Rose-Hulman ScholarCopyright (c) 2022 Rose-Hulman Institute of Technology All rights reserved.
https://scholar.rose-hulman.edu
Recent documents in Rose-Hulman Scholaren-usFri, 28 Jan 2022 01:38:35 PST3600Common Spatial Pattern Detection of Concept Semantic Relatedness Using Combined Event-Related Potentials and Frequency Spectrum Features
https://scholar.rose-hulman.edu/abbe_grad_theses/9
https://scholar.rose-hulman.edu/abbe_grad_theses/9Fri, 21 Jan 2022 11:43:00 PSTMichael DoyelDecomposable Model Spaces and a Topological Approach to Curvature
https://scholar.rose-hulman.edu/rhumj/vol22/iss2/8
https://scholar.rose-hulman.edu/rhumj/vol22/iss2/8Tue, 28 Dec 2021 13:29:47 PST
This research investigates a model space invariant known as k-plane constant vector curvature, traditionally studied when k=2, and introduces a new invariant, (m,k)-plane constant vector curvature. We prove that the sets of k-plane and (m,k)-plane constant vector curvature values are connected, compact subsets of the real numbers and establish several relationships between the curvature values of a decomposable model space and its component spaces. We also prove that every decomposable model space with a positive-definite inner product has k-plane constant vector curvature for some integer k>1. In two examples, we provide the first instance of a model space with (m,k)-plane constant vector curvature and leverage our theorems to efficiently calculate the k-plane constant vector curvature values of a decomposable model space. This research further characterizes model spaces by assigning new basis-independent values to its various subspaces and allows us to easily construct model spaces with prescribed curvature values.
]]>
Kevin M. TullyWinning Strategy For Multiplayer And Multialliance Geometric Game
https://scholar.rose-hulman.edu/rhumj/vol22/iss2/7
https://scholar.rose-hulman.edu/rhumj/vol22/iss2/7Tue, 28 Dec 2021 12:39:59 PST
The Geometric Sequence with common ratio 2 is one of the most well-known geometric sequences. Every term is a nonnegative power of 2. Using this popular sequence, we can create a Geometric Game which contains combining moves (combining two copies of the same terms into the one copy of next term) and splitting moves (splitting three copies of the same term into two copies of previous terms and one copy of the next term). For this Geometric Game, we are able to prove that the game is finite and the final game state is unique. Furthermore, we are able to calculate the upper bound and lower bound of the length of Geometric Game. We are also able to prove some interesting results in terms of the winning strategy of 2-player games, and some special cases of multiplayer games and multialliance games.
]]>
Jingkai YeHurwitz Actions on Reflection Factorizations in Complex Reflection Group G6
https://scholar.rose-hulman.edu/rhumj/vol22/iss2/6
https://scholar.rose-hulman.edu/rhumj/vol22/iss2/6Tue, 28 Dec 2021 12:03:40 PST
We show that in the complex reflection group G_{6}, reflection factorizations of a Coxeter element that have the same length and multiset of conjugacy classes are in the same Hurwitz orbit. This confirms one case of a conjecture of Lewis and Reiner.
]]>
Gaurav Gawankar et al.Lie-Derivations of Three-Dimensional Non-Lie Leibniz algebras
https://scholar.rose-hulman.edu/rhumj/vol22/iss2/5
https://scholar.rose-hulman.edu/rhumj/vol22/iss2/5Tue, 28 Dec 2021 11:40:18 PST
The concept of Lie-derivation was recently introduced as a generalization of the notion of derivations for non-Lie Leibniz algebras. In this project, we determine the Lie algebras of Lie-derivations of all three-dimensional non-Lie Leibniz algebras. As a result of our calculations, we make conjectures on the basis of the Lie algebra of derivations of Lie-solvable non-Lie Leibniz algebras.
