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Full-Text Articles in Physical Sciences and Mathematics

Investigating The Pharmacokinetics And Biological Distribution Of Silver-Loaded Polyphosphoester-Based Nanoparticles Using 111ag As A Radiotracer, Tolulope Aweda, Shiyi Zhang, Chiedza Mupanomunda, Jennifer Burkemper, Gyu Heo, Nilantha Bandara, Mai Lin, Cathy Cutler, Carolyn Cannon, Wiley Youngs, Karen Wooley, Suzanne Lapi Sep 2015

Investigating The Pharmacokinetics And Biological Distribution Of Silver-Loaded Polyphosphoester-Based Nanoparticles Using 111ag As A Radiotracer, Tolulope Aweda, Shiyi Zhang, Chiedza Mupanomunda, Jennifer Burkemper, Gyu Heo, Nilantha Bandara, Mai Lin, Cathy Cutler, Carolyn Cannon, Wiley Youngs, Karen Wooley, Suzanne Lapi

Wiley J. Youngs

Purified 111Ag was used as a radiotracer to investigate silver loading and release, pharmacokinetics, and biodistribution of polyphosphoester-based degradable shell crosslinked knedel-like (SCK) nanoparticles as a comparison to the previously reported small molecule, N-heterocyclic silver carbene complex analog (SCC1) for the delivery of therapeutic silver ions in mouse models. Biodistribution studies were conducted by aerosol administration of 111Ag acetate, [111Ag]SCC1, and [111Ag]SCK doses directly into the lungs of C57BL/6 mice. Nebulization of the 111Ag antimicrobials resulted in an average uptake of 1.07 ± 0.12% of the total aerosolized dose given per mouse. The average dose taken into the lungs of …

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Preparation And In Vitro Antimicrobial Activity Of Silver-Bearing Degradable Polymeric Nanoparticles Of Polyphosphoester-Block-Poly(L-Lactide), Young Lim, Kristin Tiemann, Gyu Heo, Patrick Wager, Yohannes Rezenom, Shiyi Zhang, Fuwu Zhang, Wiley Youngs, David Hunstad, Karen Wooley Sep 2015

Preparation And In Vitro Antimicrobial Activity Of Silver-Bearing Degradable Polymeric Nanoparticles Of Polyphosphoester-Block-Poly(L-Lactide), Young Lim, Kristin Tiemann, Gyu Heo, Patrick Wager, Yohannes Rezenom, Shiyi Zhang, Fuwu Zhang, Wiley Youngs, David Hunstad, Karen Wooley

Wiley J. Youngs

The development of well-defined polymeric nanoparticles (NPs) as delivery carriers for antimicrobials targeting human infectious diseases requires rational design of the polymer template, an efficient synthetic approach, and fundamental understanding of the developed NPs, e.g., drug loading/release, particle stability, and other characteristics. Herein, we developed and evaluated the in vitro antimicrobial activity of silver-bearing, fully biodegradable and functional polymeric NPs. A series of degradable polymeric nanoparticles (dNPs), composed of phosphoester and l-lactide and designed specifically for silver loading into the hydrophilic shell and/or the hydrophobic core, were prepared as potential delivery carriers for three different types of silver-based antimicrobials–silver acetate …

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Structure And Conformation Of The Medium-Sized Chlorophosphazene Rings, Bowers, David Bowers, Brian Wright, Vincenzo Scionti, Anthony Schultz, Matthew Panzner, Eric Twum, Lin-Lin Li, Bryan Katzenmeyer, Benjamin Thome, Peter Rinaldi, Chrys Wesdemiotis, Wiley Youngs, Claire Tessier Sep 2015

Structure And Conformation Of The Medium-Sized Chlorophosphazene Rings, Bowers, David Bowers, Brian Wright, Vincenzo Scionti, Anthony Schultz, Matthew Panzner, Eric Twum, Lin-Lin Li, Bryan Katzenmeyer, Benjamin Thome, Peter Rinaldi, Chrys Wesdemiotis, Wiley Youngs, Claire Tessier

Claire A. Tessier

No abstract provided.

