Computer Monitored Problem Solving Dialogues,
2011
Valparaiso University
Computer Monitored Problem Solving Dialogues, Lisa Dion, Jeremy Jank, Nicole Rutt
Symposium on Research and Creative Expression (SORCE)
This project looks over the shoulder at students collaboratively engaged in a math problem-solving activity. One task we looked at was mechanically classifying the students current activity or knowledge state, of which we have identified 15 different categories. We have produced an automatic classifier that examines student sentences and is 55% accurate in identifying utterances as containing certain bits of knowledge or evidence of certain activities. The classifier was built from a corpus of student-written reports. Treating each sentence as a bag of words, we built vector space models of the word co-occurrence matrix using both non-negative matrix factorization (NMF) …
Non-Contiguous Pattern Avoidance In Binary Trees,
2011
Valparaiso University
Non-Contiguous Pattern Avoidance In Binary Trees, Michael Dairyko, Samantha Tyner, Casey Wynn
Symposium on Research and Creative Expression (SORCE)
We consider the enumeration of binary trees avoiding non-contiguous binary tree patterns. We begin by modifying a known algorithm that counts binary trees avoiding a single contiguous tree pattern. Next, we use this algorithm to prove several theorems about the generating function whose nth coefficient gives the number of n-leaf trees avoiding a pattern. In addition, we investigate and structurally explain the recurrences that arise from these generating functions. Finally, we examine the enumeration of binary trees avoiding multiple tree patterns.
Modeling Infectious Diseases : Two Strain Diseases In Metapopulations,
2011
Valparaiso University
Modeling Infectious Diseases : Two Strain Diseases In Metapopulations, Daniel Rossi, Sydney Philipps, Rachel Vonarb
Symposium on Research and Creative Expression (SORCE)
Infectious diseases often mutate and are carried between regions. We consider a mathematical model which begins to account for these factors. We assume two disjoint populations that only occasionally comingle, and two strains of a disease present in these populations. Of interest are the equations describing the dynamics of this system, the conditions under which epidemics will occur, and the long term behavior of the system under various initial conditions. We find that in many ways this system is similar to a simpler one-population model. However, we find evidence that there may be conditions under which both disease strains can …
Properties Of Rd-Projective And Rd-Injective Modules,
2011
TÜBİTAK
Properties Of Rd-Projective And Rd-Injective Modules, Lixin Mao
Turkish Journal of Mathematics
In this paper, we first study RD-projective and RD-injective modules using, among other things, covers and envelopes. Some new characterizations for them are obtained. Then we introduce the RD-projective and RD-injective dimensions for modules and rings. The relations between the RD-homological dimensions and other homological dimensions are also investigated.
Krull Dimension Of Types In A Class Of First-Order Theories,
2011
TÜBİTAK
Krull Dimension Of Types In A Class Of First-Order Theories, Domenico Zambella
Turkish Journal of Mathematics
We study a class of first-order theories whose complete quantifier-free types with one free variable either have a trivial positive part or are isolated by a positive quantifier-free formula---plus a few other technical requirements. The theory of vector spaces and the theory fields are examples. We prove the amalgamation property and the existence of a model-companion. We show that the model-companion is strongly minimal. We also prove that the length of any increasing sequence of prime types is bounded, so every formula has finite Krull dimension.
Some Properties Of Associate And Presimplifiable Rings,
2011
TÜBİTAK
Some Properties Of Associate And Presimplifiable Rings, Manal Ghanem
Turkish Journal of Mathematics
In this paper we study some properties of associate and presimplifiable rings. We give a characterization of the associate (resp., domainlike) pullback P of R_1 \rightarrow{R_3} \leftarrow{R_2}, where R_1 and R_2 are two presimplifiable (resp., domainlike) rings. We prove that R is presimplifiable ring if and only if the factor ring R/{nil(R)} is presimplifiable and the ideal nil(R) is presimplifiable. Then we investigate the associate and presimplifiable property of the dual rings {R[x]/\langle{x^2}\rangle} and its modules through the base ring R and its modules.
Module Classes And The Lifting Property,
2011
TÜBİTAK
Module Classes And The Lifting Property, Muhammet Tamer Koşan
Turkish Journal of Mathematics
Let R be a ring. A collection of R-modules containing the zero module and closed under isomorphisms will be denoted by X. An R-module M is said to be X-lifting if for every X-submodule N of M there exists A \leq N such that M=A \oplus B and N \cap B is small in B [11]. In the present paper, we consider the question: Can we characterize X-lifting modules via objects of the class X?
