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Synthesis And Characterization Of Amphiphiles For Mammalian Cell Transfection And Antimicrobial Activity, Joseph William Meisel Aug 2016

Synthesis And Characterization Of Amphiphiles For Mammalian Cell Transfection And Antimicrobial Activity, Joseph William Meisel

Dissertations

Amphiphiles are molecules that contain both water-soluble and water-insoluble components. The dual nature of these molecules engenders remarkable properties including the ability to self-assemble into ordered structures. Cell membranes are composed of amphiphilic phospholipids that organize into a bilayer motif. Synthetic amphiphiles can interact with natural membranes and influence the transport of molecules across the cell membrane. The work elaborated in this report employs amphiphiles to co-assemble with DNA and transport the genetic material across cell membranes. First, a simplified method for interacting DNA with amphiphiles was developed. Second, a series of known ion-transporting compounds were assayed for their interaction …


Reproductive Ecology Of Dragonfishes (Family: Stomiidae) In The Gulf Of Mexico, Alex D. Marks Jul 2016

Reproductive Ecology Of Dragonfishes (Family: Stomiidae) In The Gulf Of Mexico, Alex D. Marks

HCNSO Student Theses and Dissertations

The most speciose group of fishes in the Gulf of Mexico is the dragonfishes (Family: Stomiidae). These fishes are dominant mesopelagic predators occurring throughout the world’s oceans, including the Antarctic seas. Little is known regarding their reproductive ecology, a consequence attributed to insufficient sample sizes of mature adults due to inadequacies of sampling gear; larger, sexually mature stomiid adults are more adept at net avoidance, thereby obfuscating synoptic reproductive biology studies. Between 2010-2011, the Offshore Nekton Sampling and Analysis Program was initiated in the northern Gulf of Mexico over all four seasons using a discrete-depth sampling system (MOCNESS) and a …


Gene Set Enrichment And Projection: A Computational Tool For Knowledge Discovery In Transcriptomes, Karl Douglas Stamm Jul 2016

Gene Set Enrichment And Projection: A Computational Tool For Knowledge Discovery In Transcriptomes, Karl Douglas Stamm

Dissertations (1934 -)

Explaining the mechanism behind a genetic disease involves two phases, collecting and analyzing data associated to the disease, then interpreting those data in the context of biological systems. The objective of this dissertation was to develop a method of integrating complementary datasets surrounding any single biological process, with the goal of presenting the response to a signal in terms of a set of downstream biological effects. This dissertation specifically tests the hypothesis that computational projection methods overlaid with domain expertise can direct research towards relevant systems-level signals underlying complex genetic disease. To this end, I developed a software algorithm named …


Studies On Purification And Functionalization Of Carbon Nanotubes And Their Aqueous Phase Behavior, Zheqiong Wu May 2016

Studies On Purification And Functionalization Of Carbon Nanotubes And Their Aqueous Phase Behavior, Zheqiong Wu

Dissertations

Carbon nanotubes (CNTs) are known to have unique mechanical, thermal and electrical properties which make them attractive for a wide range of applications ranging from batteries to sensors. CNTs are rolled up graphene sheets where the single-walled CNTs (SWCNTs) and multi-walled CNTs (MWCNTs) are classified according to the number of concentric rings. In this dissertation, the focus is on several different aspects of MWCNTs. These include purification, functionalization and colloidal behavior.

MWCNTs are insoluble in solvents and therefore some degree of functionalization is required prior to their real-world applications. Oxidation debris is generated during carboxylation which is usually the first …


Nano-Photonic Waveguides For Chemical And Biomedical Sensing, Surya Venkatasekhar Cheemalapati May 2016

Nano-Photonic Waveguides For Chemical And Biomedical Sensing, Surya Venkatasekhar Cheemalapati

USF Tampa Graduate Theses and Dissertations

In this dissertation, advances in the fields of Photonics, and Plasmonics, and specifically, single cell analysis and waveguide sensing will be addressed. The first part of the dissertation is on Finite Difference Time Domain (FDTD) optimization and experimental demonstration of a nano-scale instrument that allows sensing at the cellular and subcellular levels. A new design of plasmonic coupler into a nanoscale waveguide is proposed and optimized using FDTD simulations. Following this, a subcellular nanoendoscope that can locally excite fluorescence in labelled cell organelles and collect the emitted fluorescent light for detailed spectrum analysis is fabricated and tested. The nanoendoscope has …


