A Cardinal Sin: The Infinite in Spinoza\u27s Philosophy

One of the greatest developments in mathematics was Georg Cantor\u27s theory of infinity. His work provided a new framework to think about age-old problems in both mathematics and philosophy. Given these developments, it is tempting to write off previous thinkers has having a primitive and undeveloped theory of infinity. However, this attitude undermines the complexity and importance of the theories which existed prior to Cantor. Benedict Spinoza is one philosopher who had a highly developed theory, despite lacking the mathematical tools developed by Cantor. He held that there were three different kinds of infinity, each with different properties and roles to play in his metaphysical system. This thesis examines these types of infinity and how they interact with Spinoza\u27s overall philosophy. The first chapter focuses on a letter Spinoza wrote which outlines his views on infinity. By attending to the ways Spinoza understood infinity, new solutions and problems emerge in Spinoza scholarship, which are covered in the second and third chapters. The final chapter covers Spinoza\u27s legacy and shows the influence that his thought had on Leibniz, as well as Georg Cantor

A non-dispersive Raman D-band activated by well-ordered interlayer interactions in rotationally stacked bi-layer Graphene

Raman measurements on monolayer graphene folded back upon itself as an ordered but skew-stacked bilayer (i.e. with interlayer rotation) presents new mechanism for Raman scattering in sp2 carbons that arises in systems that lack coherent AB interlayer stacking. Although the parent monolayer does not exhibit a D-band, the interior of the skewed bilayer produces a strong two-peak Raman feature near 1350 cm-1; one of these peaks is non-dispersive, unlike all previously observed D-band features in sp2 carbons. Within a double-resonant model of Raman scattering, these unusual features are consistent with a skewed bilayer coupling, wherein one layer imposes a weak but well-ordered perturbation on the other. The discrete Fourier structure of the rotated interlayer interaction potential explains the unusual non-dispersive peak near 1350 cm-1

Dirac points with giant spin-orbit splitting in the electronic structure of two-dimensional transition-metal carbides

Two-dimensional (2D) materials, especially their most prominent member, graphene, have greatly influenced many scientific areas. Moreover, they have become a base for investigating the relativistic properties of condensed matter within the emerging field of Dirac physics. This has ignited an intense search for new materials where charge carriers behave as massless or massive Dirac fermions. Here, we theoretically show the existence of Dirac electrons in a series of 2D transition-metal carbides, known as MXenes. They possess twelve conical crossings in the 1st Brillouin zone with giant spin-orbit splitting. Our findings indicate that the 2D band structure of MXenes is protected against external perturbations and preserved even in multilayer phases. These results, together with the broad possibilities to engineer the properties of these materials phases, make Dirac MXenes a potential candidate for studying and developing novel Dirac-physics-based technologies.Comment: 4 figures and supplementar

Customer Portfolio Analysis Using the SOM

In order to compete for profitable customers, companies are looking to add value using Customer Relationship Management (CRM). One subset of CRM is customer segmentation, which is the process of dividing customers into groups based upon common features or needs. Segmentation methods can be used for customer portfolio analysis (CPA), the process of analyzing the profitability of customers. This study was made for a case organization, who wanted to identify their profitable and unprofitable customers, in order to gain knowledge on how to develop their marketing strategies. Data about the customers were gathered from the case organization’s own database. The Self-Organizing Map (SOM) was used to divide the customers into segments, which were then analyzed in light of product sales information

Reversible Fluorination of Graphene: towards a Two-Dimensional Wide Bandgap Semiconductor

We report the synthesis and evidence of graphene fluoride, a two-dimensional wide bandgap semiconductor derived from graphene. Graphene fluoride exhibits hexagonal crystalline order and strongly insulating behavior with resistance exceeding 10 G$\Omega$ at room temperature. Electron transport in graphene fluoride is well described by variable-range hopping in two dimensions due to the presence of localized states in the band gap. Graphene obtained through the reduction of graphene fluoride is highly conductive, exhibiting a resistivity of less than 100 k$\Omega$ at room temperature. Our approach provides a new path to reversibly engineer the band structure and conductivity of graphene for electronic and optical applications.Comment: 7 pages, 5 figures, revtex, to appear in PR

Direct observation and imaging of a spin-wave soliton with p−p-like symmetry

The prediction and realization of magnetic excitations driven by electrical currents via the spin transfer torque effect, enables novel magnetic nano-devices where spin-waves can be used to process and store information. The functional control of such devices relies on understanding the properties of non-linear spin-wave excitations. It has been demonstrated that spin waves can show both an itinerant character, but also appear as localized solitons. So far, it was assumed that localized solitons have essentially cylindrical, $s-$like symmetry. Using a newly developed high-sensitivity time-resolved magnetic x-ray microscopy, we instead observe the emergence of a novel localized soliton excitation with a nodal line, i.e. with $p-$like symmetry. Micromagnetic simulations identify the physical mechanism that controls the transition from $s-$ to $p-$like solitons. Our results suggest a potential new pathway to design artificial atoms with tunable dynamical states using nanoscale magnetic devices