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Articles 2821 - 2850 of 27237
Full-Text Articles in Entire DC Network
Recreational Mathematics: Where Is The Error?, Florentin Smarandache
Recreational Mathematics: Where Is The Error?, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
This short note is a funny problem for the trigonometry students!.
Soft Sets Extensions Used In Bioinformatics, Florentin Smarandache, Daniela Gifu
Soft Sets Extensions Used In Bioinformatics, Florentin Smarandache, Daniela Gifu
Branch Mathematics and Statistics Faculty and Staff Publications
This comprehensive review delves into the intricate realm of Soft Sets and their extensions, including HyperSoft Set, IndetermSoft Set, IndetermHyperSoft Set, and TreeSoft Set, within the context of biomedical data analysis. Soft Sets serve as a foundational framework for managing the inherent uncertainty and imprecision inherent in biological data, thereby facilitating informed decision-making and knowledge discovery. The exploration of Soft Set Products, particularly in the context of multiple soft sets, underscores their pivotal role in advancing biomedical research. By extending these concepts to HyperSoft Sets, researchers can unlock deeper insights into complex biological phenomena, enabling more accurate predictions and classification.
Logical Pluralism And Neutrosophy: Reflections On The Nature Of Truth, Florentin Smarandache
Logical Pluralism And Neutrosophy: Reflections On The Nature Of Truth, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
The article explores the shift from classical binary logic (true and false) to a more complex landscape of logical frameworks. It introduces logical pluralism, which suggests that no single, universally accepted system of logic exists. The paper connects this idea to neutrosophy, a framework that extends fuzzy logic by incorporating a third value: indeterminacy. This triadic approach, where every proposition has a degree of truth (T), falsity (F), and indeterminacy (I), is particularly useful for managing incomplete or contradictory information. The author argues that different logical systems, like different tools, are suited for different problems, and that the …
The Deep Bsde Method, Daniel Kovach
The Deep Bsde Method, Daniel Kovach
Masters Theses
"The curse of dimensionality is the non-linear growth in computing time as the dimension of a problem increases. Using the Deep Backwards Stochastic Differential Equation (Deep BSDE) method developed in [HJE18], I approximate the solution at an initial time to a one-dimensional diffusion equation. Although we only approximate a one-dimensional equation, this method extends well to higher dimensions because it overcomes the curse of dimensionality by evaluating the given partial differential equation along "random characteristics''. In addition to the implementation, I also present most of the mathematical theory needed to understand this method"-- Abstract, p. iii
The Exponential Function In Discrete Fractional Calculus Under The Delta Operator, Brayton James Link
The Exponential Function In Discrete Fractional Calculus Under The Delta Operator, Brayton James Link
Masters Theses
"Previously the exponential problem in discrete fractional calculus under the nabla operator was solved with the discrete Mittag--Leffler function. We now show the solution to the exponential problem in discrete fractional calculus under the delta operator, providing multiple derivations of the solution with recursion and Laplace transforms. We also share some computational and numerical results of experiments with different orders of difference to display the nature of the solution" -- Abstract, p. iii
Symmetries And Integrable Systems, Sen-Yue Lou, Bao-Feng Feng
Symmetries And Integrable Systems, Sen-Yue Lou, Bao-Feng Feng
School of Mathematical & Statistical Sciences Faculty Publications
Symmetry plays key roles in modern physics especially in the study of integrable systems because of the existence of infinitely many local and nonlocal generalized symmetries. In addition to the fundamental role to find exact group invariant solutions via Lie point symmetries, some important new developments on symmetries and conservation laws are reviewed. The recursion operator method is important to find infinitely many local and nonlocal symmetries of (1+1)-dimensional integrable systems. In this paper, it is pointed out that a recursion operator may be obtained from one key symmetry, say, a residual symmetry. For (2+1)-dimensional integrable systems, the master-symmetry approach …
Structure Of Fine Selmer Groups In Abelian P-Adic Lie Extensions, Debanjana Kundu, Filippo Alberto Edoardo Nuccio Mortarino Majno Di Capriglio, Sujatha Ramdorai
Structure Of Fine Selmer Groups In Abelian P-Adic Lie Extensions, Debanjana Kundu, Filippo Alberto Edoardo Nuccio Mortarino Majno Di Capriglio, Sujatha Ramdorai
School of Mathematical & Statistical Sciences Faculty Publications
This paper studies fine Selmer groups of elliptic curves in abelian p -adic Lie extensions. A class of elliptic curves are provided where both the Selmer group and the fine Selmer group are trivial in the cyclotomic Z p -extension. The fine Selmer groups of elliptic curves with complex multiplication are shown to be pseudonull over the trivializing extension in some new cases. Finally, a relationship between the structure of the fine Selmer group for some CM elliptic curves and the Generalized Greenberg's Conjecture is clarified.
