Open Access. Powered by Scholars. Published by Universities.®

Digital Commons Network™

Open Access. Powered by Scholars. Published by Universities.®

Theses

Discipline
Institution
Keyword
Publication Year
Publication Type

Articles 31 - 60 of 16553

Full-Text Articles in Entire DC Network

Ikaros: See Through Time, Aisha F. A. Alnouri Aug 2026

Ikaros: See Through Time, Aisha F. A. Alnouri

Theses

Conventional heritage interpretation often relies on static signage, creating an "information void" where physical ruins sit uncontextualized. This thesis addresses this issue by proposing an interactive spatial information system designed to dynamically display, and contextualize architectural heritage in real time. Designed as a global framework, Failaka Island in Kuwait serves as the primary case study, driven by a personal cultural connection and the need to bridge the island's post-war generational disconnect. Positioned at the intersection of information design, interactive media, and spatial visualization, the system, Ikaros, utilizes Hellenistic Temple B, a 3rd-century BCE sanctuary, as its core testbed. The touchscreen …


Effects Of Disorder On The Magnetic And Electronic Structure Of Kagome Alloy Fe2mnsn., Thayne Dean Aug 2026

Effects Of Disorder On The Magnetic And Electronic Structure Of Kagome Alloy Fe2mnsn., Thayne Dean

Theses

Iron-based magnets with the Kagome lattice are a rich set of materials due to their non-trivial topology combined with high magnetic ordering temperature (Tc). Previously, we identified and synthesized Fe2MnSn as a promising material with high magnetic anisotropy characterized by a high Tc. The desirable magnetic properties of ternary alloys are controlled by atomic-level antisite disorder and are sensitive to stoichiometry as well. To illustrate the role of disorder in Fe2MnSn, we performed DFT calculations using 64-atom supercells, which enabled us to probe changes in the density of states and magnetic moments by design. Our data show that substitution of …


Combining Citizen Science And Machine Learning: The Blueprint For An Emission Line Detection Algorithm, Alex Kiely Aug 2026

Combining Citizen Science And Machine Learning: The Blueprint For An Emission Line Detection Algorithm, Alex Kiely

Theses

Extragalactic spectroscopy provides us with information about the properties of galaxies and the fundamental nature of the universe. By analyzing galaxy spectra, we gain insight into a galaxy’s evolution through measures of its star formation rate (SFR), metallicity (Z), ionization parameter (U), gas pressure, dust extinction, electron density, and redshift (z). Redshift, in particular, can provide us with information about a galaxy’s velocity and distance, the formation of baryonic matter, dark matter halos, and the variation of galaxy properties with redshift. The analysis of these spectra is often an incredibly demanding, time-intensive, and potentially inaccurate process, further complicated by the …


Building A Multiwavelength Catalog Of Active Galactic Nuclei For The Cosmos Field, Thresa Kelly Aug 2026

Building A Multiwavelength Catalog Of Active Galactic Nuclei For The Cosmos Field, Thresa Kelly

Theses

Active galactic nuclei (AGNs) are capable of producing highly luminous emission across the entirety of the electromagnetic spectrum. Each waveband has characteristic features that can be used to separate AGNs from typical, inactive galaxies. However, each AGN has a unique combination of physical characteristics--such as the black hole mass, accretion rate, obscuring column density, orientation angle, and/or presence of relativistic jets--that create a unique spectral shape. Thus, a single AGN identification technique using a single wavelength will fail to find all types of AGNs. The resulting sample will bias the results of larger statistical studies. Therefore, it is critical to …


Deep Analog: Open-Set Film Emulation With Reference-Conditioned 3d Luts, Yitong Mu Aug 2026

Deep Analog: Open-Set Film Emulation With Reference-Conditioned 3d Luts, Yitong Mu

Theses

Film emulation reproduces the look of an analog film stock on a new digital photograph. We target its open-set form—matching the look of any reference film frame from a single example—with a 3D lookup table (LUT) predicted from that reference. Real-time image enhancement has converged on one recipe for the color step: predict per-image weights over a fixed bank of 3D LUTs and blend them. We show this construction is a gated mixture of experts—specialist tables chosen per image by a learned gate—and it inherits the corresponding failure: trained end-to-end against reconstruction, the gate collapses onto a single expert, so …


