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2026

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Pd-L1-Centric Whole Blood-Based Immune Signature Profiles Of Tuberculosis Patients During Therapy, Johanna Eggeling, Martina Sester, Christoph Lange, Jan Heyckendorf, Barbara Kalsdorf, Anna M Mandalakas, Andrew R Dinardo, David Lewinsohn, Dagmar Schaub, Tina Schmidt, Eva Tolosa, Maja Reimann, Patricia M Sánchez Carballo Jan 2026

Pd-L1-Centric Whole Blood-Based Immune Signature Profiles Of Tuberculosis Patients During Therapy, Johanna Eggeling, Martina Sester, Christoph Lange, Jan Heyckendorf, Barbara Kalsdorf, Anna M Mandalakas, Andrew R Dinardo, David Lewinsohn, Dagmar Schaub, Tina Schmidt, Eva Tolosa, Maja Reimann, Patricia M Sánchez Carballo

Faculty, Staff and Students Publications

This prospective study investigated whole blood-based immune cell biomarkers for pulmonary tuberculosis (TB) immunoprofiling. Blood samples from 34 healthy controls and 51 tuberculosis patients were analyzed at three timepoints: Prior to therapy (T0), after 14 days of therapy (T1), and at the end of treatment (Te). Using multiparameter flow cytometry, 386 immune cell populations were analyzed. Predictive models were developed using two machine learning algorithms. A TB5LF change score, which was based on five cell populations, effectively distinguished tuberculosis patients from controls (AUC = 0.89) and tuberculosis patients before and at the end of treatment (AUC = 0.92). Similarly, the …


"Chatcbt”: Understanding The Implications Of Artificial Intelligence In Cognitive Behavioral Therapy, Esther R. Goldberg Jan 2026

"Chatcbt”: Understanding The Implications Of Artificial Intelligence In Cognitive Behavioral Therapy, Esther R. Goldberg

Scripps Senior Theses

The proposed study is intended to explore the impacts of artificial intelligence (AI) tools when used in cognitive behavioral therapy (CBT) to treat anxiety in American adults. The research is designed to measure whether AI systems such as large language models (LLMs) provide sufficient therapy through the factors of empathy, coping skills, and anxiety symptom reduction. Human therapists are hypothesized to surpass chatbots in all three. Through an experimental design, participants will be placed in either an AI therapy condition or human therapy condition. Participants will undergo a 12-week CBT program, after which they will measure anxiety reduction, perceived empathy …


Doikayt And The Ethics Of Belonging: Lessons In Place-Making From The Jewish Labor Bund, Zoë L. Jacobs Jan 2026

Doikayt And The Ethics Of Belonging: Lessons In Place-Making From The Jewish Labor Bund, Zoë L. Jacobs

Scripps Senior Theses

This thesis traces the evolution of doikayt—the Bundist principle of hereness—from its origins in the Jewish Labor Bund to contemporary applications in North America. Rooted in a refusal of both assimilation and nationalist escape, doikayt emphasizes cultivating safety, solidarity, and belonging through collective responsibility rather than territorial claims.

Building on this foundation, the exploration situates hereness within a settler-colonial context, where ethical dwelling is complicated by Indigenous dispossession. Drawing on Alexis Shotwell alongside Indigenous thinkers Vanessa Watts and Kyle Whyte, I examine how inhabiting place requires confronting historical injustices and ongoing relational responsibilities. Chapter 3 analyzes Linke Fligl (2016–2022) as …


Effects Of Teacher Training On Identifying Inattentive Type Adhd In Afab Students, Gabrielle A. Boles Jan 2026

Effects Of Teacher Training On Identifying Inattentive Type Adhd In Afab Students, Gabrielle A. Boles

Scripps Senior Theses

Teachers are more likely to detect hyperactive ADHD symptoms than inattentive ones, which often results in students, especially girls with inattentive symptoms, being under-referred (Willcut, 2012). This study evaluates whether a targeted, inattentive-focused, and gender responsive teacher training reduces gendered and symptom-based biases in referral decisions. K-5 teachers will be randomly assigned to receive either standard general ADHD identification training or an inattentive-focused, gender-responsive training, and will then be asked to review vignettes depicting children with hyperactive and inattentive symptoms, with varying student genders. Referral accuracy and knowledge of ADHD will be measured. Training condition, symptom presentation, and student gender …