Optimizing Energy Consumption In Smart Homes Using Ga-Lstm, Akibor Junior Chukwuka, Bakare-Bolaji Moyosoreoluwa, Baboucarr Dibba
Optimizing Energy Consumption In Smart Homes Using Ga-Lstm, Akibor Junior Chukwuka, Bakare-Bolaji Moyosoreoluwa, Baboucarr Dibba
School of Mathematical & Statistical Sciences Faculty Publications
The need to optimize energy consumption arises from the inadequate energy supply many homes face. However, to optimize energy consumption in a home, one must be equipped with the knowledge of the energy consumption rate and energy supply rate in the home. This paper proposed the use of a Long Short-Term Memory (LSTM) model optimized by Genetic Algorithm (GA) to optimize the energy consumption in a smart home. The model was designed using 8 input variables, which were observed weather information of a given region over a span of 350 days. The data set was split into a training data …
Investigating Preservice Teachers’ Conceptualizations Of Mathematical Knowledge For Teaching Through Video Analysis, Bima Sapkota
Investigating Preservice Teachers’ Conceptualizations Of Mathematical Knowledge For Teaching Through Video Analysis, Bima Sapkota
School of Mathematical & Statistical Sciences Faculty Publications
Mathematics Preservice Teachers’ (M-PSTs) conceptions of Mathematical Knowledge for Teaching (MKT) enhance their reflective skills because they utilize such conceptions to reflect on how to contextualize content knowledge during secondary mathematics teaching. While previous studies suggested M-PSTs develop MKT, including pedagogical content knowledge by analyzing teaching in video lessons, how M-PSTs enhance their conceptions of MKT through such analysis is underexplored. I used a collective case study approach to investigate how four secondary M-PSTs conceptualized MKT when they analyzed and discussed teaching represented in a video lesson using the MKT framework. The findings indicated that the M-PSTs often described teacher …
Self-Exciting Point Processes In Real Estate, Ian Fraser
Self-Exciting Point Processes In Real Estate, Ian Fraser
Theses and Dissertations (Comprehensive)
This thesis introduces a novel approach to analyzing residential property sales through the lens of stochastic processes by employing point processes. Herein, property sales are treated as point patterns, using self-exciting point process models and a variety of statistical tools to uncover underlying patterns in the data. Key findings include the identification and explanation of clustering in both space and time, and the efficacy of a temporal Hawkes process with a sinusoidal background in predicting home sale occurrences. The temporal analysis starts by employing the state of art techniques for time series data like regression, autoregressive, and autoregressive integrated moving …
The Atiyah-Hitchin-Singer Theorem And An 8-Dimensional Generalization, Timothy Ponepal
The Atiyah-Hitchin-Singer Theorem And An 8-Dimensional Generalization, Timothy Ponepal
Theses and Dissertations (Comprehensive)
The Atiyah-Hitchin-Singer theorem states that the twistor almost complex structure on a certain S2 bundle over an oriented Riemannian 4-manifold (M, g) is integrable if and only if the Weyl curvature tensor of g is self-dual. These ideas were developed by Roger Penrose connecting 4-dimensional Riemannian geometry with complex geometry. We present a new approach to the Atiyah-Hitchin-Singer theorem using horizontal lifts and their respective flows, cross products and the quaternions to show that the Nijenhuis tensor vanishes if and only if the Weyl curvature tensor of g is anti-self-dual. An eight dimensional generalization is presented when the …
Recoloring In Hereditary Graph Classes: Structure And Decomposition, Manoj Belavadi
Recoloring In Hereditary Graph Classes: Structure And Decomposition, Manoj Belavadi
Theses and Dissertations (Comprehensive)
In this thesis we study reconfiguration problems in graph theory. A reconfiguration problem is generally defined on the solution space of a problem for which a configuration can be defined as a feasible solution, for example, a coloring of a graph. In Chapters 1 through 4 we study the reconfiguration of vertex colorings. The reconfiguration graph of the k-colorings, denoted Rk(G), is the graph whose vertices are the k-colorings of G and two colorings are adjacent in Rk(G) if they differ on exactly one vertex. The basic question investigated here …
Key Factor Analysis For Base Patterns In Minibridge By Reinforcement Learning, Thanathat Dechakulkamjorn
Key Factor Analysis For Base Patterns In Minibridge By Reinforcement Learning, Thanathat Dechakulkamjorn
Chulalongkorn University Theses and Dissertations (Chula ETD)
No abstract provided.
