Physical Sciences and Mathematics Commons^™

Exploring International Educators' Learning About Local And Global Social Justice In A Virtual Community Of Practice, Bima Sapkota, Xuwei Luo, Muna Sapkota, Murat Akarsu, Emmanuel Deogratias, Daphne Fauber, Rose Mbewe, Fidelis Mumba, Ram Krishna Panthi, Jill Newton

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this chapter, the authors report themes that emerged when a cross-cultural team of researchers involved in a virtual international community of practice (Global Social Justice in Education-GSJE) investigated reflections on activities focused on social justice in local and global contexts. The findings suggested that the activities elicited GSJE community members' understandings of the complexities of social justice associated with naming practices, privilege, and the arts within their own and across contexts. The authors discuss implications of the activities to advance diverse educators' understanding of social justice in global and local contexts. They also unpack the opportunities and challenges that …

Hierarchical Neural Networks, P-Adic Pdes, And Applications To Image Processing, Wilson A. Zuniga-Galindo, B. A. Zambrano-Luna, Baboucarr Dibba

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The first goal of this article is to introduce a new type of p-adic reaction-diffusion cellular neural network with delay. We study the stability of these networks and provide numerical simulations of their responses. The second goal is to provide a quick review of the state of the art of p-adic cellular neural networks and their applications to image processing.

Investigating Preservice Teachers’ Conceptualizations Of Mathematical Knowledge For Teaching Through Video Analysis, Bima Sapkota

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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 …

Sparse Representer Theorems For Learning In Reproducing Kernel Banach Spaces, Rui Wang, Yuesheng Xu, Mingsong Yan

Mathematics & Statistics Faculty Publications

Sparsity of a learning solution is a desirable feature in machine learning. Certain reproducing kernel Banach spaces (RKBSs) are appropriate hypothesis spaces for sparse learning methods. The goal of this paper is to understand what kind of RKBSs can promote sparsity for learning solutions. We consider two typical learning models in an RKBS: the minimum norm interpolation (MNI) problem and the regularization problem. We first establish an explicit representer theorem for solutions of these problems, which represents the extreme points of the solution set by a linear combination of the extreme points of the subdifferential set, of the norm function, …

Advanced Techniques In Time Series Forecasting: From Deterministic Models To Deep Learning, Xue Bai

Graduate Theses, Dissertations, and Problem Reports

This dissertation discusses three instances of temporal prediction, applied to population dynamics and deep learning.

In population modeling, dynamic processes are frequently represented by systems of differential equations, allowing for the analysis of various phenomena. The first application explores modeling cloned hematopoiesis in chronic myeloid leukemia (CML) via a nonlinear system of differential equations. By tracking the evolution of different cell compartments, including cycling and quiescent stem cells, progenitor cells, differentiated cells, and terminally differentiated cells, the model captures the transition from normal hematopoiesis to the chronic and accelerated-acute phases of CML. Three distinct non-zero steady states are identified, representing …

Analyzing Imprecise Data From Wireless Temperature Sensor, Usama Afzal, Muhammad Aslam, Muhammad Ahmed Shehzad, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Various sensors play an important role in the monitoring and development of robotic technology. We present a contemporary statistical analysis method for evaluating datasets generated by robotic systems. Specifically, this data set originates from the physical structure of the robot and is acquired by a wireless temperature sensor. The data collection process spans a temporal period of 1 to 10 hours during the operational period of the robot. The collected data is subjected to a rigorous analysis using neutrosophic methodology. To facilitate this, a modern neutrosophic formula has been devised, drawing on definitions established within the field. To benchmark the …

Super Hiper Funcion Y Super Hiper Estructura Y Sus Correspondientes Super Hiper Funcion Neutrosofica Y Super Hiper Estructura Neutrosofica, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

El n-ésimo Conjunto Potencia de un Conjunto {o Pn(S)} describe mejor nuestro mundo real, porque un sistema S (que puede ser una empresa, institución, asociación, país, sociedad, conjunto de objetos/plantas/animales/seres, conjunto de conceptos/ideas/proposiciones, etc.) está formado por subsistemas, que a su vez están formados por sub-subsistemas, y así sucesivamente. Demostramos que la Super Hiper Función es una generalización de la Función clásica, Super Función y la Hiper Función. Y el Super Hiper Álgebra, Super Hiper Gráfico son parte de la Super Hiper Estructura. Casi todas las estructuras en nuestro mundo real son Super Hiper Estructuras Neutrosóficas ya que tienen …

Resolving The Paradoxism With The Logic Of “Not” In Javanese Puppetry: A Re-Reading Of Wrekodoro And Dewaruci’S Mytology, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

