Mathematics Commons^™

A Review On Possible Physical Meaning Of Elastic-Electromagnetic Mathematical Equivalences, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

It is known, despite special theory of relativity has been widely accepted, in our recent draft submitted to this journal it is shown that some experiments have been carried out suggesting superluminal wave propagation, which make Minkowski lightcone not valid anymore. Therefore, it seems worth to reconsider the connection between elastic wave and electromagnetic wave equations, as in their early development. In this paper we will start with Maxwell-Dirac isomorphism, then we will find its connection with elastic wave equations.

Godel, Escherian Staircase And Possibility Of Quantum Wormhole With Liquid Crystalline Phase Of Iced-Water - Part Ii: Experiment Description, Victor Christianto, T. Daniel Chandra, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The present article was partly inspired by G. Pollack’s book, and also Dadoloff, Saxena & Jensen (2010). As a senior physicist colleague and our friend, Robert N. Boyd, wrote in a journal (JCFA, Vol. 1, No. 2, 2022), for example, things and Beings can travel between Universes, intentionally or unintentionally [4]. In this short remark, we revisit and offer short remark to Neil Boyd’s ideas and trying to connect them with geometry of musical chords as presented by D. Tymoczko and others, then to Escherian staircase and then to Jacob’s ladder which seems to pointto possibility to interpret Jacob’s vision …

Godel, Escherian Staircase And Possibility Of Quantum Wormhole With Liquid Crystalline Phase Of Iced-Water - Part I: Theoretical Underpinning, Victor Christianto, T. Daniel Chandra, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

As a senior physicist colleague and our friend, Robert N. Boyd, wrote in a journal (JCFA, Vol. 1,. 2, 2022), Our universe is but one page in a large book [4]. For example, things and Beings can travel between Universes, intentionally or unintentionally. In this short remark, we revisit and offer short remark to Neil’s ideas and trying to connect them with geometrization of musical chords as presented by D. Tymoczko and others, then to Escher staircase and then to Jacob’s ladder which seems to point to possibility to interpret Jacob’s vision as described in the ancient book of Genesis …

Exploring Non-Orientable Topology: Deriving The Poincaré Conjecture And Possibility Of Experimental Vindication With Liquid Crystal, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This review investigates the potential of non-orientable topology as a fundamental framework for understanding the Poincaré conjecture and its implications across various scientific disciplines. Integrating insights from Dokuchaev (2020), Rapoport, Christianto, Chandra, Smarandache (under review), and other pioneering works, this article explores the theoretical foundations linking non-orientable spaces to resolving the Poincaré conjecture and its broader implications in theoretical physics, geology, cosmology, and biology.

The Encyclopedia Of Neutrosophic Researchers, 5th Volume, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy.

In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical engineering, investment problems, economic forecasting, social science, humanistic and practical achievements.

There are about 7,000 neutrosophic researchers, within 89 countries around the …

Probabilistic Modeling Of Social Media Networks, Distinguishing Phylogenetic Networks From Trees, And Fairness In Service Queues, Md Rashidul Hasan

Mathematics & Statistics ETDs

In this dissertation, three primary issues are explored. The first subject exposes who-saw-from-whom pathways in post-specific dissemination networks in social media platforms. We describe a network-based approach for temporal, textual, and post-diffusion network inference. The conditional point process method discovers the most probable diffusion network. The tool is capable of meaningful analysis of hundreds of post shares. Inferred diffusion networks demonstrate disparities in information distribution between user groups (confirmed versus unverified, conservative versus liberal) and local communities (political, entrepreneurial, etc.). A promising approach for quantifying post-impact, we observe discrepancies in inferred networks that indicate the disproportionate amount of automated bots. …

Modified Geometries, Clifford Algebras And Graphs: Their Impact On Discreteness, Locality And Symmetr, Roma Sverdlov

Mathematics & Statistics ETDs

In this dissertation I will explore the question whether various entities commonly used in quantum field theory can be “constructed". In particular, can spacetime be “constructed" out of building blocks, and can Berezin integral be “constructed" in terms of Riemann integrals.