Specifying The Desired Attributes Of Solutions To Vehicle Routing Problems With Time Windows Using Machine Learning, Teerapong Chaochanglek
Specifying The Desired Attributes Of Solutions To Vehicle Routing Problems With Time Windows Using Machine Learning, Teerapong Chaochanglek
Chulalongkorn University Theses and Dissertations (Chula ETD)
A vehicle routing problem with time windows (VRPTW) has been studied widely in the literature. Most effective methods to find a solution are still heuristics, which are constructed from the inventor’s ideas of how a good solution should be obtained, and their efficiency is quantified only by empirical data. However, these ideas may or may not yield a near-optimal solution. It would be better if we can identify some characteristics of a solution to VRPTW to help guide the heuristic in the right direction. Arnold and Sörensen had proposed a statistical learning model to determine a characteristic of a near-optimal …
Simulation Of Optimal Control Of Vaccination For Svihr Covid-19 Epidemic Model, Kantanop Yimfan
Simulation Of Optimal Control Of Vaccination For Svihr Covid-19 Epidemic Model, Kantanop Yimfan
Chulalongkorn University Theses and Dissertations (Chula ETD)
Infectious disease modeling plays a crucial role in understanding and managing epidemic outbreaks. Mathematical models, combined with control strategies, can help guide effective interventions and policy making. In this study, we examined an epidemic model, so-called SV IHR, which is an extended SIR model with additional states to incorporate vaccination and treatment. Our goal is to determine parameters known as controls; specifically, the vaccination proportion, through the framework of the optimal control problems. We defined an objective function and explored the control strategies that optimize it. Numerical simulations were then performed to illustrate the dynamics of the epidemic both with …
Boundaries Of Overlapping Isosceles Triangles, Kirati Sriamorn
Boundaries Of Overlapping Isosceles Triangles, Kirati Sriamorn
Chulalongkorn University Theses and Dissertations (Chula ETD)
No abstract provided.
Rupert Property Of Some Solids In Higher Dimensions, Pongbunthit Tonpho
Rupert Property Of Some Solids In Higher Dimensions, Pongbunthit Tonpho
Chulalongkorn University Theses and Dissertations (Chula ETD)
We say that a solidS has the Rupert property if a hole could be cut into one copy of S so that another copy of S can be passed through this hole. In recent years, many solids in R$ have been shown to have the Rupert property. However, not much is known about the Rupert property in higher dimensions. This dissertation investigates the Rupert property for some solids in R". We introduce lemmas that help to verify this property. In particular, we prove that some particular n-simplices, the generalized n-octahedrons/and the two-way cones in In have the Rupert property.
Certain Incident Matrices For Lines Intersecting On Plane, Anawin Chongaumklang
Certain Incident Matrices For Lines Intersecting On Plane, Anawin Chongaumklang
Chulalongkorn University Theses and Dissertations (Chula ETD)
This work studies arrangements of lines on the plane, focusing on Fourier’s 17 lines problem, which involves constructing 101 intersection points with 17 lines. We use code notation and incident matrices to classify possible configurations and develop algorithms to determine which codes are drawable. Special attention is given to the role of multiple points and parallel families in these arrangements. Out of 924 possible codes, 658 are confirmed drawable using a combination of theoretical analysis and computer verification. For the remaining cases, new lemmas are proposed to construct additional intersection points. Our findings offer both theoretical insights and practical algorithms …
Splitness Of The Characteristic Polynomial Of 2×2 Normal Matrices Over A Finite Field, Sarawut Therdchanthuk
