the formulation is such a simple
generalization of the classic complex case. It also shows that hypercomplex
discrete Fourier transforms may be computed using standard matrix arithmetic
packages without the need for a hypercomplex library, which is of importance in
providing a reference implementation for verifying implementations based on
hypercomplex code.Comment: The paper has been revised since the second version to make some of
the reasons for the paper clearer, to include reviews of prior hypercomplex
transforms, and to clarify some points in the conclusion
Laser Lithotripsy â The New Wave
Currently more than 90% of all common bile duct concrements
can he removed via the endoscopic retrograde route by means of endoscopic
papillotomy, stone extraction by baskets and balloon catheters, or mechanical
lithotripsy. Oversized, very hard or impacted stones however often st ill resist
conventional endoscopic therapy. Laser lithotripsy represents a promising new
endoscopic approach to the nonsurgical treatment of those common bile duct
stones. Currently only short-pulsed laser systems with high power peaks but low
potential for thermal tissue damage are used for stone fragmentation. Systems in
clinical applications are the pulsed free-running-mode neodymium YAG
(Nd:YAG) laser (1064 nm, 2 ms) and the dye laser (504 nm, 1 to 1.5 ÎŒs). Energy
transmission via highly flexible 200 ĂŹm quartz fibres allows an endoscopic
retrograde approach to the stone via conventional duodenoscope or mother-baby-scope systems. New systems currently in preclinical and first clinical testing
are the Q-switched Nd:YAG laser (1064 nm, 20 ns) and the Alexandrite laser
(700 to 815 nm, 30 to 500 ns). By means of extremely short nanosecond pulses
(10-9 s) for the induction of local shock waves at the stone surface, possible tissue
damage is even more reduced. No complications have been reported so far after
applying laser lithotripsy clinically in about 120 patients worldwide. Compared
to extracorporeal shock wave treatment, laser lithotripsy can be executed in any
endoscopy unit in the scope of the endoscopic pretreatment and does not require
general anesthesia, which is often necessary for extracorporeal shock wave
lithotripsy
Instantaneous frequency and amplitude of complex signals based on quaternion Fourier transform
The ideas of instantaneous amplitude and phase are well understood for
signals with real-valued samples, based on the analytic signal which is a
complex signal with one-sided Fourier transform. We extend these ideas to
signals with complex-valued samples, using a quaternion-valued equivalent of
the analytic signal obtained from a one-sided quaternion Fourier transform
which we refer to as the hypercomplex representation of the complex signal. We
present the necessary properties of the quaternion Fourier transform,
particularly its symmetries in the frequency domain and formulae for
convolution and the quaternion Fourier transform of the Hilbert transform. The
hypercomplex representation may be interpreted as an ordered pair of complex
signals or as a quaternion signal. We discuss its derivation and properties and
show that its quaternion Fourier transform is one-sided. It is shown how to
derive from the hypercomplex representation a complex envelope and a phase.
A classical result in the case of real signals is that an amplitude modulated
signal may be analysed into its envelope and carrier using the analytic signal
provided that the modulating signal has frequency content not overlapping with
that of the carrier. We show that this idea extends to the complex case,
provided that the complex signal modulates an orthonormal complex exponential.
Orthonormal complex modulation can be represented mathematically by a polar
representation of quaternions previously derived by the authors. As in the
classical case, there is a restriction of non-overlapping frequency content
between the modulating complex signal and the orthonormal complex exponential.
