The symbolic model for algebra : functions and mechanisms

The symbolic mode of reasoning in algebra, as it emerged during the sixteenth century, can be considered as a form of model-based reasoning. In this paper we will discuss the functions and mechanisms of this model and show how the model relates to its arithmetical basis. We will argue that the symbolic model was made possible by the epistemic justification of the basic operations of algebra as practiced within the abbaco tradition. We will also show that this form of model-based reasoning facilitated the expansion of the number concept from Renaissance interpretations of number to the full notion of algebraic numbers

Open-Source ANSS Quake Monitoring System Software

ANSS stands for the Advanced National Seismic System of the U.S.A., and ANSS Quake Monitoring System (AQMS) is the earthquake management system (EMS) that most of its member regional seismic networks (RSNs) use. AQMS is based on Earthworm, but instead of storing files on disk, it uses a relational database with replication capability to store pick, amplitude, waveform, and event parameters. The replicated database and other features of AQMS make it a fully redundant system. A graphical user interface written in Java, Jiggle, is used to review automatically generated picks and event solutions, relocate events, and recalculate magnitudes. Add‐on mechanisms to produce various postearthquake products such as ShakeMaps and focal mechanisms are available as well. It provides a configurable automatic alarming and notification system. The Pacific Northwest Seismic Network, one of the Tier 1 ANSS RSNs, has modified AQMS to be compatible with a freely available, capable, open‐source database system, PostgreSQL, and is running this version successfully in production. The AQMS Software Working Group has moved the software from a subversion repository server hosted at the California Institute of Technology to a public repository at gitlab.com. The drawback of AQMS as a whole is that it is complex to fully configure and comprehend. Nevertheless, the fact that it is very capable, documented, and now free to use, might make it an attractive EMS choice for many seismic networks

Visions of the Possible: Reflections on the Faculty/Student Co-Inquirer Relationship

This manuscript is a reflection on the processes and outcomes inherent in the faculty/student co-inquirer relationship. Authors briefly describe their SoTL research project. Subsequently, learning outcomes from the student co-inquirer are discussed in terms of: understanding research and the research process, the impact of the research experience on the student\u27s own teaching and learning, and the impact of the research experience on the student\u27s future professional plans. Lessons learned are shared for future student co-inquirers

Polarimetric nonregularity of evanescent waves

Three-dimensional polarization states of random light can be classified into regular and nonregular according to the structure of the related 3 × 3 polarization matrix. Here we show that any purely evanescent wave excited in total internal reflection of a partially polarized plane-wave field is always in a nonregular polarization state. The degree of nonregularity of such evanescent waves is also studied in terms of a recently advanced measure. Nonregular evanescent waves uncover new aspects of the polarimetric structure and dimensional character of electromagnetic near fields, with potential applications in nanoscale surface optics

Intensity and spin anisotropy of three-dimensional polarization states

Anisotropy is a natural feature of polarization states, and only fully random three-dimensional (3D) states exhibit complete isotropy. In general, differences between the strengths of the electric field components along the three orthogonal directions give rise to intensity anisotropy. Moreover, polarization states involve an average spin whose inherent vectorial nature constitutes a source of spin anisotropy. In this work, appropriate descriptors are identified to characterize quantitatively the levels of intensity anisotropy and spin anisotropy of a general 3D polarization state, leading to a novel interpretation for the degree of polarimetric purity as a measure describing the overall polarimetric anisotropy of a 3D optical field. The mathematical representation, as well as the physical features of completely intensity-isotropic 3D polarization states with a maximum spin anisotropy, are also examined. The results provide new insights into the polarimetric field structure of random 3D electromagnetic light states. (C) 2019 Optical Society of Americ

Phase transitions and the internal noise structure of nonlinear Schr\"odi nger equation solitons

