Mathematics Commons^™

Level 17 Ramanujan-Sato Series, Timothy Huber, Daniel Schultz, Dongxi Ye

School of Mathematical & Statistical Sciences Faculty Publications

Two level 17 modular functions r=q2∏n=1∞(1−qn)(n17),s=q2∏n=1∞(1−q17n)3(1−qn)3 are used to construct a new class of Ramanujan–Sato series for 1/π. The expansions are induced by modular identities similar to those level of 5 and 13 appearing in Ramanujan’s Notebooks. A complete list of rational and quadratic series corresponding to singular values of the parameters is derived.

Mathematical Modeling Of Nonlinear Blood Glucose-Insulin Dynamics With Beta Cells Effect, Gabriela Urbina, Daniel N. Riahi, Dambaru Bhatta

School of Mathematical & Statistical Sciences Faculty Publications

We consider mathematical modeling of blood glucose-insulin regulatory system with the additional effect of the secreted insulin by the pancreatic beta cells and in the presence of an external energy input to such system. Such modeling system is investigated to determine the time-dependent nonlinear dynamics that take place by the quantities, which represent the glucose and insulin concentrations in the blood, insulin action as well as in the absence or presence of secreted insulin due to the pancreatic beta cells. Using both analytical and numerical procedures, we determine such quantities versus time for both diabetes patients and normal human and …

Characterizing Quantum Physics Students’ Conceptual And Procedural Knowledge Of The Characteristic Equation, Kaitlyn Stephens Serbin, Brigitte Johana Sánchez Robayo, Julia Victoria Truman, Kevin Lee Watson, Megan Wawro

School of Mathematical & Statistical Sciences Faculty Publications

Research on student understanding of eigentheory in linear algebra has expanded recently, yet few studies address student understanding of the Characteristic Equation. In this study, we explore quantum physics students’ conceptual and procedural knowledge of deriving and using the Characteristic Equation. We developed the Conceptual and Procedural Knowledge framework for classifying the quality of students’ conceptual and procedural knowledge of both deriving and using the Characteristic Equation along a continuum. Most students exhibited deeper conceptual and procedural knowledge of using the Characteristic Equation than of deriving the Characteristic Equation. Furthermore, most students demonstrated deeper procedural knowledge than conceptual knowledge of …

Universal Constraints Of Kleinian Groups And Hyperbolic Geometry, Hala Alaqad

Dissertations

Recent advances in geometry have shown the wide application of hyperbolic geometry not only in Mathematics but also in real-world applications. As in two dimensions, it is now clear that most three-dimensional objects (configuration spaces and manifolds) are modelled on hyperbolic geometry. This point of view explains a great many things from large-scale cosmological phenomena, such as the shape of the universe, right down to the symmetries of groups and geometric objects, and various physical theories. Kleinian groups are basically discrete groups of isometries associated with tessellations of hyperbolic space. They form the fundamental groups of hyperbolic manifolds. Over the …

Structure For Regular Inclusions. Ii Cartan Envelopes, Pseudo-Expectations And Twists, David R. Pitts

Department of Mathematics: Faculty Publications

We introduce the notion of a Cartan envelope for a regular inclusion (C,Ɗ). When a Cartan envelope exists, it is the unique, minimal Cartan pair into which (C,Ɗ) regularly embeds. We prove a Cartan envelope exists if and only if (C,Ɗ) has the unique faithful pseudo-expectation property and also give a characterization of the Cartan envelope using the ideal intersection property.

For any covering inclusion, we construct a Hausdorff twisted groupoid using appropriate linear functionals and we give a description of the Cartan envelope for (C,Ɗ) in terms of a twist …

Expected Resurgence Of Ideals Defining Gorenstein Rings, Eloísa Grifo, Craig Huneke, Vivek Mukundan

Department of Mathematics: Faculty Publications

Building on previous work by the same authors, we show that certain ideals defining Gorenstein rings have expected resurgence, and thus satisfy the stable Harbourne Conjecture. In prime characteristic, we can take any radical ideal defining a Gorenstein ring in a regular ring, provided its symbolic powers are given by saturations with the maximal ideal. While this property is not suitable for reduction to characteristic p, we show that a similar result holds in equicharacteristic 0 under the additional hypothesis that the symbolic Rees algebra of I is noetherian.

