Mathematics Commons^™

New Types Of Neutrosophic Set/Logic/Probability, Neutrosophic Over-/ Under-/ Off Set, Neutrosophic Refined Set, And Their Extension To Plithogenic Set/Logic/Probability, With Applications, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This international collective massive book, edited by Florentin Smarandache, has 716 pages, and represents the special issue on neutrosophic environment at SYMMETRY international journal (Scopus, Web of Science, IF: 2.143). The book contains 37 published papers, by 73 authors and coauthors, from 13 countries from around the world, in alphabetical order: China, Cuba, Ecuador, Egypt, India, Jordan, Korea, Malaysia, Pakistan, Romania, Saudi Arabia, United Kingdom, and United States of America.

Special Subset Vertex Multisubgraphs For Multi Networks, Florentin Smarandache, W.B. Vasantha Kandasamy, Ilanthenral K

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors study special type of subset vertex multi subgraphs; these multi subgraphs can be directed or otherwise. Another special feature of these subset vertex multigraphs is that we are aware of the elements in each vertex set and how it affects the structure of both subset vertex multisubgraphs and edge multisubgraphs. It is pertinent to record at this juncture that certain ego centric directed multistar graphs become empty on the removal of one edge, there by theorising the importance, and giving certain postulates how to safely form ego centric multi networks. Given any subset vertex multigraph we …

Advances Of Standard And Nonstandard Neutrosophic Theories, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this book, we approach different topics related to neutrosophics, such as: Neutrosophic Set, Intuitionistic Fuzzy Set, Inconsistent Intuitionistic Fuzzy Set, Picture Fuzzy Set, Ternary Fuzzy Set, Pythagorean Fuzzy Set, Atanassov’s Intuitionistic Fuzzy Set of second type, Spherical Fuzzy Set, n-HyperSpherical Neutrosophic Set, q-Rung Orthopair Fuzzy Set, truth-membership, indeterminacy-membership, falsehood-nonmembership, Regret Theory, Grey System Theory, ThreeWays Decision, n-Ways Decision, Neutrosophy, Neutrosophication, Neutrosophic Probability, Refined Neutrosophy, Refined Neutrosophication, Nonstandard Analysis; Extended Nonstandard Analysis; Open and Closed Monads to the Left/Right; Pierced and Unpierced Binads; MoBiNad Set; infinitesimals; infinities; nonstandard reals; standard reals; Nonstandard Neutrosophic Lattices of First Type (as poset) and …

Modeling Of Hiv, Sir And Sis Epidemics On Time Scales And Oscillation Theory, Gülşah Yeni

Doctoral Dissertations

"We study higher dimensional systems of first order dynamic equations on time scales together with their applications. In particular, we focus on epidemic models such as HIV (Human Immunodeficiency Virus), SIS (Susceptible-Infected-Susceptible) and SIR (Susceptible-Infected-Recovered).

First, we generalize the early studied continuous three dimensional linear model of drug therapy for HIV-1 decline on time scales in order to derive new discrete models that predict the total concentration of plasma virus as a function of time. We compare these models to explore the impact of the theory of time scales. After fitting the models to the data collected at a clinical …

Some Results On Partial Difference Sets And Partial Geometries, Eric J. Neubert Jr

Dissertations, Master's Theses and Master's Reports

This thesis shows results on 3 different problems involving partial difference sets (PDS) in abelian groups, and uses PDS to study partial geometries with an abelian Singer group. First, the last two undetermined cases of PDS on abelian groups with k ≤ 100, both of order 216, were shown not to exist. Second, new parameter bounds for k and ∆ were found for PDS on abelian groups of order p^n , p an odd prime, n odd. A parameter search on p^5 in particular was conducted, and only 5 possible such cases remain for p < 250. Lastly, the existence of rigid type partial geometries with an abelian Singer group are examined; existence is left undetermined for 11 cases with α ≤ 200. This final study led to the determination of nonexistence for an infinite class of cases which impose a negative Latin type PDS.