As far as “constructing" spacetime out of building blocks, it has been attempted by multiple scientific communities and various models were proposed. But the common downfall is they break the principles of relativity. I will explore the ways of doing so in such a way that principles of relativity are respected. One of my approaches is to replace points …

Multilevel Optimization With Dropout For Neural Networks, Gary Joseph Saavedra

Mathematics & Statistics ETDs

Large neural networks have become ubiquitous in machine learning. Despite their widespread use, the optimization process for training a neural network remains com-putationally expensive and does not necessarily create networks that generalize well to unseen data. In addition, the difficulty of training increases as the size of the neural network grows. In this thesis, we introduce the novel MGDrop and SMGDrop algorithms which use a multigrid optimization scheme with a dropout coarsening operator to train neural networks. In contrast to other standard neural network training schemes, MGDrop explicitly utilizes information from smaller sub-networks which act as approximations of the full …

Using Physics-Informed Neural Networks For Multigrid In Time Coarse Grid Equations, Jonathan P. Gutierrez

Mathematics & Statistics ETDs

For parallel-in-time integration methods, the multigrid-reduction-in-time (MGRIT) method has shown promising results in both improved convergence and increased computational speeds when solving evolution problems. However, one problem the MGRIT algorithm currently faces is it struggles solving hyperbolic problems efficiently. In particular, hyperbolic problems are generally solved using explicit methods and this causes issues on the coarser multigrid levels, where larger (coarser) time step sizes can violate the stability condition. In this thesis, physics-informed neural networks (PINNs) are used to evaluate the coarse grid equations in the MGRIT algorithm with the goal to improve convergence for problems with hyperbolic behavior, as …

The Computational Model Of Nanofluid Considering Heat Transfer And Entropy Generation Across A Curved And Fat Surface, Sayer Obaid Alharbi, Florentin Smarandache, Awatif M.A. Elsiddieg, Aisha M. Alqahtani, M. Riaz Khan, V. Puneeth, Nidhal Becheikh

Branch Mathematics and Statistics Faculty and Staff Publications

The entropy generation analysis for the nanofluid flowing over a stretching/shrinking curved region is performed in the existence of the cross-diffusion effect. The surface is also subjected to second-order velocity slip under the effect of mixed convection. The Joule heating that contributes significantly to the heat transfer properties of nanofluid is incorporated along with the heat source/sink. Furthermore, the flow is assumed to be governed by an exterior magnetic field that aids in gaining control over the flow speed. With these frameworks, the mathematical model that describes the flow with such characteristics and assumptions is framed using partial differential equations …

Medical Diagnosis Via Refined Neutrosophic Fuzzy Logic: Detection Of Illness Using Neutrosophic Sets, K. Hemabala, B. Srinivasa Kumar, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The objective of the paper is to implement and validate diagnosis in the medical field via refined neutrosophic fuzzy logic (RNFL). As such, we have proposed a Max-Min composition (MMC) method in RNFL. This method deals with the diagnosis under certain constraints like uncertainty and indeterminacy. Further, we have considered the diagnosis problems to validate the sensitivity analysis of the novel multi attribute decision-making technique. Finally, we gave the graphical representations and compared the obtained results with other existing measures in refined neutrosophic fuzzy sets.

The Fluid Margin Between Physical Causal Closure And Non-Physical Causal Closure, Extended To The Neutrosophic Causal Closure Principle, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

We plead for a fluid margin, or mixed/indeterminate buffer zone, between Physical and Non-Physical Causal Closures, and for a Neutrosophic Causal Closure Principle claiming that the chances of all physical effects are determined by their prior partially physical and partially non-physical causes.

Linguistic Multidimensional Spaces, W. B. Vasantha Kandasamy, Ilanthenral K., Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This book extends the concept of linguistic coordinate geometry using linguistic planes or semi-linguistic planes. In the case of coordinate planes, we are always guaranteed of the distance between any two points in that plane. However, in the case of linguistic and semi-linguistic planes, we can not always determine the linguistic distance between any two points. This is the first limitation of linguistic planes and semi-linguistic planes.

