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Articles 91 - 120 of 434
Full-Text Articles in Statistics and Probability
Analysis Of Ibnr Liabilities With Interevent Times Depending On Claim Counts, Daniel J. Geiger, Akim Adekpedjou
Analysis Of Ibnr Liabilities With Interevent Times Depending On Claim Counts, Daniel J. Geiger, Akim Adekpedjou
Mathematics and Statistics Faculty Research & Creative Works
We extend a recently proposed stochastic loss reserving model for liabilities from incurred but not reported (IBNR) micro-level claims. We propose viewing the number of claims from an event as a measure of catastrophic severity. This view covers catastrophes with arbitrarily many classes of magnitude. Our Markovian model allows the time between disasters to depend on the previous event's level of severity. Simultaneously, we let the discount rate vary in the same manner. First, we find the moments of IBNR liabilities in our model. Then, we permit a later time horizon for IBNR claims when considered jointly with incurred and …
Joint Control Of Manufacturing And Onsite Microgrid System Via Novel Neural-Network Integrated Reinforcement Learning Algorithms, Jiaojiao Yang, Zeyi Sun, Wenqing Hu, Louis Steinmeister
Joint Control Of Manufacturing And Onsite Microgrid System Via Novel Neural-Network Integrated Reinforcement Learning Algorithms, Jiaojiao Yang, Zeyi Sun, Wenqing Hu, Louis Steinmeister
Mathematics and Statistics Faculty Research & Creative Works
Microgrid is a promising technology of distributed energy supply system, which consists of storage devices, generation capacities including renewable sources, and controllable loads. It has been widely investigated and applied for residential and commercial end-use customers as well as critical facilities. In this paper, we propose a joint state-based dynamic control model on microgrids and manufacturing systems where optimal controls for both sides are implemented to coordinate the energy demand and supply so that the overall production cost can be minimized considering the constraint of production target. Markov Decision Process (MDP) is used to formulate the decision-making procedure. The main …
Combining Cardiac Monitoring With Actigraphy Aids Nocturnal Arousal Detection During Ambulatory Sleep Assessment In Insomnia, Lara Rösler, Glenn Van Der Lande, Jeanne Leerssen, Austin G. Vandegriffe, Oti Lakbila-Kamal, Jessica C. Foster-Dingley, Anne C.W. Albers, Eus J.W. Van Someren
Combining Cardiac Monitoring With Actigraphy Aids Nocturnal Arousal Detection During Ambulatory Sleep Assessment In Insomnia, Lara Rösler, Glenn Van Der Lande, Jeanne Leerssen, Austin G. Vandegriffe, Oti Lakbila-Kamal, Jessica C. Foster-Dingley, Anne C.W. Albers, Eus J.W. Van Someren
Mathematics and Statistics Faculty Research & Creative Works
Study Objectives: The objective assessment of insomnia has remained difficult. Multisensory devices collecting heart rate (HR) and motion are regarded as the future of ambulatory sleep monitoring. Unfortunately, reports on altered average HR or heart rate variability (HRV) during sleep in insomnia are equivocal. Here, we evaluated whether the objective quantification of insomnia improves by assessing state-related changes in cardiac measures. Methods: We recorded electrocardiography, posture, and actigraphy in 33 people without sleep complaints and 158 patients with mild to severe insomnia over 4 d in their home environment. At the microscale, we investigated whether HR changed with proximity to …
Periodicity On Isolated Time Scales, Martin Bohner, Jaqueline Mesquita, Sabrina Streipert
Periodicity On Isolated Time Scales, Martin Bohner, Jaqueline Mesquita, Sabrina Streipert
Mathematics and Statistics Faculty Research & Creative Works
In this work, we formulate the definition of periodicity for functions defined on isolated time scales. The introduced definition is consistent with the known formulations in the discrete and quantum calculus settings. Using the definition of periodicity, we discuss the existence and uniqueness of periodic solutions to a family of linear dynamic equations on isolated time scales. Examples in quantum calculus and for mixed isolated time scales are presented.
On Inclusions With Monotone-Type Mappings In Nonreflexive Banach Spaces, Vy Khoi Le
On Inclusions With Monotone-Type Mappings In Nonreflexive Banach Spaces, Vy Khoi Le
Mathematics and Statistics Faculty Research & Creative Works
We are concerned in this article with the existence of solutions to inclusions containing generalized pseudomonotone perturbations of maximal monotone mappings in general Banach spaces. Our approach is based on a truncation–regularization technique and an extension of the Moreau–Yosida–Brezis–Crandall–Pazy regularization for maximal monotone mappings in general Banach spaces. We also consider some applications to multivalued variational inequalities containing elliptic operators with rapidly growing coefficients in Orlicz–Sobolev spaces.
