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Characterization Of An Inorganic Powder-Based Scintillation Detector Under A Uhdr Electron Beam, Daline Tho, Sam Beddar

Faculty, Staff and Student Publications

Background: Ultra-high dose rate (UHDR) radiation therapy needs a reliable dosimetry solution and scintillation detectors are promising candidates. In this study, we characterized an inorganic powder-based scintillation detector under a 9 MeV UHDR electron beam.

Methods: A mixture of ZnS:Ag powder and optic glue was coupled to an 8 m Eska GH-4001-P polymethyl methacrylate (PMMA) optical fiber. We evaluated the dependence of the detector on dose per pulse (DPP), pulse repetition frequency (PRF), and pulse width (PW). Additionally, we determined the stability and the reproducibility of the detector.

Results: The signal ratio between the PMMA clear optical fiber and the …

A Computational And Mathematical Approach To The Preclinical Development Of Alpha Emitting Radiopharmaceutical Therapies, Abdulaziz Said

McKelvey School of Engineering Graduate Student Theses & Dissertations

Numerous candidate nuclides have been undergoing rigorous preclinical development in the pursuit of novel targeted therapies. Successful development of these drugs relies on the understanding of physiological impacts at the macro and micro scales, in addition to a scalable process for their production. Here, mathematical and computerized approaches have been developed to guide this preclinical development. In this report, two alpha emitting nuclides Pb-212 and Ra-223 are modeled. Radium-223 dichloride citrate a newly approved ion indicated for treatment of bone metastatic castrate resistant prostate cancer, irradiates lesions through targeted uptake in bone at sites of disease. We have undertaken the …

Gene Expression Regulation By Au-Rich Elements And Au-Rich Element Binding Proteins, Courtney Fay Jungers

Arts & Sciences Graduate Student Theses and Dissertations

The regulation of messenger RNA (mRNA) splicing, stability, and translation efficiency are major modes for controlling gene expression – which is essential for life. RNA-binding proteins (RBPs) and microRNAs (miRNAs) are trans-acting factors that bind to cis-elements influencing the stability and translation of the mRNA transcript. AU-rich elements (AREs) are cis-elements that are targeted by AU-rich element binding proteins (ARE-BPs). Here, I show a novel role for AREs and AU-rich element binding protein 1 (AUF1) during alternative splicing and report on interactions of RBPs and miRNAs to design a new treatment for breast cancer by interrupting these interactions in the …

A Filter-Based Model Of Visual Recognition, Olivia Rose Bockler

Arts & Sciences Graduate Student Theses and Dissertations

Visual recognition, a key perceptual process, enables primates to identify faces, food, tools, and potential threats in their environment. Cortical neurons along the ventral visual stream—spanning from early visual cortex (V1) through inferotemporal cortex (IT), with long-range projections to ventrolateral prefrontal cortex (vlPFC)—are essential for visual recognition. Traditional models propose that neuronal representations increase in complexity in each stage of this pathway, culminating in object-specific representations in higher-order cortex. However, this hypothesis remains debated, particularly as artificial visual models have countered that individual neurons along this pathway may function more as filters contributing to distributed representations of objects. Thus, this …

Aging, Fast And Slow: Gene Expression Signatures Of Physiological Age Vs. Future Lifespan In Caenorhabditis Elegans, Matthew Mosley

Arts & Sciences Graduate Student Theses and Dissertations

An outstanding question in the field of aging biology is the origin of variability in lifespans among members of the same species. Traditional wisdom dictates that differences in one individual’s genes or environment, “nature” and “nurture,” could predispose that individual to a long or short life. However, these explanations are radically incomplete. Even in a model system as homogenous as C. elegans, using an isogenic population in a lab-controlled environment, we observe a distribution in lifespans comparable to that seen in outbred human populations. The first part of this dissertation focuses on characterizing this non-genetic, non-environmental variability in the aging …

Sensitivity And Application Of Frequency Domain High-Density Diffuse Optical Tomography (Fd Hd-Dot), Weihao Fan

