Geometry of the SL(3,ℂ)-character variety of torus knots.

Let G be the fundamental group of the complement of the torus knot of type (m, n). It has a presentation G = . We find a geometric description of the character variety X(G) of characters of representations of G into SL(3,ℂ), GL(3,ℂ) and PGL(3,ℂ).

Analysis of the spectral response of fractal antennas related with its geometry and current paths

Fractal antennas have been proposed to improve the bandwidth of resonant structures and optical antennas. Their multiband characteristics are of interest in radiofrequency and microwave technologies. In this contribution we link the geometry of the current paths built-in the fractal antenna with the spectral response. We have seen that the actual currents owing through the structure are not limited to the portion of the fractal that should be geometrically linked with the signal. This fact strongly depends on the design of the fractal and how the different scales are arranged within the antenna. Some ideas involving materials that could actively respond to the incoming radiation could be of help to spectrally select the response of the multiband design.

The influence of magnetic field geometry on magnetars X-ray spectra

Nowadays, the analysis of the X-ray spectra of magnetically powered neutron stars or magnetars is one of the most valuable tools to gain insight into the physical processes occurring in their interiors and magnetospheres. In particular, the magnetospheric plasma leaves a strong imprint on the observed X-ray spectrum by means of Compton up-scattering of the thermal radiation coming from the star surface. Motivated by the increased quality of the observational data, much theoretical work has been devoted to develop Monte Carlo (MC) codes that incorporate the effects of resonant Compton scattering (RCS) in the modeling of radiative transfer of photons through the magnetosphere. The two key ingredients in this simulations are the kinetic plasma properties and the magnetic field (MF) configuration. The MF geometry is expected to be complex, but up to now only mathematically simple solutions (self-similar solutions) have been employed. In this work, we discuss the effects of new, more realistic, MF geometries on synthetic spectra. We use new force-free solutions [14] in a previously developed MC code [9] to assess the influence of MF geometry on the emerging spectra. Our main result is that the shape of the final spectrum is mostly sensitive to uncertain parameters of the magnetospheric plasma, but the MF geometry plays an important role on the angle-dependence of the spectra.

Reverse Geometry Hybrid Contact Lens Fitting in a Case of Donor-Host Misalignment after Keratoplasty

Purpose: To report the successful outcome obtained after fitting a new hybrid contact lens in a cornea with an area of donor-host misalignment and significant levels of irregular astigmatism after penetrating keratoplasty (PKP). Materials and methods: A 41-year-old female with bilateral asymmetric keratoconus underwent PKP in her left eye due to the advanced status of the disease. One year after surgery, the patient referred a poor visual acuity and quality in this eye. The fitting of different types of rigid gas permeable contact lenses was performed, but with an unsuccessful outcome due to contact lens stability problems and uncomfortable wear. Scheimpflug imaging evaluation revealed that a donor-host misalignment was present at the nasal area. Contact lens fitting with a reverse geometry hybrid contact lens (Clearkone, SynergEyes Carlsbad) was then fitted. Visual, refractive, and ocular aberrometric outcomes were evaluated during a 1-year period after the fitting. Results: Uncorrected distance visual acuity improved from a prefitting value of 20/200 to a best corrected postfitting value of 20/20. Prefitting manifest refraction was +5.00 sphere and -5.50 cylinder at 75°, with a corrected distance visual acuity of 20/30. Higher order root mean square (RMS) for a 5 mm pupil changed from a prefitting value of 6.83 µm to a postfitting value of 1.57 µm (5 mm pupil). The contact lens wearing was referred as comfortable, with no anterior segment alterations. Conclusion: The SynergEyes Clearkone contact lens seems to be another potentially useful option for the visual rehabilitation after PKP, especially in cases of donor-host misalignment.

