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Physical Sciences and Mathematics Commons™
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- Academic retention (1)
- At dimension (1)
- Aztec rectangle (1)
- Calculus (1)
- Caputo nabla fractional difference equation (1)
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- Diagnostic activity (1)
- Dual graph (1)
- Ecological production function; Ecological risk assessment; Ecosystem service; Environmental management; Mechanistic effects model (1)
- Existence (1)
- Frobenius map (1)
- Generalized quasi-linearization (1)
- Graphical con- densation (1)
- Hexagonal dungeon. (1)
- Homotopical Loewy length. (1)
- Mastery grading (1)
- Perfect matching (1)
- Rapid convergence (1)
- Schauder’s fixed point theorem (1)
- Tiling (1)
- Undergraduate mathematics (1)
Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
Perfect Matchings Of Trimmed Aztec Rectangles, Tri Lai
Perfect Matchings Of Trimmed Aztec Rectangles, Tri Lai
Department of Mathematics: Faculty Publications
We consider several new families of subgraphs of the square grid whose matchings are enumerated by powers of several small prime numbers: 2, 3, 5, and 11. Our graphs are obtained by trimming two opposite corners of an Aztec rectangle. The result yields a proof of a conjecture posed by Ciucu. In addition, we reveal a hidden connection between our graphs and the hexagonal dungeons introduced by Blum.
Existence And Rapid Convergence Results For Nonlinear Caputo Nabla Fractional Difference Equations, Xiang Liu, Baoguo Jia, Lynn Erbe, Allan Peterson
Existence And Rapid Convergence Results For Nonlinear Caputo Nabla Fractional Difference Equations, Xiang Liu, Baoguo Jia, Lynn Erbe, Allan Peterson
Department of Mathematics: Faculty Publications
This paper is concerned with finding properties of solutions to initial value problems for nonlinear Caputo nabla fractional difference equations. We obtain existence and rapid convergence results for such equations by use of Schauder’s fixed point theorem and the generalized quasi-linearization method, respectively. A numerical example is given to illustrate one of our rapid convergence results.
Detecting Finite Flat Dimension Of Modules Via Iterates Of The Frobenius Endomorphism, Douglas J. Dailey, Srikanth B. Iyengar, Thomas Marley
Detecting Finite Flat Dimension Of Modules Via Iterates Of The Frobenius Endomorphism, Douglas J. Dailey, Srikanth B. Iyengar, Thomas Marley
Department of Mathematics: Faculty Publications
It is proved that a module M over a Noetherian ring R of positive characteristic p has finite flat dimension if there exists an integer t > 0 such that Tor R (M, fe R) = 0 for t < i< t + dim R and infinitely many e. This extends results of Herzog, who proved it when M is finitely generated. It is also proved that when R is a Cohen-Macaulay local ring, it suffices that the Tor vanishing holds for one e > logp e(R) is the multiplicity of R.
A Framework For Predicting Impacts On Ecosystem Services From (Sub)Organismal Responses To Chemicals, Valery E. Forbes, Chris J. Salice, Bjorn Birnir, Randy J.F. Bruins, Peter Calow, Virginie Ducrot, Nika Galic, Kristina Garber, Bret C. Harvey, Henriette Jager, Andrew Kanarek, Robert Pastorok, Steve F. Railsback, Richard Rebarber, Pernille Thorbek
A Framework For Predicting Impacts On Ecosystem Services From (Sub)Organismal Responses To Chemicals, Valery E. Forbes, Chris J. Salice, Bjorn Birnir, Randy J.F. Bruins, Peter Calow, Virginie Ducrot, Nika Galic, Kristina Garber, Bret C. Harvey, Henriette Jager, Andrew Kanarek, Robert Pastorok, Steve F. Railsback, Richard Rebarber, Pernille Thorbek
Department of Mathematics: Faculty Publications
Protection of ecosystem services is increasingly emphasized as a risk-assessment goal, but there are wide gaps between current ecological risk-assessment endpoints and potential effects on services provided by ecosystems. The authors present a framework that links common ecotoxicological endpoints to chemical impacts on populations and communities and the ecosystem services that they provide. This framework builds on considerable advances in mechanistic effects models designed to span multiple levels of biological organization and account for various types of biological interactions and feedbacks. For illustration, the authors introduce 2 case studies that employ well-developed and validated mechanistic effects models: the inSTREAM individual-based …
Gene Expression Noise Enhances Robust Organization Of The Early Mammalian Blastocyst, William R. Holmes, Nabora Soledad Reyes De Mochel, Qixuan Wang, Huijing Du, Tao Peng, Michael Chiang, Olivier Cinquin, Ken Cho, Qing Nie
Gene Expression Noise Enhances Robust Organization Of The Early Mammalian Blastocyst, William R. Holmes, Nabora Soledad Reyes De Mochel, Qixuan Wang, Huijing Du, Tao Peng, Michael Chiang, Olivier Cinquin, Ken Cho, Qing Nie
Department of Mathematics: Faculty Publications
A critical event in mammalian embryo development is construction of an inner cell mass surrounded by a trophoectoderm (a shell of cells that later form extraembryonic structures). We utilize multi-scale, stochastic modeling to investigate the design principles responsible for robust establishment of these structures. This investigation makes three predictions, each supported by our quantitative imaging. First, stochasticity in the expression of critical genes promotes cell plasticity and has a critical role in accurately organizing the developing mouse blastocyst. Second, asymmetry in the levels of noise variation (expression fluctuation) of Cdx2 and Oct4 provides a means to gain the benefits of …
An Early Semester Mastery Activity And Intervention In First-Year Calculus, Allan P. Donsig, Nathan Wakefield
An Early Semester Mastery Activity And Intervention In First-Year Calculus, Allan P. Donsig, Nathan Wakefield
Department of Mathematics: Faculty Publications
Success in first-year mathematics courses is essential for students to pursue STEM careers, including teaching careers. We investigate a mastery activity given during the first two weeks of a first-year calculus course at the research site. Previous work showed a model using this activity in College Algebra, together with ACT and high school rank, was predictive of student success in precalculus. Here we do a similar analysis for such an activity in calculus, including an intervention for students who do not complete the activity. We also investigate the intervention’s effectiveness. These results show that the early mastery activity, especially when …