At The Interface Of Algebra And Statistics, Tai-Danae Bradley

Dissertations, Theses, and Capstone Projects

This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. The starting point is a passage from classical probability theory to quantum probability theory. The quantum version of a probability distribution is a density operator, the quantum version of marginalizing is an operation called the partial trace, and the quantum version of a marginal probability distribution is a reduced density operator. Every joint probability distribution on a finite set can be modeled as a rank one density operator. By applying the partial trace, we obtain reduced density operators whose diagonals …

Symmetric Rigidity For Circle Endomorphisms With Bounded Geometry And Their Dual Maps, John Adamski

Dissertations, Theses, and Capstone Projects

Let $f$ be a circle endomorphism of degree $d\geq2$ that generates a sequence of Markov partitions that either has bounded nearby geometry and bounded geometry, or else just has bounded geometry, with respect to normalized Lebesgue measure. We define the dual symbolic space $\S^*$ and the dual circle endomorphism $f^*=\tilde{h}\circ f\circ{h}^{-1}$, which is topologically conjugate to $f$. We describe some properties of the topological conjugacy $\tilde{h}$. We also describe an algorithm for generating arbitrary circle endomorphisms $f$ with bounded geometry that preserve Lebesgue measure and their corresponding dual circle endomorphisms $f^*$ as well as the conjugacy $\tilde{h}$, and implement it …

Towards Realism Interpretation Of Wave Mechanics Based On Maxwell Equations In Quaternion Space And Some Implications, Including Smarandache’S Hypothesis, Florentin Smarandache, Victor Christianto, Yunita Umniyati

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Derivable Single Valued Neutrosophic Graphs Based On Km-Fuzzy Metric, Florentin Smarandache, Mohammad Hamidi

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we consider the concept of KM-fuzzy metric spaces and we introduce a novel concept of KM-single valued neutrosophic metric graphs based on KM-fuzzy metric spaces. Then we investigate the finite KM-fuzzy metric spaces with respect to KM-fuzzy metrics and we construct the KMfuzzy metric spaces on any given non-empty sets. We try to extend the concept of KM-fuzzy metric spaces to a larger class of KM-fuzzy metric spaces such as union and product of KM-fuzzy metric spaces and in this regard we investigate the class of products of KM-single valued neutrosophic metric graphs. In the final, we …

Optimal Control Of A Rumor Propagation Model With Different Propagation Degrees In Social Network, Yingfeng Tang

Student Works (2020-2029)

Rumor is a social interaction of information, and its development is of great significance to human beings. In this paper, by studying the D K model and a rumor model spreading with rumor latent period, deduces the rumor model with differe nt propagation degrees of the spreaders. The two equilibrium points in the system are found through derivation. In real life, enterprises often ignore the reasonable planning of the cost of rumor control. By means of public education and media technology u sing by the authorities to debunk rumors, an optimal control problem i s established. The Pontryagin’s maximum principle …

Pemahaman Ungkapan Algebra Dalam Kalangan Murid Tingkatan Dua, Hamid Azizah

Student Works (2020-2029)

Pemahaman tentang konsep ungkapan algebra penting bagi murid sekolah menengah kerana ia merupakan asas kepada pembelajaran matematik di peringkat menengah dan peringkat pengajian tinggi memandangkan kesukaran dalam pembelajaran algebra menjadi semakin kritikal. Kajian ini adalah untuk mengenal pasti pemahaman murid Tingkatan Dua tentang ungkapan algebra dengan berlandaskan konstruktivisme radikal. Penyelidikan ini menggunakan kajian kes sebagai reka bentuk kajian, yang membabitkan data berbentuk kualitatif. Peserta kajian membabitkan enam murid dari tiga kategori pencapaian akademik dengan menggunakan teknik persampelan bertujuan. Data kajian terkumpul melalui tiga sesi temu duga klinikal dengan menggunakan perakam video, catatan murid dan pengkaji. Data kajian dianalisis dengan menggunakan …

Pemahaman Murid Tingkatan Lima Tentang Konsep Dalam Topik Janjang Aritmetik, Edwar Siti Zaharah

Student Works (2020-2029)

Janjang Aritmetik merupakan tajuk yang sangat penting bagi murid Tingkatan Lima yang mengambil matapelajaran elektif Matematik Tambahan. Tujuan kajian ini dijalankan adalah untuk mengetahui pemahaman murid Tingkatan Lima tentang konsep dalam topik janjang aritmetik. Seramai empat orang murid Tingkatan Lima dipilih dalam kajian ini menggunakan kaedah persampelan bertujuan. Mereka belajar di sebuah sekolah menengah di Selangor. Kajian ini dijalankan berlandaskan teori konstruktivisme radikal. Kajian kes digunakan bagi mengumpulkan data melalui empat sesi temu bual klinikal yang melibatkan gambaran mental, perwakilan, makna dan penyelesaian masalah. Setiap sesi temu duga dirakam dengan alat perakam video. Data kajian dalam bentuk jawapan bertulis dan …