A Multigrid Multilevel Monte Carlo Method For Stokes–Darcy Model With Random Hydraulic Conductivity And Beavers–Joseph Condition, Zhipeng Yang, Ju Ming, Changxin Qiu, Maojun Li, Xiaoming He
A Multigrid Multilevel Monte Carlo Method For Stokes–Darcy Model With Random Hydraulic Conductivity And Beavers–Joseph Condition, Zhipeng Yang, Ju Ming, Changxin Qiu, Maojun Li, Xiaoming He
Mathematics and Statistics Faculty Research & Creative Works
A multigrid multilevel Monte Carlo (MGMLMC) method is developed for the stochastic Stokes–Darcy interface model with random hydraulic conductivity both in the porous media domain and on the interface. Three interface conditions with randomness are considered on the interface between Stokes and Darcy equations, especially the Beavers–Joesph interface condition with random hydraulic conductivity. Because the randomness through the interface affects the flow in the Stokes domain, we investigate the coupled stochastic Stokes–Darcy model to improve the fidelity. Under suitable assumptions on the random coefficient, we prove the existence and uniqueness of the weak solution of the variational form. To construct …
The Beverton-Hold Model On Isolated Time Scales, Martin Bohner, Jaqueline Mesquita, Sabrina Streipert
The Beverton-Hold Model On Isolated Time Scales, Martin Bohner, Jaqueline Mesquita, Sabrina Streipert
Mathematics and Statistics Faculty Research & Creative Works
In this work, we formulate the Beverton-Holt model on isolated time scales and extend existing results known in the discrete and quantum calculus cases. Applying a recently introduced definition of periodicity for arbitrary isolated time scales, we discuss the effects of periodicity onto a population modeled by a dynamic version of the Beverton-Holt equation. The first main theorem provides conditions for the existence of a unique !-periodic solution that is globally asymptotically stable, which addresses the first Cushing-Henson conjecture on isolated time scales. The second main theorem concerns the generalization of the second Cushing-Henson conjecture. It investigates the effects of …
Optimal Equivalence Testing In Exponential Families, Renren Zhao, Robert L. Paige
Optimal Equivalence Testing In Exponential Families, Renren Zhao, Robert L. Paige
Mathematics and Statistics Faculty Research & Creative Works
We develop uniformly most powerful unbiased (UMPU) two sample equivalence test for a difference of canonical parameters in exponential families. This development involves a non-unique reparameterization. We address this issue via a novel characterization of all possible reparameterizations of interest in terms of a matrix group. Furthermore, our procedure involves an intractable conditional distribution which we reproduce to a high degree of accuracy using saddle point approximations. The development of this saddle point-based procedure involves a non-unique reparameterization, but we show that our procedure is invariant under choice of reparameterization. Our real data example considers the mean-to-variance ratio for normally …
On The Hartogs Extension Theorem For Unbounded Domains In CN, Al Boggess, Roman Dwilewicz, Egmont Porten
On The Hartogs Extension Theorem For Unbounded Domains In CN, Al Boggess, Roman Dwilewicz, Egmont Porten
Mathematics and Statistics Faculty Research & Creative Works
Let Ω ⊂ Cn, n > 2, be a domain with smooth connected boundary. If Ω is relatively compact, the Hartogs–Bochner theorem ensures that every CR distribution on ∂Ω has a holomorphic extension to Ω. For unbounded domains this extension property may fail, for example if Ω contains a complex hypersurface. The main result in this paper tells that the extension property holds if and only if the envelope of holomorphy of Cn \ Ω is Cn. It seems that it is the first result in the literature which gives a geometric characterization of unbounded domains in Cn for which the …
Fundamental Structure Of General Stochastic Dynamical Systems: High-Dimension Case, Haoyu Wang, Xiaoliang Gan, Wenqing Hu, Ping Ao
Fundamental Structure Of General Stochastic Dynamical Systems: High-Dimension Case, Haoyu Wang, Xiaoliang Gan, Wenqing Hu, Ping Ao
Mathematics and Statistics Faculty Research & Creative Works
No one has proved that mathematically general stochastic dynamical systems have a special structure. Thus, we introduce a structure of a general stochastic dynamical system. According to scientific understanding, we assert that its deterministic part can be decomposed into three significant parts: the gradient of the potential function, friction matrix and Lorenz matrix. Our previous work proved this structure for the low-dimension case. In this paper, we prove this structure for the high-dimension case. Hence, this structure of general stochastic dynamical systems is fundamental.