We predict phase-transitions in the quantum noise characteristics of systems described by the quantum nonlinear Schr\"odinger equation, showing them to be related to the solitonic field transition at half the fundamental soliton amplitude. These phase-transitions are robust with respect to Raman noise and scattering losses. We also describe the rich internal quantum noise structure of the solitonic fields in the vicinity of the phase-transition. For optical coherent quantum solitons, this leads to the prediction that eliminating the peak side-band noise due to the electronic nonlinearity of silica fiber by spectral filtering leads to the optimal photon-number noise reduction of a fundamental soliton.Comment: 10 pages, 5 figure

Nonlinear directional coupler for polychromatic light

We demonstrate that nonlinear directional coupler with special bending of waveguide axes can be used for all-optical switching of polychromatic light with very broad spectrum covering all visible region. The bandwidth of suggested device is enhanced five times compared to conventional couplers. Our results suggest novel opportunities for creation of all-optical logical gates and switches for polychromatic light with white-light and super-continuum spectrum.Comment: 3 pages, 3 figure

Fourier Transform NMR Self-diffusion Studies Of A Nonaqueous Microemulsion System

Self-diffusion coefficients of the components of the microemulsion system glycerol/hexanol/sodium dodecyl sulfate (SDS) were determined in the presence and absence of an oil, p-xylene, and the results were compared with those from corresponding aqueous systems (i.e., glycerol replaced by water). In the aqueous system, the water in the hexanol rich isotropic liquid showed a diffusion coefficient less than 10% of that of free water, while that of hexanol was roughly 80% of that of free hexanol; such restricted motion of the water is consistent with the presence of water as discrete droplets. Partial substitution of p-xylene for hexanol did not affect the diffusion coefficient of water appreciably. In the nonaqueous three-component system, the diffusion coefficients of glycerol, SDS, and hexanol all decreased in concert as the glycerol content increased, e.g., that of hexanol goes from 1.75 x 10-10 m2 s-1 to 2.7 x 10-11 m2 s-1 as the glycerol content ranges from 10 to 80%. The diffusion coefficient of glycerol was always greater than that of neat glycerol by a factor of 5 to 45. As the diffusion coefficients of all components were within a factor of 2, the idea of segregating one or more components into disconnected domains is not supported. There is no support for glycerol droplets but these microemulsions appear to be structureless. © 1987

Comparison of Lives Saved Tool model child mortality estimates against measured data from vector control studies in sub-Saharan Africa

<p>Abstract</p> <p>Background</p> <p>Insecticide-treated mosquito nets (ITNs) and indoor-residual spraying have been scaled-up across sub-Saharan Africa as part of international efforts to control malaria. These interventions have the potential to significantly impact child survival. The Lives Saved Tool (LiST) was developed to provide national and regional estimates of cause-specific mortality based on the extent of intervention coverage scale-up. We compared the percent reduction in all-cause child mortality estimated by LiST against measured reductions in all-cause child mortality from studies assessing the impact of vector control interventions in Africa.</p> <p>Methods</p> <p>We performed a literature search for appropriate studies and compared reductions in all-cause child mortality estimated by LiST to 4 studies that estimated changes in all-cause child mortality following the scale-up of vector control interventions. The following key parameters measured by each study were applied to available country projections: baseline all-cause child mortality rate, proportion of mortality due to malaria, and population coverage of vector control interventions at baseline and follow-up years.</p> <p>Results</p> <p>The percent reduction in all-cause child mortality estimated by the LiST model fell within the confidence intervals around the measured mortality reductions for all 4 studies. Two of the LiST estimates overestimated the mortality reductions by 6.1 and 4.2 percentage points (33% and 35% relative to the measured estimates), while two underestimated the mortality reductions by 4.7 and 6.2 percentage points (22% and 25% relative to the measured estimates).</p> <p>Conclusions</p> <p>The LiST model did not systematically under- or overestimate the impact of ITNs on all-cause child mortality. These results show the LiST model to perform reasonably well at estimating the effect of vector control scale-up on child mortality when compared against measured data from studies across a range of malaria transmission settings. The LiST model appears to be a useful tool in estimating the potential mortality reduction achieved from scaling-up malaria control interventions.</p