Arts & Sciences Graduate Student Theses and Dissertations

Functional near-infrared spectroscopy (fNIRS) is a non-invasive imaging technique that measures hemodynamic responses in the brain, similar to functional magnetic resonance imaging (fMRI) but with distinct advantages. By utilizing near-infrared light, fNIRS can penetrate biological tissues and detect changes in oxygenated and deoxygenated hemoglobin. Additionally, fNIRS is portable, noninvasive and inexpensive. Within the realm of fNIRS, several measurement techniques exist, including Continuous Wave (CW), Frequency Domain (FD), and Time Domain (TD) methods. In this dissertation, we focused on the effects, fundamental principles and applications of FD designs. We provided the introduction in Chapter 1, and discussed the background theory and …

Recent Trends And Biases In Mesophotic Ecosystem Research, Veronica Z. Radice, Alejandra Hernández-Agreda, Gonzalo Pérez-Rosales, Ryan Booker, Jessica Bellworthy, Manon Broadribb, Gaby E. Carpenter, Clara Diaz, Ryan J. Eckert, Nicola L. Foster, Johanna C. Gijsbers, Erika Gress, Jack H. Laverick, Valerio Micaroni, Miriam Pierotti, Héloïse Rouzé, Angela Stevenson, Alexis B. Sturm, Pim Bongaerts

School of Biological and Marine Sciences

Mesophotic ecosystems (approx. 30-150 m) represent a significant proportion of the world's oceans yet have long remained understudied due to challenges in accessing these deeper depths. Owing to advances in underwater technologies and a growing scientific and management interest, there has been a major expansion in research of both (sub)tropical mesophotic coral ecosystems and temperate mesophotic ecosystems. Here, we characterize the recent global trends in mesophotic research through an updated release of the 'mesophotic.org' database (www.mesophotic.org) where we reviewed and catalogued 1500 scientific publications. In doing so, we shed light on four major research biases: a gross imbalance in (a) …

Terrestrial Evidence For Volcanogenic Sulfate-Driven Cooling Event ~30 Ka Before The Cretaceous–Paleogene Mass Extinction: Volcanism-Induced Cooling ~30 Ka Pre-K–Pg Boundary, Lauren O'Connor, Rhodri Jerrett, Gregory Price, Tyler Lyson, Sabine Lengger, Francien Peterse, Bart Van Dongen

School of Geography, Earth and Environmental Sciences

Alongside the Chicxulub meteorite impact, Deccan volcanism is considered a primary trigger for the Cretaceous–Paleogene (K–Pg) mass extinction. Models suggest that volcanic outgassing of carbon and sulfur—potent environmental stressors—drove global temperature change, but the relative timing, duration, and magnitude of such change remains uncertain. Here, we use the organic paleothermometer MBT′5me and the carbon-isotope composition of two K–Pg-spanning lignites from the western Unites States, to test models of volcanogenic air temperature change in the ~100 kyr before the mass extinction. Our records show long-term warming of ~3°C, probably driven by Deccan CO2 emissions, and reveal a transient (<10 kyr) ~5°C cooling event, coinciding with the peak of the Poladpur “pulse” of Deccan eruption ~30 kyr before the K–Pg boundary. This cooling was likely caused by the aerosolization of volcanogenic sulfur. Temperatures returned to pre-event values before the mass extinction, suggesting that, from the terrestrial perspective, volcanogenic climate change was not the primary cause of K–Pg extinction.

Engagement And Access To Support For Oral Health, Substance Use, Smoking And Diet By People With Severe And Multiple Disadvantage: A Qualitative Study, Neha Jain, Emma A. Adams, Emma C. Joyes, Gillian Mclellan, Martin Burrows, Martha Paisi, Laura J. Mcgowan, Lorenzo Iafrate, David Landes, Richard Watt, Falko F. Sniehotta, Eileen Kaner, Sheena E. Ramsay

Peninsula Dental School

Background Severe and multiple disadvantage (SMD) is the combined effect of experiencing homelessness, substance use and repeat offending. People experiencing SMD have high burden of physical and mental health issues. Oral health is one of the most common health problems in people experiencing SMD which interacts with substance use, smoking, and unhealthy diet to create a cycle of harm and disadvantage. However, burden of these conditions is worsened by poor access to health services. This study aimed to identify pathways to improve engagement and access to health interventions, for oral health, substance and alcohol use, smoking and diet. Methods Using …