We show that, under these conditions, modulation in the time domain is
equivalent to a frequency shift in the quaternion Fourier domain. Examples are
presented to demonstrate these concepts
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AzĂșcar y nervios: Explanatory models and treatment experiences of Hispanics with diabetes and depression
This study examined the explanatory models of depression, perceived relationships between diabetes and depression, and depression treatment experiences of low-income, Spanish-speaking, Hispanics with diabetes and depression. A purposive sample (n = 19) was selected from participants enrolled in a randomized controlled trial conducted in Los Angeles, California (United States) testing the effectiveness of a health services quality improvement intervention. Four focus groups followed by 10 in-depth semi-structured qualitative interviews were conducted. Data were analyzed using the methodology of coding, consensus, co-occurrence, and comparison, an analytical strategy rooted in grounded theory. Depression was perceived as a serious condition linked to the accumulation of social stressors. Somatic and anxiety-like symptoms and the cultural idiom of nervios were central themes in low-income Hispanics' explanatory models of depression. The perceived reciprocal relationships between diabetes and depression highlighted the multiple pathways by which these two illnesses impact each other and support the integration of diabetes and depression treatments. Concerns about depression treatments included fears about the addictive and harmful properties of antidepressants, worries about taking too many pills, and the stigma attached to taking psychotropic medications. This study provides important insights about the cultural and social dynamics that shape low-income Hispanics' illness and treatment experiences and support the use of patient-centered approaches to reduce the morbidity and mortality associated with diabetes and depression
On harmonic analysis of vector-valued signals
A vectorâvalued signal in N dimensions is a signal whose value at any time instant is an Nâdimensional vector, that is, an element of urn:x-wiley:mma:media:mma3938:mma3938-math-0001. The sum of an arbitrary number of such signals of the same frequency is shown to trace an ellipse in Nâdimensional space, that is, to be confined to a plane. The parameters of the ellipse (major and minor axes, represented by Nâdimensional vectors; and phase) are obtained algebraically in terms of the directions of oscillation of the constituent signals, and their phases. It is shown that the major axis of the ellipse can always be determined algebraically. That is, a vector, whose value can be computed algebraically (without decisions or comparisons of magnitude) from parameters of the constituent signals, always represents the major axis of the ellipse. The ramifications of this result for the processing and Fourier analysis of signals with vector values or samples are discussed, with reference to the definition of Fourier transforms, particularly discrete Fourier transforms, such as have been defined in several hypercomplex algebras, including Clifford algebras. The treatment in the paper, however, is entirely based on signals with values in urn:x-wiley:mma:media:mma3938:mma3938-math-0002. Although the paper is written in terms of vector signals (which are taken to include images and volumetric images), the analysis clearly also applies to a superposition of simple harmonic motions in N dimensions
On harmonic analysis of vector-valued signals
A vectorâvalued signal in N dimensions is a signal whose value at any time instant is an Nâdimensional vector, that is, an element of urn:x-wiley:mma:media:mma3938:mma3938-math-0001. The sum of an arbitrary number of such signals of the same frequency is shown to trace an ellipse in Nâdimensional space, that is, to be confined to a plane. The parameters of the ellipse (major and minor axes, represented by Nâdimensional vectors; and phase) are obtained algebraically in terms of the directions of oscillation of the constituent signals, and their phases. It is shown that the major axis of the ellipse can always be determined algebraically. That is, a vector, whose value can be computed algebraically (without decisions or comparisons of magnitude) from parameters of the constituent signals, always represents the major axis of the ellipse. The ramifications of this result for the processing and Fourier analysis of signals with vector values or samples are discussed, with reference to the definition of Fourier transforms, particularly discrete Fourier transforms, such as have been defined in several hypercomplex algebras, including Clifford algebras. The treatment in the paper, however, is entirely based on signals with values in urn:x-wiley:mma:media:mma3938:mma3938-math-0002. Although the paper is written in terms of vector signals (which are taken to include images and volumetric images), the analysis clearly also applies to a superposition of simple harmonic motions in N dimensions
Comparing laparoscopic antireflux surgery with esomeprazole in the management of patients with chronic gastro-oesophageal reflux disease: a 3-year interim analysis of the LOTUS trial
BACKGROUND: With the introduction of laparoscopic antireflux surgery (LARS) for gastro-oesophageal reflux disease (GORD) along with the increasing efficacy of modern medical treatment, a direct comparison is warranted. The 3-year interim results of a randomised study comparing both the efficacy and safety of LARS and esomeprazole (ESO) are reported.
METHODS: LOTUS is an open, parallel-group multicentre, randomised and controlled trial conducted in dedicated centres in 11 European countries. LARS was completed according to a standardised protocol, comprising a total fundoplication and a crural repair. Medical treatment comprised ESO 20 mg once daily, which could be increased stepwise to 40 mg once daily and then 20 mg twice daily in the case of incomplete GORD control. The primary outcome variable was time to treatment failure (Kaplan-Meier analysis). Treatment failure was defined on the basis of symptomatic relapse requiring treatment beyond that stated in the protocol.
RESULTS: 554 patients were randomised, of whom 288 were allocated to LARS and 266 to ESO. The two study arms were well matched. The proportions of patients who remained in remission after 3 years were similar for the two therapies: 90% of surgical patients compared with 93% medically treated for the intention to treat population, p = 0.25 (90% vs 95% per protocol). No major unexpected postoperative complications were experienced and ESO was well tolerated. However, postfundoplication complaints remain a problem after LARS.
CONCLUSIONS: Over the first 3 years of this long-term study, both laparoscopic total fundoplication and continuous ESO treatment were similarly effective and well-tolerated therapeutic strategies for providing effective control of GORD
Excitonic Photoluminescence in Semiconductor Quantum Wells: Plasma versus Excitons
Time-resolved photoluminescence spectra after nonresonant excitation show a
distinct 1s resonance, independent of the existence of bound excitons. A
microscopic analysis identifies excitonic and electron-hole plasma
contributions. For low temperatures and low densities the excitonic emission is
extremely sensitive to even minute optically active exciton populations making
it possible to extract a phase diagram for incoherent excitonic populations.Comment: 9 pages, 4 figure
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