Digital Commons Network^™

Prescribed Fire Effects On Resource Selection By Cattle In Mesic Sagebrush Steppe. Part 1: Spring Grazing, Patrick Clark, Jaechoul Lee, Kyungduk Ko, Ryan Nielson, Douglas Johnson, David Ganskopp, Joe Chigbrow, Frederick Pierson, Stuart Hardegree

Kyungduk Ko

Prescribed fire is commonly applied world-wide as a tool for enhancing habitats and altering resource-selection patterns of grazing animals. A scientific basis for this practice has been established in some ecosystems but its efficacy has not been rigorously evaluated on mesic sagebrush steppe. Beginning in 2003, resource-selection patterns of beef cows were investigated using global positioning system (GPS) collars for 2 years before and for 5 years after a fall prescribed burn was applied to mesic sagebrush steppe in the Owyhee Mountains of southwestern Idaho, USA. Resource-selection functions (RSF) developed from these data indicated cattle selected for lightly to moderately …

Localized Bases For Kernel Spaces On The Unit Sphere, E. Fuselier, T. Hangelbroek, F. J. Narcowich, J. D. Ward, G. B. Wright

Grady Wright

Approximation/interpolation from spaces of positive definite or conditionally positive definite kernels is an increasingly popular tool for the analysis and synthesis of scattered data and is central to many meshless methods. For a set of N scattered sites, the standard basis for such a space utilizes N globally supported kernels; computing with it is prohibitively expensive for large N. Easily computable, well-localized bases with “small-footprint” basis elements—i.e., elements using only a small number of kernels—have been unavailable. Working on S2, with focus on the restricted surface spline kernels (e.g., the thin-plate splines restricted to the sphere), we construct easily computable, …

Digital Images: They're Not Just For Viewing, Lori Ziegelmeier

Lori Beth Ziegelmeier

No abstract provided.

Mathematicians Playing A Role In Math Education: What We Learned At The Ime/Mime Workshop, Anna Bargagliotti, Rama Chidambaram, Gizem Karaali

Anna Bargagliotti

In Hollywood, some actors are regularly cast as mean, others as sweet and endearing, and some typically play innocent big-eyed youths who inevitably succeed after awakening to the particular facts of life that their producer wants them to awaken to. It is unusual and difficult for actors to cross the bridge between different types on a regular basis. However, there are always exceptions to the rule. In the seemingly unrelated world of academics, mathematics faculty may find themselves playing different roles. People with different skills and interests strive to balance their careers in ways that will be uniquely fulfilling to …

Folding Corners Of The Habits Of Mind, Peter S. Wiles

Peter S. Wiles

X2 Tests For The Choice Of The Regularization Parameter In Nonlinear Inverse Problems, J. L. Mead, C. C. Hammerquist

Jodi Mead

We address discrete nonlinear inverse problems with weighted least squares and Tikhonov regularization. Regularization is a way to add more information to the problem when it is ill-posed or ill-conditioned. However, it is still an open question as to how to weight this information. The discrepancy principle considers the residual norm to determine the regularization weight or parameter, while the χ2 method [J. Mead, J. Inverse Ill-Posed Probl., 16 (2008), pp. 175–194; J. Mead and R. A. Renaut, Inverse Problems, 25 (2009), 025002; J. Mead, Appl. Math. Comput., 219 (2013), pp. 5210–5223; R. A. Renaut, I. Hnetynkova, and J. L. …

Bayesian Analysis Of Hypothesis Testing Problems For General Population: A Kullback–Leibler Alternative, Naveen Bansal, Gholamhossein Hamedani, Ru Sheng

Naveen Bansal

We consider a hypothesis problem with directional alternatives. We approach the problem from a Bayesian decision theoretic point of view and consider a situation when one side of the alternatives is more important or more probable than the other. We develop a general Bayesian framework by specifying a mixture prior structure and a loss function related to the Kullback–Leibler divergence. This Bayesian decision method is applied to Normal and Poisson populations. Simulations are performed to compare the performance of the proposed method with that of a method based on a classical z-test and a Bayesian method based on the …

Creating Composite Age Groups To Smooth Percentile Rank Distributions Of Small Samples, Francesca Lopez, Amy Olson, Naveen Bansal