Asymptotic Properties Of Kneser Solutions To Third-Order Delay Differential Equations, Martin Bohner, John R. Graef, Irena Jadlovská
Asymptotic Properties Of Kneser Solutions To Third-Order Delay Differential Equations, Martin Bohner, John R. Graef, Irena Jadlovská
Mathematics and Statistics Faculty Research & Creative Works
The aim of this paper is to extend and complete the recent work by Graef et al. (J. Appl. Anal. Comput., 2021) analyzing the asymptotic properties of solutions to third-order linear delay differential equations. Most importantly, the authors tackle a particularly challenging problem of obtaining lower estimates for Kneser-type solutions. This allows improvement of existing conditions for the nonexistence of such solutions. As a result, a new criterion for oscillation of all solutions of the equation studied is established.
Oscillation Of Nonlinear Third-Order Difference Equations With Mixed Neutral Terms, Jehad Alzabut, Martin Bohner, Said R. Grace
Oscillation Of Nonlinear Third-Order Difference Equations With Mixed Neutral Terms, Jehad Alzabut, Martin Bohner, Said R. Grace
Mathematics and Statistics Faculty Research & Creative Works
In this paper, new oscillation results for nonlinear third-order difference equations with mixed neutral terms are established. Unlike previously used techniques, which often were based on Riccati transformation and involve limsup or liminf conditions for the oscillation, the main results are obtained by means of a new approach, which is based on a comparison technique. Our new results extend, simplify, and improve existing results in the literature. Two examples with specific values of parameters are offered.
Predicting Lifespan Of Drosophila Melanogaster: A Novel Application Of Convolutional Neural Networks And Zero-Inflated Autoregressive Conditional Poisson Model, Yi Zhang, V. A. Samaranayake, Gayla R. Olbricht, Matthew S. Thimgan
Predicting Lifespan Of Drosophila Melanogaster: A Novel Application Of Convolutional Neural Networks And Zero-Inflated Autoregressive Conditional Poisson Model, Yi Zhang, V. A. Samaranayake, Gayla R. Olbricht, Matthew S. Thimgan
Mathematics and Statistics Faculty Research & Creative Works
A model to classify the lifespan of Drosophila, the fruit fly, into short- and long-lived categories based on a sleep characteristic, extracted from activity data, is developed using a two-stage process. Stage 1 models the per-minute activity counts of each fly using a zero-inflated autoregressive conditional Poisson model. These probabilities are allowed to vary hourly, reflecting the circadian and other cycles present in a fly's sleep architecture. A 5-day moving window is used to model data allowing the model parameters to vary over the course of the fly's life. The resulting probabilities capture information about changes in sleep patterns with …
Generalization Of Mitrinović–Pečarić Inequalities On Time Scales, Ahmed A. El-Deeb, Elvan Akin, Billur Kaymakçalan
Generalization Of Mitrinović–Pečarić Inequalities On Time Scales, Ahmed A. El-Deeb, Elvan Akin, Billur Kaymakçalan
Mathematics and Statistics Faculty Research & Creative Works
We prove some new inequalities of Mitrinović–Pečarić inequalities for convex functions on an arbitrary time scale using delta integrals. These inequalities extend and improve some known dynamic inequalities in the literature. The main results will be proved by using Hölder and Jensen inequalities and a simple consequence of Keller's and Poetzsche's chain rules on time scales.