The Dunning-Kruger Effect In Sixth Grade Adolescents: Improving Metacognition For Self-Regulated Learning, Julie H. Chen Jan 2026

The Dunning-Kruger Effect In Sixth Grade Adolescents: Improving Metacognition For Self-Regulated Learning, Julie H. Chen

Scripps Senior Theses

The Dunning-Kruger (DK) effect is a cognitive bias where low-performing individuals overestimate their own abilities, and top-performing individuals underestimate their own abilities relative to their peers. The purpose of this proposed study is to investigate the DK effect in sixth grade adolescents and to use metacognition as an intervention to improve self-assessment calibrations. This study will investigate adolescents in Piaget’s formal operational stage, aiming to improve metacognition levels. The study will occur over 12 weeks, and participants will be given a preparation handbook with or without metacognition activities for the purpose of preparing for the California Assessment of Student Performance …


Polysemicolon; Novice Programmers And Java Keywords, Briana C. Bettin Jan 2026

Polysemicolon; Novice Programmers And Java Keywords, Briana C. Bettin

Michigan Tech Publications

Most industrial programming languages leverage the English language for reserved keywords – words which a program compiler recognizes as specific execution commands. The divide between expert and novice programmers showcases an intriguing middle-ground by which the polysemy of many keywords becomes revealed. This essay explores a sampling of the multitude of keyword interpretations that a novice programmer may derive from the Java language’s syntactic style and keywords specifically, and how the polysemy of both “English” and “code” meanings to these terms affects the novice-expert programmer transition.The transition from novice to expert, and the mapping of the career of metaphor to …


Real Interpolation: An Approximate Introduction, Madeline Anderson Jan 2026

Real Interpolation: An Approximate Introduction, Madeline Anderson

Scripps Senior Theses

This thesis provides an introduction to real interpolation. We establish

relevant notions in functional analysis first, and use these concepts to study

real interpolation using J. Peetre’s 𝐾-functional in some detail. We also

explore the basics of approximation theory, in particular the connection

between approximation and interpolation results.


Optimal Takeoff Trajectory Prediction Of Electric Drones Based On A Fully Automated Optimal Experimental Design Method, Jiachen Wang, Dheeraj Paramkusham, Xiaosong Du Jan 2026

Optimal Takeoff Trajectory Prediction Of Electric Drones Based On A Fully Automated Optimal Experimental Design Method, Jiachen Wang, Dheeraj Paramkusham, Xiaosong Du

Mechanical and Aerospace Engineering Faculty Research & Creative Works

Electric vertical takeoff and landing (eVTOL) aircraft is attracting great interest as a viable solution to promote urban aerial mobility with promising flexibility as well as emission reductions. However, the low specific energy of the current battery is still a strong constraint on the range and endurance of eVTOL flights, especially considering the significant power demands during the takeoff process. Engineering design optimization permits promising solutions for the minimum takeoff energy consumption but can be computationally intensive due to iteratively evaluating simulation models. Surrogate-based design optimization is efficient but still relies on optimization iterations which prohibit real-time decision-making. To fill …


Phy Engineering, Clas Jan 2026

Phy Engineering, Clas

Executive Actions

No abstract provided.


Ba Psy, Clas Jan 2026

Ba Psy, Clas

Executive Actions

No abstract provided.


Ba Psy Revised Program, Clas Jan 2026

Ba Psy Revised Program, Clas

Executive Actions

No abstract provided.


Csm 2170, Clas Jan 2026

Csm 2170, Clas

Executive Actions

No abstract provided.


Associations Of Blood Pressure Level And Variability With Cortical Thickness: A Cross-Sectional Analysis From The Maracaibo Aging Study, Romeo De Leon, Shana Garza, Silvia Mejia-Arango, Kristina Vatcheva, Sokratis Charisis, Claudia L. Satizabal, Luis J. Mena, Joseph H. Lee, Joseph D. Terwilliger, Eron Manusov Jan 2026

Associations Of Blood Pressure Level And Variability With Cortical Thickness: A Cross-Sectional Analysis From The Maracaibo Aging Study, Romeo De Leon, Shana Garza, Silvia Mejia-Arango, Kristina Vatcheva, Sokratis Charisis, Claudia L. Satizabal, Luis J. Mena, Joseph H. Lee, Joseph D. Terwilliger, Eron Manusov

School of Medicine Publications

Background: Although high blood pressure (BP) level and variability are associated with Alzheimer's Disease (AD), their relationship with cortical thickness in brain regions that are associated with AD is unclear. Furthermore, the role of 24-hour BP has not been examined. We investigated the associations of office and ambulatory BP measures with cortical thickness in brain regions implicated in AD.

Methods: We performed a cross sectional analysis of 304 participants without dementia from a population-based study with office and 24-hour BP and magnetic resonance imaging (MRI) data. We considered cortical thickness values derived from 10 regions throughout the frontal, parietal, and …


Una Nueva Herramienta Para Estimar El Volumen Muscular Independientemente De La Edad, El Sexo Y El Nivel De Actividad Física, José J. Rivera-Sánchez, Laura P. Burgos-Morelos, Daniel Castillo-Castillo, Gerardo Méndez-Suárez, Juan C. Lopez-Alvarenga, Damián Carrillo-Ruíz Jan 2026

Una Nueva Herramienta Para Estimar El Volumen Muscular Independientemente De La Edad, El Sexo Y El Nivel De Actividad Física, José J. Rivera-Sánchez, Laura P. Burgos-Morelos, Daniel Castillo-Castillo, Gerardo Méndez-Suárez, Juan C. Lopez-Alvarenga, Damián Carrillo-Ruíz

School of Medicine Publications

Antecedentes: Actualmente, la evaluación del volumen muscular requiere técnicas invasivas o de imagen, lo que aumenta los costos y retrasa la evaluación, y las mediciones antropométricas con frecuencia son inexactas.

Objetivo: Desarrollar una fórmula matemática para estimar el volumen del cuádriceps.

Material y métodos: Se evaluaron 127 sujetos: 40 adultos sedentarios de 20 a 35 años, 47 atletas adultos de 20 a 45 años y 40 adultos sedentarios de 70 a 94 años. Se dividieron en grupos de desarrollo y de validación. Se realizaron mediciones de variables antropométricas y fuerza de agarre, y se desarrolló la fórmula de predicción del …


Large Language Models For Neurology: A Mini Review, Donald C. Wunsch, Daniel B. Hier Jan 2026

Large Language Models For Neurology: A Mini Review, Donald C. Wunsch, Daniel B. Hier

Electrical and Computer Engineering Faculty Research & Creative Works

Large language models have the potential to transform neurology by augmenting diagnostic reasoning, streamlining documentation, and improving workflow efficiency. This Mini Review surveys emerging applications of large language models in Alzheimer's disease, Parkinson's disease, multiple sclerosis, and epilepsy, with emphasis on ambient documentation, multimodal data integration, and clinical decision support. Key barriers to adoption include bias, privacy, reliability, and regulatory alignment. Looking ahead, neurology-focused language models may develop greater fluency in biomedical ontologies and FHIR standards, improving data interoperability and supporting more seamless collaboration between clinicians and AI systems. Two future developments have the potential to be particularly impactful: (1) …


Safe Optimal Control Framework For Cooperative Manipulation Of Objects In Human–Robot Teams, Irfan Ganie, Sarangapani Jagannathan Jan 2026

Safe Optimal Control Framework For Cooperative Manipulation Of Objects In Human–Robot Teams, Irfan Ganie, Sarangapani Jagannathan

Electrical and Computer Engineering Faculty Research & Creative Works

This article introduces a distributed deep neural network (NN)-based adaptive control framework for cooperative object manipulation in human–robot teams with unknown agent dynamics by using three distinct multilayer NN observers (MNNOs). The first observer, termed the reference point estimator, enables each robotic agent to estimate the object's reference center using consensus-based learning, even without direct access to global reference trajectories. The second observer, referred to as the human force-to-trajectory estimator, uses human-applied forces to infer the intended position, velocity, and acceleration of the object, enabling real-time estimation of human intent. Together, these two observers allow distributed estimation of human-intended motion. …


Waveguide-Assisted Single-Mode Fiber Bragg Gratings In A Highly Multimode Coreless Fiber Via Femtosecond Laser Inscription For Extreme Temperature Quasi-Distributed Thermal Sensing, Farhan Mumtaz, Koustav Dey, Bohong Zhang, Jeffrey D. Smith, Ronald J. O'Malley, Jie Huang Jan 2026

Waveguide-Assisted Single-Mode Fiber Bragg Gratings In A Highly Multimode Coreless Fiber Via Femtosecond Laser Inscription For Extreme Temperature Quasi-Distributed Thermal Sensing, Farhan Mumtaz, Koustav Dey, Bohong Zhang, Jeffrey D. Smith, Ronald J. O'Malley, Jie Huang