A Fredholm Alternative-Like Result On Power Bounded Operators,
2011
TÜBİTAK
A Fredholm Alternative-Like Result On Power Bounded Operators, Ali̇ Ülger, Onur Yavuz
Turkish Journal of Mathematics
Let X be a complex Banach space and T:X\rightarrow X be a power bounded operator, i.e., \sup_{n \geq 0}\ T^n\
A Beurling-Type Theorem In Bergman Spaces,
2011
TÜBİTAK
A Beurling-Type Theorem In Bergman Spaces, Ali Abkar
Turkish Journal of Mathematics
It is known that Beurling's theorem concerning invariant subspaces is not true in the Bergman space (in contrast to the Hardy space case). However, Aleman, Richter, and Sundberg proved that every cyclic invariant subspace in the Bergman space \lpad, 0
Universal Inequalities And Bounds For Weighted Eigenvalues Of The Schrödinger Operator On The Heisenberg Group,
2011
TÜBİTAK
Universal Inequalities And Bounds For Weighted Eigenvalues Of The Schrödinger Operator On The Heisenberg Group, Hejun Sun
Turkish Journal of Mathematics
For a bounded domain \Omega in the Heisenberg group H^n, we investigate the Dirichlet weighted eigenvalue problem of the Schrödinger operator - \Delta_{H^n} +V, where \Delta_{H^n} is the Kohn Laplacian and V is a nonnegative potential. We establish a Yang-type inequality for eigenvalues of this problem. It contains the sharpest result for \Delta_{H^n} in [17] of Soufi, Harrel II and Ilias. Some estimates for upper bounds of higher order eigenvalues and the gaps of any two consecutive eigenvalues are also derived. Our results are related to some previous results for the Laplacian \Delta and the Schrödinger operator -\Delta+V on a …
Hypersurfaces With Constant Mean Curvature In A Real Space Form,
2011
TÜBİTAK
Hypersurfaces With Constant Mean Curvature In A Real Space Form, Shichang Shu, Sanyang Liu
Turkish Journal of Mathematics
Let M^n be an n\(n \geq 3)-dimensional complete connected and oriented hypersurface in M^{n+1}(c)(c \geq 0) with constant mean curvature H and with two distinct principal curvatures, one of which is simple. We show that (1) if c=1 and the squared norm of the second fundamental form of M^n satisfies a rigidity condition (1.3), then M^n is isometric to the Riemannian product S^1(\sqrt{1-a^2}) \times S^{n-1}(a); (2) if c=0, H \neq 0 and the squared norm of the second fundamental form of M^n satisfies S \geq n^2H^2/(n-1), then M^n is isometric to the Riemannian product S^{n-1}(a)\times R or S^1(a) \times R^{n-1}
On Generalized Witt Algebras In One Variable,
2011
TÜBİTAK
On Generalized Witt Algebras In One Variable, Ki Bong Nam, Jonathan Pakianathan
Turkish Journal of Mathematics
We study a class of infinite dimensional Lie algebras called generalized Witt algebras (in one variable). These include the classical Witt algebra and the centerless Virasoro algebra as important examples. We show that any such generalized Witt algebra is a semisimple, indecomposable Lie algebra which does not contain any abelian Lie subalgebras of dimension greater than one. We develop an invariant of these generalized Witt algebras called the spectrum, and use it to show that there exist infinite families of nonisomorphic, simple, generalized Witt algebras and infinite families of nonisomorphic, nonsimple, generalized Witt algebras. We develop a machinery that can …
On The Uniqueness Of Strongly Flat Covers Of Cyclic Acts,
2011
TÜBİTAK
On The Uniqueness Of Strongly Flat Covers Of Cyclic Acts, Majid Ershad, Roghaieh Khosravi
Turkish Journal of Mathematics
In [1], strongly flat covers of cyclic acts are discussed and it is asked if strongly flat covers are unique. From this point of view, in this paper we give numerous classes of monoids over which strongly flat covers of cyclic acts are unique.
Weingarten Quadric Surfaces In A Euclidean 3-Space,
2011
TÜBİTAK
Weingarten Quadric Surfaces In A Euclidean 3-Space, Min Hee Kim, Dae Won Yoon
Turkish Journal of Mathematics
In this paper, we study quadric surfaces in a Euclidean 3-space. Furthermore, we classify quadric surfaces in a Euclidean 3-space in terms of the Gaussian curvature and the mean curvature.