Discrete Fractional Boundary Value Problems And Inequalities, Martin Bohner, Nick Fewster-Young
Discrete Fractional Boundary Value Problems And Inequalities, Martin Bohner, Nick Fewster-Young
Mathematics and Statistics Faculty Research & Creative Works
In this paper, a general nonlinear discrete fractional boundary value problem is considered, of order between one and two. The main result is an existence theorem, proving the existence of at least one solution to the boundary value problem, subject to validity of a certain key inequality that allows unrestricted growth in the problem. The proof of this existence theorem is accomplished by using Brouwer's fixed point theorem as well as two other main results of this paper, namely, first, a result showing that the solutions of the boundary value problem are exactly the solutions to a certain equivalent integral …
Estimating Average Treatment Effect On The Treated Via Sufficient Dimension Reduction, Lu Li, Wei Luo, Xuerong Meggie Wen, Zhou Yu
Estimating Average Treatment Effect On The Treated Via Sufficient Dimension Reduction, Lu Li, Wei Luo, Xuerong Meggie Wen, Zhou Yu
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we propose to use sufficient dimension reduction (SDR) in conjunction with nonparametric techniques to estimate the average treatment effect on the treated (ATT), a parameter of common interest in causal inference. The proposed method is applicable under a general low-dimensional structure in the data and avoids both the risk of model misspecification and the "curse of dimensionality," for which it often outperforms the existing parametric and nonparametric methods. We develop the theoretical properties of the proposed method, including its asymptotic normality, its asymptotic super-efficiency, and its equivalent form as an augmented inverse probability weighting estimator. We also …
Oscillation And Nonoscillation Criteria For Four-Dimensional Advanced And Delay Time-Scale Systems, Elvan Akin, Gülşah Yenpi
Oscillation And Nonoscillation Criteria For Four-Dimensional Advanced And Delay Time-Scale Systems, Elvan Akin, Gülşah Yenpi
Mathematics and Statistics Faculty Research & Creative Works
We obtain oscillation and Non oscillation criteria for solutions to four-dimensional advanced and delay systems of first-order dynamic equations on time scales. To establish oscillation criteria, we eliminate Non oscillatory solutions of the systems based on the sign of components of the solutions. Furthermore, some of our results are new in the discrete case.
Conservative Unconditionally Stable Decoupled Numerical Schemes For The Cahn-Hilliard-Navier-Stokes-Darcy-Boussinesq System, Wenbin Chen, Daozhi Han, Xiaoming Wang, Yichao Zhang
Conservative Unconditionally Stable Decoupled Numerical Schemes For The Cahn-Hilliard-Navier-Stokes-Darcy-Boussinesq System, Wenbin Chen, Daozhi Han, Xiaoming Wang, Yichao Zhang
Mathematics and Statistics Faculty Research & Creative Works
We propose two mass and heat energy conservative, unconditionally stable, decoupled numerical algorithms for solving the Cahn-Hilliard-Navier-Stokes-Darcy-Boussinesq system that models thermal convection of two-phase flows in superposed free flow and porous media. The schemes totally decouple the computation of the Cahn-Hilliard equation, the Darcy equations, the heat equation, the Navier-Stokes equations at each time step, and thus significantly reducing the computational cost. We rigorously show that the schemes are conservative and energy-law preserving. Numerical results are presented to demonstrate the accuracy and stability of the algorithms.
Dynamics Of Plane Waves In The Fractional Nonlinear Schrödinger Equation With Long-Range Dispersion, Siwei Duo, Taras I. Lakoba, Yanzhi Zhang
Dynamics Of Plane Waves In The Fractional Nonlinear Schrödinger Equation With Long-Range Dispersion, Siwei Duo, Taras I. Lakoba, Yanzhi Zhang
Mathematics and Statistics Faculty Research & Creative Works
We analytically and numerically investigate the stability and dynamics of the plane wave solutions of the fractional nonlinear Schrödinger (NLS) equation, where the long-range dispersion is described by the fractional Laplacian (−∆)α/2 . The linear stability analysis shows that plane wave solutions in the defocusing NLS are always stable if the power α ∈ [1, 2] but unstable for α ∈ (0, 1). In the focusing case, they can be linearly unstable for any α ∈ (0, 2]. We then apply the split-step Fourier spectral (SSFS) method to simulate the nonlinear stage of the plane waves dynamics. In agreement with …
Confluent Projections And Connectedness Of Inverse Limits, Włodzimierz J. Charatonik, Daria Michalik
Confluent Projections And Connectedness Of Inverse Limits, Włodzimierz J. Charatonik, Daria Michalik
Mathematics and Statistics Faculty Research & Creative Works
V. Nall proved that connectedness is preserved under inverse limits if the bounding functions are unions of functions with connected images. We show that for such functions the projections from the graph onto domain are confluent and we investigate relationships between functions satisfying this or similar conditions with confluence or openness of projections.