Electrical and Computer Engineering Faculty Research & Creative Works

This research reports a potential quasi-distributed thermal mapping optical sensing system for extreme temperatures, leveraging femtosecond (fs) laser inscribed single-mode fiber Bragg gratings (FBGs) and a waveguide within coreless, highly multimode optical fiber, resulting in a single-mode structure. Unlike doped single-mode fibers, coreless fibers composed of silica rods prevent issues associated with dopant migration and ensure data accuracy. The strategic placement of point-by-point FBGs in a cascaded formation on the fs-laser inscribed waveguide facilitates localized multipoint sensing. The long-term stability of the proposed waveguide-assisted FBG system was assessed over 24 hours at elevated temperatures (1000°C), showing no hysteresis during heating …


Online Lifelong Optimal Adaptive Control Of Partially Uncertain Strict Feedback Discrete-Time Systems With Application To Quadrotor Uavs, Maxwell Geiger, Sarangapani Jagannathan Jan 2026

Online Lifelong Optimal Adaptive Control Of Partially Uncertain Strict Feedback Discrete-Time Systems With Application To Quadrotor Uavs, Maxwell Geiger, Sarangapani Jagannathan

Electrical and Computer Engineering Faculty Research & Creative Works

This article considers the infinite time horizon optimal adaptive tracking control of partially uncertain strict feedback discrete-time (DT) systems with application to quadrotor uncrewed aerial vehicles (UAVs). First, the strict feedback DT system is transformed into an equivalent affine nonlinear DT system in terms of the tracking error dynamics. The optimal adaptive tracking control problem is solved using an augmented system approach, where a horizon of future bounded reference trajectory points is used in the augmented state, when compared to using a single point. It is assumed that the internal dynamics of the strict feedback system are unknown, but the …


Enhancing Measurement Accuracy: The Impact Of Missing Data On Parameter Estimation In Mass-Spring-Damper Systems, Michkath Omanda Bouraima, Steven Thompson, Maciej J. Zawodniok Jan 2026

Enhancing Measurement Accuracy: The Impact Of Missing Data On Parameter Estimation In Mass-Spring-Damper Systems, Michkath Omanda Bouraima, Steven Thompson, Maciej J. Zawodniok

Electrical and Computer Engineering Faculty Research & Creative Works

In sensor-driven dynamic systems, missing data can severely degrade parameter estimation accuracy. This article investigates the impact of missing data on phase estimation in a mass-spring-damper system using an information-theoretic framework based on the Cramér-Rao Lower Bound (CRLB). Closed-form CRLB expressions are derived for four scenarios: complete data, missing completely at random (MCAR) deletion, MCAR-based imputation, and missing at random (MAR) missingness via a selection-weighted formulation. These bounds are used as theoretical benchmarks to evaluate classical imputation methods (last observation carried forward (LOCF), linear interpolation) and advanced approaches (Kalman filtering, Rauch-Tung-Striebel (RTS) smoothing, Bayesian inference, and transformer-based imputation) through Monte …


Rf-Attennet: A Hybrid Attention-Enhanced Network For Mixed Signal Classification In Uav Swarm Detection, Prajoy Podder, Mohammad Atikur Rahman, Maciej Zawodniok, Sanjay Madria Jan 2026

Rf-Attennet: A Hybrid Attention-Enhanced Network For Mixed Signal Classification In Uav Swarm Detection, Prajoy Podder, Mohammad Atikur Rahman, Maciej Zawodniok, Sanjay Madria

Electrical and Computer Engineering Faculty Research & Creative Works

The continuous increase of UAVs, particularly in swarms, creates significant challenges for security and airspace regulation. Traditional RF fingerprinting methods struggle to detect and classify UAV swarms due to overlapping signals and interference. This study introduces RF-AttenNet, a hybrid deep learning model designed to classify mixed UAV signals by analyzing composite RF spectrograms. RF-AttenNet uses dual attention mechanisms, channel and spatial attention to focus on critical spectral features, enabling the model to effectively separate and identify overlapping UAV signals. We have developed custom composite UAV datasets that simulate real-world swarm interference, incorporating both single and mixed UAV classes. RF-AttenNet achieves …