The Effect Of Hofmeister Series Counterions On The Colloidal And Antimicrobial Properties Of Triple-Headed Cationic Amphiphiles, Kirstie A. Thompson May 2016

The Effect Of Hofmeister Series Counterions On The Colloidal And Antimicrobial Properties Of Triple-Headed Cationic Amphiphiles, Kirstie A. Thompson

Senior Honors Projects, 2010-2019

Antibacterial resistance is becoming increasingly prominent, causing a great need for novel antibacterial products. This work focuses on developing an understanding of the relationship between counterion identity on colloidal and antibacterial activity for cationic amphiphiles. In an amphiphile series with three hydrophilic quaternary ammonium bromide head groups and one hydrophobic tail, the amphiphile with a linear hydrocarbon chain with 18 carbons is more antibacterial than those with longer or shorter tails. Counterion exchange of the bromide counterions with various Hofmeister series anions significantly affects both antibacterial and colloidal activity. The logarithm of critical aggregation concentration [log(CAC)] was found to have …


Algal Growth Response To Nutrient Loading On The Lower Boise River, Idaho, Ian Penn May 2016

Algal Growth Response To Nutrient Loading On The Lower Boise River, Idaho, Ian Penn

Boise State University Theses and Dissertations

Nitrate and phosphate concentrations in the Lower Boise River become increasingly elevated with distance downstream. While there is correlative evidence that there is algal growth from elevated nutrients, no one has formally evaluated the algal growth response from nutrient loading. We quantified algal biomass in response to increased nutrient concentrations by sampling benthic algal biomass from natural substrata (rocks) and artificial substrata that also assessed nutrient limitation along a 64 mile reach from near Diversion Dam to the city of Parma that exhibited an increase of nitrate (0.01 mg/L to 3.40 mg/L) and phosphate (below detection to 0.56 mg/L). Samples …


A Model For Collective Dynamics In Ant Raids, Shawn D. Ryan May 2016

A Model For Collective Dynamics In Ant Raids, Shawn D. Ryan

Mathematics and Statistics Faculty Publications

Ant raiding, the process of identifying and returning food to the nest or bivouac, is a fascinating example of collective motion in nature. During such raids ants lay pheromones to form trails for others to find a food source. In this work a coupled PDE/ODE model is introduced to study ant dynamics and pheromone concentration. The key idea is the introduction of two forms of ant dynamics: foraging and returning, each governed by different environmental and social cues. The model accounts for all aspects of the raiding cycle including local collisional interactions, the laying of pheromone along a trail, and …


Is Metabolism Goal-Directed? Investigating The Validity Of Modeling Biological Systems With Cybernetic Control Via Omic Data, Frank T. Devilbiss Apr 2016

Is Metabolism Goal-Directed? Investigating The Validity Of Modeling Biological Systems With Cybernetic Control Via Omic Data, Frank T. Devilbiss

Open Access Dissertations

Cybernetic models are uniquely juxtaposed to other metabolic modeling frameworks in that they describe the time-dependent regulation of cellular reactions in terms of dynamic "metabolic goals." This approach contrasts starkly with purely mechanistic descriptions of metabolic regulation which seek to explain metabolic processes in high resolution — a clearly daunting undertaking. Over a span of three decades, cybernetic models have been used to predict metabolic phenomena ranging from resource consumption in mixed-substrate environments to intracellular reaction fluxes of intricate metabolic networks. While the cybernetic approach has been validated in its utility for the prediction of metabolic phenomena, its central feature, …


Photochemical Electrocyclic Ring Closure And Elimination Reactions Of N-(Oxothioxanthenyl)Naphthothiophene Carboxamides, Himali Devika Jayasekara Apr 2016

Photochemical Electrocyclic Ring Closure And Elimination Reactions Of N-(Oxothioxanthenyl)Naphthothiophene Carboxamides, Himali Devika Jayasekara

Dissertations (1934 -)

Photochemical cleavage reactions have found a widespread used in biological applications that require the photorelease of biologically active molecules such as proteins, peptides, neurotransmitters, and nucleotide phosphates. This research focuses on the design of photoremovable protecting groups which can be utilized to release these biomolecules by photolysis. These biomolecules are attached to the photoremovable protecting group at the sites of functional groups that are present within these substrates. Such functional groups are carboxylates, phosphates, thiolates, or phenolates, which upon exposure to light, are released as anions of varying basicities. The photochemical reaction involved is an electrocyclic ring closure between aromatic …