Naveen Bansal

Individually administered tests are often normed on small samples, a process that may result in irregularities within and across various age or grade distributions. Test users often smooth distributions guided by Thurstone assumptions (normality and linearity) to result in norms that adhere to assumptions made about how the data should look. Test users, however, may come across particular tests or sets of data in which the Thurstone assumptions are untenable. When users expect deviations from normality within age or grade, an alternate method is desirable. The authors present a relatively simple procedure that allows the user to treat observed raw …

Mathematical Reasoning: Writing And Proof, Ted Sundstrom

Ted Sundstrom, Professor of Mathematics

Mathematical Reasoning: Writing and Proof is designed to be a text for the first course in the college mathematics curriculum that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics. The primary goals of the text are to help students: • Develop logical thinking skills and to develop the ability to think more abstractly in a proof oriented setting. • Develop the ability to construct and write mathematical proofs using standard methods of mathematical proof including direct proofs, proof by contradiction, mathematical induction, case analysis, and counterexamples. • Develop the ability …

Sections Of Surface Bundles And Lefschetz Fibrations, Inanc Baykur, Mustafa Korkmaz, Naoyuki Monden

Inanc Baykur

We investigate the possible self-intersection numbers for sections of surface bundles and Lefschetz fibrations over surfaces. When the fiber genus g and the base genus h are positive, we prove that the adjunction bound 2h−2 is the only universal bound on the self-intersection number of a section of any such genus g bundle and fibration. As a side result, in the mapping class group of a surface with boundary, we calculate the precise value of the commutator lengths of all powers of a Dehn twist about a boundary component, concluding that the stable commutator length of such a Dehn twist …

A Study Of Non-Central Skew T Distributions And Their Applications In Data Analysis And Change Point Detection, Abeer Hasan

Abeer Hasan

Mathematics Libguide, Sandra Barclay

Sandra Barclay

Welcome to the Horace W. Sturgis Library and the Mathematics Libguide at Kennesaw State University! To get started with your math research, this is the place to go. We hope you will find this information helpful. Please let us know what other resources you could use.

Early Investigations In Conformal And Differential Geometry, Raymond T. Walter

Raymond Walter

Quantitative Interpretation Of A Genetic Model Of Carcinogenesis Using Computer Simulations, Donghai Dai, Brandon Beck, Xiaofang Wang, Cory Howk, Yi Li

Donghai Dai

The genetic model of tumorigenesis by Vogelstein et al. (V theory) and the molecular definition of cancer hallmarks by Hanahan and Weinberg (W theory) represent two of the most comprehensive and systemic understandings of cancer. Here, we develop a mathematical model that quantitatively interprets these seminal cancer theories, starting from a set of equations describing the short life cycle of an individual cell in uterine epithelium during tissue regeneration. The process of malignant transformation of an individual cell is followed and the tissue (or tumor) is described as a composite of individual cells in order to quantitatively account for intra-tumor …

A High-Order Kernel Method For Diffusion And Reaction-Diffusion Equations On Surfaces, Edward J. Fuselier, Grady B. Wright

Grady Wright

In this paper we present a high-order kernel method for numerically solving diffusion and reaction-diffusion partial differential equations (PDEs) on smooth, closed surfaces embedded in R^d . For two-dimensional surfaces embedded in R³ , these types of problems have received growing interest in biology, chemistry, and computer graphics to model such things as diffusion of chemicals on biological cells or membranes, pattern formations in biology, nonlinear chemical oscillators in excitable media, and texture mappings. Our kernel method is based on radial basis functions and uses a semi-discrete approach (or the method-of-lines) in which the surface derivative operators that …

Inverse Problems For Unilevel Block $\Alpha$-Circulants, William F. Trench

William F. Trench

No abstract provided.

Discontinuous Parameter Estimates With Least Squares Estimators, J. L. Mead

Jodi Mead

We discuss weighted least squares estimates of ill-conditioned linear inverse problems where weights are chosen to be inverse error covariance matrices. Least squares estimators are the maximum likelihood estimate for normally distributed data and parameters, but here we do not assume particular probability distributions. Weights for the estimator are found by ensuring its minimum follows a χ2 distribution. Previous work with this approach has shown that it is competitive with regularization methods such as the L-curve and Generalized Cross Validation (GCV) [20]. In this work we extend the method to find diagonal weighting matrices, rather than a scalar regularization parameter. …

College Algebra In Context With Applications To The Managerial, Life, And Social Sciences, Lisa Yocco, Ronald Harshbarger

Lisa S. Yocco

No abstract provided.