Cross-Layer Security And Responsive Evaluation Architectures For Quantum Resistance In Connected Vehicles, Geoff Twardokus Aug 2026

Cross-Layer Security And Responsive Evaluation Architectures For Quantum Resistance In Connected Vehicles, Geoff Twardokus

Theses

Connected vehicle (CV) technologies are emerging as a crucial technology for improving safety on future roadways. Wireless vehicle-to-everything (V2X) communication allows CVs to exchange information that provides enhanced awareness and supports better driving decisions, especially in high-risk or non-line-of-sight scenarios. However, V2X also exposes new surfaces to physical layer attacks and increasingly sophisticated, potentially quantum-capable threat actors. As human or autonomous CV drivers will make split-second safety-critical decisions based on the contents of V2X messages, ensuring their authenticity, as well as their reliable and timely delivery, is crucial. Otherwise, malicious attackers may interfere with safety services or spoof messages to …


Design And Verification Of A Reconfigurable Cryptographic Hardware Accelerator, Nicholas Merante Aug 2026

Design And Verification Of A Reconfigurable Cryptographic Hardware Accelerator, Nicholas Merante

Theses

Cryptographic operations are used throughout computing systems to protect data confidentiality and integrity. Although software implementations provide flexibility, dedicated hardware can offer more predictable execution time and reduce the processing burden placed on a general-purpose processor. This thesis presents the design and verification of a Reconfigurable Cryptographic Hardware Accelerator (RCHA) that integrates AES-128, ChaCha20, SHA-256, and BLAKE2s within a single Verilog/SystemVerilog design. A top-level interface shared by the four cores manages algorithm selection, inputs, outputs, status, protocol errors, cycle measurement, and known-answer self-tests. Verification combined primitive-level tests, integrated UVM regressions, randomized stimulus, directed coverage tests, and OpenSSL-based C++ reference models …


Asynchronous Methods For Reducing Dynamic Power In Sparse Systems, Braley Lachner Aug 2026

Asynchronous Methods For Reducing Dynamic Power In Sparse Systems, Braley Lachner

Theses

While a strong history of computer development has maximized architecture performance, modern computing is fundamentally constrained by thermal limits and power consumption. This is especially true in power sensitive edge applications, which often have low activity. Asynchronous architectures offer a pathway to take advantage of sparsity within hardware to drastically reduce dynamic power through fine-grain selective activation of only necessary hardware. Despite these advantages, the semiconductor industry relies heavily on Electronic Design Automation (EDA) toolchains, which have been developed with many synchronous assumptions. The traditional overhead and strict incompatibility with standard EDA toolchains have limited adoption of asynchronous technologies in …


Poppies In Bloom: Gathering Galaxies From Jwst Parallel Fields, Anika Kumar Aug 2026

Poppies In Bloom: Gathering Galaxies From Jwst Parallel Fields, Anika Kumar

Theses

A major goal of extragalactic astrophysics is connecting the Big Bang to the present by under- standing the evolution of star formation (SF) across cosmic time. The correlation between SF and the stellar mass buildup in galaxies, or the star forming main sequence relation (SFMS), highlights the various mechanisms that drive galaxy evolution. Deviations like quiescent galaxies, which have ceased forming stars, and starburst galaxies, which undergo an exceptionally high rate of SF compared to their normal star formation histories (SFH), offer key clues to the catalysts of galaxy evolution (e.g., mergers, gas accretion, supernovae feedback). Our understanding of early …


Impact Of Chiral Chain Conformations On The Self-Assembly Of Helical Polymers, Michael J. Grant Aug 2026

Impact Of Chiral Chain Conformations On The Self-Assembly Of Helical Polymers, Michael J. Grant

Theses

Polymers are a soft material with diverse applications across a spectrum of technologies including, but not limited to, packaging, drug-delivery, optics, lithography and templating. This ubiquity stems from over a century of in-depth theoretical and experimental investigations relating polymer size, stiffness and architecture to their emergent material properties. Interestingly, unlike small organic molecules where solution behavior is predominantly a function of hydrophobicity, in polymers, adjusting the aforementioned features can have a dramatic impact on their interactions with neighboring molecules. In turn, this allows for a tunable parameter space enabling the ability to achieve specific engineering goals. Yet, while the impact …


Uvm Verification Of A 4-Stage Asynchronous Risc-V Processor, Yashaswini Suresha Aug 2026