3D geometry of growth strata in a fault-propagation fold: insights into space–time evolution of the Crevillente Fault (Abanilla-Alicante sector), Betic Cordillera, Spain

This work presents a 3D geometric model of growth strata cropping out in a fault-propagation fold associated with the Crevillente Fault (Abanilla-Alicante sector) from the Bajo Segura Basin (eastern Betic Cordillera, southern Spain). The analysis of this 3D model enables us to unravel the along-strike and along-section variations of the growth strata, providing constraints to assess the fold development, and hence, the fault kinematic evolution in space and time. We postulate that the observed along-strike dip variations are related to lateral variation in fault displacement. Along-section variations of the progressive unconformity opening angles indicate greater fault slip in the upper Tortonian–Messinian time span; from the Messinian on, quantitative analysis of the unconformity indicate a constant or lower tectonic activity of the Crevillente Fault (Abanilla-Alicante sector); the minor abundance of striated pebbles in the Pliocene-Quaternary units could be interpreted as a decrease in the stress magnitude and consequently in the tectonic activity of the fault. At a regional scale, comparison of the growth successions cropping out in the northern and southern limits of the Bajo Segura Basin points to a southward migration of deformation in the basin. This means that the Bajo Segura Fault became active after the Crevillente Fault (Abanilla-Alicante sector), for which activity on the latter was probably decreasing according to our data. Consequently, we propose that the seismic hazard at the northern limit of the Bajo Segura Basin should be lower than at the southern limit.

Notebook on geometry, geography, astronomy, and navigation, ca. 1714-1718

This heavily illustrated notebook contains entries on the following topics: geometrical definitions and axioms, geographical and astronomical definitions, compasses, plain sailing, parallel sailing, and Mercator's sailing. It also contains pages designated for notes on "Currents, Lee Way, & Variation," but these pages have been left blank. The back cover contains calculations which appear to relate to charting a course from Jamaica to "Lizzard."

[Natural Philosophy book list, 1790]

One leaf containing a handwritten list of books marked "Natural Philosophy." Entries contain the author's last name and abbreviated title; five books have dates. The page is inscribed "Callender" and likely refers to John Callender (Harvard AB 1790).

[Ethics and Moral Philosophy book list, 1790]

One leaf containing a handwritten list of books with one column marked "Ethics" and the other column marked "Moral Philosophy." Entries contain the author's last name and abbreviated title. The page is inscribed "Vose," likely referring to Roger Vose (Harvard AB 1790), and the verso has a fragment of a poem.

[Ethics and moral philosophy book list, 1790]

One leaf containing a handwritten list of books generally on ethics and moral philosophy, though no subject is identified. Entries contain the author's last name and abbreviated title. The page is inscribed "Paine," likely referring to Robert Treat Paine (Harvard AB 1792), and the verso has a fragment of a student essay on the theme "An undevout astronomer is mad," signed "Paine."

Abiel Holmes's book: bought Decem'r 23'd anno domini 1780 : manuscript, 1780-1783 and undated

Commonplace book containing excerpts on religion, philosophy, geometry and other subjects; with two fold-out tables, one concerning the "partition of sciences" and the other "grand divisions of Europe."

A catalogue of books in the College library: [which Benjamin Welles wished to read], 1797

In this small paper-bound catalog, Benjamin Welles (1781-1860) listed books in the Harvard College Library which he wished to read. He presumably compiled the list by consulting the Library's 1790 printed catalog, as the works are categorized according to subjects outlined in that catalog (Antiquities, Astronomy, Ancient Authors, Biography, Sacred Criticism, Ethics, Geography, Geometry, History, Nature, Travels / Voyages, Natural Law, Logic, Metaphysics, Miscellaneous Works, Dramatic, Phililogy, Natural Philosophy, Poetry, Rhetoric, and Theology). The final pages of Welles' catalog, which he titles "Another Selection," list additional volumes he wished to read. These are listed alphabetically, A - G. Some titles throughout the catalog have been marked with a "+" perhaps to indicate that Welles had read them.

The summary of a course of experimental lectures in natural philosophy by Dr. John Winthrop (manuscript copy), 1772-1774

Notebook with a handwritten copy of lecture summaries for a physics course given by Harvard Professor John Winthrop. The notes were made by Timothy Foster in 1772 and 1773. The volume contains twenty-five lectures with some diagrams.

Elements of geometry : manuscript, 1798

Contains work on geometry, trigonometry, surveying, mensuration of heights and distances, and navigation. The graphs and diagrams illustate story problems and navigational examples.