There are a large number of text collections in Indonesia, related to wayang theme, cf Zoetmulder (1971). And the text collections do not consist only of wayang purwa but also variations of this theme, including wayang wahyu etc. In the mean time, a Japanese scholar Shoshichi Nagatomo proposed the concept of "Asian Logic" which differs from Western logic. In Western thought, things are often seen as black or white, good or bad. However, Asian logic embraces certain degree of ambiguity. Here, "good" characters can exhibit flaws, and "bad" characters can possess redeeming qualities; especially among Javanese people preference is given …

An Innovative Approach On Yao’S Three-Way Decision Model Using Intuitionistic Fuzzy Sets For Medical Diagnosis, Wajid Ali, Tanzeela Shaheen, Iftikhar Ul Haq, Florentin Smarandache, Hamza Ghazanfar Toor, Faiza Asif

Branch Mathematics and Statistics Faculty and Staff Publications

In the realm of medical diagnosis, intuitionistic fuzzy data serves as a valuable tool for representing information that is uncertain and imprecise. Nevertheless, decision-making based on this kind of knowledge can be quite challenging due to the inherent vagueness of the data. To address this issue, we employ power aggregation operators, which prove effective in combining several sources of data, such as expert thoughts and patient information. This allows for a more correct diagnosis; a particularly crucial aspect of medical practice where precise and timely diagnoses can significantly impact medication policy and patient results. In our research, we introduce a …

Eevmc: An Energy Efficient Virtual Machine Consolidation Approach For Cloud Data Centers, Attique Ur Rehman, Songfeng Lu, Mubashir Ali, Florentin Smarandache, Sultan S. Alshamrani, Abdullah Alshehri, Farrukh Arslan

Branch Mathematics and Statistics Faculty and Staff Publications

The dynamic landscape of cloud computing design presents significant challenges regarding power consumption and quality of service (QoS). Virtual machine (VM) consolidation is essential for reducing power usage and enhancing QoS by relocating VMs between hosts. OpenStack Neat, a leading framework for VM consolidation, employs the Modified Best-Fit Decreasing (MBFD) VM placement technique, which faces issues related to energy consumption and QoS. To address these issues, we propose an Energy Efficient VM Consolidation (EEVMC) approach. Our method introduces a novel host selection criterion based on the incurred loss during VM placement to identify the most efficient host. For validation, we …

A Few Lessons From Venezuela: Introducing A New Path Of Appropriate Farming And Appropriate Renewable Energy, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In development economics literatures, there is a known term for developing countries which tend to mismanage natural resources, that term is called natural resources curse. And two examples which have been discussed quite often is Venezuela and Norway. Here we also discuss other countries as well, including Argentina and a few lessons for Indonesia in choosing the next course of development path, especially with appropriate farming and appropriate renewable energy.

Single-Valued Neutrosophic Ideal Approximation Spaces, Yaser Saber, Mohamed Abusalih, Esam Bader, Tawfik Elmasry, Abdelaziz Babiker, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we defined the basic idea of the single-valued neutrosophic upper, single-valued neutrosophic lower and single-valued neutrosophic boundary sets of a rough single-valued neutrosophic set in a single-valued neutrosophic approximation space. We joined the single-valued neutrosophic ideal notion with the single-valued neutrosophic approximation spaces and then introduced the single-valued neutrosophic ideal approximation closure and interior operators associated with a rough single-valued neutrosophic set, single-valued neutrosophic ideal approximation connectedness and the single-valued neutrosophic ideal approximation continuity between single-valued neutrosophic ideal approximation spaces are introduced. The concepts of single-valued neutrosophic groups and their approximations have also been applied in the …

Unveiling Quantum Communication: From Bell's Inequality To Neutrosophic Logic, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this mini-review, we delve into the intriguing realm of quantum communication, spurred by China's recent development of the Tiantong communication satellite. This satellite, shrouded in secrecy, hints at a revolutionary approach to communication that transcends the limitations of conventional signal transmission. We explore the foundational concepts of Bell's inequality and neutrosophic logic, elucidating their roles in understanding the non-local phenomena of quantum entanglement and its potential for secure and rapid communication. Additionally, we examine the connection between Bell's inequality and Shannon information entropy, unveiling the intricate relationship between quantum mechanics and information theory. Through this exploration, we glimpse a …

Ermakov Equations Can Be Derived From Zel’Dovich Pancake, And They Are Cold And Nonlocal Through Using Neutrosophic Venn Diagram, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

As we argue in a previous article, the labyrinthine worlds of Jorge Luis Borges are more than captivating narratives; they are portals to a deeper understanding of existence. By weaving elements of science-fiction fantasy with philosophical and ethical inquiries, Borges's short stories bridge the seemingly disparate realms of physics and the humanities, offering fertile ground for contemporary physics research. The present-day universe consists of galaxies, galaxy clusters, one-dimensional filaments and two-dimensional sheets or pancakes, all of which combine to form the cosmic web. The so called ”Zeldovich pancakes”, are very difficult to observe, because their overdensity is only slightly greater …

The Paradoxist Movement, Precursor Of Neutrosophy, In The Shadow Of A Totalitarian Regime, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Physics thrives on precision, but paradoxes in set theory reveal limitations in our understanding of well-defined boundaries. Neutrosophic logic, challenging the excluded middle principle, introduces the concept of "betweenness" and partial belonging. This article explores, among other things, what is less known, i.e., Paradoxism emerged as a radical artistic and literary movement in Romania during the late 1980s and continues even today. It arose within the stifling and highly controlled environment of Nicolae Ceaușescu's socialist regime, offering a rebellious outlet and a means to subvert the prevailing ideology. Understanding the Paradoxist Movement necessitates a contextual understanding of the Nicolae Ceaușescu …

Integrating Contradictory Perspectives In Latin American Philosophy: A Multialism Approach, Maikel Yelandi Leyva Vázquez, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This study explores the integration of indigenous philosophies and postcolonial modernist theories within the framework of MultiAlism, highlighting the potential for dialogue and synthesis between these diverse philosophical traditions in Latin America. MultiAlism, a concept developed by Florentin Smarandache, is utilized to bridge the gaps and contradictions between these systems by focusing on areas of neutrality such as cultural diversity and power structure critiques. The research emphasizes the importance of incorporating both ancestral wisdom and modern critiques to foster a deeper understanding and appreciation of Latin America’s rich philosophical heritage. This integrative approach offers practical insights for developing inclusive policies …

Bv2trs Appraiser Model: Enforcing Bharat Version2 In Tree Soft Modelling For Appraising E-Mobility Hurdles, Mona Mohamed, Florentin Smarandache, Michael Gr. Voskoglou

Branch Mathematics and Statistics Faculty and Staff Publications

Electric vehicles (EVs) are being introduced to lessen greenhouse gas (GHG) emissions, air pollution, and reliance on fossil fuels. As a result of the government's aggressive promotion of EVs and rising environmental consciousness, EVs are quickly rising to the top of the low-carbon transportation market. Several viewpoints suggested that shifting to electric vehicles has been seen as a potential way to achieve sustainable mobility. Nevertheless, many studies discussed the obstacles and hurdles that obstruct the embracing of various electric-mobility (E-mobility) as EVs and electric-scooters (E-scooters) as eco-friendly means. Herein, we discussed these hurdles and determined them through surveys for prior …

Automated Livestock Practices: Incorporation Emerging Contemporary Technologies Toward Sustainable Livestock In Era Of Smart Cities, Asmaa Elsayed, Mona Mohamed, Florentin Smarandache, Michael Gr. Voskoglou

Branch Mathematics and Statistics Faculty and Staff Publications

Currently, numerous spheres now face a wider range of needs due to the increasingly competitive and globalized global market. Moreover, digital technologies are necessary for analysis and comprehension in many sectors of contemporary society. For instance, Internet of Things (IoT) has the potential to revolutionize livestock management, including the dairy cattle industry, by providing real-time data and enabling data-driven decisions to improve animal welfare, increase productivity, and promote sustainable farming practices. The main components of IoT-enabled livestock management include sensors, communication systems, data storage, and analysis systems. These components of IoT-enabled livestock management improve animal welfare, increase productivity, and reduce …

Assuming Photon As Extended Point Particle In The Hypersoft Topological Space And Other Hypotheses: Issues And Trend Analysis, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Following our preceding article, where we discussed alternative interpretations of the advanced perihelion of Mercury, the present article revisits the 1919 solar eclipse expedition led by Arthur Eddington, which famously provided the first observational confirmation of Einstein's theory of general relativity. We focus on the deflection of starlight data obtained during the eclipse, a cornerstone of this validation. Here, we explore three alternative explanations for the observed light bending that challenge the sole attribution to general relativity. Firstly, the paper begins by arguing based on criticisms raised by Tullio Levi-Civita, a contemporary mathematician, regarding Einstein's use of pseudo-tensors in his …

Distinctions Between Various Types Of Fuzzy-Extension Hypersoft Sets, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

We define the universes of discourses for all fuzzy and fuzzy-extension sets. Then present many types of Plithogenic Universes of discourse and their connections to HyperSoft Sets. Afterward, we make distinctions between various hybrid forms of HyperSoft Sets.

Two Applications Of The Concepts Of Pole And Polar With Respect To A Circle, Ion Pătrașcu, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this article, we present in a unified form the theoretical results regarding the concepts of pole and polar with respect to a circle, and as applications of these, we offer a demonstration of Newton’s theorem related to the circumscribed quadrilateral and a demonstration of a theorem usually derived as a particular case of Pascal’s theorem related to the inscribed hexagon.