Splitness Of The Characteristic Polynomial Of 2×2 Normal Matrices Over A Finite Field, Sarawut Therdchanthuk
Chulalongkorn University Theses and Dissertations (Chula ETD)
เราได้ทฤษฎีบทสเปกตรัมสำหรับเมทริกซ์ขนาด 2x2 เหนือฟีลด์จำกัดที่มีลักษณะเฉพาะเท่ากับ 2 โดยการตรวจสอบการแตกตัวของพหุนามลักษณะเฉพาะเหนือฟีลด์ดังกล่าว ซึ่งใช้ข้อเท็จจริงเสริมบางประการเกี่ยวกับพหุนามกำลังสองและเมทริกซ์เหนือฟีลด์ดังกล่าว พหุนามลักษณะเฉพาะจะสะท้อนให้เห็นถึงรูปแบบบัญญัติของเมทริกซ์เหล่านี้ เป็นผลให้สามารถแยกชั้นความคล้ายของเมทริกซ์ปรกติได้ และสำหรับเมทริกซ์ปรกติที่แปลงเป็นทแยงมุมได้ เราให้ข้อความที่สมมูลกับการทำให้เป็นเมทริกซ์ที่แปลงเป็นทแยงมุมแบบยูนิแทรีได้
Developing Test Statistics For Familial Dna Searches Through Multinomial Logistic Regression Model, Akaraphon Jantaraphum
Developing Test Statistics For Familial Dna Searches Through Multinomial Logistic Regression Model, Akaraphon Jantaraphum
Chulalongkorn University Theses and Dissertations (Chula ETD)
In hypothesis testing for familial DNA searches, the likelihood ratio (LR) is a commonly used statistic that requires allele frequency distributions. However, since the population background of a forensic sample is generally unknown, the appropriate allele frequency distribution is uncertain. To address this issue, various LR-based methods—such as those using local allele frequencies (LRLAF), or selecting maximum, minimum, or average LRs (LRMAX, LRMIN, LRAVG), and Naive Bayes classification (LRNB)—have been developed. In this study, we introduce a family of LR-based statistics incorporating multinomial logistic regression classification (LRMLR). DNA samples are classified into subpopulations using multinomial logistic regression, and the likelihood …
Two-Step-Change Pivot Rule For Simplex Method, Rawit Chaiareekij
Two-Step-Change Pivot Rule For Simplex Method, Rawit Chaiareekij
Chulalongkorn University Theses and Dissertations (Chula ETD)
The simplex method is a fundamental method for solving linear programming problems proposed by George B. Dantzig in 1963. The simplex method’s efficiency hinges on the choice of the entering variable, determined by the pivot rule. Dantzig’s original pivot rule, while effective in many cases, can exhibit exponential behavior on certain problems. To address this problem, this thesis proposes a new pivot rule for the simplex method, called the two-step-change pivot rule. The idea is to obtain the two-step-change improvement from the objective value by computing the direction of change for each entering variable to determine the cost per unit. …
Closed-Form Formulas For Conditional Moments Of Stochastic Volatility Markovswitching Model And Applications, Supavit Kiatteerarat
Closed-Form Formulas For Conditional Moments Of Stochastic Volatility Markovswitching Model And Applications, Supavit Kiatteerarat
Chulalongkorn University Theses and Dissertations (Chula ETD)
In the present day, the regime-switching model plays a crucial role in the financial world. This thesis studies a stochastic volatility model with regime switching, specifically examining a Markovian regime-switching process known as Cox-Ingersoll-Ross. Analytical formulas for the conditional moment generation function of the process are developed, presenting both a linearly closed-form and an exponentially closed-form. The formulas are derived by solving a partial differential equation (PDE) that obtains the Feynman-Kac Theorem. We also present the relationship between these two closed-forms, demonstrated by using the formula by Faà Bruno. Additionally, a numerical validation, the Monte Carlo method, is employed to …
Creating A Positive Learning Environment: Preliminary Results, Kien H. Lim, Hilda Y. Sotelo
Creating A Positive Learning Environment: Preliminary Results, Kien H. Lim, Hilda Y. Sotelo
Departmental Papers (Math)
No abstract provided.
Continuous-Variable Quantum Computation Of The O(3) Model In 1+1 Dimensions, Raghav G. Jha, Felix Ringer, George Siopsis, Shane Thompson
Continuous-Variable Quantum Computation Of The O(3) Model In 1+1 Dimensions, Raghav G. Jha, Felix Ringer, George Siopsis, Shane Thompson
Physics Faculty Publications
We formulate the O(3) nonlinear sigma model in 1+1 dimensions as a limit of a three-component scalar field theory restricted to the unit sphere in the large squeezing limit. This allows us to describe the model in terms of the continuous-variable (CV) approach to quantum computing. We construct the ground state and excited states using the coupled-cluster Ansatz and find excellent agreement with the exact diagonalization results for a small number of lattice sites. We then present the simulation protocol for the time evolution of the model using CV gates and obtain numerical results using a photonic quantum simulator. We …
Integrable Symplectic Maps With A Polygon Tessellation, T. Zolkin, Y. Kharkov, S. Nagaitsev
Integrable Symplectic Maps With A Polygon Tessellation, T. Zolkin, Y. Kharkov, S. Nagaitsev
Physics Faculty Publications
Identifying integrable dynamics remains a formidable challenge, and despite centuries of research, only a handful of examples are known to date. In this article, we explore a distinct form of area-preserving (symplectic) mappings derived from the stroboscopic Poincaré cross section of a kicked rotator—an oscillator subjected to an external force periodically switched on in short pulses. The significance of this class of problems extends to various applications in physics and mathematics, including particle accelerators, crystallography, and studies of chaos. Notably, Suris's theorem constrains the integrability within this category of mappings, outlining potential scenarios with analytic invariants of motion. In this …
Decompositions Of Nonlinear Input-Output Systems To Zero The Output, W. Steven Gray, Kurusch Ebrahimi-Fard, Alexander Schmeding
Decompositions Of Nonlinear Input-Output Systems To Zero The Output, W. Steven Gray, Kurusch Ebrahimi-Fard, Alexander Schmeding
Electrical & Computer Engineering Faculty Publications
Consider an input–output system where the output is the tracking error given some desired reference signal. It is natural to consider under what conditions the problem has an exact solution, that is, the tracking error is exactly the zero function. If the system has a well defined relative degree and the zero function is in the range of the input–output map, then it is well known that the system is locally left invertible, and thus, the problem has a unique exact solution. A system will fail to have relative degree when more than one exact solution exists. The general goal …
Generalized Functions In The Study Of Signals And Systems, Erik I. Verriest, Gunther Dirr, W. Steven Gray
Generalized Functions In The Study Of Signals And Systems, Erik I. Verriest, Gunther Dirr, W. Steven Gray
Electrical & Computer Engineering Faculty Publications
We collect three instances where the theory of generalized functions may still make contributions to the study of signals and systems. In the first, a purely algebraic approach is presented for LTI-ODE's, in terms of two operators, D and T, respectively the differentiation operator and the multiplication-by-the-independent-variable operator. This formalism adds simplicity, a duality theory, and nicely generalizes to other classes of operator equations and their solutions. In the second part we extend the classical bilateral Laplace transform to include Bohl functions with support in ℝ by invoking Sato's hyperfunctions. Finally, in the third case we use the Colombeau algebra …
Modeling The Effect Of Observational Social Learning On Parental Decision-Making For Childhood Vaccination And Diseases Spread Over Household Networks, Tamer Oraby, Andras Balogh
Modeling The Effect Of Observational Social Learning On Parental Decision-Making For Childhood Vaccination And Diseases Spread Over Household Networks, Tamer Oraby, Andras Balogh
School of Mathematical & Statistical Sciences Faculty Publications
In this paper, we introduce a novel model for parental decision-making about vaccinations against a childhood disease that spreads through a contact network. This model considers a bilayer network comprising two overlapping networks, which are either Erdős–Rényi (random) networks or Barabási–Albert networks. The model also employs a Bayesian aggregation rule for observational social learning on a social network. This new model encompasses other decision models, such as voting and DeGroot models, as special cases. Using our model, we demonstrate how certain levels of social learning about vaccination preferences can converge opinions, influencing vaccine uptake and ultimately disease spread. In addition, …
Conditional Constrained And Unconstrained Quantization For Probability Distributions, Megha Pandey, Mrinal Kanti Roychowdhury
Conditional Constrained And Unconstrained Quantization For Probability Distributions, Megha Pandey, Mrinal Kanti Roychowdhury
School of Mathematical & Statistical Sciences Faculty Publications
In this paper, we present the idea of conditional quantization for a Borel probability measure P on a normed space Rk. We introduce the concept of conditional quantization in both constrained and unconstrained scenarios, along with defining the conditional quantization errors, dimensions, and coefficients in each case. We then calculate these values for specific probability distributions. Additionally, we demonstrate that for a Borel probability measure, the lower and upper quantization dimensions and coefficients do not depend on the conditional set of the conditional quantization in both constrained and unconstrained quantization.
Flow And Stability Of Three-Dimensional Rotating Viscoelastic Jet, Daniel N. Riahi
Flow And Stability Of Three-Dimensional Rotating Viscoelastic Jet, Daniel N. Riahi
School of Mathematical & Statistical Sciences Faculty Publications
We consider rotationally driven nonlinear viscoelastic jet. In contrast to previous unrealistic planar studies with no gravity effect, we investigate here realistic three-dimensional jet with gravity effect. Using theoretical and computational methods, we develop models for such jet and its stability and determine the solutions. We find three-dimensional jet with gravity effect leads to faster and thinner jet. For jet arc length higher than its exit diameter, our calculation with typical parameter values shows that jet radius is smaller by a factor of more than 1.4 and jet speed is higher by factor of more than 2 as are compared …