Beta Linear Failure Rate Geometric Distribution With Applications, Broderick O. Oluyede, Ibrahim Elbatal, Shujiao Huang Apr 2016

Beta Linear Failure Rate Geometric Distribution With Applications, Broderick O. Oluyede, Ibrahim Elbatal, Shujiao Huang

Mathematical Sciences: Faculty Publications

This paper introduces the beta linear failure rate geometric (BLFRG) distribution, which contains a number of distributions including the exponentiated linear failure rate geometric, linear failure rate geometric, linear failure rate, exponential geometric, Rayleigh geometric, Rayleigh and exponential distributions as special cases. The model further generalizes the linear failure rate distribution. A comprehensive investigation of the model properties including moments, conditional moments, deviations, Lorenz and Bonferroni curves and entropy are presented. Estimates of model parameters are given. Real data examples are presented to illustrate the usefulness and applicability of the distribution.


Study Of The Seasonal And Interannual Variability Of Phytoplankton Bloom In Arabian Gulf Using Modisdata, Malik Mutasim Malik Gasim Apr 2016

Study Of The Seasonal And Interannual Variability Of Phytoplankton Bloom In Arabian Gulf Using Modisdata, Malik Mutasim Malik Gasim

Theses

The Arabian Gulf is a semi enclosed large water body that experiences seasonal

variations and reversal of it water currents flow circulation. The Gulf waters are characterized by having high primary productivity and strong phytoplankton blooms at particular seasons within the year. Phytoplankton is a base of the food chain for marine species, providing an essential food resource for aquatic life. Marine phytoplankton affects the diversity of any marine ecosystem and drives its functioning and is strongly correlated with fishery yields. The primary

objectives of this research study are to answer key research questions related to phytoplankton blooms in the …


Synthesis And Mechanistic Investigations Of Transition Metal Complexes And Ligands For Chemotherapeutic Applications, Jimmie Lee Bullock Jr. Apr 2016

Synthesis And Mechanistic Investigations Of Transition Metal Complexes And Ligands For Chemotherapeutic Applications, Jimmie Lee Bullock Jr.

Chemistry & Biochemistry Theses & Dissertations

Transition metal complexes have played a critical role in antitumor therapy with many complexes incorporating platinum, ruthenium, and lanthanum having been investigated in preclinical and clinical trials. The best known transition metal therapeutic is cisplatin, which is utilized in nearly 50% of all cancer therapies, despite its significant toxic side effects. The toxic side effects of current FDA approved platinum-based chemotherapeutics are often overlooked due to the “special status” granted to these drugs due to their ability to fight, what is often considered an incurable disease with life expectancies often measured in months. Oncology drug development has therefore now focused …


05. Chemistry, Northeastern State University Jan 2016

05. Chemistry, Northeastern State University

Oklahoma Research Day Abstracts

No abstract provided.


03. Biology, Northeastern State University Jan 2016

03. Biology, Northeastern State University

Oklahoma Research Day Abstracts

No abstract provided.


Novel Photodynamic Cancer Therapy Agent And Biochemical Phosphate Sensor Based On Nanomaterials, Alaa Fadhel Jan 2016

Novel Photodynamic Cancer Therapy Agent And Biochemical Phosphate Sensor Based On Nanomaterials, Alaa Fadhel

Electronic Theses and Dissertations

Biochemical research and clinical studies have revolutionized the field of medicine in both diagnosis and therapy. Researchers in the field of biochemistry and biotechnology are using nanomaterials in different applications to develop devices and materials that offer benefits to both patients and the health care industry. These include biochemical sensors, enzyme encapsulation, biomarkers, and drug delivery improvements for the treatment of cancer. This dissertation focuses on investigating two biochemical aspects using nanomaterials; namely therapy and clinical diagnosis. For therapy purposes, Silica nanoparticles were used as drug delivery system to develop a new photodynamic cancer therapy agent photo-acid generator (PAG) that …


Characterization Of An Al$^{3+}$-Selective Fluorescent Probe Based On A Benzoyl Hydrazine Derivative And Its Application In Cell Imaging, Yuxiang Ji, Chunwei Yu, Shaobai Wen, Jun Zhang Jan 2016

Characterization Of An Al$^{3+}$-Selective Fluorescent Probe Based On A Benzoyl Hydrazine Derivative And Its Application In Cell Imaging, Yuxiang Ji, Chunwei Yu, Shaobai Wen, Jun Zhang

Turkish Journal of Chemistry

A fluorescent probe based on benzoyl hydrazine was synthesized and characterized as an Al$^{3+}$-selective fluorescent probe. This probe showed good selectivity towards Al$^{3+\, }$compared to other common ions. Under optimized experimental conditions, the probe exhibited a linear dynamic response for Al$^{3+}$ from 5.0 $\times $ 10$^{-7}$ to 4.5 $\times $ 10$^{-6}$ M with a detection limit of 1.3 $\times $ 10$^{-7}$ M in ethanol-water solution (9:1, v:v, pH 6.8, 20 mM HEPES). Furthermore, it was used for imaging of Al$^{3+}$ in living cells with satisfying results.


Changes In Wetland Conditions And Wetland Plant Communities In The Prairie Pothole Region After 50 Years, Ryann Cressey Jan 2016

Changes In Wetland Conditions And Wetland Plant Communities In The Prairie Pothole Region After 50 Years, Ryann Cressey

Electronic Theses and Dissertations

Wetlands in Stutsman County, North Dakota were revisited after 50 years to assess changes in wetland conditions and plant communities within wetland zones in the Prairie Pothole Region. In 1961-1966, Robert E. Stewart and Harold A. Kantrud conducted a study to investigate the relationship of wetland plant communities to variations of water permanence and chemistry on three study areas: Crystal Springs, Cottonwood, and Mt. Moriah. Within in this region, a severe drought occurred in 1988- 1992 followed by the longest deluge starting in 1993 with wetlands still impacted today. In 2013 and 2014, I revisited 80 of the original wetlands …


An In Vitro Study On The Effect Of Synthesized Tin (Iv) Complexes On Glioblastoma, Colorectal, And Skin Cancer Cell Lines, Jennie L. Williams, Lesley C. Lewis-Alleyne, Melinda Solomon, Long Nguyen, Robert Johnson, Jennifer Vital, Ping Ji, John Durant, Camille Cooper, Patrice Cagle, Patrick Martin, Don Vanderveer, William L. Jarrett, Alvin A. Holder Jan 2016

An In Vitro Study On The Effect Of Synthesized Tin (Iv) Complexes On Glioblastoma, Colorectal, And Skin Cancer Cell Lines, Jennie L. Williams, Lesley C. Lewis-Alleyne, Melinda Solomon, Long Nguyen, Robert Johnson, Jennifer Vital, Ping Ji, John Durant, Camille Cooper, Patrice Cagle, Patrick Martin, Don Vanderveer, William L. Jarrett, Alvin A. Holder

Chemistry & Biochemistry Faculty Publications

((E)-2-(2-hydroxybenzylideneamino)phenolato-2,2-diphenyl-6-aza-1,3-dioxa-2-stanna-[d,h]dibenzocyclononene, [Sn(Ph₂SB)] (compound 1, where Ph₂SB=(E)-2-(2-hydroxybenzylideneamino)phenolato Schiff base) and two novel compounds, [[SnPh2(F-azoSB)] (compound 2, where F-azoSB=4-((E)-(4-fluorophenyl)diazenyl)-2-((E)-(2-hydroxyphenylimino)methyl)phenolato Schiff base), [[SnPh2(sulf-azoSB)]0.125CHCl₃ (compound 3, where sulfamerazineazosalSB=4-((E)-(4-hydroxy-3-((E)-(2-hydroxyphenylimino)methyl)phenyl)diazenyl)-N-(4-methylpyrimidin-2-yl) benzenesulfonamide Schiff base), and the control compound, cisplatin (compound 4) were analysed to comparatively determine their effect on cancer cell growth. Anti-cancer properties of compounds 1-4 were examined using glioblastoma (U-1242 MG), colorectal (HT-29 and HCT-116), and skin (A431) human cancer cell lines. With regards to human glioblastoma cells, compounds 1 and 3 demonstrated anti-proliferative capacity in the cell line tested. Specifically, compounds 1 and 3 inhibited cell proliferation by 50% at …


Bioinformatics Investigation On The Role Of Obox Gene Family In Preimplantation Embryo Development, Wei Wang Jan 2016

Bioinformatics Investigation On The Role Of Obox Gene Family In Preimplantation Embryo Development, Wei Wang

Electronic Theses and Dissertations

Preimplantation embryo development (PED) refers to the period from fertilization to implantation in mammals. This complex process is critical for successful implantation and pregnancy. Although studies on PED have been conducted, using mainly the mouse as a model organism, the gene regulatory mechanisms are still not well understood. The next-generation sequencing technologies enable researchers to obtain the genome-wide expression profiling with single-cell resolution, which are powerful tools to study early embryogenesis. We used the single-cell RNA sequencing datasets that are available in the public domain and conducted bioinformatics analysis of expression profiling from zygote to blastocyst. Through hierarchical clustering of …


Application Of Encoded Microparticles Fabricated By Standard Lithography On Multiplexed Bioassay, Muhan He Jan 2016

Application Of Encoded Microparticles Fabricated By Standard Lithography On Multiplexed Bioassay, Muhan He

Legacy Theses & Dissertations (2009 - 2024)

Suspension microarray, has become a popular candidate for multiplexed bioassay since its advent. Unlike traditional planar microarray, suspension microarray permits the probes suspended in aqueous solution while keeping their addresses, and possesses many advantages such as large available binding surface, rapid reaction rate, high multiplexing ability, and high sensitivity and specificity. Photolithography, the technology widely utilized for production of abundant microparticles as carrier in suspension microarray, was investigated by many researchers. However, there was still not a mature, efficient method to produce microparticles with low background, easily recognized identity and good hybridization capacity. To address those issues, we developed a …


The Update, January-March 2016, University Of Northern Iowa. College Of Humanities, Arts And Sciences. Jan 2016

The Update, January-March 2016, University Of Northern Iowa. College Of Humanities, Arts And Sciences.

Update

Inside This Issue:

--CHAS Briefs
--Spotlight – Faculty Kyle Gray
--CHAS News Diversity Training
--Biology Celeste Underriner
--Featured Story: IEEE Demonstration Awards
--Spotlight – Alumni Meghan Reynolds
--Spotlight – Student Alyssa Adamac
--Theater – Rent
--Spotlight – Student Kyle Spurgeon
--ABC Competition
--UNI Construction
--Management Club


The Science Of Cute: What Makes Us Say "Aww!", Allison Murphy Jan 2016

The Science Of Cute: What Makes Us Say "Aww!", Allison Murphy

The Synapse: Intercollegiate science magazine

No abstract provided.


Spatial Variation In Tooth Shape Of Miocene Populations Of Carcharocles Megalodon Across Ocean Basins, Maxwell John Bertsos Jan 2016

Spatial Variation In Tooth Shape Of Miocene Populations Of Carcharocles Megalodon Across Ocean Basins, Maxwell John Bertsos

Browse all Theses and Dissertations

The extinct Lamniform species, Carcharocles megalodon, were some of the most geographically widespread apex predators in the fossil record. However, whether this cosmopolitan distribution was related to population level differences is unknown. The objective of this study is to assess whether variation in tooth morphology coincided with geographic dispersal. The underlying hypothesis is that variation in an aspect of functional morphology, such as tooth shape, suggests some level of population structuring. Detecting this relationship could potentially provide a mechanism that links population to functional relationships inherent in tooth morphology that may reflect period differences in ocean basins. This would offer …


Geographically Isolated Wetlands Are Part Of The Hydrological Landscape, Mark Rains, S. G. Leibowitz, M. J. Cohen, I. F. Creed, H. E. Golden, J. W. Jawitz, P. Kalla, C. R. Lane, M. W. Lang, D. L. Mclaughlin Jan 2016

Geographically Isolated Wetlands Are Part Of The Hydrological Landscape, Mark Rains, S. G. Leibowitz, M. J. Cohen, I. F. Creed, H. E. Golden, J. W. Jawitz, P. Kalla, C. R. Lane, M. W. Lang, D. L. Mclaughlin

School of Geosciences Faculty and Staff Publications

No abstract provided.


Novel Dynamic Partial Reconfiguration Implementations Of The Support Vector Machine Classifier On Fpga, Hanaa Hussain, Khaled Benkrid, Hüseyi̇n Şeker Jan 2016

Novel Dynamic Partial Reconfiguration Implementations Of The Support Vector Machine Classifier On Fpga, Hanaa Hussain, Khaled Benkrid, Hüseyi̇n Şeker

Turkish Journal of Electrical Engineering and Computer Sciences

The support vector machine (SVM) is one of the highly powerful classifiers that have been shown to be capable of dealing with high-dimensional data. However, its complexity increases requirements of computational power. Recent technologies including the postgenome data of high-dimensional nature add further complexity to the construction of SVM classifiers. In order to overcome this problem, hardware implementations of the SVM classifier have been proposed to benefit from parallelism to accelerate the SVM. On the other hand, those implementations offer limited flexibility in terms of changing parameters and require the reconfiguration of the whole device. The latter interrupts the operation …


Design, Synthesis And Physicochemical Analysis Of Ruthenium(Ii) Polypyridyl Complexes For Application In Phototherapy And Nucleic Acid Sensing, Erin Melissa Wachter Jan 2016

Design, Synthesis And Physicochemical Analysis Of Ruthenium(Ii) Polypyridyl Complexes For Application In Phototherapy And Nucleic Acid Sensing, Erin Melissa Wachter

Theses and Dissertations--Chemistry

Current chemotherapeutics exhibit debilitating side effects as a result of their toxicity to healthy tissues. Reducing these side effects by developing chemotherapeutics with selectivity for cancer cells is an active area of research. Phototherapy is one promising modality for selective treatment, where drug molecules are “turned on” when irradiated with light, reducing damage to healthy tissues by spatially restricting the areas exposed to irradiation. A second approach to improve selectivity is to exploit the differences in cancerous versus healthy cells, such as increased metabolism and/or upregulation of cell surface receptors. Ruthenium(II) polypyridyl complexes are candidates for phototherapy due to their …


Impacts Of Environmental Changes To The Middle Rio Grande Landscape On Ysleta Del Sur Pueblo's Cultural And Cermonial Sustainability, Andrea L. Everett Jan 2016

Impacts Of Environmental Changes To The Middle Rio Grande Landscape On Ysleta Del Sur Pueblo's Cultural And Cermonial Sustainability, Andrea L. Everett

Open Access Theses & Dissertations

Given future climate scenarios, this Thesis investigates how plausible climate changes will further impact the Native American community of Ysleta del Sur Pueblo's (Tiguas) cultural continuity and access to riparian ecosystem services along the Rio Grande River (specific to Tigua tradition; riparian vegetation used in ceremony, i.e. Gooding's and Coyote willow). The project aims to (1) describe and understand the relationship between regional climatic changes, anthropogenic changes, and major events in Tigua history, (2) identify rates and patterns of riparian vegetation changes, (3) evaluate impacts on cultural and provisioning ecosystem services relevant to Tigua culture, and relate these to climate …


Design, Synthesis And Biological Applications Of Polypeptoids And Boron Dipyrromethenes, Sunting Xuan Jan 2016

Design, Synthesis And Biological Applications Of Polypeptoids And Boron Dipyrromethenes, Sunting Xuan

LSU Doctoral Dissertations

The dissertation is about the design, synthesis and biological applications of polypeptoids and boron dipyrromethenes (BODIPYs). The dissertation is divided into seven chapters reporting various aspects of the background to my field of study and the results obtained during my PhD program. Chapter 1 is a concise overview of the fundamental concepts of polypeptoids and hydrogels, as well as their recent developments on synthetic strategies, property investigations, and biological applications in different fields. Chapter 2 presents the design, synthesis and potential application as tissue engineering scaffold of thermoreversible ABC polypeptoid hydrogels. A series of ABC copolypeptoids were synthesized and their …


Evaluation Of Ray-Path Integrals In Geometrical Optics, John A. Adam, Michael Pohrivchak Jan 2016

Evaluation Of Ray-Path Integrals In Geometrical Optics, John A. Adam, Michael Pohrivchak

Mathematics & Statistics Faculty Publications

A brief summary of the physical context to this paper is provided, and the deviation angle undergone by an incident ray after k internal reflections inside a transparent unit sphere is formulated. For radially inhomogeneous spheres (in particular) this angle is related to a ray-path integral; an improper integral for which there are relatively few known exact analytical forms, even for simple refractive index profiles n(r). Thus for a linear profile the integral is a combination of incomplete elliptic integrals of the first and third kinds (though not all are as complicated as this). The ray-path integral is evaluated …