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Tuning The Mobility Coupling Of Quaternized Polyvinylpyridine And Anionic Phospholipids In Supported Lipid Bilayers, Xiaojun Shi, Xiaosi Li, Megan Kaliszewski, Xiaodong Zhuang, Adam Smith Sep 2015

Tuning The Mobility Coupling Of Quaternized Polyvinylpyridine And Anionic Phospholipids In Supported Lipid Bilayers, Xiaojun Shi, Xiaosi Li, Megan Kaliszewski, Xiaodong Zhuang, Adam Smith

Adam W. Smith

Binding of biomacromolecules to anionic lipids in the plasma membrane is a common motif in many cell signaling pathways. Previous work has shown that macromolecules with cationic sequences can form nanodomains with sequestered anionic lipids, which alters the lateral distribution and mobility of the membrane lipids. Such sequestration is believed to result from the formation of a lipid–macromolecule complex. To date, however, the molecular structure and dynamics of the lipid–polymer interface are poorly understood. We have investigated the behavior of polycationic quaternized polyvinylpyridine (QPVP) on supported lipid bilayers doped with phosphatidylserine (PS) or phosphatidylinositol phosphate (PIP) lipids using time-resolved fluorescence …

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Contrasting Patterns Of Coupling Between The Ch Stretches And The Large-Amplitude Motions In The Molecules, Ch3nh2, Ch3oh2+ And Ch3ch2radical Dot, Mahesh Dawadi, Ram Bhatta, David Perry Sep 2015

Contrasting Patterns Of Coupling Between The Ch Stretches And The Large-Amplitude Motions In The Molecules, Ch3nh2, Ch3oh2+ And Ch3ch2radical Dot, Mahesh Dawadi, Ram Bhatta, David Perry

David S. Perry

In each of the title molecules, torsional and inversion tunneling occurs between six equivalent minima. The coupling between these large-amplitude motions and the CH stretch vibrations stems from the variation of the CH stretching force constants as a function of the torsional and inversion coordinates. First principles 2D maps of the variation of the CH-stretch force constants are reported. Although the torsional barriers differ by more than a factor of 20, the torsion–inversion–vibration coupling is similar for two of the species, CH3NH2 and CH3CH2, but is much weaker and qualitatively different in form …

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Inflammation Triggers Production Of Dimethylsphingosine From Oligodendrocytes, Leah Shriver, Alexandra Taraboletti, S Hill, Y Chen, H Huang, K Cho, R Gallo, M Manchester, G Patti Sep 2015

Inflammation Triggers Production Of Dimethylsphingosine From Oligodendrocytes, Leah Shriver, Alexandra Taraboletti, S Hill, Y Chen, H Huang, K Cho, R Gallo, M Manchester, G Patti

Leah Shriver

Neuropathic pain is a chronic, refractory condition that arises after damage to the nervous system. We previously showed that an increased level of the endogenous metabolite N,N-dimethylsphingosine (DMS) in the central nervous system (CNS) is sufficient to induce neuropathic pain-like behavior in rats. However, several important questions remain. First, it has not yet been demonstrated that DMS is produced in humans and its value as a therapeutic target is therefore unknown. Second, the cell types within the CNS that produce DMS are currently unidentified. Here we provide evidence that DMS is present in human CNS tissue. We show that DMS …

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Unexpected Synthesis Of 1,3,5-Triarly-1,5-Diketones From Aryl Ketones Via Di-Enamine Mechanism, Bin Liu, Junfeng Wang, Yi Pang, Zemei Ge, Runtao Li Sep 2015

Unexpected Synthesis Of 1,3,5-Triarly-1,5-Diketones From Aryl Ketones Via Di-Enamine Mechanism, Bin Liu, Junfeng Wang, Yi Pang, Zemei Ge, Runtao Li

Yi Pang

An unexpected reaction of aryl ketone with acetohydrazone of aromatic aldehyde via 1,2-di-enamine/diiminium mechanism was discovered, leading to efficient synthesis of 1,3,5-triaryl-1,5-diketones in good to excellent yields. (C) 2014 Elsevier Ltd. All rights reserved.