Uvm Verification Of A 4-Stage Asynchronous Risc-V Processor, Yashaswini Suresha

Theses

Functional verification often takes more effort than designing the system itself, especially when the design departs from the synchronous, globally clocked style that verification tools assume. Asynchronous or clockless circuits are an example of this. They use local request and acknowledge handshaking instead of a global clock, which reduces dynamic power and eliminates clock-distribution and skew problems. However, this also means that standard verification methods that rely on a single periodic clock no longer apply. This thesis introduces a constrained-random, coverage-driven verification environment for a four-stage asynchronous RISC-V processor. The environment is built in SystemVerilog using the Universal Verification Methodology …


Characterizing Heavy Water Displacement In Molecular Sieve Drying Beds For Practical Trace Tritium Capture Methods, Brandon M. Massett Aug 2026

Characterizing Heavy Water Displacement In Molecular Sieve Drying Beds For Practical Trace Tritium Capture Methods, Brandon M. Massett

Theses

Tritium plays a crucial role in nuclear fusion power plant designs, and adsorption beds are essential tools for managing tritiated water vapor. A series of tests was performed to investigate whether a saturated adsorption bed preferentially adsorbs heavy water vapor. The design of passive tritium control systems could potentially rely on adsorption beds preferentially trapping heavier isotopologues of water. This work investigates the displacement phenomenon and the effects of carrier gas superficial velocity on bed performance. Significant displacement was observed when a humid stream containing heavy water was diverted through a bed pre-saturated with light water, as indicated by changes …


Carbon Credits, Capture And Storage Markets In The Uae, Fatema Adnan Majed Aug 2026

Carbon Credits, Capture And Storage Markets In The Uae, Fatema Adnan Majed

Theses

The growing urgency to address climate change has placed carbon markets and carbon capture technologies at the core of global climate strategies. This thesis looks into whether the United Arab Emirates can develop its emerging carbon credit framework into a platform that supports viable private investment and national sustainability goals. While systems that are established, such as the EU Emission Trading System (EU ETS) and voluntary schemes, such as Verra's Verified Carbon Standard (VCS), provide mature models, the UAE shows a unique case: a market still in its early stages yet backed by ambitious climate commitments and world-class hydrocarbon infrastructure. …


Analysis Of Gwtc-3 With Multiple Quasicircular Next-Generationwaveform Models, Noah M. Manning Aug 2026

Analysis Of Gwtc-3 With Multiple Quasicircular Next-Generationwaveform Models, Noah M. Manning

Theses

The interpretation of gravitational wave sources depends on the specific choice of model used to interpret signals. For example, previous analyses of GWTC-3 event candidates using the SEOBNRv4PHM, IMRPhenomXPHM, and NRSur7dq4 models have arrived at sometimes notably di!erent conclusions about event properties. Unfortunately, subtle analysis settings and code di!erences can also produce notable di!erences in event properties. Previous work on GWTC-3 has not yet used a consistent analysis framework to reassess all events with state-of- the-art models. In this work, we revisit GWTC-3, reassessing every event using three waveform models: two state-of-the-art models (SEOBNRv5PHM and IMRPhenomTPHM) and one older waveform …


The Interactions That Shape Us: An Investigation Of The Supernova Engine’S Effect On Bbh Mergers, And Of Stellar Encounters In The Disks Of Active Galactic Nuclei, Zoe A. Rosenberg Aug 2026

The Interactions That Shape Us: An Investigation Of The Supernova Engine’S Effect On Bbh Mergers, And Of Stellar Encounters In The Disks Of Active Galactic Nuclei, Zoe A. Rosenberg

Theses

Mergers and other close interactions between astrophysical objects such as black holes and stars are powerful and energetic occurrences, capable of creating heavy elements, forming intriguing remnants, and shaping the populations of stars and compact objects around them. In this thesis, we describe two studies which examine two types of close gravitational events: isolated binary black hole mergers and dynamic stellar interactions in a dense environment. For our first study, we investigate how modifying the speed of convection in the engine behind core-collapse supernova explosions affects the population of merging binary black holes. To get an accurate picture of this …


Detecting Eccentric Kozai–Lidov Imprints On Gravitational Waves From An Intermediate–Stellar-Mass Binary Black Hole Around A Supermassive Black Hole, Zainab Mangi Aug 2026

Detecting Eccentric Kozai–Lidov Imprints On Gravitational Waves From An Intermediate–Stellar-Mass Binary Black Hole Around A Supermassive Black Hole, Zainab Mangi

Theses

The gravitational-wave signal of a compact binary carries the imprint of its environment. In a galactic nucleus, the tidal field of the central supermassive black hole (SMBH) drives Kozai--Lidov (KL) oscillations in the eccentricity of an orbiting binary, modulating the emitted signal. As a proof of concept, previous work showed that for an IMBH--stellar-mass black hole binary, this modulation is detectable with LISA out to about a megaparsec (Deme et al. 2020). This detectability depends on the parameters of the triple; among them, the outer eccentricity plays a special role: it switches on the octupole order of the secular approximation, …


Population Inference Of Compact Binaries With Eccentricity, Muhammad Zeeshan Aug 2026

Population Inference Of Compact Binaries With Eccentricity, Muhammad Zeeshan

Theses

Gravitational waves opened a new window to study the properties of compact binary systems, providing insights into their astrophysical formation and evolution. Initially, population studies relied on mass and spin distributions to distinguish between isolated, dynamical, and hierarchical merger channels; however, orbital eccentricity offers a complementary probe of binary formation scenarios. Historically, eccentricity received limited attention due to the lack of eccentric wave- form models and the absence of strong observational evidence within the LIGO–Virgo–KAGRA sensitivity band. A growing catalog, recent advances in eccentric waveform modeling, and analyses reporting candidates consistent with non-zero eccentricity motivate a systematic population-level study with …


Harnessing Airborne And Spaceborne Lidar For Large-Area Assessment Of Canopy Structural Complexity, Tahrir Ibraq Siddiqui Aug 2026

Harnessing Airborne And Spaceborne Lidar For Large-Area Assessment Of Canopy Structural Complexity, Tahrir Ibraq Siddiqui

Theses

Forests play a vital role in global carbon cycling, biodiversity conservation, and the provision of ecosystem services. Accurate quantification of forest carbon sequestration rates – or forest production – therefore is essential for understanding ecosystem dynamics and informing sustainable forest management practices. Light detection and ranging (LiDAR) systems, as an active remote sensing modality, have emerged as a powerful tool for capturing detailed structural information of forests. Studies employing terrestrial LiDAR demonstrated that canopy structural complexity (CSC) metrics are strongly correlated with forest production at stand to landscape scales. While terrestrial LiDAR systems provide highly detailed maps of internal canopy …


Factors Influencing Employee Engagement And Performance In Hybrid Work Environments, Saif Alblooshi Aug 2026

Factors Influencing Employee Engagement And Performance In Hybrid Work Environments, Saif Alblooshi

Theses

The widespread adoption of hybrid work arrangements, in which employees divide their working time between remote and office-based settings, has fundamentally altered how organisations manage, measure, and sustain workforce engagement and performance. While hybrid models offer tangible benefits such as increased autonomy, reduced commuting burden, and greater scheduling flexibility, they simultaneously introduce a set of organisational challenges that conventional management frameworks were not designed to address. Chief among these challenges is the difficulty of maintaining consistent levels of employee engagement across distributed work settings, where informal communication, social connection, and direct managerial oversight are structurally constrained. The absence of robust, …


A Hyperpipeline For Joint Inference Of The Equation Of State And Population Of Binary Neutron Stars, Marc Ebiri Aug 2026

A Hyperpipeline For Joint Inference Of The Equation Of State And Population Of Binary Neutron Stars, Marc Ebiri

Theses

The extreme environment within neutron stars presents the opportunity to probe the nuclear equation of state at high densities and study the nature of stellar remnants near 1 solar mass. Parameter inference for the equation of state has received abundant attention in previous studies, but only a fraction of those have employed nontrivial population models in their priors. In this work, we introduce an upgrade to the generalized version of the popular RIFT algorithm known as HyperPipe, enabling the inclusion of flexible, user-provided priors within preexisting likelihood marginalization scripts that will facilitate joint inference of the equation of state and …


A Scalable And Physically Interpretable Machine Learning Approach To Analyzing Agn Spectra, Liza Maria Matrecito Salcedo Aug 2026

A Scalable And Physically Interpretable Machine Learning Approach To Analyzing Agn Spectra, Liza Maria Matrecito Salcedo

Theses

The broad-line region (BLR) is a sub-parsec region in an Active Galactic Nucleus (AGN) where dense, optically thick gas clouds produce broad emission lines (BELs). BELs are important probes of physical processes near the central supermassive black hole (SMBH); however, a complete understanding of the BLR’s structure and dynamics remains lacking. The observed diversity in BEL profile shapes suggests substantial differences in BLR properties across AGN. The availability of large-scale spectroscopic databases provides a valuable opportunity to systematically study these properties in large samples of AGN. They also offer the opportunity to identify rare but important systems, such as SMBH …


Investigations Into The Structure-Property Relationships Of Magnetic Fe2mnsn And Gradient Copt Thin Films For Next-Generation Magnetic Technologies, Lance Griswold Aug 2026

Investigations Into The Structure-Property Relationships Of Magnetic Fe2mnsn And Gradient Copt Thin Films For Next-Generation Magnetic Technologies, Lance Griswold

Theses

e study of spin-based electronic phenomena, or spintronics, has become increasingly important in materials science and condensed matter physics due to its potentialto enable next-generation magnetic technologies, including advanced memory devices and quantum computing. Central to this field is the relationship between a material’s atomic structure and its physical properties, which requires precise control over synthesis conditions to achieve desired magnetic and electronic behavior. In this work, I investigate the structure–property relationships of several magnetic thin-film systems, each designed to address a specific technological challenge. All films were synthesized using magnetron co-sputtering from elemental magnetic and non-magnetic targets, either at …


Radiometric Dating And Isotope Analysis To Determine The Source And Timing Of Rare Earth Element-Bearing Fluid Mineralization At Hicks Dome, Hardin County, Illinois, Kristina M. Kohl Aug 2026

Radiometric Dating And Isotope Analysis To Determine The Source And Timing Of Rare Earth Element-Bearing Fluid Mineralization At Hicks Dome, Hardin County, Illinois, Kristina M. Kohl

Theses

The Hicks Dome structure of Hardin County, Illinois, located within the Illinois-Kentucky Fluorspar District (IKFD), is one of the most perplexing geological features in the mid-continental U.S. Composed of uplifted Devonian strata intruded by a Ca-rich magma and ultramafic dikes, the dome is recognized as part of the Wauboukigou Igneous Province (WIP) and has been shown to host an abundance of rare earth element (REE) mineralization, particularly Dy, Y, and Sc. Despite extensive prior studies on REE concentrations and the link between fluorite mineralization in the IKFD and igneous activity at Hicks Dome, the absolute timing and relationship among REE …


Measurement Of Kerr Rotation Using A Variable-Angle Polarizer Method, Shusmita Podder Pooza Aug 2026

Measurement Of Kerr Rotation Using A Variable-Angle Polarizer Method, Shusmita Podder Pooza

Theses

The magneto-optical Kerr effect (MOKE) occurs when polarized light is reflected from a magnetized surface, causing changes in polarization angle (called Kerr rotation) and its state (linear vs elliptical, for example). In a simple version, MOKE measurement involves measuring the intensity of the reflected beam off the surface of a sample as an external magnetic field is swept through it. We record a change in the reflected intensity when the magnetization of the material changes. While easily measurable using modern electronics methods, the Kerr rotation is minimal, only of the order of milliradians (~0.1 deg), and is a characteristic of …


The Impact Of Built-Environment Walkability On Obesity Among Women In Pakistan: A Cross-Sectional Analysis Using Demographic Health Surveys (Dhs) Data, Areej Arshad Jul 2026

The Impact Of Built-Environment Walkability On Obesity Among Women In Pakistan: A Cross-Sectional Analysis Using Demographic Health Surveys (Dhs) Data, Areej Arshad

Theses

Pakistan is the fifth most populous country in the world, with a population of over 247 million people in 2023. According to the World Health Organization, 23% of Pakistan’s population is obese, with higher prevalence among women (26%) compared to men (19.9%). Recent research in high-income countries has identified built-environment as an important factor impacting physical activity, as well as health outcomes like obesity rates. However, work linking built-environment and health outcomes is scattered for low- and middle- income countries. This study, therefore, aimed to construct a consistent and simple built-environment walkability score for Pakistan using Demographic Health Surveys (DHS) …