]]>
Emily H. BelangerThe Optimal Double Bubble for Density $r^p$
https://scholar.rose-hulman.edu/rhumj/vol22/iss2/4
https://scholar.rose-hulman.edu/rhumj/vol22/iss2/4Tue, 28 Dec 2021 09:40:05 PST
In 2008 Reichardt proved that the optimal Euclidean double bubble---the least-perimeter way to enclose and separate two given volumes---is three spherical caps meeting along a sphere at 120 degrees. We consider R^{n}with densityr^{p}, joining the surge of research on manifolds with density after their appearance in Perelman's 2006 proof of the Poincaré Conjecture. Boyer et al. proved that the best single bubble is a sphere through the origin. We conjecture that the best double bubble is the Euclidean solution with the singular sphere passing through the origin, for which we have verified equilibrium (first variation or ``first derivative'' zero). To prove the exterior of the minimizer connected, it would suffice to show that least perimeter is increasing as a function of the prescribed areas. We give the first direct proof of such monotonicity in the Euclidean plane. Such arguments were important in the 2002 Annals proof of the double bubble in Euclidean 3-space.
]]>
Jack Hirsch et al.A Proof of a Generalization of Niven's Theorem Using Algebraic Number Theory
https://scholar.rose-hulman.edu/rhumj/vol22/iss2/3
https://scholar.rose-hulman.edu/rhumj/vol22/iss2/3Fri, 24 Dec 2021 06:53:29 PST
Niven’s theorem states that the sine, cosine, and tangent functions are rational for only a few rational multiples of π. Specifically, for angles θ that are rational multiples of π, the only rational values of sin(θ) and cos(θ) are 0, ±½, and ±1. For tangent, the only rational values are 0 and ±1. We present a proof of this fact, along with a generalization, using the structure of ideals in imaginary quadratic rings. We first show that the theorem holds for the tangent function using elementary properties of Gaussian integers, before extending the approach to other imaginary quadratic rings. We then show for which rational multiples of π the squares of the sine, cosine, and tangent functions are rational, providing a generalized form of Niven’s theorem. We end with a discussion of a few related combinatorial identities.
]]>
Caroline NunnA Mathematical Model Regarding Change in Preferences of Refugee Settlements
https://scholar.rose-hulman.edu/rhumj/vol22/iss2/2
https://scholar.rose-hulman.edu/rhumj/vol22/iss2/2Fri, 17 Dec 2021 15:33:36 PST
Where cultures meet, there is bound to be conflict to some extent. This especially applies in the case of refugees grouped together when seeking asylum, with different styles of life, socialization, and conflict resolution meeting in one place. This paper focuses specially on three types of conflict resolution(negotiation, mediation, and arbitration) and constructs a differential equation model to study how the interactions between populations cause the number of people following each resolution method to shift. It was found that when there is no existing outside authority or environmental bias towards a resolution method, the method with the greatest number of followers will also be the one to take over the final population. However, in the presence of an outside force promoting or discouraging certain methods, although some groups will be given advantages over others, the final outcome is also still partially under the influence of the initial population. Outside of stable equilibria representing situations where one method ends up taking over the entire population, we also found certain unstable equilibria that carry key information about the basins of attraction of the stable equilibria.
]]>
Raaghav Malik et al.Convergence Properties of Solutions of a Length-Structured Density-Dependent Model for Fish
https://scholar.rose-hulman.edu/rhumj/vol22/iss2/1
https://scholar.rose-hulman.edu/rhumj/vol22/iss2/1Fri, 17 Dec 2021 15:20:05 PST
We numerically study solutions to a length-structured matrix model for fish populations in which the probability that a fish grows into the next length class is a decreasing nonlinear function of the total biomass of the population. We make conjectures about the convergence properties of solutions to this equation, and give numerical simulations which support these conjectures. We also study the distribution of biomass in the different age classes as a function of the total biomass.
]]>
Geigh ZollicofferComputer Program Simulation of a Quantum Turing Machine with Circuit Model
https://scholar.rose-hulman.edu/math_mstr/177
https://scholar.rose-hulman.edu/math_mstr/177Tue, 07 Dec 2021 16:30:53 PST
Molina and Watrous present a variation of the method to simulate a quantum Turing machine employed in Yao’s 1995 publication “Quantum Circuit Complexity”. We use a computer program to implement their method with linear algebra and an additional unitary operator defined to complete the details. Their method is verified to be correct on a quantum Turing machine.