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Biocompatible Flavone-Based Fluorogenic Probes For Quick Wash-Free Mitochondria! Imaging In Living Cells, Bin Liu, Mickey Shah, Ge Zhang, Qin Liu, Yi Pang Sep 2015

Biocompatible Flavone-Based Fluorogenic Probes For Quick Wash-Free Mitochondria! Imaging In Living Cells, Bin Liu, Mickey Shah, Ge Zhang, Qin Liu, Yi Pang

Yi Pang

Mitochondria, vital organelles existing in almost all eukaryotic cells, play a crucial role in energy metabolism and apoptosis of aerobic organisms. In this work, we report two new flavone-based fluorescent probes, MC-Mito1 and MC-Mito2, for monitoring mitochondria in living cells. These two probes exhibit remarkably low toxicity, good cell permeability, and high specificity; these probes complement the existing library of mitochondrial imaging agents. The new dyes give nearly no background fluorescence, and their application does not require tedious postwashing after cell staining. The appreciable tolerance of MC-Mito2 encourages a broader range of biological applications for understanding the cell degeneration and …

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A Single Molecular Probe For Multi-Analyte (Cr3+, Al3+ And Fe3+) Detection In Aqueous Medium And Its Biological Application, Junfeng Wang, Yingbo Li, Nikul Patel, Ge Zhang, Demin Zhou, Yi Pang Sep 2015

A Single Molecular Probe For Multi-Analyte (Cr3+, Al3+ And Fe3+) Detection In Aqueous Medium And Its Biological Application, Junfeng Wang, Yingbo Li, Nikul Patel, Ge Zhang, Demin Zhou, Yi Pang

Yi Pang

An ESIPT based fluorescent sensor 1 was developed, which could selectively detect and differentiate trivalent metal ions Cr3+, Al3+ and Fe3+ in aqueous medium. The cell imaging experiments confirmed that 1 can be used for monitoring intracellular Cr3+ and Al3+ levels in living cells.

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Mercury Metallation Of The Copper Protein Azurin And Structural Insight Into Possible Heavy Metal Reactivity., Anthony Zampino, Francesca Masters, Erika Bladholm, Matthew Panzner, Steven Berry, Thomas Leeper, Christopher Ziegler Sep 2015

Mercury Metallation Of The Copper Protein Azurin And Structural Insight Into Possible Heavy Metal Reactivity., Anthony Zampino, Francesca Masters, Erika Bladholm, Matthew Panzner, Steven Berry, Thomas Leeper, Christopher Ziegler

Thomas C Leeper

Mercury(II) metallation of Pseudomonas aeruginosa azurin has been characterized structurally and biochemically. The X-ray crystal structure at 1.5 Å of mercury(II) metallated azurin confirms the coordination of mercury at the copper binding active site and a second surface site. These findings are further validated by NMR, Matrix-assisted laser desorption/ionization spectrometry (MALDI), and UV–visible spectroscopic methods indicating copper displacement from the wild-type protein. Bioinformatic analysis has identified homologous human protein domains computationally, and compared them to the structure of azurin, providing a model for human mercury interactions. Study of the mercury–azurin adduct, in combination with other known examples of protein–heavy metal …

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Mitoneet As A Novel Drug Target For Mitochondrial Dysfunction, Werner Geldenhuys, Thomas Leeper, Richard Carroll Sep 2015

Mitoneet As A Novel Drug Target For Mitochondrial Dysfunction, Werner Geldenhuys, Thomas Leeper, Richard Carroll

Thomas C Leeper

Mitochondrial dysfunction plays an important part in the pathology of several diseases, including Alzheimer's disease and Parkinson's disease. Targeting mitochondrial proteins shows promise in treating and attenuating the neurodegeneration seen in these diseases, especially considering their complex and pleiotropic origins. Recently, the mitochondrial protein mitoNEET [also referred to as CDGSH iron sulfur domain 1 (CISD1)] has emerged as the mitochondrial target of thiazolidinedione drugs such as the antidiabetic pioglitazone. In this review, we evaluate the current understanding regarding how mitoNEET regulates cellular bioenergetics as well as the structural requirements for drug compound association with mitoNEET. With a clear understanding of …

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Structural Libraries Of Protein Models For Multiple Species To Understand Evolution Of The Renin-Angiotensin System, Jeremy Prokop, Victoria Petri, Mary Shimoyama, Ingrid Watanabe, Dulce Casarini, Thomas Peeper, Stephanie Bilinovich, Howard Jacob, Robson Santos, Almir Martins, Fabiano Araujo, Fernando Reis, Amy Milsted Sep 2015

Structural Libraries Of Protein Models For Multiple Species To Understand Evolution Of The Renin-Angiotensin System, Jeremy Prokop, Victoria Petri, Mary Shimoyama, Ingrid Watanabe, Dulce Casarini, Thomas Peeper, Stephanie Bilinovich, Howard Jacob, Robson Santos, Almir Martins, Fabiano Araujo, Fernando Reis, Amy Milsted

Thomas C Leeper

The details of protein pathways at a structural level provides a bridge between genetics/molecular biology and physiology. The renin-angiotensin system is involved in many physiological pathways with informative structural details in multiple components. Few studies have been performed assessing structural knowledge across the system. This assessment allows use of bioinformatics tools to fill in missing structural voids. In this paper we detail known structures of the renin-angiotensin system and use computational approaches to estimate and model components that do not have their protein structures defined. With the subsequent large library of protein structures, we then created a species specific protein …

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Biocompatible Flavone-Based Fluorogenic Probes For Quick Wash-Free Mitochondria! Imaging In Living Cells, Bin Liu, Mickey Shah, Ge Zhang, Qin Liu, Yi Pang Sep 2015

Biocompatible Flavone-Based Fluorogenic Probes For Quick Wash-Free Mitochondria! Imaging In Living Cells, Bin Liu, Mickey Shah, Ge Zhang, Qin Liu, Yi Pang

Ge Zhang

Mitochondria, vital organelles existing in almost all eukaryotic cells, play a crucial role in energy metabolism and apoptosis of aerobic organisms. In this work, we report two new flavone-based fluorescent probes, MC-Mito1 and MC-Mito2, for monitoring mitochondria in living cells. These two probes exhibit remarkably low toxicity, good cell permeability, and high specificity; these probes complement the existing library of mitochondrial imaging agents. The new dyes give nearly no background fluorescence, and their application does not require tedious postwashing after cell staining. The appreciable tolerance of MC-Mito2 encourages a broader range of biological applications for understanding the cell degeneration and …

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A Single Molecular Probe For Multi-Analyte (Cr3+, Al3+ And Fe3+) Detection In Aqueous Medium And Its Biological Application, Junfeng Wang, Yingbo Li, Nikul Patel, Ge Zhang, Demin Zhou, Yi Pang Sep 2015

A Single Molecular Probe For Multi-Analyte (Cr3+, Al3+ And Fe3+) Detection In Aqueous Medium And Its Biological Application, Junfeng Wang, Yingbo Li, Nikul Patel, Ge Zhang, Demin Zhou, Yi Pang

Ge Zhang

An ESIPT based fluorescent sensor 1 was developed, which could selectively detect and differentiate trivalent metal ions Cr3+, Al3+ and Fe3+ in aqueous medium. The cell imaging experiments confirmed that 1 can be used for monitoring intracellular Cr3+ and Al3+ levels in living cells.

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The Quasi-Static Deformation, Failure, And Fracture Behavior Of Titanium Alloy Gusset Plates Containing Bolt Holes, Therese Hurtuk, Craig Menzemer, Anil Patnaik, Tirumalai Srivatsan, Kannan Manigandan, T. Quick Aug 2015

The Quasi-Static Deformation, Failure, And Fracture Behavior Of Titanium Alloy Gusset Plates Containing Bolt Holes, Therese Hurtuk, Craig Menzemer, Anil Patnaik, Tirumalai Srivatsan, Kannan Manigandan, T. Quick

Anil Patnaik

In this article, the influence of bolt holes, specifically their number and layout on strength, deformation, and final fracture behavior of titanium alloy gusset plates under the influence of an external load is presented and discussed. Several plates having differences in both the number and layout of the bolt holes were precision machined and then deformed under quasi-static loading. The specific influence of number of bolt holes and their layout on maximum load-carrying capability and even fracture load was determined. The conjoint influence of bolt number, bolt layout pattern, nature of loading, contribution from local stress concentration, and intrinsic microstructural …

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Innovation Mashups: Academic Rigor Meets Social Networking Buzz, Dejan Milojicic, Martin Arlitt, Dorée Seligmann, George Thiruvathukal, Christian Timmerer Aug 2015

Innovation Mashups: Academic Rigor Meets Social Networking Buzz, Dejan Milojicic, Martin Arlitt, Dorée Seligmann, George Thiruvathukal, Christian Timmerer

George K. Thiruvathukal

Exploring new options for publishing and content delivery offers an enormous opportunity to improve the state of the art and further modernize academic and professional publications. Traditional organizations such as the IEEE Computer Society, ACM, and Usenix have been encountering increasing competition from new ways of rapid publishing and dissemination, including social networking sites (Facebook, Twitter, LinkedIn, Google+), blogs with enabled commenting, video posting (YouTube), Slashdot, and many other types of media. "Liking" is replacing traditional impact factors, comments left on authors' webpages or blogs are replacing formal reviews, and site visits have more relevance than the number of article …

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Software Engineering Need Not Be Difficult, Jeffrey Carver, George Thiruvathukal Aug 2015

Software Engineering Need Not Be Difficult, Jeffrey Carver, George Thiruvathukal

George K. Thiruvathukal

"Progress in scientific research is dependent on the quality and accessibility of software at all levels" (the overall premise of the workshop). We argue that true progress depends on embracing the best traditional--and emergent-- practices in software engineering, especially agile practices that intersect with the tradition of software engineering. Software engineering as practiced today is more than the stereotypical monolithic lifecycle processes (e.g. waterfall, spiral, etc.) that historically have impeded progress for small/medium sized development efforts. In addition, the discipline and practice of software engineering includes software quality (with an established tradition of software metrics). Software processes can be …

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Introduction To Computer Science In C#, Andrew Harrington, George Thiruvathukal Aug 2015

Introduction To Computer Science In C#, Andrew Harrington, George Thiruvathukal

George K. Thiruvathukal

Drs. Harrington and Thiruvathukal created a living textbook to introduce computer science and programming principles (using the C# language from Microsoft, read C-sharp, as in music) to computer science at Loyola University Chicago (and beyond). This book is a work in progress but has been used since AY 2012 to teach COMP 170 at Loyola University Chicago.

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Bioactive Surface Modification Of Metal Oxides Via Catechol-Bearing Modular Peptides: Multivalent-Binding, Surface Retention, And Peptide Bioactivity, Wen Tang, Gina Policastro, Geng Hua, Kai Guo, Chrys Wesdemiotis, Gary Doll, Matthew Becker Aug 2015

Bioactive Surface Modification Of Metal Oxides Via Catechol-Bearing Modular Peptides: Multivalent-Binding, Surface Retention, And Peptide Bioactivity, Wen Tang, Gina Policastro, Geng Hua, Kai Guo, Chrys Wesdemiotis, Gary Doll, Matthew Becker

Gary L. Doll

A series of multivalent dendrons containing a bioactive osteogenic growth peptide (OGP) domain and surface-binding catechol domains were obtained through solid phase synthesis, and their binding affinity to hydroxyapatite, TiO2, ZrO2, CeO2, Fe3O4 and gold was characterized using a quartz crystal microbalance with dissipation (QCM-d). Using the distinct difference in binding affinity of the bioconjugate to the metal oxides, TiO2-coated glass slides were selectively patterned with bioactive peptides. Cell culture studies demonstrated the bioavailability of the OGP and that OGP remained on the surface for at least 2 weeks under in vitro cell culture conditions. Bone sialoprotein (BSP) and osteocalcein …

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Detection And Counting Of Micro Scale Particles And Pollen Using A Multi-Aperture Coulter Counter, Ashish Jagtiani, Jiang Zhe, Jun Hu, Joan Carletta Aug 2015

Detection And Counting Of Micro Scale Particles And Pollen Using A Multi-Aperture Coulter Counter, Ashish Jagtiani, Jiang Zhe, Jun Hu, Joan Carletta

Joan Carletta

We demonstrate a high throughput, all-electronic Coulter-type sensor with four sensing microapertures to detect and count micro-scale particles. Four particle samples are utilized for this study: polymethacrylate particles 40 µm and 20 µm in diameter, Juniper Scopulorum (Rocky Mountain Juniper) pollen and Cottonwood pollen particles. The two types of pollen particles are roughly 20 µm in diameter. The particles are mixed with deionized water and forced to pass through the microapertures. Voltage pulses across all four apertures are recorded and analysed. Results demonstrate that the sensor can detect and count particles through its four sensing apertures simultaneously. Thus, the counting …

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Rapid Door-To-Balloon Time (≤ 30 Minutes) In The Treatment Of Acute St-Elevation Myocardial Infarction (Stemi) Is Associated With Reduced Length Of Hospital Stay And Improved Clinical Outcomes, Yassir Nawaz Md, Ataul Qureshi Md, Navin K. Subrayappa Md, Orlando E. Rivera Rn, Bruce Feldman Do, Nainesh C. Patel Md Aug 2015

Rapid Door-To-Balloon Time (≤ 30 Minutes) In The Treatment Of Acute St-Elevation Myocardial Infarction (Stemi) Is Associated With Reduced Length Of Hospital Stay And Improved Clinical Outcomes, Yassir Nawaz Md, Ataul Qureshi Md, Navin K. Subrayappa Md, Orlando E. Rivera Rn, Bruce Feldman Do, Nainesh C. Patel Md

Bruce A. Feldman DO

No abstract provided.

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Skew-Product Dynamical Dystems: Applications To Difference Equations, Saber Elaydi, Robert Sacker Aug 2015

Skew-Product Dynamical Dystems: Applications To Difference Equations, Saber Elaydi, Robert Sacker

Saber Elaydi

No abstract provided.

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Asymptotic Solutions Of A Discrete Schrödinger Equation Arising From A Dirac Equation With Random Mass, Bernd Aulbach, Saber Elaydi, Klaus Ziegler Aug 2015

Asymptotic Solutions Of A Discrete Schrödinger Equation Arising From A Dirac Equation With Random Mass, Bernd Aulbach, Saber Elaydi, Klaus Ziegler

Saber Elaydi

For a Dirac particle in one dimension with random mass, the time evolution for the average wavefunction is considered. Using the supersymmetric representation of the average Green’s function, we derive a fourth order linear difference equation for the low-energy asymptotics of the average wavefunction. This equation is of Poincar´e type, though highly critical and therefore not amenable to standard methods. In this paper we show that, nevertheless, asymptotic expansions of its solutions can be obtained.

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Difference Equations Versus Differential Equations, A Possible Equivalence For The Rössler System?, Christophe Letellier, Saber Elaydi, Luis Aguirre, Aziz Alaoui Aug 2015

Difference Equations Versus Differential Equations, A Possible Equivalence For The Rössler System?, Christophe Letellier, Saber Elaydi, Luis Aguirre, Aziz Alaoui

Saber Elaydi

When a set of non linear differential equations is investigated, most of the time there is no analytical solution and only numerial integration techniques can provide accurate numerical solutions. In a general way the process of numerical integration is the replacement of a set of differential equations with a continuous dependence on the time by a model for which these time variable is discrete. When only a numerical solution is researched, a fourth-order Runge-Kutta integration scheme is usually sufficient. Nevertheless, sometimes a set of differential equations may be required and, in this case, standard schemes like the forward Euler, backward …

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Is The World Evolving Discretely?, Saber Elaydi Aug 2015

Is The World Evolving Discretely?, Saber Elaydi

Saber Elaydi

No abstract provided.