Realizations Of Holomorphic And Slice Hyperholomorphic Functions: The Krein Space Case, Daniel Alpay, Fabrizio Colombo, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we treat realization results for operator-valued functions which are analytic in the complex sense or slice hyperholomorphic over the quaternions. In the complex setting, we prove a realization theorem for an operator-valued function analytic in a neighborhood of the origin with a coisometric state space operator thus generalizing an analogous result in the unitary case. A main difference with previous works is the use of reproducing kernel Krein spaces. We then prove the counterpart of this result in the quaternionic setting. The present work is the first paper which presents a realization theorem with a state space …

Data Assimilation For Conductance-Based Neuronal Models, Matthew Moye

Dissertations

This dissertation illustrates the use of data assimilation algorithms to estimate unobserved variables and unknown parameters of conductance-based neuronal models. Modern data assimilation (DA) techniques are widely used in climate science and weather prediction, but have only recently begun to be applied in neuroscience. The two main classes of DA techniques are sequential methods and variational methods. Throughout this work, twin experiments, where the data is synthetically generated from output of the model, are used to validate use of these techniques for conductance-based models observing only the voltage trace. In Chapter 1, these techniques are described in detail and the …

Analysis Of Gameplay Strategies In Hearthstone: A Data Science Approach, Connor W. Watson

Theses

In recent years, games have been a popular test bed for AI research, and the presence of Collectible Card Games (CCGs) in that space is still increasing. One such CCG for both competitive/casual play and AI research is Hearthstone, a two-player adversarial game where players seeks to implement one of several gameplay strategies to defeat their opponent and decrease all of their Health points to zero. Although some open source simulators exist, some of their methodologies for simulated agents create opponents with a relatively low skill level. Using evolutionary algorithms, this thesis seeks to evolve agents with a higher skill …

Price Vs Quantity: Essays On Strategic Choice In Differentiated Oligopoly., Arindam Paul Dr.

Doctoral Theses

Industrial economists are often interested in comparing different market structures which are primarily based on their market outcomes and then try to determine the best market structure considering either the society’s welfare or the firm’s profit and sometimes considering both. In this context, the "Cournot-Bertrand comparison" is one such important comparison that has often been analyzed in the literature of industrial economics. The main structural difference between Cournot competition and Bertrand competition arises due to the strategic variable through which firms interact with each other in the market. To be more specific, in case of Cournot competition, firms compete with …

Acoustic Versus Electromagnetic Field Theory: Scalar, Vector, Spinor Representations And The Emergence Of Acoustic Spin, Lucas Burns, Konstantin Y. Bliokh, Franco Nori, Justin Dressel

Mathematics, Physics, and Computer Science Faculty Articles and Research

We construct a novel Lagrangian representation of acoustic field theory that describes the local vector properties of longitudinal (curl-free) acoustic fields. In particular, this approach accounts for the recently-discovered nonzero spin angular momentum density in inhomogeneous sound fields in fluids or gases. The traditional acoustic Lagrangian representation with a scalar potential is unable to describe such vector properties of acoustic fields adequately, which are however observable via local radiation forces and torques on small probe particles. By introducing a displacement vector potential analogous to the electromagnetic vector potential, we derive the appropriate canonical momentum and spin densities as conserved Noether …

Radio Graceful Labelling Of Graphs, Laxman Saha, Alamgir Rahaman Basunia

Theory & Applications of Graphs

Radio labelling problem of graphs have their roots in communication problem known as Channel Assignment Problem. For a simple connected graph G=(V(G), E(G)), a radio labeling is a mapping f : V(G) →{0,1,2,…} such that |f(u)-f(v)|≥ diam(G)+1-d(u,v) for each pair of distinct vertices u,v ∈ V(G), where diam(G) is the diameter of G and d(u,v) is the distance between u and v. A radio labeling f of a graph G is a radio graceful labeling of G if f(V(G)) = {0,1,… |V(G)|-1}. A graph for which a radio graceful labeling exists is called radio graceful. …

"Fireworks And Quadratic Functions”, Kelly W. Remijan

Teacher Resources

No abstract provided.