A New Type Of Neutrosophic Set In Pythagorean Fuzzy Environment And Applications To Multi-Criteria Decision Making, Mahmut Can Bozyıgıt, Murat Olgun, Florentin Smarandache, Mehmet Unver

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we introduce the concepts of Pythagorean fuzzy valued neutrosophic set (PFVNS) and Pythagorean fuzzy valued neutrosophic (PFVNV) constructed by considering Pythagorean fuzzy values (PFVs) instead of numbers for the degrees of the truth, the indeterminacy and the falsity, which is a new extension of intuitionistic fuzzy valued neutrosophic set (IFVNS). By means of PFVNSs, the degrees of the truth, the indeterminacy and the falsity can be given in Pythagorean fuzzy environment and more sensitive evaluations are made by a decision maker in decision making problems compared to IFVNSs. In other words, such sets enable a decision maker …

New Types Of Topologies And Neutrosophic Topologies, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we recall the six new types of topologies that we introduced in the last years (2019-2022), such as: Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, NeutroTopology, AntiTopology, SuperHyperTopology, and Neutrosophic SuperHyperTopology.

Neutrosophic Superhyperalgebra And New Types Of Topologies, Florentin Smarandache, Memet Sahin, Derya Bakbak, Vakkas Uluçay, Abdullah Kargı

Branch Mathematics and Statistics Faculty and Staff Publications

In general, a system S (that may be a company, association, institution, society, country, etc.) is formed by sub-systems Si { or P(S), the powerset of S }, and each sub-system Si is formed by sub-sub-systems Sij { or P(P(S)) = P^2(S) } and so on.

That’s why the n-th PowerSet of a Set S { defined recursively and denoted by P^n(S) = P(P^(n-1)(S) } was introduced, to better describes the organization of people, beings, objects etc. in our real world.

The n-th PowerSet was used in defining the SuperHyperOperation, SuperHyperAxiom, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyperAxiom in order …

Nidus Idearum. Scilogs, Xii: Seed & Heed, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this twelfth book of scilogs – called seed & heed –, one may find topics on Neutrosophy, Superluminal Physics, Mathematics, Information Fusion, Philosophy, or Sociology – email messages to research colleagues, or replies, notes, comments, remarks about authors, articles, or books, spontaneous ideas, and so on.

Perceptual Anthropomorphic Walking Robot Platform For Navigation In Unstructured And Undifferentiated Environments, Luige Vladareanu, Mihai Rădulescu, Marius Pandelea, Hongbo Wang, Florentin Smarandache, Yongfei Feng, Ionel-Alexandru Gal, Alexandra C. Ciocîrlan

Branch Mathematics and Statistics Faculty and Staff Publications

This scientific presentation studies the VIPRO Platform for control of Anthropomorphic Walking Robots (AWR), the architecture control system of the SiMeLA MP robot motion, and shows several experimental results.

The Encyclopedia Of Neutrosophic Researchers, Vol. 6, Florentin Smarandache, Maikel Yelandi Leyva Vázquez, Jesús Estupiñán Ricardo

Branch Mathematics and Statistics Faculty and Staff Publications

Este es el Sexto volumen de la Enciclopedia de Investigadores Neutróficos, editados a partir de materiales ofrecidos por los autores que respondieron a la invitación del editor. Los autores se enumeran alfabéticamente. La introducción contiene una breve historia de la neutrosófica, y en especial se sus impacto en latinoamérica junto con enlaces a los principales artículos y libros. Conjunto neutrosófico, lógica neutrosófica, probabilidad neutrosófica, estadística neutrosófica, medida neutrosófica, precálculo neutrosófico, cálculo neutrosófico, psicología neutrosófica, sociología neutrosófica etc., están ganando una atención significativa en resolver muchos problemas de la vida real que implican incertidumbre, imprecisión, vaguedad, incompletitud, inconsistencia e indeterminación. En …