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Global Stability Of Periodic Orbits Of Non-Autonomous Difference Equations And Population Biology, Saber Elaydi, Robert Sacker Aug 2015

Global Stability Of Periodic Orbits Of Non-Autonomous Difference Equations And Population Biology, Saber Elaydi, Robert Sacker

Saber Elaydi

Elaydi and Yakubu showed that a globally asymptotically stable(GAS) periodic orbit in an autonomous difference equation must in fact be a fixed point whenever the phase space is connected. In this paper we extend this result to periodic nonautonomous difference equations via the concept of skew-product dynamical systems. We show that for a k-periodic difference equation, if a periodic orbit of period r is GAS, then r must be a divisor of k. In particular sub-harmonic, or long periodic, oscillations cannot occur. Moreover, if r divides k we construct a non-autonomous dynamical system having minimum period k and which has …

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Periodic Difference Equations, Population Biology And The Cushing-Henson Conjectures, Saber Elaydi, Robert Sacker Aug 2015

Periodic Difference Equations, Population Biology And The Cushing-Henson Conjectures, Saber Elaydi, Robert Sacker

Saber Elaydi

We show that for a k-periodic difference equation, if a periodic orbit of period r is globally asymptotically stable (GAS), then r must be a divisor of k. In particular sub-harmonic, or long periodic, oscillations cannot occur. Moreover, if r divides k we construct a non-autonomous dynamical system having minimum period k and which has a GAS periodic orbit with minimum period r. Our method uses the technique of skew-product dynamical systems. Our methods are then applied to prove two conjectures of J. Cushing and S. Henson concerning a non-autonomous Beverton-Holt equation which arises in the study of the response …

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Nonautonomous Beverton-Holt Equations And The Cushing-Henson Conjectures, Saber Elaydi, Robert Sacker Aug 2015

Nonautonomous Beverton-Holt Equations And The Cushing-Henson Conjectures, Saber Elaydi, Robert Sacker

Saber Elaydi

In [3] Jim Cushing and Shandelle Henson published two conjectures (see Section 3) related to the Beverton-Holt difference equation (with growth parameter exceeding one), which said that the B-H equation with periodically varying coefficients (a) will have a globally asymptotically stable periodic solution and (b) the average of the state variable along the periodic orbit will be strictly less than the average of the carrying capacities of the individual maps. They had previously [2] proved both statements for period 2.

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An Extension Of Sharkovsky’S Theorem To Periodic Difference Equations, Ziyad Alsharawi, James Angelos, Saber Elaydi, Leela Rakesh Aug 2015

An Extension Of Sharkovsky’S Theorem To Periodic Difference Equations, Ziyad Alsharawi, James Angelos, Saber Elaydi, Leela Rakesh

Saber Elaydi

We present an extension of Sharkovsky’s Theorem and its converse to periodic difference equations. In addition, we provide a simple method for constructing a p-periodic difference equation having an r-periodic geometric cycle with or without stability properties.

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Asymptotic Stability Of Linear Difference Equations Of Advanced Type, Fozi Dannan, Saber Elaydi Aug 2015

Asymptotic Stability Of Linear Difference Equations Of Advanced Type, Fozi Dannan, Saber Elaydi

Saber Elaydi

Necessary and sufficient conditions are obtained for the asymptotic stability of difference equations of advanced typen of the form x(n) - ax(n+1) + bx(n+k) = 0, n = 0, 1, .. where a and b are arbitrary real numbers and k > 1. For a = 1, we establish an analogue of a result by Levin and May.

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