Fixed-Time Consensus Tracking For Nonlinear Multi-Agent Systems Under Aperiodically Intermittent Control, Lei Xue, Tong Wu, Wenwen Jia, Donald C. Wunsch Jan 2026

Fixed-Time Consensus Tracking For Nonlinear Multi-Agent Systems Under Aperiodically Intermittent Control, Lei Xue, Tong Wu, Wenwen Jia, Donald C. Wunsch

Electrical and Computer Engineering Faculty Research & Creative Works

This article explores the problem of fixed-time consensus tracking (FT-CT) for nonlinear multi-agent systems utilizing the a periodically intermittent control (AIC) strategy. In contrast to existing control algorithms, the proposed algorithm utilizes the AIC strategy instead of the conventional continuous-time control strategy, effectively reducing the consumption of communication resources. Moreover, the problem of intermittent FT-CT is well handled by proposing the average control rate of the AIC strategy. Two theorems based on the cases of directed and undirected graphs are proposed, respectively. Finally, the validity of these results is confirmed through numerical simulations on a general nonlinear system and a …


Resolving Stiffness Trade-Offs In Simultaneous Pressure And Vibration Sensing Using A Corrugated-Tube Fiber-Optic Sensor, Yizheng Chen, Yan Tang, Jie Huang, Qi Zhang, Biyao Shi, Zewei Wu Jan 2026

Resolving Stiffness Trade-Offs In Simultaneous Pressure And Vibration Sensing Using A Corrugated-Tube Fiber-Optic Sensor, Yizheng Chen, Yan Tang, Jie Huang, Qi Zhang, Biyao Shi, Zewei Wu

Electrical and Computer Engineering Faculty Research & Creative Works

This article proposes and experimentally demonstrates a corrugated-tube-based fiber-optic sensor capable of measuring pressure, vibration, or both simultaneously. To address the limited sensitivity of conventional diaphragm-based designs, the sensor incorporates an optimized corrugated tube that balances the conflicting stiffness requirements for pressure and vibration measurements. The corrugated tube, acting as a mechanical transducer, is integrated with an extrinsic fiber-optic Fabry–Perot interferometer (EFPI). The EFPI cavity is formed between a reflective surface at the sealed end of the corrugated tube and the cleaved end face of an optical fiber fixed within a mounting assembly. In this configuration, displacement of the corrugated …


Nash Equilibrium Strategies For Multicluster Pursuit–Evasion Game With Disturbances: A Prescribed-Time Convergence Approach, Lei Xue, Xian Yu, Yongbao Wu, Jian Liu, Changyin Sun, D. C. Wunsch Jan 2026

Nash Equilibrium Strategies For Multicluster Pursuit–Evasion Game With Disturbances: A Prescribed-Time Convergence Approach, Lei Xue, Xian Yu, Yongbao Wu, Jian Liu, Changyin Sun, D. C. Wunsch

Electrical and Computer Engineering Faculty Research & Creative Works

This article investigates the problem of prescribed-time Nash equilibrium (NE) seeking for a multicluster pursuit–evasion game (PEG) subject to external disturbances. To mitigate the impact of disturbances and reach the NE within a user-defined prescribed time, a prescribed-time disturbance observer (PTDO) is devised to estimate and compensate for them. Based on this observation, a novel control algorithm is developed, which facilitates collaboration among multiple pursuers to capture multiple evaders within the prescribed time. It is theoretically demonstrated that the designed algorithm ensures prescribed-time convergence to the NE of the multicluster PEG with disturbances. Finally, numerical simulations are conducted to verify …


Deep Learning Based High-Resolution Electromagnetic Inversion Imaging Using Deep Convolutional Double-Module Structure, He Ming Yao, Shiji Song, Lijun Jiang, Michael Ng Jan 2026

Deep Learning Based High-Resolution Electromagnetic Inversion Imaging Using Deep Convolutional Double-Module Structure, He Ming Yao, Shiji Song, Lijun Jiang, Michael Ng

Electrical and Computer Engineering Faculty Research & Creative Works

In this paper, a novel deep learning (DL) approach has been proposed to realize high-resolution electromagnetic (EM) inversion imaging. The newly proposed approach is based on the deep convolutional double-module structure (DCDMS), consisting of the pixel-interpolating module and the corresponding quality-improving module. While the pixel-interpolating module roughly increases the 'resolution' of the initial input, the following quality-improving module realizes quantitative EM imaging in high resolution. The input of the proposed DCDMS adopts the mixed input scheme, consisting of the received EM scattered field and the initial reconstruction in much low resolution computed from Gauss-Newton method. The output of the proposed …


