Evaluating A Class Of Balanced $Q$-Series,
2018
TÜBİTAK
Evaluating A Class Of Balanced $Q$-Series, Wenchang Chu
Turkish Journal of Mathematics
By means of the modified Abel lemma on summation by parts, we examine a class of terminating balanced $q$-series. Two transformation formulae are established that contain ten summation formulae as consequences.
Corrigendum And Addendum To "Modules Whose $P$-Submodules Are Direct Summands",
2018
TÜBİTAK
Corrigendum And Addendum To "Modules Whose $P$-Submodules Are Direct Summands", Yeli̇z Kara
Turkish Journal of Mathematics
This paper is written to correct the proof of Lemma 2.1$(i)$ in \cite{K} and to add some decomposition results for the class of $PD$-modules defined in \cite{K}.
A Note On The Associated Primes Of Local Cohomology Modules For Regular Local Rings,
2018
TÜBİTAK
A Note On The Associated Primes Of Local Cohomology Modules For Regular Local Rings, Yubin Gao
Turkish Journal of Mathematics
Let $R$ be a regular local ring. In this note, we prove that $Ass_RH^2_I(R)$ is finite for any ideal $I$ of $R$. We also give a sufficient condition for $Ass_RH^3_{(x,y,z)}(R)$ to be finite for $x, y$ an $R$-regular sequence and $z\in R$, which would imply that Lyubeznik's conjecture is true in the regular local rings case.
On $3$-Dimensional $\Jt$-Tangent Centro-Affine Hypersurfaces And $\Jt$-Tangent Affine Hyperspheres With Some Null-Directions,
2018
TÜBİTAK
On $3$-Dimensional $\Jt$-Tangent Centro-Affine Hypersurfaces And $\Jt$-Tangent Affine Hyperspheres With Some Null-Directions, Zuzanna Szancer
Turkish Journal of Mathematics
Let $\Jt$ be the canonical para-complex structure on $\R^4$. In this paper we study $3$-dimensional centro-affine hypersurfaces with a $\Jt$-tangent centro-affine vector field (sometimes called $\Jt$-tangent centro-affine hypersurfaces) as well as $3$-dimensional $\Jt$-tangent affine hyperspheres with the property that at least one null-direction of the second fundamental form coincides with either $\DD^+$ or $\DD^-$. The main purpose of this paper is to give a full local classification of the above-mentioned hypersurfaces. In particular, we prove that every nondegenerate centro-affine hypersurface of dimension $3$ with a $\Jt$-tangent centro-affine vector field that has two null-directions $\DD^+$ and $\DD^-$ must be both an …
Influence Of Reading Proficiency On Placement And Success In Online Developmental Mathematics,
2018
Walden University
Influence Of Reading Proficiency On Placement And Success In Online Developmental Mathematics, Diane Marie Stryk
Walden Dissertations and Doctoral Studies
Community college leaders have spent years trying to improve success rates for students in developmental mathematics (DM) courses, but with little progress. This quantitative study, using a pre-experimental static-group research design, examined if a change in a community college district's policy and practices for student placement into DM courses could improve student success in online DM courses. Bounded rationality theory provided the lens to view how students' decision making is influenced by the lack of timely and appropriate information during the placement process. The study addressed whether a composite placement score, the result of combining the ACCUPLACER placement scores for …
On A Pseudodifferential Calculus With Modest Boundary Decay Condition,
2018
Binghamton University--SUNY
On A Pseudodifferential Calculus With Modest Boundary Decay Condition, Binbin Huang
Graduate Dissertations and Theses
A boundary decay condition, called vanishing to infinite logarithmic order is introduced. A pseudodifferential calculus, extending the b-calculus of Melrose, is proposed based on this modest decay condition. The mapping properties, composition rule, and normal operators are studied. Instead of functional analytic methods, a geometric approach is invoked in pursuing the Fredholm criterion. As an application, a detailed proof of the Atiyah-Patodi-Singer index theorem, including a review of Dirac operators of product type and construction of the heat kernel, is presented.
Automating The Calculation Of Hilbert-Kunz Multiplicities And F-Signatures,
2018
University of Mississippi. Sally McDonnell Barksdale Honors College
Automating The Calculation Of Hilbert-Kunz Multiplicities And F-Signatures, Gabriel Johnson
Honors Theses
We describe an application written to automate a calculation for the mathematical research of Dr. Spiroff of University of Mississippi & Dr. Enescu of Georgia State University. This work represents a way to overcome the barriers of the mathematical calculations in obtaining theoretical results.
Complex-Valued Time Series Modeling For Improved Activation Detection In Fmri Studies,
2018
Grand Valley State University
Complex-Valued Time Series Modeling For Improved Activation Detection In Fmri Studies, Daniel W. Adrian, Ranjan Maitra, Daniel B. Rowe
Mathematical and Statistical Science Faculty Research and Publications
A complex-valued data-based model with th order autoregressive errors and general real/imaginary error covariance structure is proposed as an alternative to the commonly used magnitude-only data-based autoregressive model for fMRI time series. Likelihood-ratio-test-based activation statistics are derived for both models and compared for experimental and simulated data. For a dataset from a right-hand finger-tapping experiment, the activation map obtained using complex-valued modeling more clearly identifies the primary activation region (left functional central sulcus) than the magnitude-only model. Such improved accuracy in mapping the left functional central sulcus has important implications in neurosurgical planning for tumor and epilepsy patients. Additionally, we …
On Extended Quadratic Hazard Rate Distribution: Development, Properties, Characterizations And Applications,
2018
National College of Business Administration and Economic
On Extended Quadratic Hazard Rate Distribution: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Wenhui Sheng, Munir Ahmad
Mathematical and Statistical Science Faculty Research and Publications
In this paper, we propose a flexible extended quadratic hazard rate (EQHR) distribution with increasing, decreasing, bathtub and upside-down bathtub hazard rate function. The EQHR density is arc, right-skewed and symmetrical shaped. This distribution is also obtained from compounding mixture distributions. Stochastic orderings, descriptive measures on the basis of quantiles, order statistics and reliability measures are theoretically established. Characterizations of the EQHR distribution are studied via different techniques. Parameters of the EQHR distribution are estimated using the maximum likelihood method. Goodness of fit of this distribution through different methods is studied.
On The Composition Of Derivatives,
2018
West Virginia University
On The Composition Of Derivatives, Krzysztof Ciesielski
Faculty & Staff Scholarship
We show that there exists a derivative f : [0, 1] → [0, 1] such that the graph of f ◦ f is dense in [0, 1]2 , so not a Gδ-set. In particular, f ◦ f is everywhere discontinuous, so not of Baire class 1, and hence it is not a derivative.
Simultaneous Small Coverings By Smooth Functions Under The Covering Property Axiom,
2018
West Virginia University
Simultaneous Small Coverings By Smooth Functions Under The Covering Property Axiom, Krzysztof Ciesielski
Faculty & Staff Scholarship
The covering property axiom CPA is consistent with ZFC: it is satisfied in the iterated perfect set model. We show that CPA implies that for every ν ∈ ω ∪ {∞} there exists a family Fν ⊂ C ν (R) of cardinality ω1 < c such that for every g ∈ D ν (R) the set g \ S Fν has cardinality ≤ ω1. Moreover, we show that this result remains true for partial functions g (i.e., g ∈ D ν (X) for some X ⊂ R) if, and only if, ν ∈ {0, 1}. The proof of this result is based on the following theorem of independent interest (which, for ν 6= 0, seems to have been previously unnoticed): for every X ⊂ R with no isolated points, every ν-times differentiable function g : X → R admits a ν-times differentiable extension ¯g : B → R, where B ⊃ X is a Borel subset of R. The presented arguments rely heavily on a Whitney’s Extension Theorem for the functions defined on perfect subsets of R, which short but fully detailed proof is included. Some open questions are also posed.
Special Values Of Ibukiyama-Saito L-Functions,
2018
CUNY New York City College of Technology
Special Values Of Ibukiyama-Saito L-Functions, Brad Isaacson
Publications and Research
Following the method of Arakawa, we express the special values of an L-function originally introduced by Arakawa and Hashimoto and later generalized by Ibukiyama and Saito at non-positive integers by finite sums of products of Bernoulli polynomials. As a corollary, we prove an infinite family of identities expressing finite sums of products of Bernoulli polynomials by generalized Bernoulli numbers.
A Survey On Monochromatic Connections Of Graphs,
2018
Nankai University
A Survey On Monochromatic Connections Of Graphs, Xueliang Li, Di Wu
Theory & Applications of Graphs
The concept of monochromatic connection of graphs was introduced by Caro and Yuster in 2011. Recently, a lot of results have been published about it.
In this survey, we attempt to bring together all the results that dealt with it.
We begin with an introduction, and then classify the results into the following categories: monochromatic connection coloring of edge-version, monochromatic connection coloring of vertex-version, monochromatic index, monochromatic connection coloring of total-version.
Classical And Quantum Kac’S Chaos,
2018
University of South Carolina
Classical And Quantum Kac’S Chaos, Rade Musulin
Theses and Dissertations
In 1956 Kac studied the Boltzmann equation, an integro-differential equation which describes the density function of the distribution of the velocities of the molecules of dilute monoatomic gases under the assumption that the energy is only transferred via collisions between the molecules. In an attempt at a solution to the Boltzmann equation, Kac introduced a property of the density function that he called the “Boltzmann property" which describes the behavior of the density function at a given fixed time as the number of particles tends to infinity. The Boltzmann property has been studied extensively since then, and has been abstracted …
Theory, Computation, And Modeling Of Cancerous Systems,
2018
University of South Carolina
Theory, Computation, And Modeling Of Cancerous Systems, Sameed Ahmed
Theses and Dissertations
This dissertation focuses on three projects. In Chapter 1, we derive and implement the compact implicit integration factor method for numerically solving partial differential equations. In Chapters 2 and 3, we generalize and analyze a mathematical model for the nonlinear growth kinetics of breast cancer stem cells. And in Chapter 4, we develop a novel mathematical model for the HER2 signaling pathway to understand and predict breast cancer treatment. Due to the high order spatial derivatives and stiff reactions, severe temporal stability constraints on the time step are generally required when developing numerical methods for solving high order partial differential …
Special Fiber Rings Of Certain Height Four Gorenstein Ideals,
2018
University of South Carolina
Special Fiber Rings Of Certain Height Four Gorenstein Ideals, Jaree Hudson
Theses and Dissertations
Let S be a set of four variables, k a field of characteristic not equal to two such that k contains all square roots, and I a height four Gorenstein ideal of k[S] generated by nine quadratics so that I has a Gorenstein-linear resolution. We define a complex X• so that each module of X• is the tensor product of a certain polynomial ring Q in nine variables and a direct sum of indecomposable k[Sym(S)]-modules and the differential maps are Q- and k[Sym(S)]-module homomorphisms. Work with the Macaulay2 software suggests that H0(X•) is the special fiber ring of I and …
Pbw Bases And Marginally Large Tableaux In Type D,
2018
Central Michigan University
Pbw Bases And Marginally Large Tableaux In Type D, Ben Salisbury, Adam Schultze, Peter Tingley
Mathematics and Statistics: Faculty Publications and Other Works
We give an explicit description of the unique crystal isomorphism between two realizations of B(∞) in type D: that using marginally large tableaux and that using PBW monomials with respect to one particularly nice reduced expression of the longest word
How Often Does The Best Team Win? A Unified Approach To Understanding Randomness In North American Sport,
2018
Skidmore College
How Often Does The Best Team Win? A Unified Approach To Understanding Randomness In North American Sport, Michael J. Lopez, Gregory J. Matthews, Benjamin S. Baumer
Mathematics and Statistics: Faculty Publications and Other Works
Statistical applications in sports have long centered on how to best separate signal (e.g., team talent) from random noise. However, most of this work has concentrated on a single sport, and the development of meaningful cross-sport comparisons has been impeded by the difficulty of translating luck from one sport to another. In this manuscript we develop Bayesian state-space models using betting market data that can be uniformly applied across sporting organizations to better understand the role of randomness in game outcomes. These models can be used to extract estimates of team strength, the between-season, within-season and game-to-game variability of team …
How Often Does The Best Team Win? A Unified Approach To Understanding Randomness In North American Sport,
2018
Skidmore College
How Often Does The Best Team Win? A Unified Approach To Understanding Randomness In North American Sport, Michael J. Lopez, Gregory J. Matthews, Benjamin S. Baumer
Mathematics and Statistics: Faculty Publications and Other Works
Statistical applications in sports have long centered on how to best separate signal (e.g. team talent) from random noise. However, most of this work has concentrated on a single sport, and the development of meaningful cross-sport comparisons has been impeded by the difficulty of translating luck from one sport to another. In this manuscript, we develop Bayesian state-space models using betting market data that can be uniformly applied across sporting organizations to better understand the role of randomness in game outcomes. These models can be used to extract estimates of team strength, the between-season, within-season, and game-to-game variability of team …
Logic -> Proof -> Rest,
2018
The College of Wooster
Logic -> Proof -> Rest, Maxwell Taylor
Senior Independent Study Theses
REST is a common architecture for networked applications. Applications that adhere to the REST constraints enjoy significant scaling advantages over other architectures. But REST is not a panacea for the task of building correct software. Algebraic models of computation, particularly CSP, prove useful to describe the composition of applications using REST. CSP enables us to describe and verify the behavior of RESTful systems. The descriptions of each component can be used independently to verify that a system behaves as expected. This thesis demonstrates and develops CSP methodology to verify the behavior of RESTful applications.