Pixel Weave: Explore The Craft, Share The Story, Janki Akbari Jul 2026

Pixel Weave: Explore The Craft, Share The Story, Janki Akbari

Theses

Traditional craft practices are often preserved as finished objects rather than experienced as active systems of knowledge. As a result, the techniques, visual logic, and cultural meaning behind these crafts become less accessible to broader audience. Pixel Weave addresses this challenge by translating the double ikat (a premium, highly complex weaving technique in which both the warp (vertical) and weft (horizontal) yarns are individually resist-dyed to a preplanned pattern before being placed on the loom, so that the design only fully emerges once the two dyed yarn sets are woven together) weaving logic of Patan Patola, a centuries old textile …


The Mediating Role Of Moral Disengagement In The Relationship Between Facets Of Empathy And Aggression, Romiere J. Horace Jul 2026

The Mediating Role Of Moral Disengagement In The Relationship Between Facets Of Empathy And Aggression, Romiere J. Horace

Theses

Aggression is a major social and public health concern with economic, psychological, and interpersonal implications. Extensive research has examined the potential antecedents for aggressive behavior, with many different environmental, biological, and intrapsychic factors being significantly associated with aggression. Researchers have also focused on cognitive mechanisms, like empathy, as a protective factor for aggression. More specifically, research has linked lower levels of empathy to higher levels of aggression; however, the underlying mechanisms of this relationship remain underexplored. A potential explanatory mechanism is moral disengagement, which allows individuals to justify harmful behaviors and avoid self-sanctions. However, limited research has examined these constructs …


Bridging The Gap: Using A Regional Pediatric Intensive To Improve Rural Nursing Students’ Self-Efficacy, Hannah J. Sasser, Will Brewer Jul 2026

Bridging The Gap: Using A Regional Pediatric Intensive To Improve Rural Nursing Students’ Self-Efficacy, Hannah J. Sasser, Will Brewer

Theses

Abstract

Introduction: Valuable clinical learning opportunities is essential, yet often an unmet goal in nursing education, especially within rural associate degree nursing (ADN) programs, where access to high-acuity and diverse clinical experiences is limited.

Background: Nursing students in geographically isolated areas face limited access to specialty clinicals, including pediatrics, creating inadequacies in clinical learning and preparedness (Institute of Pediatric Nursing, 2021).

Purpose: The purpose of this project was to evaluate the effect of a two-day pediatric intensive, incorporating simulation scenarios and micro-learning activities, on the self-efficacy and satisfaction with learning of students in a rural ADN program. …


Machine Learning For Practical Quantum Computing: Adaptive Mitigation And Data-Driven Noise Characterization, Steven Szachara Jul 2026

Machine Learning For Practical Quantum Computing: Adaptive Mitigation And Data-Driven Noise Characterization, Steven Szachara

Theses

Quantum error mitigation (QEM) is essential for reliable near-term quantum computing, yet practical deployment requires balancing mitigation strength against runtime overhead under nonstationary noise. This work introduces GSC-QEMit, a telemetry-driven context–forecast–bandit framework that adaptively selects mitigation intensity using unsupervised context discovery, uncertainty-aware Gaussian process forecasting, and a cost-aware contextual bandit. Evaluated on benchmark quantum circuits under drifting noise in simulation, the approach improves logical fidelity while reducing unnecessary intervention cost. Complementing this systems-level contribution, we apply unsupervised machine learning to broadband cryogenic transient dielectric spectroscopy data to analyze two-level system (TLS) noise mechanisms. Through clustering, dimensionality reduction, and spectral analysis, …


Numerical Range Of Rank-1 Partial Isometries And Elliptical Range Theorem, Lucas Saone Jul 2026

Numerical Range Of Rank-1 Partial Isometries And Elliptical Range Theorem, Lucas Saone

Theses

The Elliptical Range Theorem states that the numerical range of a 2x2 complex matrix A is an elliptical disc with foci at the eigenvalues of A and center at tr(A)/2. Many proofs have been offered for this theorem. In this paper, we provide another one. The strategy we will use is to decompose the matrix A into the sum of rank-1 operators of the form YxX*, where X and Y are in 2-D complex vectors. When analyzing the numerical range of a rank-1 operator of this form, three results can happen: i) the numerical range forms a disc at the …