A Kinetic Model For Blood Biomarker Levels After Mild Traumatic Brain Injury, Sima Azizi, Daniel B. Hier, Blaine Allen, Tayo Obafemi-Ajayi, Gayla R. Olbricht, Matthew S. Thimgan, Donald C. Wunsch
A Kinetic Model For Blood Biomarker Levels After Mild Traumatic Brain Injury, Sima Azizi, Daniel B. Hier, Blaine Allen, Tayo Obafemi-Ajayi, Gayla R. Olbricht, Matthew S. Thimgan, Donald C. Wunsch
Mathematics and Statistics Faculty Research & Creative Works
Traumatic brain injury (TBI) imposes a significant economic and social burden. The diagnosis and prognosis of mild TBI, also called concussion, is challenging. Concussions are common among contact sport athletes. After a blow to the head, it is often difficult to determine who has had a concussion, who should be withheld from play, if a concussed athlete is ready to return to the field, and which concussed athlete will develop a post-concussion syndrome. Biomarkers can be detected in the cerebrospinal fluid and blood after traumatic brain injury and their levels may have prognostic value. Despite significant investigation, questions remain as …
Efficient, Positive, And Energy Stable Schemes For Multi-D Poisson–Nernst–Planck Systems, Hailiang Liu, Wumaier Maimaitiyiming
Efficient, Positive, And Energy Stable Schemes For Multi-D Poisson–Nernst–Planck Systems, Hailiang Liu, Wumaier Maimaitiyiming
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we design, analyze, and numerically validate positive and energy-dissipating schemes for solving the time-dependent multi-dimensional system of Poisson–Nernst–Planck equations, which has found much use in the modeling of biological membrane channels and semiconductor devices. The semi-implicit time discretization based on a reformulation of the system gives a well-posed elliptic system, which is shown to preserve solution positivity for arbitrary time steps. The first order (in time) fully discrete scheme is shown to preserve solution positivity and mass conservation unconditionally, and energy dissipation with only a mild O (1) time step restriction. The scheme is also shown to …
Photoelectron Sheath Near The Lunar Surface: Fully Kinetic Modeling And Uncertainty Quantification Analysis, Jianxun Zhao, Xinpeng Wei, Zhangli Hu, Xiaoming He, Daoru Frank Han, Zhen Hu, Xiaoping Du
Photoelectron Sheath Near The Lunar Surface: Fully Kinetic Modeling And Uncertainty Quantification Analysis, Jianxun Zhao, Xinpeng Wei, Zhangli Hu, Xiaoming He, Daoru Frank Han, Zhen Hu, Xiaoping Du
Mathematics and Statistics Faculty Research & Creative Works
This paper presents a modeling and uncertainty quantification (UQ) study of the photoelectron sheath near the lunar surface. A fully kinetic 3-D finite-difference (FD) particle-in-cell (PIC) code is utilized to simulate the plasma interaction near the lunar surface and the resulting photoelectron sheath. For the uncertainty quantification analysis, this FD-PIC code is treated as a black box providing high-fidelity quantities of interest, which are also used to construct efficient reduced-order models to perform UQ analysis. 1-D configuration is chosen to present the analytic sheath solution as well as to demonstrate the procedure and capability of the UQ analysis.
Fully-Kinetic Particle-In-Cell Simulations Of Photoelectron Sheath On Uneven Lunar Surface, Jianxun Zhao, Xinpeng Wei, Xiaoming He, Daoru Frank Han, Xiaoping Du
Fully-Kinetic Particle-In-Cell Simulations Of Photoelectron Sheath On Uneven Lunar Surface, Jianxun Zhao, Xinpeng Wei, Xiaoming He, Daoru Frank Han, Xiaoping Du
Mathematics and Statistics Faculty Research & Creative Works
This paper presents a modeling and simulation study of the photoelectron sheath near uneven lunar surface. A fully kinetic 3-D finite-difference (FD) particle-in-cell (PIC) code is utilized to simulate the plasma interaction with local uneven surface terrain on the lunar surface in 2-D photoelectron sheaths. The code is first validated using a 1-D plasma charging and sheath problem by comparing with a semi-analytic solution. Good agreement is obtained. The 2-D FD-PIC simulations present the distributions of electric potential and charged species densities near the uneven lunar surface. It shows that the surface potential is highly influenced by the exposure to …
Stokes-Darcy System, Small-Darcy-Number Behaviour And Related Interfacial Conditions, Wenqi Lyu, Xiaoming Wang
Stokes-Darcy System, Small-Darcy-Number Behaviour And Related Interfacial Conditions, Wenqi Lyu, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