Covers And Envelopes With Respect To A Semidualizing Module,
2011
TÜBİTAK
Covers And Envelopes With Respect To A Semidualizing Module, Xiaoguang Yan, Xiaosheng Zhu
Turkish Journal of Mathematics
Let R be a commutative ring and C be a semidualizing R-module. For a given class of R-modules Q, we define a class Q_C by M \in Q_C \Leftrightarrow Hom_R(C,M) \in Q. We prove that if Q \subseteq (R) is a Kaplansky class and closed under direct sums, then Q_C^{\bot} is special preenveloping. As corollaries, we can show that p_C^{n \bot} and f_C^{n \bot} are both special preenveloping. Finally, we show that I_C^n is covering, I_C^{n \bot} is enveloping and special preenveloping provided R is Noetherian.
Some Results On G-Frames In Hilbert Spaces,
2011
TÜBİTAK
Some Results On G-Frames In Hilbert Spaces, Abdolaziz Abdollahi, Elham Rahimi
Turkish Journal of Mathematics
In this paper we show that every g-frame for a Hilbert space H can be represented as a linear combination of two g-orthonormal bases if and only if it is a g-Riesz basis. We also show that every g-frame can be written as a sum of two tight g-frames with g-frame bounds one or a sum of a g-orthonormal basis and a g-Riesz basis for H. We further give necessary and sufficient conditions on g-Bessel sequences {\Lambda_i \in L (H,H_i) : i \in J} and {\Gamma_i \in L(H,H_i): i \in J} and operators L_1, L_2 on H so that {\Lambda_iL_1+\Gamma_iL_2: …
Conjugate Convolution And Characterizations Of Inner Amenable Locally Compact Groups,
2011
TÜBİTAK
Conjugate Convolution And Characterizations Of Inner Amenable Locally Compact Groups, Bahram Mohammadzadeh
Turkish Journal of Mathematics
For locally compact group G, we give some characterizations of inner amenability of G by conjugate convolution operations. Moreover, we study multiples of positive elements in group algebra L^1(G), whenever G is inner amenable.
An Exploration Of Modeling Techniques For The Study Of The Dynamics Of E-Mail Viruses,
2011
Montclair State University
An Exploration Of Modeling Techniques For The Study Of The Dynamics Of E-Mail Viruses, Karin Weule
Theses, Dissertations and Culminating Projects
We analyze real data sets from two e-mail viruses, the Magistr.b and the Sircam.a to explore how we can use mathematical models to predict the behavior described by the data. Analysis of the data is conducted primarily with computer programming in MatLab. We focus mainly on the use of two continuous models commonly used in the study of biological diseases, the SIS and the SIR models. A discrete modeling approach using agent-based simulations is also explored and revealed to be potentially useful in developing a compartmentalized model that incorporates both SIS and SIR model behavior. The theory behind the continuous …
Providing Preservice Teachers With Worthwhile Field-Based Experiences In Mathematics,
2011
University of Northern Iowa
Providing Preservice Teachers With Worthwhile Field-Based Experiences In Mathematics, Glenn Nelson
Faculty Work
Providing preservice teachers with worthwhile field-based experiences is recognized as an important component in their development as good teachers. Because mathematics instruction in general has moved from a teacher-directed, procedurally-focused process to a more student-centered, conceptually-oriented approach, preservice mathematics education classes – especially methods courses - should reflect this shift as well. Field-based opportunities can be instances for preservice teachers to personally experience such a shift to real-world relevance.
On Lower Bounds Of The Chung-Diaconis-Graham Random Process,
2011
University at Albany, State University of New York
On Lower Bounds Of The Chung-Diaconis-Graham Random Process, Richard Eugene Neville
Legacy Theses & Dissertations (2009 - 2024)
Chung, Diaconis, and Graham considered random processes of the form X_(n+1)=(a_n)X_n+b_n (mod p) where p is odd, X_0=0, b_n are i.i.d. for n=0,1,2,... with P(b_n=0)=P(b_n=1)=P(b_n=-1)=1/3, and a_n=2 always. Later, Hildebrand was able to establish a lower bound for this process as p approaches infinity. This paper will prove the following conclusions on lower bounds of the Chung-Diaconis-Graham random process:
