Finite Lorentz Transformations, Automorphisms, and Division Algebras

We give an explicit algebraic description of finite Lorentz transformations of vectors in 10-dimensional Minkowski space by means of a parameterization in terms of the octonions. The possible utility of these results for superstring theory is mentioned. Along the way we describe automorphisms of the two highest dimensional normed division algebras, namely the quaternions and the octonions, in terms of conjugation maps. We use similar techniques to define $SO(3)$ and $SO(7)$ via conjugation, $SO(4)$ via symmetric multiplication, and $SO(8)$ via both symmetric multiplication and one-sided multiplication. The non-commutativity and non-associativity of these division algebras plays a crucial role in our constructions.Comment: 24 pages, Plain TeX, 2 figures on 1 page submitted separately as uuencoded compressed tar fil

Is There an Innovative Solution to the Opioid Epidemic?

There are innovative ways and solutions to the current opioid epidemic. This affects people of every walk of life and is a huge problem in our country.https://digitalcommons.misericordia.edu/research_posters2020/1048/thumbnail.jp

Scaled Synthetic Aperture Rader Development

Several previous Cal Poly thesis projects involve synthetic aperture radar (SAR), automatic target recognition (ATR), and tracking. SAR data was either accessed from a publicly available database or generated using complex computer modeling software. The motivation for this dual thesis project is to design and construct a scaled SAR system to support Cal Poly radar projects. Ideally this is a low-cost, high resolution SAR architecture that produces raw range Doppler data for any desired target area. To that end, a scaled SAR system was successfully designed, built, and tested. The current SAR system, however, does not perform azimuthal compression and range cell migration correction. These functionalities can be pursued by future students joining the ongoing radar project. The system built for this thesis is a 1 GHz bandwidth SAR system. The system is comprised of analog/RF front end circuitry, two antennas, a mechanical rail platform, power supplies, an oscilloscope, and control and image processing software. This thesis covers the design and evaluation of the analog/radio frequency (RF) front end circuitry and signal processing software. RF amplifier integrated circuits (ICs) were evaluated for two purposes: increasing transmitted signal strength and improving system signal-to-noise ratio (SNR). A voltage-controlled oscillator’s (VCO) tuning characteristic and bandwidth were measured to verify its ability to support system specifications. A ramp generator circuit was designed, assembled and tested. Multiple ultra wide band (UWB) band pass filters were investigated for received signal image rejection. A low pass filter (LPF) was designed, assembled and tested for noise reduction. The overall system was tested with multiple known target locations. This thesis is a joint project with Ryan Green, MSEE student. To understand the entire project, refer to both thesis documents. The overall project is covered broadly in both papers but each report specializes in selected areas. Ryan Green’s thesis document focuses on the system control software, antenna design, and mechanical rail platform. This thesis document focuses on the RF circuitry, analog circuitry, and image processing. The introductory section introduces radar system concepts and the SAR system layout. The remaining sections describe component designs, component performance and system results

A Gift from God: An Analysis of Social Media Policies Adopted by Catholic Institutions of Higher Education and How They Cover Faculty

This dissertation investigates the development of social media policies in higher education. This study differentiates itself from existing social media policy research by analyzing the content of social media policies themselves, focusing on how social media policies cover faculty, and examining policies at Catholic higher education institutions. Using multiple data sources and quantitative content analysis, this study found 28.7 percent of Catholic higher education institutions have a published social media policy and 27.5 percent of Catholic higher education institutions have a social media policy that covers faculty. Related to social media policies at Catholic higher education institutions, this study revealed that doctorate-granting universities make up the largest percentage of institutions that have a social media policy. Policies frequently mentioned particular social media sites, with Facebook and Twitter among the most likely named. Policies typically applied to all those associated with the institution (including faculty). Members of the community were advised to post appropriate content, represent the institution positively, and to ensure posts comply with the law

A Gift from God: An Analysis of Social Media Policies Adopted by Catholic Institutions of Higher Education and How They Cover Faculty

This dissertation investigates the development of social media policies in higher education. This study differentiates itself from existing social media policy research by analyzing the content of social media policies themselves, focusing on how social media policies cover faculty, and examining policies at Catholic higher education institutions. Using multiple data sources and quantitative content analysis, this study found 28.7 percent of Catholic higher education institutions have a published social media policy and 27.5 percent of Catholic higher education institutions have a social media policy that covers faculty. Related to social media policies at Catholic higher education institutions, this study revealed that doctorate-granting universities make up the largest percentage of institutions that have a social media policy. Policies frequently mentioned particular social media sites, with Facebook and Twitter among the most likely named. Policies typically applied to all those associated with the institution (including faculty). Members of the community were advised to post appropriate content, represent the institution positively, and to ensure posts comply with the law

A study of prospective entrepreneurs\u27 perceptions of knowledge required for success : and its implications for curriculum development and revision

The purpose of this study was to provide information to secondary, post-secondary and vocational teachers on what instructional areas should be taught to prospective entrepreneurs involved in pre-venture training. In addition it was hoped that information gained from the study would add to the existing body of knowledge on entrepreneurship education and validate entrepreneurship education practices in Oregon

High Speed Control of Atom Transfer Sequence from Magneto-Optical to Dipole Trap for Quantum Computing

Two circuits were designed, built, and tested for the purpose of aiding in the transfer of 87Rb atoms from a MOT to dipole traps and for characterizing the final dipole traps. The first circuit was a current switch designed to quickly turn the magnetic fields of the MOT off. The magnetic coil switch was able to reduce the magnetic field intensity to 5 % of its initial value after 81 μs. The second circuit was an analog signal switch designed to turn the modulation signal of an AOM off. The analog switch was able to reduce the modulation signal intensity to 8.5 % of its initial magnitude in ~25μs. The performances of the two circuits discussed in this paper are sufficient for future atom transfer research based on predicted experimental requirements

The Construction of Spinor Fields on Manifolds with Smooth Degenerate Metrics

We examine some of the subtleties inherent in formulating a theory of spinors on a manifold with a smooth degenerate metric. We concentrate on the case where the metric is singular on a hypersurface that partitions the manifold into Lorentzian and Euclidean domains. We introduce the notion of a complex spinor fibration to make precise the meaning of continuity of a spinor field and give an expression for the components of a local spinor connection that is valid in the absence of a frame of local orthonormal vectors. These considerations enable one to construct a Dirac equation for the discussion of the behavior of spinors in the vicinity of the metric degeneracy. We conclude that the theory contains more freedom than the spacetime Dirac theory and we discuss some of the implications of this for the continuity of conserved currents.Comment: 24 pages, LaTeX (RevTeX 3.0, no figures), To appear in J. Math. Phy

Finite action Yang-Mills solutions on the group manifold

We demonstrate that the left (and right) invariant Maurer-Cartan forms for any semi-simple Lie group enable one to construct solutions of the Yang-Mills equations on the group manifold equipped with the natural Cartan-Killing metric. For the unitary unimodular groups the Yang-Mills action integral is finite for such solutions. This is explicitly exhibited for the case of SU(3)

Finding Octonionic Eigenvectors Using Mathematica

The eigenvalue problem for 3x3 octonionic Hermitian matrices contains some surprises, which we have reported elsewhere. In particular, the eigenvalues need not be real, there are 6 rather than 3 real eigenvalues, and the corresponding eigenvectors are not orthogonal in the usual sense. The nonassociativity of the octonions makes computations tricky, and all of these results were first obtained via brute force (but exact) Mathematica computations. Some of them, such as the computation of real eigenvalues, have subsequently been implemented more elegantly; others have not. We describe here the use of Mathematica in analyzing this problem, and in particular its use in proving a generalized orthogonality property for which no other proof is known.Comment: LaTeX2e, 22 pages, 8 PS figures (uses included PS prolog; needs elsart.cls and one of epsffig, epsf, graphicx