Neutrosophical Plant Hybridization In Decision-Making Problems, M. Arockia Dasan, E. Bementa, Florentin Smarandache, X. Tubax

Branch Mathematics and Statistics Faculty and Staff Publications

Florentin Smarandache developed the neutrosophic set theory to study inconsistency, incomplete, and uncertainty information by using truth-membership, indeterminacy-membership, and falsity-membership functions. One of the main objectives of this chapter is to develop a new methodological approach of neutrosophic sets in multi-criteria decision-making problems. This method considers neutrosophic sets with their unions in the direct direction and the complements of given neutrosophic sets with their intersections are also considered in the reverse direction. Using these collections, single-valued neutrosophic score functions are computed in both directions. After this process, all the alternatives are ranked in the ascending order arrangement to find the …

Multi-Criteria Group Decision-Making With Electre-Iii Method For Selection Of Female Spouse In Pythagorean Neutrosophic Environment, Rajesh Kumar Saini, Ashik Ahirwar, Florentin Smarandache, Mukesh Kushwaha

Branch Mathematics and Statistics Faculty and Staff Publications

Selecting a female partner in the 21st century is more challenging as compared to the 20th century. The globalized world, changing societal norms, and technology have increased the pool of potential partners, making it harder to find a compatible match. The prevalence of social media and online dating has also changed how people interact, leading to new challenges in establishing genuine connections. This paper presents a novel Multiple-Criteria Group Decision Making (MCGDM) model for selecting a female spouse using the ELECTRE-III method in a Pythagorean neutrosophic environment. The proposed model takes into account multiple criteria and addresses the challenges of …

Evaluating Blockchain Cybersecurity Based On Tree Soft And Opinion Weight Criteria Method Under Uncertainty Climate, Florentin Smarandache, Mona Mohamed, Michael Gr. Voskoglou

Branch Mathematics and Statistics Faculty and Staff Publications

In the era of digital transformation (DT), many digital technologies have emerged and have had a positive impact on society. Nevertheless, because of certain issues with existing technologies, innovative technology has developed to eradicate them. Fog computing (FC) plays a vital role as an intermediate between edge layer and cloud computing (CC) to resolve limited resources and capabilities. In the same vein, blockchain technology (BCT) is responsible for resolving privacy and security issues that IoT suffers from. Due to using cryptography rules and hashing which is utilized in BCT to prevent any trickery. Hence, BC shows promise as a possible …

The Enduring Power Of Giving And Caring From Cavemen To Kind Hearts: A Neutrosophic Multi-Criteria Decision Making Approach, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Giving and caring are not just warm and fuzzy feelings; they are the bedrock of a healthy society. By understanding the neuroscience and sociology behind these behaviors, we can cultivate a world that prioritizes cooperation, compassion, and the well-being of all its members. We used the single valued neutrosophic sets (SVNSs) with the multi-criteria decision making (MCDM) method for evaluating the giving and caring impacts. We used TreeSoft to divide the problems as a tree. The SVNSs were used to overcome uncertain information in the evaluation process. The SVNSs were integrated with the DEMATEL method to compute the relationships between …

Act Chapter 29: Art And Science And Theology In Dialogue, V. Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Where does a sparkling idea come to us, so out of the blue? Divine inspiration? I want a scientific explanation... Maybe, at present, with our current level of science, we are not able to understand the paranormal, or what we think is fantastic, but in fact it is real. A reality that we cannot reach with understanding, because of our low level... Are we not perhaps relevant and do we understand the incomprehensible? Some are connected to the universe better than others, do they have extra senses? How can we “gather” ideas from “air”? How does the spark in the …

Foundation Of Appurtenance And Inclusion Equations For Constructing The Operations Of Neutrosophic Numbers Needed In Neutrosophic Statistics Foundation Of Appurtenance And Inclusion Equations For Constructing The Operations Of Neutrosophic Numbers Needed In Neutrosophic Statistics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

We introduce for the first time the appurtenance equation and inclusion equation, which help in understanding the operations with neutrosophic numbers within the frame of neutrosophic statistics. The way of solving them resembles the equations whose coefficients are sets (not single numbers).

Symmetries And Integrable Systems, Sen-Yue Lou, Bao-Feng Feng

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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 …

Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen

Theses and Dissertations (Comprehensive)

The complex nature of the human brain, with its intricate organic structure and multiscale spatio-temporal characteristics ranging from synapses to the entire brain, presents a major obstacle in brain modelling. Capturing this complexity poses a significant challenge for researchers. The complex interplay of coupled multiphysics and biochemical activities within this intricate system shapes the brain's capacity, functioning within a structure-function relationship that necessitates a specific mathematical framework. Advanced mathematical modelling approaches that incorporate the coupling of brain networks and the analysis of dynamic processes are essential for advancing therapeutic strategies aimed at treating neurodegenerative diseases (NDDs), which afflict millions of …

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 …