Modeling Hourly Electricity Prices: A Structural Time Series Approach Incorporating Modified Garch Innovations,
2011
Missouri University of Science and Technology
Modeling Hourly Electricity Prices: A Structural Time Series Approach Incorporating Modified Garch Innovations, Edirisinghe Mudiyanselage Asitha Edirisinghe
Doctoral Dissertations
"The main objective of this research is to develop time series based procedures for modeling day-ahead and real-time hourly electricity prices. Such empirical processes exhibit features that make the direct application of standard time series models infeasible. Four years of hourly day-ahead and real-time electricity price data from the region supplied by the American Electric Power (AEP) company through the PJM Regional Transmission Organization (RTO) and one half years of real-time electricity prices from the MISO RTO are utilized as an empirical basis for developing such procedures. The price data show several features, such as irregular seasonal behavior, weekly and …
Normal And Δ-Normal Configurations In Toric Algebra,
2011
Oberlin College
Normal And Δ-Normal Configurations In Toric Algebra, Liam Solus
Honors Papers
Toric algebra is a field of study that lies at the intersection of algebra, geometry, and combinatorics. Thus, the algebraic properties of the toric ideal IA defined by the vector configuration A are often characterizable via the geometric and combinatorial properties of its corresponding toric variety and A, respectively. Here, we focus on the property of normality of A. A normal vector configuration defines the toric ideal of a normal toric variety. However, the definition of normality of A is based entirely on the algebraic structures associated with A without regard to any of its combinatorial properties. In this paper, …
Optimal Summer Camp Layout,
2011
Oberlin College
Optimal Summer Camp Layout, Anthony Bonifonte
Honors Papers
Convex optimization is an important branch of operations research. It generalizes linear programming and offers powerful tools for modelling problems and discovering optimal solutions to real world problems. Mathematically it is an interesting topic because it ties together many branches: linear algebra, multivariable calculus, and numerical analysis, to name a few. Modelling a problem as a convex optimization problem can be challenging but offers many benefits. Algorithm design is critically important to ensure precision of solutions that solve with minimal computation power. From an engineering perspective it is also incredibly useful, since many more situations can be modeled than with …
Equality Of P-Partition Generating Functions,
2011
Bucknell University
Equality Of P-Partition Generating Functions, Ryan Ward
Honors Theses
To every partially ordered set (poset), one can associate a generating function, known as the P-partition generating function. We find necessary conditions and sufficient conditions for two posets to have the same P-partition generating function. We define the notion of a jump sequence for a labeled poset and show that having equal jumpsequences is a necessary condition for generating function equality. We also develop multiple ways of modifying posets that preserve generating function equality. Finally, we are able to give a complete classification of equalities among partially ordered setswith exactly two linear extensions.
A Topological Constructions For All Two-Row Springer Varieties,
2011
University of Richmond
A Topological Constructions For All Two-Row Springer Varieties, Heather M. Russell
Department of Math & Statistics Faculty Publications
Springer varieties appear in both geometric representation theory and knot theory. Motivated by knot theory and categorification, Khovanov provides a topological construction of (m,m) Springer varieties. Here we extend his construction to all two-row Springer varieties. Using the combinatorial and diagrammatic properties of this construction we provide a particularly useful homology basis and construct the Springer representation using this basis. We also provide a skein-theoretic formulation of the representation in this case.
The Jordan Curve Theorem Is Non-Trivial,
2011
University of Richmond
The Jordan Curve Theorem Is Non-Trivial, Fiona Ross, William T. Ross
Department of Math & Statistics Faculty Publications
The formal mathematical definition of a Jordan curve (a non-self-intersecting continuous loop in the plane) is so simple that one is often lead to the unimaginative view that a Jordan curve is nothing more than a circle or an ellipse. In this paper, we pursue the theme that a Jordan curve can be quite fantastical in the sense that there are some bizarre properties such a curve might have (jagged at every point, space filling, etc.) or that such a curve can have a difficult to discover inside and outside as promised by the celebrated Jordan Curve Theorem (JCT). We …
Adjusted Empirical Likelihood Models With Estimating Equations For Accelerated Life Tests,
2011
University of Richmond
Adjusted Empirical Likelihood Models With Estimating Equations For Accelerated Life Tests, Ni Wang, Jye-Chyi Lu, Di Chen, Paul H. Kvam
Department of Math & Statistics Faculty Publications
This article proposes an adjusted empirical likelihood estimation (AMELE) method to model and analyze accelerated life testing data. This approach flexibly and rigorously incorporates distribution assumptions and regression structures by estimating equations within a semiparametric estimation framework. An efficient method is provided to compute the empirical likelihood estimates, and asymptotic properties are studied. Real-life examples and numerical studies demonstrate the advantage of the proposed methodology.
Multi-Cause Degradation Path Model: A Case Study On Rubidium Lamp Degradation,
2011
University of Richmond
Multi-Cause Degradation Path Model: A Case Study On Rubidium Lamp Degradation, Sun Quan, Paul H. Kvam
Department of Math & Statistics Faculty Publications
At the core of satellite rubidium standard clocks is the rubidium lamp, which is a critical piece of equipment in a satellite navigation system. There are many challenges in understanding and improving the reliability of the rubidium lamp, including the extensive lifetime requirement and the dearth of samples available for destructive life tests. Experimenters rely on degradation experiments to assess the lifetime distribution of highly reliable products that seem unlikely to fail under the normal stress conditions, because degradation data can provide extra information about product reliability. Based on recent research on the rubidium lamp, this article presents a multi‐cause …
Inverse Limits With Set Valued Functions,
2011
University of Richmond
Inverse Limits With Set Valued Functions, Van C. Nall
Department of Math & Statistics Faculty Publications
We begin to answer the question of which continua can be homeomorphic to an inverse limit with a single upper semi-continuous bonding map from [O, 1) to 2(O,l). Several continua including (0, 1) x (0, 1) and all compact manifolds with dimension greater than one cannot be homeomorphic to such an inverse limit. It is also shown that if the upper semi-continuous bonding maps have only zero dimensional point values, then the dimension of the inverse limit does not exceed the dimension of the factor spaces.
The Dynamics Of Integrate-And-Fire: Mean Vs. Variance Modulations And Dependence On Baseline Parameters,
2011
University of Richmond
The Dynamics Of Integrate-And-Fire: Mean Vs. Variance Modulations And Dependence On Baseline Parameters, Joanna R. Wares, Todd W. Troyer
Department of Math & Statistics Faculty Publications
The leaky integrate-and-fire (LIF) is the simplest neuron model that captures the essential properties of neuronal signaling. Yet common intuitions are inadequate to explain basic properties of LIF responses to sinusoidal modulations of the input. Here we examine responses to low - and moderate-frequency modulations of both the mean and variance of the input current and quantify how these responses depend on baseline parameters. Across parameters, responses to modulations in the mean current are low pass, approaching zero in the limit of high frequencies. For very low baseline firing rates, the response cutoff frequency matches that expected from membrane integration. …
Springer Representations On The Khovanov Springer Varieties,
2011
University of Richmond
Springer Representations On The Khovanov Springer Varieties, Heather M. Russell, Julianna Tymoczko
Department of Math & Statistics Faculty Publications
Springer varieties are studied because their cohomology carries a natural action of the symmetric group Sn and their top-dimensional cohomology is irreducible. In his work on tangle invariants, Khovanov constructed a family of Springer varieties Xn as subvarieties of the product of spheres (S2)n. We show that if Xn is embedded antipodally in (S2)n then the natural Sn-action on (S2)n induces an Sn-representation on the image of H*(Xn). This representation is the Springer representation. Our construction admits an elementary (and geometrically …
Adjusted Hazard Rate Estimator Based On A Known Censoring Probability,
2011
University of Richmond
Adjusted Hazard Rate Estimator Based On A Known Censoring Probability, Ülkü Gürler, Paul H. Kvam
Department of Math & Statistics Faculty Publications
In most reliability studies involving censoring, one assumes that censoring probabilities are unknown. We derive a nonparametric estimator for the survival function when information regarding censoring frequency is available. The estimator is constructed by adjusting the Nelson–Aalen estimator to incorporate censoring information. Our results indicate significant improvements can be achieved if available information regarding censoring is used. We compare this model to the Koziol–Green model, which is also based on a form of proportional hazards for the lifetime and censoring distributions. Two examples of survival data help to illustrate the differences in the estimation techniques.
An Ethnographic Study Of In-Service And Pre-Service Teacher Collaboration In The Development And Execution Of Mathematics Lessons,
2011
Utah State University
An Ethnographic Study Of In-Service And Pre-Service Teacher Collaboration In The Development And Execution Of Mathematics Lessons, Jessica Munns
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
While much is known about effective strategies for teaching mathematics, less is understood about how to lead new teachers to employ research-based practices in their work. To address this issue we followed a Methods of Teaching Secondary and Middle School Mathematics course at Utah State University where collaboration between inservice and pre-service teachers was emphasized. This report documents examples of the implementation of research-based teaching practices by collaborative groups during the course. The structure of collaboration followed a lesson study model involving research and planning, execution and observation, and reflection and revision of lessons. Preservice and in-service teachers met twice …
Longitudinal Investigation Of The Curricular Effect: An Analysis Of Student Learning Outcomes From The Liecal Project In The United States,
2011
University of Delaware
Longitudinal Investigation Of The Curricular Effect: An Analysis Of Student Learning Outcomes From The Liecal Project In The United States, Jinfa Cai, Ning Wang, John Moyer, Chuang Wang, Bikai Nie
Mathematics, Statistics and Computer Science Faculty Research and Publications
In this article, we present the results from a longitudinal examination of the impact of a Standards-based or reform mathematics curriculum (called CMP) and traditional mathematics curricula (called non-CMP) on students’ learning of algebra using various outcome measures. Findings include the following: (1) students did not sacrifice basic mathematical skills if they are taught using a Standards-based or reform mathematics curriculum like CMP; (2) African American students experienced greater gain in symbol manipulation when they used a traditional curriculum; (3) the use of either the CMP or a non-CMP curriculum improved the mathematics achievement of all students, including …
Probability Theory On Time Scales And Applications To Finance And Inequalities,
2011
Missouri University of Science and Technology
Probability Theory On Time Scales And Applications To Finance And Inequalities, Thomas Matthews
Doctoral Dissertations
"In this dissertation, the recently discovered concept of time scales is applied to probability theory, thus unifying discrete, continuous and many other cases. A short introduction to the theory of time scales is provided. Following this preliminary overview, the moment generating function is derived using a Laplace transformation on time scales. Various unifications of statements and new theorems in statistics are shown. Next, distributions on time scales are defined and their properties are studied. Most of the derived formulas and statements correspond exactly to those from discrete and continuous calculus and extend the applicability to many other cases. Some theorems …
Null Mannheim Curves In The Minkowski 3-Space E_1^3,
2011
TÜBİTAK
Null Mannheim Curves In The Minkowski 3-Space E_1^3, Handan Özteki̇n, Mahmut Ergüt
Turkish Journal of Mathematics
In this study, we give the definition of null Mannheim curve with timelike or spacelike Mannheim partner curve in the Minkowski 3-space E _1^3. We get the necessary and sufficient conditions for the null Mannheim curves. Then we investigate the null and timelike or spacelike generalized helix as the null Mannheim curve and timelike or spacelike Mannheim partner curve, respectively.
Slant Lightlike Submanifolds Of Indefinite Kenmotsu Manifolds,
2011
TÜBİTAK
Slant Lightlike Submanifolds Of Indefinite Kenmotsu Manifolds, Ram Gupta, Sharfuddin Ahamad
Turkish Journal of Mathematics
In this paper, we introduce the notion of a slant lightlike submanifold of an indefinite Kenmotsu manifold. We provide a non-trivial example and obtain necessary and sufficient conditions for the existence of a slant lightlike submanifold. Also, we give an example of a minimal slant lightlike submanifold of R_2^{9} and prove some characterization theorems.
Products Of Multiplication, Composition And Differentiation Between Weighted Bergman-Nevanlinna And Bloch-Type Spaces,
2011
TÜBİTAK
Products Of Multiplication, Composition And Differentiation Between Weighted Bergman-Nevanlinna And Bloch-Type Spaces, Ajay K. Sharma
Turkish Journal of Mathematics
Let \varphi and \psi be holomorphic maps on D such that \varphi ( D ) \subset D . Let C_{\varphi} , M_{\psi} and D be the composition, multiplication and differentiation operators, respectively. In this paper, we consider linear operators induced by products of these operators from Bergman-Nevanlinna spaces A^{\beta}_N to Bloch-type spaces. In fact, we prove that these operators map A^{\beta}_N compactly into Bloch-type spaces if and only if they map A^{\beta}_N boundedly into these spaces.
Some Products Involving The Fourth Greek Letter Family Element \Tilde{\Delta}_S In The Adams Spectral Sequence,
2011
TÜBİTAK
Some Products Involving The Fourth Greek Letter Family Element \Tilde{\Delta}_S In The Adams Spectral Sequence, Xiu-Gui Liu, He Wang
Turkish Journal of Mathematics
Let p be an odd prime and A be the mod p Steenrod algebra. For computing the stable homotopy groups of spheres with the classical Adams spectral sequence, we must compute the E_2-term of the Adams spectral sequence, Ext_A^{\ast,\ast} (Z_p,Z_p). In this paper we prove that in the cohomology of A, the product k_0 h_n \tilde \delta _{s + 4} \in Ext_A^{s + 7, t(s,n) + s} (Z_p, Z_p), is nontrivial for n \geq 5, and trivial for n=3, 4, where \tilde\delta_{s + 4} is actually \tilde\alpha_{s + 4}^{(4)} described by Wang and Zheng, p \geq 11, 0 \leq s < p - 4 and t(s,n)=2(p-1)[(s + 2) + (s + 4)p + (s + 3)p^2 + (s + 4)p^3 + p^n].
Pseudo Pq-Injective Modules,
2011
TÜBİTAK
Pseudo Pq-Injective Modules, Zhanmin Zhu
Turkish Journal of Mathematics
A module M_R is called Pseudo PQ-injective (or PPQ-injective for short) if every monomorphism from a principal submodule of M to M extends to an endomorphism of M. Some characterizations and properties of this class of modules are investigated, PPQ-injective modules with some additional conditions are studied, semisimple artinian rings are characterized by PPQ-injective modules.