Some Properties Of Uniform Fuzzy Modules And Semiuniform Fuzzy Modules, Burhan Chemat

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we study some properties of uniform fuzzy modules and semiuniform fuzzy modules. Let R be a ring with the identity and M a right R-module. A submodule A of a right R-module M is called an essential submodule of M, if any non-zero submodule B of M, A∩B≠{θ} where θ is the zero element in M. A right R-module M is called a uniform module, if any non-zero submodule of M is an essential submodule of M. A submodule α of a fuzzy module μ in a right R-module M is called an essential submodule of μ, …

Distance Powers Of Partial Unitary Cayley Graphs, Muntiranee Mongkolsin

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

Pressure Versus Impulse Graph For Blast-Induced Traumatic Brain Injury And Correlation To Observable Blast Injuries, Barbara Rutter

Doctoral Dissertations

"With the increased use of explosive devices in combat, blast induced traumatic brain injury (bTBI) has become one of the signature wounds in current conflicts. Animal studies have been conducted to understand the mechanisms in the brain and a pressure versus time graph has been produced. However, the role of impulse in bTBIs has not been thoroughly investigated for animals or human beings.

This research proposes a new method of presenting bTBI data by using a pressure versus impulse (P-I) graph. P-I graphs have been found useful in presenting lung lethality regions and building damage thresholds. To present the animal …

Decoupling Methods For The Time-Dependent Navier-Stokes-Darcy Interface Model, Changxin Qiu

Doctoral Dissertations

"In this research, several decoupling methods are developed and analyzed for approximating the solution of time-dependent Navier-Stokes-Darcy (NS-Darcy) interface problems. This research on decoupling methods is motivated to efficiently solve the complex Stokes-Darcy or NS-Darcy type models, which arise from many interesting real world problems involved with or even dominated by the coupled porous media flow and free flow. We first discuss a semi-implicit, multi-step non-iterative domain decomposition (NIDDM) to solve a coupled unsteady NS-Darcy system with Beavers-Joseph-Saffman-Jones (BJSJ) interface condition and obtain optimal error estimates. Second, a parallel NIDDM is developed to solve unsteady NS-Darcy model with Beavers-Joseph (BJ) …

Long-Time Behavior Of A Nonlocal Dispersal Equation, Aussacha Dintawong

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, study the nonlocal dispersal equation [equation] with a non-homogeneous boundary condition. We generalize the result of J.W. Sun (2015), where in this work the kernel J has a non-compact support. The global well-posedness and comparison principles (both time-dependent and stationary problems) are established. The main result is the long-time behavior of solutions, which is proved to depend on the boundary data.

Augmented Sensors For Particulate Matter Concentration Prediction Using Supervised Learning Models, Chadaphim Photphanloet

Chulalongkorn University Theses and Dissertations (Chula ETD)

Particulate matter concentration prediction models have been researched, developed, and applied to data from various topography around the world. The characteristics of different topography make a model suitable for each specific topography. This dissertation proposes a novel method to predict particulate matter concentration with a diameter smaller than 10 microns in Nan Province of Thailand that integrates feature selection method, supervised learning model, and modified depth-first search algorithm. Unlike the traditional supervised learning models, the proposed method is able to accept multi-dimensional data as input which consist of particulate matter concentration, air pollutants, and air qualities. These features are the …

Uniform Distribution Of Fractional Parts Of Average Of Kth Power Of Prime Divisors, Chitpanu Chairatanagul

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we prove that for every positive integer k greater than or equal to two, the sequence of the fractional parts of the arithmetic mean of the kth power of prime divisors of n counted with or without multiplicity, as n runs through all positive integers, is uniformly distributed modulo one.

Boundaries Of Overlapping Reuleaux Triangles, Jirapat Kaewkam

Chulalongkorn University Theses and Dissertations (Chula ETD)

where R1 and R2 are two congruent Reuleaux triangle such that Int(R1)∩Int(R2) ̸= ∅. Denote ∂Ri and Int(Ri) the boundary and the interior of Ri , respectively. We finish the proof when R2 is a translated copy R1 and we obtain some interesting results when R1 and R2 intersect in general position.

Spectra Of Unitary Cayley Graphs Of Matrices Over Finite Commutative Rings, Jitsupat Rattanakangwanwong

Chulalongkorn University Theses and Dissertations (Chula ETD)

For a finite ring R with identity, the unitary Cayley graph of R, CR, is the graph with vertex set R and for each x, y ∈ R, x and y are adjacent if and only if x − y is a unit of R. In this thesis, we determine some eigenvalues of CMn(F) , where F is a finite field, by using the additive characters and use these eigenvalues to analyze strong regularity, hyperenergetic graphs and Ramanujan graphs. Next, we extend the results to CMn(R) , where R is a local ring. We characterize all local rings R and …

Classification Of Aircraft With Shadow Using Keypoint Descriptor From Remote Sensing Images, Natnicha Meeboonmak

Chulalongkorn University Theses and Dissertations (Chula ETD)