We show that the Stokes-Darcy system, which governs flows through adjacent porous and pure-fluid domains in the two-domain approach without forced filtration, can be recovered from the Helmholtz minimal dissipation principle. While the continuity of normal velocity across the interface is imposed explicitly for mass conservation, only the Beavers-Joseph-Saffman-Jones (BJSJ) interface boundary condition is imposed implicitly, and the balance of the normal-force interface boundary condition appears naturally in the variational process. This set of interface boundary conditions is well-accepted in the mathematics community. We show that these interfacial boundary conditions, at the physically important small-Darcy-number regime, are consistent with continuity …
New Proper Orthogonal Decomposition Approximation Theory For Pde Solution Data, Sarah Locke, John R. Singler
New Proper Orthogonal Decomposition Approximation Theory For Pde Solution Data, Sarah Locke, John R. Singler
Mathematics and Statistics Faculty Research & Creative Works
In our previous work [J. R. Singler, SIAM J. Numer. Anal., 52 (2014), pp. 852- 876], we considered the proper orthogonal decomposition (POD) of time varying PDE solution data taking values in two different Hilbert spaces. We considered various POD projections of the data and obtained new results concerning POD projection errors and error bounds for POD reduced order models of PDEs. In this work, we improve on our earlier results concerning POD projections by extending to a more general framework that allows for nonorthogonal POD projections and seminorms. We obtain new exact error formulas and convergence results for POD …
A Natural Frenet Frame For Null Curves On The Lightlike Cone In Minkowski Space ℝ⁴₂, Nemat Abazari, Martin Bohner, Ilgin Sağer, Alireza Sedaghatdoost, Yusuf Yayli
A Natural Frenet Frame For Null Curves On The Lightlike Cone In Minkowski Space ℝ⁴₂, Nemat Abazari, Martin Bohner, Ilgin Sağer, Alireza Sedaghatdoost, Yusuf Yayli
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we investigate the representation of curves on the lightlike cone ℚ³₂ in Minkowski space ℝ⁴₂ by structure functions. In addition, with this representation, we classify all of the null curves on the lightlike cone ℚ³₂ in four types, and we obtain a natural Frenet frame for these null curves. Furthermore, for this natural Frenet frame, we calculate curvature functions of a null curve, especially the curvature function κ₂ = 0 , and we show that any null curve on the lightlike cone is a helix. Finally, we find all curves with constant curvature functions.
Hereditarily Irreducible Maps, Hussam Abobaker, Włodzimierz J. Charatonik
Hereditarily Irreducible Maps, Hussam Abobaker, Włodzimierz J. Charatonik
Mathematics and Statistics Faculty Research & Creative Works
A map f:X→Y from a continuum X onto a continuum Y is said to be hereditarily irreducible, if f(A)⊊f(B) for any subcontinua A and B such that A⊊B. We investigate properties of hereditarily irreducible maps between continua. Special attention is given to maps between graphs and maps from the interval.
Student Preclass Preparation By Both Reading The Textbook And Watching Videos Online Improves Exam Performance In A Partially Flipped Course, Kaleb Bassett, Gayla R. Olbricht, Katie Shannon
Student Preclass Preparation By Both Reading The Textbook And Watching Videos Online Improves Exam Performance In A Partially Flipped Course, Kaleb Bassett, Gayla R. Olbricht, Katie Shannon
Mathematics and Statistics Faculty Research & Creative Works
The flipped classroom has the potential to improve student performance. Because flipping involves both preclass preparation and problem solving in the classroom, the means by which increased learning occurs and whether the method of delivering content matters is of interest. In a partially flipped cell biology course, students were assigned online videos before the flipped class and textbook reading before lectures. Low-stakes assessments were used to incentivize both types of preclass preparation. We hypothesized that more students would watch the videos than read the textbook and that both types of preparation would positively affect exam performance. A multiple linear regression …
Inverse Limits And Atomic Projections, Włodzimierz J. Charatonik, Faruq A. Mena, Robert Paul Roe
Inverse Limits And Atomic Projections, Włodzimierz J. Charatonik, Faruq A. Mena, Robert Paul Roe
Mathematics and Statistics Faculty Research & Creative Works
We consider generalized inverse limits of continua with bonding functions Fn that have the projection of Graph (Fn) onto the second (first) factor atomic and images (pre-image) of points are zero-dimensional. For such bonding functions we show that under some easily verified conditions that if the first (all) factor space(s) has a certain property then the inverse limit space must have this property. The properties considered include hereditary decomposability, hereditary indecomposability, hereditary unicoherence, arc-likeness, and tree-likeness. We illustrate the theorems by several examples.