Event-Based Predefined-Time Synchronization For Complex Networks With Deception Attacks: An Asynchronously Intermittent Strategy, Lei Xue, Jiong Yu, Haoyu Zhou, Yongbao Wu, Jian Liu, Donald C. Wunsch Jan 2026

Event-Based Predefined-Time Synchronization For Complex Networks With Deception Attacks: An Asynchronously Intermittent Strategy, Lei Xue, Jiong Yu, Haoyu Zhou, Yongbao Wu, Jian Liu, Donald C. Wunsch

Electrical and Computer Engineering Faculty Research & Creative Works

This article studies the practical predefined-time synchronization (PPTS) for complex networks (CNs) under deception attacks based on the asynchronously intermittent event-triggered control (AIE-TC). Notably, AIE-TC effectively integrates the advantages of asynchronously intermittent control (AIC) and event-triggered control, where AIC provides each subsystem node with independent control and rest intervals. Besides, all synchronization errors of the CNs converge to an adjustable neighborhood within the predefined time by designing a bounded time-varying function into the controller. Moreover, this article considers that the transmission network is subjected to stochastic deception attacks modeled by a Markov process, which captures the state-driven dynamic transition characteristics …


Gender-Inclusive Language In Spanish: A Data-Informed Sociolinguistic Exploration Of Naming Variation, Silvia Rivera Alfaro, Jonathan Hanon Jan 2026

Gender-Inclusive Language In Spanish: A Data-Informed Sociolinguistic Exploration Of Naming Variation, Silvia Rivera Alfaro, Jonathan Hanon

Publications and Research

ABSTRACT

This paper presents a data-informed sociolinguistic exploration of the variation in the names given to gender-inclusive language in Spanish. We use publicly available Google Trends (GT) data to describe the frequency of usage of different names over time and explore their geographical distribution. To account for the challenges and limitations of using Google Trends, we compare the data with information from two large linguistic corpora (CORPES XXI and Google Books Ngram Viewer). Using these tools, we generate small datasets to explore the intricacies of the topic addressed in this paper. In our literature review, we identified 17 names for …


Quantum General Relativity V2, James Glimm, James Glimm Jan 2026

Quantum General Relativity V2, James Glimm, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

We construct a quantum general relativity theory.. The construction includes specification of a cosmological model. Based on type Ia supernova data, the model has zero dark energy and zero cosmological constant.

The analysis is at the level of theoretical physics, with some mathematical details omitted.


Brst Conserved Moments For Fluids, James Glimm Jan 2026

Brst Conserved Moments For Fluids, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

This note adds a missing proof for an assertion in the original paper Gauge Invariance and Repeated Time Isolated Solution Discontinuities.

The assertion is that under weak limits and within a constant energy isosurface, enstrophy is conserved up to losses due to viscous dissipation.

According to the BRST theory for quantum Yang-Mills fields, the conserved moments are exactly those with infinite vacuum expectation values. Application of the BRST theory to fluids is explored. The BRST restriction to the loop expansion (fixed space) is justified by the reqirement that a perturbative expansion can be constructed. In this case the theory predicts …


Mathematicly Rigorous Quantum General Relativity, I: Pure, James Glimm Jan 2026

Mathematicly Rigorous Quantum General Relativity, I: Pure, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

A pure general relativity (quantum or classical) is one lacking in matter. Such a field has a Lorentzian space time geometry. A renormalization perturbative expansion, truncated to all finite orders, establishes both the quantum and the general relativity theory with full mathematical rigor.


Weak Solutions Of The Navier-Stokes Equation And Their Euler Limits, James Glimm Jan 2026

Weak Solutions Of The Navier-Stokes Equation And Their Euler Limits, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

The existence of a weak solution of the incompressible isothermal Navier-Stokes equation with given initial conditions in the Sobolev space $\mathcal{H}_{-2}$ for energy fluctuations and in $\mathcal{H}_{-3}$ for enstrophy fluctuations is assumed. The existence is uniform with respect to the Euler limit of zero viscosity $\nu$. Thus, existence of weak solutions of the Euler equation with given initial conditions is established, and these Euler solutions are the zero viscosity limit of Navier-Stokes solutions, provided the Navier-Stokes solutions exist.