Presently, aircraft classification from remote sensing images is widely used in military and civilian. However, aircraft type classification is still challenging to discriminate. The reason is that the aircraft displayed in the image has different in color, shape, size, and orientation. Moreover, there is the shadow appeared over and behind the aircraft that obscures some details of aircraft. Therefore, this work proposes the classification of aircraft with shadow method. This method modifies the deeply supervised salient object detection with short connections to make the aircraft be outstanding from the shadow and other objects in the background and then segment it. …

Development Of Facial Expression Detection Model For Stroke Patients, Rawinan Praditsangthong

Chulalongkorn University Theses and Dissertations (Chula ETD)

A stroke patient should be cared and treated closely since the patient cannot speak, communicate, and move the body when needed. In addition, the number of stroke patients is increasing in Thailand and around the world. Unfortunately, the number of medical staffs does not vary by the number of stroke patient. Thus, the aim of this research is to develop a facial expression detection model for stroke patients during their treatments. This research proposes the facial expression detection model for stroke patients from facial features, such as Interpalpebral Fissure (IPF), Palpebral Fissure Length (PFL), Palpebral Fissure Region (PFR), Inner Brow …

Generalized Topologies Induced By Monotonic Maps And Hereditary Classes, Sahawat Wongkhunen

Chulalongkorn University Theses and Dissertations (Chula ETD)

It is shown in [3] that every generalized topology can be extended to a new one by using hereditary classes, called a generalized topology via a hereditary class. Following [5], the continuity on generalized topological spaces via hereditary classes was studied. In this thesis, we introduce the notion of generalized topological spaces induced by monotonic maps and hereditary classes and provide some of their properties. Also, we define and study the continuity on generalized topological spaces induced by monotonic maps and hereditary classes in various situations. Finally, we study some properties and characterizations of generalized topological spaces induced by monotonic …

Solving Interval-Valued Returns Mean Absolute Deviation Portfolio Selection Model Under Basis Stability, Songkomkrit Chaiyakan

Chulalongkorn University Theses and Dissertations (Chula ETD)

This work discusses a portfolio selection model with interval linear programming arising from the uncertainty of future rates of return and the disagreement over their estimates. The risk of the overall portfolio is proposed as an objective function to obtain a well-diversified portfolio with a certain threshold rate of return. The optimization problem employs mean absolute deviation as a risk measure for the sake of risk diversification and time complexity. The possible ranges of optimal portfolio returns and associated risks are derived. The duality theory contributes to an enclosure of the optimal portfolios. When the bounds on future rates of …

Aircraft Detection Using Single Shot Scale-Invariant Face Detector With Viridis Saliency Map From Remote Sensing Image, Teepakorn Lilek

Chulalongkorn University Theses and Dissertations (Chula ETD)

Aircraft detection from remote sensing images is a useful task and essential in many fields; for example, in the military, aircraft detection systems are used to search and inspect an enemy aircraft from remote sensing images. Nowadays, aircraft detection from remote sensing images has gained increasing research attention because this task is very challenging. This task is difficult due to many occurred problems in remote sensing images, such as a shadow, a complicated background, and various aircraft scales. In this research, we create a Viridis saliency map using many techniques from image processing such as color mapping, morphological image processing, …

Logo Classification Of Amphetamines By Surf And Bag-Of-Features Model, Tharaphon Nitijiramon

Chulalongkorn University Theses and Dissertations (Chula ETD)

An amphetamine is one of the drugs apprehended by the policemen in Thailand. At present, when an amphetamine drug seller is arrested, captured amphetamines are sent to the Scientific Crime Detection Center Region 1 to identify the amphetamines' source. Each drug is classified based on the printed character to relevant information from the source of drugs. For each case, a large volume of drugs is sent to be classified by only three staff members. It is a time-consuming task. In this work, we propose a framework for classifying the image of amphetamines based on their logo using the SURF and …

Excess Versions Of The Minkowski And Hölder Inequalities, Iosif Pinelis

Michigan Tech Publications, Part 1

Certain excess versions of the Minkowski and Hölder inequalities are given.

Normalized Hodge Laplacian Matrix And Its Spectrum, Nalinpat Ponoi

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

Automatic Model Identification For Time Series Analysis Using Deep Learning, Paisit Khanarsa

Chulalongkorn University Theses and Dissertations (Chula ETD)

Most time series data can be characterized by a linear process via the autoregressive integrated moving average model requiring a three-component vector which are the autoregressive, differencing, and moving average orders before fitting coefficients. A model identification which determines those orders is analyzed via the partial autocorrelation function to identify the autoregressive order, the autocorrelation function to identify the moving average order and an extended sample autocorrelation function to identify both orders which is a challenging problem for statisticians. Accordingly, the auto-ARIMA model was proposed to automatically vary those orders and estimates their corresponding coefficients. This thesis proposes three architectures …

Self-Balancing Recursive Partitioning Algorithm For Classification Problems, Artit Sagoolmuang

Chulalongkorn University Theses and Dissertations (Chula ETD)

Creating an effective classification model has been played an important role in knowledge discovery in a database methodology for the past several years. However, there is a critical issue that significantly affects the classification performance appearing in many real-world situations, which is called a class imbalanced problem. In this dissertation, a classification model built based on the recursive partitioning algorithm is improved under the concept of modified entropy components for handling a classification problem regardless of the class imbalanced situation. Three methodologies are introduced for achieving different purposes. The first methodology is presented to classify a binary-class imbalanced dataset dealing …

Solving System Of Linear Integro-Differential Equations By Finite Integration Method With Shifted Chebyshev Polynomials, Matinee Juytai

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we modify the finite integration method by using the shifted Chebyshev polynomial (FIM-SCP). The major tool of our FIM-SCP is the shifted Chebyshev integration matrix. It is constructed in order to be a matrix representation for integrating over interpolated points which are generated by the zeros of shifted Chebyshev polynomial of a certain degree. The efficiently numerical algorithms are then created by the modified FIM-SCP for seeking approximate solutions of a system of stiff linear ordinary differential equations, a system of linear Volterra integro-differential equations, and a system of linear Fredholm integro-differential equations under some given boundary …

Pointwise Dimension Of Archimedean Copulas, Noppawit Yanpaisan

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we introduce the pointwise dimension of a bivariate copula C at (u,v) in [0, 1]2 via its C-volume. This quantity gives a broader view of probability mass distribution than the support of a copula, the smallest closed set on which the whole mass lies. We would like to study some fundamental properties of pointwise dimension, including the equality to pointwise exponent whenever both of them exist. After that, we investigate the behavior of the pointwise dimension of copulas constructed by various methods. In the last part, we compute the pointwise dimension of Archimedean copulas, an important class …

Binomial Characterizations Of Inner Product Spaces, Saranyachakri Roekrit

Chulalongkorn University Theses and Dissertations (Chula ETD)

We study the sufficient conditions for a normed space to be an inner product space. We found that some characterizations of inner product spaces are in a form [equation] satisfy some algebraic conditions. We then introduce some characterizations of inner product spaces relating to the binomial identity and conclude that a nomed linear space (X,II.II) is an inner product space if there exist positive integers k and m with 2m

Covers For Leo Moser's Worm Problem, Thitipong Kanchai

Chulalongkorn University Theses and Dissertations (Chula ETD)

Leo Moser’s worm problem was posted in 1966 stating that “What is the region of the smallest area that can cover every unit are?”. In 2018, N. Ploymaklam and W. Wichiramala illustrated a new cover, which is currently smallest. Their cover was adapted from the cover of R. Norwood and G. Poole. In this work, we modify the region from the work of R. Norwood and G. Poole and the work of N. Ploymaklam and W. Wichiramala. Our regions are modified by changing their upper boundary. However, the regions remain satisfying properties in the work of R. Norwood and G. …

Attitudes Toward Using And Teaching Confidence Intervals: A Latent Profile Analysis On Elementary Statistics Instructors, Hyung Won Kim, Woo Jin Kim, Aaron T. Wilson, Ho Kyoung Ko

School of Mathematical & Statistical Sciences Faculty Publications

The use of confidence intervals (CIs) for making a statistical inference is gaining popularity in research communities. To evaluate college statistics instructors’ readiness to teach CIs, this study explores their attitudes toward teaching CIs in elementary statistics courses, and toward using CIs in inferential statistics. Data were collected with a survey that classifies instructors’ attitudes on the basis of three previously established pedagogical components: affective, cognitive, and behavioral. Based on the survey responses from 270 participants, we created three profiles (subgroups) via latent profile analysis, and identified each profile’s pattern of attitudes toward CIs and common characteristics of the instructors …

Blocks In The Category Of Finite-Dimensional Representations Of Principal W-Algebra For Q(2), Elena Poletaeva

School of Mathematical & Statistical Sciences Faculty Publications

We describe the blocks in the category of finite-dimensional representations of the principal finite W-algebra for the Lie superalgebra Q(2).