A Method To Dynamically Subdivide Parcels In Land Use Change Models, Rohan Wickramasuriya, Laurie Chisholm, Marji Puotinen, Nicholas Gill, Peter Klepeis

Rohan Wickramasuriya, Ph.D.

Spatial simulation models have become a popular tool in studying land use/land cover (LULC) change. An important, yet largely overlooked process in such models is the land subdivision, which is known to govern LULC change and landscape restructuring to a large extent. To fill this gap, we propose an efficient and straightforward method to simulate dynamic land subdivision in LULC change models. Key features in the proposed method are implementing a hierarchical landscape where adjacent cells of the same LULC type form patches, patches form properties, and properties form the landscape and incorporating real subdivision layouts. Furthermore, we use a …

On The Construction Of Number Sequence Identities, Tian-Xiao He, Wun-Seng Chou

Tian-Xiao He

To construct a class of identities for number sequences generated by linear recurrence relations. An alternative method based on the generating functions of the sequences is given. The equivalence between two methods for linear recurring sequences are also shown. However, the second method is not limited to the linear recurring sequences, which can be used for a wide class of sequences possessing rational generating functions. As examples, Many new and known identities of Stirling numbers of the second kind, Pell numbers, Jacobsthal numbers, etc., are constructed by using our approach. Finally, we discuss the hyperbolic expression of the identities of …

The Calculus Student: Insights From The Mathematical Association Of America National Study, David Bressoud, Marilyn Carlson, Vilma Mesa, Chris Rassmusen

David Bressoud

No abstract provided.

Uniform Gaussian Bounds For Subelliptic Heat Kernels And An Application To The Total Variation Flow Of Graphs Over Carnot Groups, Luca Capogna, Giovanna Citti, Maria Manfredini

Luca Capogna

In this paper we study heat kernels associated with a Carnot group G, endowed with a family of collapsing left-invariant Riemannian metrics σε which converge in the Gromov- Hausdorff sense to a sub-Riemannian structure on G as ε→ 0. The main new contribution are Gaussian-type bounds on the heat kernel for the σε metrics which are stable as ε→0 and extend the previous time-independent estimates in [16]. As an application we study well posedness of the total variation flow of graph surfaces over a bounded domain in a step two Carnot group (G; σε ). We establish interior and boundary …

Mixed Integer Programming Vs Logic-Based Benders Decomposition For Planning And Scheduling, John Hooker, Andre Cire

John Hooker

No abstract provided.

The First Year Of Calculus And Statistics At Macalester College, Karen Saxe, Dan Flath, Tom Halverson, Daniel Kaplan

Karen Saxe

No abstract provided.

Expression And Computation Of Generalized Stirling Numbers, Tian-Xiao He

Tian-Xiao He

Schroder Matrix As Inverse Of Delannoy Matrix, Tian-Xiao He, Sheng-Liang Yang, Sai-Nan Zheng, Shao-Peng Yuan

Tian-Xiao He

Functions Defined By Improper Integrals, William F. Trench

William F. Trench

This is a supplement to the author's Introduction to Real Analysis. It has been judged to meet the evaluation criteria set by the Editorial Board of the American Institute of Mathematics in connection with the Institute's Textbook Initiative. It may be copied, modified, redistributed, translated, and built upon subject to the Creative Commons license

Attribution-NonCommercial-ShareAlike 3.0 Unported License.

A complete instructor's solution manual is available by email to wtrench@trinity.edu subject to verification of the requestor's faculty status.

Determination Of Kinetic Parameters From The Thermogravimetric Data Set Of Biomass Samples, Karol Postawa, Wojciech M. Budzianowski

Wojciech Budzianowski

This article describes methods of the determination of kinetic parameters from the thermogravimetric data set of biomass samples. It presents the methodology of the research, description of the needed equipment, and the method of analysis of thermogravimetric data. It describes both methodology of obtaining quantitative data such as kinetic parameters as well as of obtaining qualitative data like the composition of biomass. The study is focused mainly on plant biomass because it is easy in harvesting and preparation. Methodology is shown on the sample containing corn stover which is subsequently pyrolysed. The investigated sample show the kinetic of first order …

Numerical Solution For Complex Systems Of Fractional Order, Habibolla Latifizadeh

H. L. Zadeh

No abstract provided.

Minimum Correlation In Construction Of Multivariate Distributions, Nevena Maric, Vanja Dukic

Nevena Maric