Structural Variant Allelic Heterogeneity In Mecp2 Duplication Syndrome Provides Insight Into Clinical Severity And Variability Of Disease Expression, Davut Pehlivan, Jesse D Bengtsson, Sameer S Bajikar, Christopher M Grochowski, Ming Yin Lun, Mira Gandhi, Angad Jolly, Alexander J Trostle, Holly K Harris, Bernhard Suter, Sukru Aras, Melissa B Ramocki, Haowei Du, Michele G Mehaffey, Kyunghee Park, Ellen Wilkey, Cemal Karakas, Jesper J Eisfeldt, Maria Pettersson, Lynn Liu, Marwan S Shinawi, Virginia E Kimonis, Wojciech Wiszniewski, Kyle Mckenzie, Timo Roser, Angela M Vianna-Morgante, Alberto S Cornier, Ahmed Abdelmoity, James P Hwang, Shalini N Jhangiani, Donna M Muzny, Tadahiro Mitani, Kazuhiro Muramatsu, Shin Nabatame, Daniel G Glaze, Jawid M Fatih, Richard A Gibbs, Zhandong Liu, Anna Lindstrand, Fritz J Sedlazeck, James R Lupski, Huda Y Zoghbi, Claudia M B Carvalho

Faculty, Staff and Students Publications

BACKGROUND: MECP2 Duplication Syndrome, also known as X-linked intellectual developmental disorder Lubs type (MRXSL; MIM: 300260), is a neurodevelopmental disorder caused by copy number gains spanning MECP2. Despite varying genomic rearrangement structures, including duplications and triplications, and a wide range of duplication sizes, no clear correlation exists between DNA rearrangement and clinical features. We had previously demonstrated that up to 38% of MRXSL families are characterized by complex genomic rearrangements (CGRs) of intermediate complexity (2 ≤ copy number variant breakpoints < 5), yet the impact of these genomic structures on regulation of gene expression and phenotypic manifestations have not been investigated.

METHODS: To study the role of the genomic rearrangement structures on an individual's clinical phenotypic variability, we employed a comprehensive …

Distinct Effects Of Extra- And Intracellular Trehalose Supplementation In Freezing Medium On The Post-Thaw Developmental Capacity Of Feline Oocytes, Saengtawan Arayatham, Wirakan Kallayanathum, Panuwat Padungros, Theerawat Tharasanit

The Thai Journal of Veterinary Medicine

Oocyte cryopreservation is a crucial technique for preserving the genetic material of female cats, yet maintaining post-thaw oocyte developmental competence remains a significant challenge. This study investigated the impact of intra- and extracellular trehalose on the developmental competence of feline oocytes following cryopreservation. In Experiment 1, immature feline oocytes were matured in vitro (IVM) with varying concentrations (0, 1.5, and 3 mM) of intracellular trehalose hexaacetate (Tre-(OAc)6). The matured oocytes were then cryopreserved and thawed prior to in vitro fertilization and embryo culture. Experiment 2 examined the effects of extracellular trehalose supplementation at concentrations of 0, 0.125, 0.25, and 0.5 …

Deinstitutionalizing The Mentally Retarded In Maine: The Inevitable Face-Off With Zoning, Pamela D. Albee

Maine Law Review

In July 1978, agencies and officials of the State of Maine entered into a federal consent judgment which terminated a class action lawsuit that had dragged on for three years. The consent judgment in Wuori v. Zitnay detailed a comprehensive plan designed to bring about speedy and meaningful relief to the plaintiff class: mentally retarded citizens of Maine involuntarily confined to Pineland Center, Maine's principal institution for the mentally retarded, and certain others who were conditionally released from Pineland and in community placements. The relief granted was a right to be provided the least restrictive and most normal living conditions …

The Relationship Between Periodontal Disease Of Feline And Oral Core Microbiome, Ziyao Zhou

The Thai Journal of Veterinary Medicine

The microbiome of the oral cavity is complex with the average adult harboring about 50 to 100 billion bacteria which represent about 200 predominant bacterial species. There are a large number of microbes in the oral cavity of the feline, normally beneficial to oral health and safety maintenance. However, when the balance of bacteria lost, it may occur feline stomatitis and periodontitis, which seriously endanger local oral health. Environmental implication, feeding model, age and genetic factors may be main factors affecting oral composition of microbiome. Filifactor alocis, Porphyromonas gingivals, Tannerella forsythia and their interactions are main pathogen that …

Approved Courses 12-17-24, Angela Brock

Individual Course Committee (ICC)

No abstract provided.

Pmp2+ Scs Maintain The Survival And Functioning Of Large-Caliber Motor Axons, Mikolaj Kozlowski

Arts & Sciences Electronic Theses and Dissertations

Neurodegenerative diseases are characterized by selective neuronal vulnerability, a phenomenon in which a specific pathology induces the death of a particular subpopulation of neurons. For example, selective neuronal vulnerability in the peripheral nervous system results in sensory, motor, or mixed peripheral neuropathies. While the intrinsic differences between neuronal subtypes cannot fully explain the basis of selective neuronal vulnerability, it is plausible that it partially stems from neuron extrinsic mechanisms such as the malfunction of distinct Schwann cell (SC) subtypes. Recently, we identified an exciting subpopulation of myelinating SCs characterized by the expression of Adamtsl1, Cldn14, and Pmp2 (hereafter referred to …

Avian Adaptation To Thermal Gradients, Justin Wheeler Baldwin

Arts & Sciences Electronic Theses and Dissertations

Life on Earth has adapted to extremely different temperatures worldwide. However, across distant branches of the tree of life, animals in similar temperature environments often share similar phenotypic traits. Specifically, traits that bear on the ratio between an individual’s surface area (e.g. appendage length) and its volume (e.g. body size) are particularly important for temperature regulation and are codified in canonical biogeographical rules. Although these global patterns of finding larger-bodied (Bergmann’s Rule) and shorter-limbed (Allen’s Rule) animals in colder regions are widely upheld, they also show substantial variation. It remains poorly understood why some animals conform to these biogeographical rules …

N-Methyl-D-Aspartate (Nmda) Receptors Control Calcium Signaling In Striatal Neurons To Guide Value-Based Learning, Alex Legaria Macal

Arts & Sciences Electronic Theses and Dissertations

N-methyl-D-aspartate receptors (NMDARs) play an essential role in neuronal function. Activation of NMDARs leads to calcium influx into postsynaptic neurons, which regu?late many fundamental aspects of neuronal physiology including synaptic plasticity, gene expression, and excitability. In the striatum, the input region of the basal ganglia, NM?DAR activity has been shown to regulate physiological function of striatal neurons, such as synaptic plasticity and excitability, and they also modulate behavior, particularly op?erant learning. However, there are many fundamental questions about the signaling and effects of NMDARs in vivo that have yet to be resolved. Moreover, the link between the physiological and behavioral …

Understanding Sequence Determinants Of Functional Protein Dynamics Using Biophysical Simulations And Experiments, Upasana Lakshmi Mallimadugula

Arts & Sciences Electronic Theses and Dissertations

Mutations in the sequence of proteins associated with a disease often increase its risk or severity. They can also be a barrier to developing effective therapeutics for such diseases. One way in which mutations affect function is by altering dynamics that elude structural studies. Observing these changes requires methods that can report on movements of the protein on various timescales and is an ongoing challenge in biophysics and biochemistry. In this study I will use both experimental and computational techniques that can report on such dynamics to explore how small sequence changes shift the conformational landscape and consequently the function …

Water Quality Assessment Of Three Ponds In The Plaster Creek Watershed, Orin Daspit, Salome Giessmann, Kennedi Pepin, Andrew Slagter, Sydney Wagenmaker

Student Papers and Reports

Ponds are commonly found in urban areas serving as both an aesthetic and ecological feature. The water quality of these ponds can make important contributions to the overall health of the watershed in which they reside. This study analyzes three ponds within the Plaster Creek Watershed: the Southbridge Condominium Association Pond, the Calvin University Seminary Pond, and the Calvin University Ecosystem Preserve Kettle Swamp. This project aims to provide the Southbridge Condo Association with data that will inform future remediation actions. Using water samples collected over three days, E. coli, pH, nutrients, and total dissolved solids were measured in each …

The Biopiracy Of Traditional Knowledge In United States Patent Law, Hannah Green

Public Land & Resources Law Review

The United States intellectual property (“IP”) system is deeply intertwined with our country’s history and constitution. t is foundational in favoring young American inventors. George Washington signed the first patent act in 1790 in hopes of promoting the innovation and progress of science and useful arts. Yet, our patent system was also built around the Western tradition of individualism and competition, which failed to recognize the communal nature and traditional knowledge of tribal communities. This disparity allows the biopiracy of traditional knowledge to be lawful. This comment will explore the harmful toll that United States patent law has taken on …

The Chinese Room And Creating Consciousness: How Recent Strides In Ai Technology Revitalize A Classic Debate, Thomas Held

Departmental Honors & Graduate Capstone Projects

Since 1950, when Alan Turing first posed the question of whether a machine could think, the possibility of artificial consciousness has sparked intense and ongoing debate, and strong positions have been staked out on each side of the argument. On the one hand, the historically popular functionalist school of thought claims that any system capable of producing suitably “conscious” behavior in a given environment should be considered conscious. On the other hand, John Searle’s famous “Chinese Room” argument insists that this cannot be the case, and that consciousness is in all likelihood not artificially reproducible. However, both positions have issues—the …

Influence Of Demographics, Health, And Self-Objectification On Body Acceptance And Body Appreciation In Older Adults, Heather Russell

Walden Dissertations and Doctoral Studies

Prior research has examined the demographic, health, and activity factors influencing how young people, particularly young women, see themselves concerning body appreciation and acceptance. However, body appreciation and acceptance as perceived by older men and women have not been well-studied. The purpose of the study was to examine the extent to which gender, age, quality of life assessment of physical and mental health, physical activity, and self-objectification influence body acceptance by others and body appreciation in adults ages 55-75. Self-objectification theory (SOT) was the framework used to examine the influence of two aspects of self-objectification (lack of autonomy and invisibility) …

The Influence Of Heat Therapy On Redox Signaling In Skeletal Muscle, Kimberly Miriam Richard

Theses and Dissertations

Reactive oxygen species (ROS) have been identified as crucial signaling molecules in skeletal muscle adaptations to exercise and signal for protective pathways within the myofiber. Pathological heat stress studies in animals demonstrate the ability of heat to increase ROS production in skeletal muscle. Limited data on the influence of therapeutic heat on ROS production and redox signaling in human skeletal muscle exists in the literature. The purpose of this study was to assess ROS production and redox signaling in human skeletal muscle following an acute, therapeutic bout of heat treatment. We hypothesized that heat would create an oxidized environment within …

Phosphorus Adsorption Capacity Of Volcanic Scoria, Easton Jeffrey Perkins

Theses and Dissertations

Phosphorus (P) pollution in stormwater runoff poses a significant threat to water quality, contributing to eutrophication and ecosystem degradation. This research evaluates the potential of volcanic scoria (VSco), an abundant and cost-effective resource in Utah, USA, to influence P concentrations in urban stormwater systems. Batch adsorption experiments examined the behavior of VSco across three particle sizes—fine (<0.841 mm), medium (0.841–2 mm), and granular (2.38–9.5 mm)—under conditions mimicking stormwater scenarios. The results reveal that fine VSco exhibited higher adsorption efficiency than medium and granular sizes, achieving notable P removal at higher concentrations. However, at lower concentrations, fine VSco showed potential for P release due to desorption of pre-existing P. Medium and granular VSco showed minimal adsorption capacity and, in some cases, acted as P sources, highlighting a dual potential depending on stormwater conditions. Adsorption isotherms indicate that the adsorption behavior of fine VSco aligns with the Langmuir model, with a finite and relatively low adsorption capacity. Calculated distribution coefficient (Kd) values for fine VSco ranged from 0.04 to 0.005 L/g, indicating weak adsorption efficiency compared to materials like activated carbon (1–10 L/g) or soils with moderate adsorption capacity (0.1–0.5 L/g). Loss-on-ignition tests confirmed that VSco’s performance is driven by its physical and chemical properties, particularly its calcium content, rather than organic matter. The study emphasizes caution in applying fine VSco for stormwater remediation due to its potential to release P under typical runoff conditions. However, fine VSco may still be viable in specific scenarios where P levels are higher, such as in stormwater hotspots or localized areas with elevated concentrations, allowing for targeted remediation. The research underscores the need for further testing to refine VSco’s applications, particularly in low-impact development (LID) practices, such as infiltration basins and rain gardens, to effectively manage P levels while supporting ecological and aesthetic goals. These findings contribute to understanding the complex role of VSco in urban stormwater systems, offering insights for sustainable water quality management and nutrient cycling in urban landscapes.

3d Reconstruction Method Of Tunnel Surrounding Rock Fracture Based On Vtk, Liu Houxiang, Su Heng

Journal of China & Foreign Highway

Fracture parameters are important reference factors for surrounding rock stability analysis.To realize the visualization analysis of surrounding rock fractures，this paper proposed a three-dimensional （3D） reconstruction method of surrounding rock fractures based on the visualization toolkit （VTK）.Firstly，the collected tunnel surrounding rock images were preprocessed by OpenCV for image grayscale and noise reduction.Secondly，the Otsu method and the open operation in morphology were used to segment the image，and the complete surrounding rock fracture map was obtained.Then，the median method was used to replace the linear interpolation method with the traditional Marching Cubes algorithm in VTK to calculate the equivalent point，and the improved Marching Cubes …

Fine-Scale Spatial Patterns Of Gelatinous Zooplankton In The Northern Gulf Of Alaska, Hannah E. Kepner

Oceanography

The Northern Gulf of Alaska (NGA) is characterized by high variability across spatial and temporal scales. In the NGA, zooplankton are a crucial link between primary production and higher trophic levels. Understanding the mechanisms that structure zooplankton assemblages is important to our overall understanding of ecosystem functioning. Nonetheless, thorough description of zooplankton abundance and distribution patterns is challenging due to the inherent variability and complexity of the marine environment. The study of gelatinous zooplankton is further complicated by the limitations of traditional plankton net sampling methods that are inefficient for the collection of high-resolution spatiotemporal data and often inflict damage …

Creating A Digital House Of Knowledge: Ensuring The Continuation And Integrity Of Indigenous Knowledge Transfers In The Digital Era, Jacquelyn C. Cordova

Indigenous Studies

Traditional Indigenous knowledge transfer systems have contributed to the sustainability of highly advanced Indigenous societies since time immemorial. These systems have been purposefully targeted since European arrival to the Americas in the late 1400s and early 1500s, consequently creating barriers for Indigenous Peoples as they strive to conduct their traditional knowledge transfer processes within their communities. These barriers, paired with the continual rise and use of global technologies, have created circumstances where many Native Elders and Knowledge Keepers experience difficulty reaching their youth and community members to ensure the successful transfer of Indigenous data and knowledge to current and future …

A Range Extension For Carex Sartwellii In Interior Alaska, Mark A. Winterstein

Biological Sciences

Mean annual temperatures and growing season length have been increasing in northern latitudes. This has impacted permafrost thaw and the water balance of northern regions, resulting in a pattern of drying lakes in the Yukon Flats, Alaska. As lakes dry, they expose lake sediments to colonization by terrestrial vegetation. Recent interest in the terrestrial response to climate change and its effects on ecosystem services led to the formation of the Yukon River Basin project. As a part of this project, we studied plant succession and diversity in the drying lake basins. In the course of our field work we encountered …

Method For Measuring The Rate Of Improvement In Survival Times Of Cancer Patients, Thobani Chaduka

Theses and Dissertations

In clinical settings, technological advancements have facilitated health care improvements in data analytics, artificial intelligence, telemedicine, health information systems, etc. This has furthered our understanding of cancer biology and treatment mechanisms. In this study, we aim to understand whether Moore’s law-like models may derive from historical cancer survival data, and how they can predict survival statistics for newly diagnosed cancer patients. Historically these predictions have previously been done with the diagnosis year as the independent variable and the survival as a dependent variable. In this study we use death year data as an independent variable and from that, we derive …

Existence And Uniqueness Of Solutions Of Fourth Order Iterative Boundary Value Problems, Zach Whaley

Theses and Dissertations

In this dissertation, we study the fourth-order iterative differential equation \begin{displaymath} x^{(4)}(t) = \f(t, x(t), x^{[2]}(t), \dots, x^{[m]}(t)) \end{displaymath} where $x^{[2]}(t) = x(x(t))$ and $x^{[j]}(t) = x(x^{[j - 1]}(t))$ for $j > 2$. We consider the above equation with multiple sets of boundary conditions, and we state results on the existence and uniqueness of solutions for each set of boundary conditions. In Chapter 2, the boundary conditions are conjugate boundary conditions, \begin{align*} &x(-a) = -a, \ x'(-a) = b, \ x''(-a) = c, \ x(a) = a \\ &x(-a) = -a, \ x(a) = a, \ x'(a) = b, \ x''(a) …