]]>
Shixin WuModeling, Design, and Fabrication of Plasmonic Coupling to a Silicon Nitride Waveguide-Photodetector
https://scholar.rose-hulman.edu/dept_optics/9
https://scholar.rose-hulman.edu/dept_optics/9Mon, 01 Nov 2021 08:02:58 PDT
This paper reports an evanescent coupling to silicon nitride-Germanium (SiN-Ge) photodetectors using surface plasmon polaritons (SPPs). Modeling, design, and fabrication of plasmonic coupling to Al nanoscale metal and light detection are included. Since 10 % of light coupled with surface plasmons is detected from poly-Si waveguides using lens fiber, Ge-photodetectors and SiN waveguides are utilized to detect light around 1550 nm wavelength with less insertion loss. Two plasmonic configurations with either Ag or Al nanoscale metal are simulated and analyzed using Lumerical FDTD simulation. Difficulty during fabricating SiN-Ge photodetectors are mentioned, and the best design and fabrication are suggested. The results in this paper can be applied to the design and fabrication of plasmonic systems with SiN-Ge photodetectors.
]]>
Jaehoon JeongDecentering Authority to Communicate Learning. Teachers Going Gradeless.
https://scholar.rose-hulman.edu/abbe_fac/240
https://scholar.rose-hulman.edu/abbe_fac/240Tue, 19 Oct 2021 12:23:31 PDTEmily Dosmar et al.Decentering Authority to Communicate Learning. Teachers Going Gradeless.
https://scholar.rose-hulman.edu/english_fac/377
https://scholar.rose-hulman.edu/english_fac/377Tue, 19 Oct 2021 12:21:09 PDTJulia WilliamsDistributed Feedback Master Oscillator Power Amplifier using Interface Polaritons
https://scholar.rose-hulman.edu/optics_grad_theses/27
https://scholar.rose-hulman.edu/optics_grad_theses/27Mon, 27 Sep 2021 11:19:27 PDT
Characterization and simulation of an innovative solid-state distributed feedback master oscillator power amplifier (solid-state DFB MOPA) are presented, using interface polaritons (IPs) that enhance wave propagations at gain-loss interfaces in active layers. The author set up the design of the fabricated device, and a company, Freedom photonics, collaborated with us, allowing me to modify some of their designed MOPA systems. The master oscillator (MO) consists of a patterned grating on a waveguiding region to transfer only a single mode of 1.550 μm wavelength. The power amplifier (PA) is fabricated with the MO to reduce power loss and tapered to amplify a single low-power mode from the MO. This PA region has a difference from other tapered PAs, containing an unpumped central area to have additional IPs. The simulation analyzes modeling characteristics of output light power, responding to different geometric parameters. The characterization includes far-field profiles, LIV, spectrum, and FWHM of the new device measured from experiments, compared with counterparts of a standard model.
]]>
Dongwon JangVolume 56 - Issue 18 - March 29, 2021
https://scholar.rose-hulman.edu/rosethorn/1259
https://scholar.rose-hulman.edu/rosethorn/1259Mon, 27 Sep 2021 08:50:28 PDTRose Thorn StaffA computational framework for understanding the roles of simplicity and rational support in people's behavior explanations
https://scholar.rose-hulman.edu/psychology_fac/20
https://scholar.rose-hulman.edu/psychology_fac/20Thu, 23 Sep 2021 09:42:13 PDTAlan Jern et al.Many Labs 5: Testing Pre-Data-Collection Peer Review as an Intervention to Increase Replicability
https://scholar.rose-hulman.edu/psychology_fac/19
https://scholar.rose-hulman.edu/psychology_fac/19Thu, 23 Sep 2021 09:42:13 PDTAlan Jern et al.Many Labs 5: Registered Multisite Replication of the Tempting-Fate Effects in Risen and Gilovich (2008)
https://scholar.rose-hulman.edu/psychology_fac/18
https://scholar.rose-hulman.edu/psychology_fac/18Thu, 23 Sep 2021 09:42:12 PDTAlan Jern et al.The Role of Electron Structure of Polymers at Their Biodegradation in Living Organisms Article Information
https://scholar.rose-hulman.edu/physics_fac/474
https://scholar.rose-hulman.edu/physics_fac/474Thu, 23 Sep 2021 09:28:22 PDTRenat Letfullin“Skill Set, Aptitude, and Desire”: Industry Perceptions of Recent Engineering Graduates as Professional Communicators
https://scholar.rose-hulman.edu/english_fac/368
https://scholar.rose-hulman.edu/english_fac/368Thu, 23 Sep 2021 09:24:01 PDTSarah Summers et al.