The Use Of Neutrosophic Methods Of Operation Research In The Management Of Corporate Work, Maissam Jdid, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The science of operations research is one of the modern sciences that have made a great revolution in all areas of life through the methods provided by it, suitable and appropriate to solve most of the problems that were facing researchers, scholars and those interested in the development of societies, and the most beneficiaries of this science were companies and institutions that are looking for scientific methods that help them manage their work so that they achieve the greatest profit and the lowest cost, and one of the important methods that have been used in the management of companies we …

N-Cylindrical Fuzzy Neutrosophic Topological Spaces, Sarannya Kumari R, Sunny Joseph Kalayathankal, Mathews George, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The objective of this study is to incorporate topological space into the realm of n-Cylindrical Fuzzy Neutrosophic Sets (n-CyFNS), which are the most novel type of fuzzy neutrosophic sets. In this paper, we introduce n-Cylindrical Fuzzy Neutrosophic Topological Spaces (n-CyFNTS), n-Cylindrical Fuzzy Neutrosophic (n-CyFN) open sets, and n-CyFN closed sets. We also defined the n-CyFN base, n-CyFN subbase, and some related theorems here.

Complex Fermatean Neutrosophic Graph And Application To Decision Making, Said Broumi, Swaminathan Mohanaselvi, Tomasz Witczak, Mohamed Talea, Assia Bakali, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Original scientific paper Abstract: A new growing area of the neutrosophic set theory called complex neutrosophic sets (CNS) provides useful tools for dealing with uncertainty in complex valued physical variables that are observed in the actual world. A CNS takes values for the truth, indeterminacy and falsity membership functions in the complex plane's unit circle. In this research, a novel concept of complex fermatean neutrosophic graph (CFNG) is established and various basic graphical ideas such as the order, size, degree and total degree of a vertex of it are introduced. Also, set theoretical operations such as complement, union, join, ring-sum …

On Neutro-La-Semihypergroups And Neutro-Hv-La-Semigroup, Saeid Mirvakili, Akbar Rezaei, Omaima Al-Shanqiti, Florentin Smarandache, Bijan Davvaz

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we extend the notion of LA-semihypergroups (resp. Hv-LA-semigroups) to neutro-LA-semihypergroups (respectively, neutro-Hv-LA-semigroups). Anti-LA-semihypergroups (respectively, anti-Hv-LA-semigroups) are studied and investigated some of their properties. We show that these new concepts are different from classical concepts by several examples. These are particular cases of the classical algebraic structures generalized to neutroalgebraic structures and antialgebraic structures (Smarandache, 2019).

Professor Cai Wen’S Extenics ( A Letter To The Editor-In-Chief), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

I had the chance and honor to meet Prof. Dr. Cai Wen (1941 - 2021), the founder of Extenics, in the summer of 2012, at the Guangdong University of Technology (GDUT), Institute of Extenics and Innovative Methods, in Guangzhou, P. R. China, where I was invited by Dr. Xingsen Li to do research on Extenics about solving contradictory problems in science.

I have passed a wonderful time in China (17 May – 15 August, 2012) presenting and listening to many scientific presentations on Extenics and their applications in various fields of knowledge, and studying new papers and book provided to …

Special Subset Linguistic Topological Spaces, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this book, authors, for the first time, introduce the new notion of special subset linguistic topological spaces using linguistic square matrices. This book is organized into three chapters. Chapter One supplies the reader with the concept of ling set, ling variable, ling continuum, etc. Specific basic linguistic algebraic structures, like linguistic semigroup linguistic monoid, are introduced. Also, algebraic structures to linguistic square matrices are defined and described with examples. For the first time, non-commutative linguistic topological spaces are introduced. The notion of a linguistic special subset of doubly non-commutative topological spaces of linguistic topological spaces is introduced in this …

Neutrosophic Transport And Assignment Issues, Florentin Smarandache, Maissam Ahmad Jdid

Branch Mathematics and Statistics Faculty and Staff Publications

We all know that problems of transportation and allocation appear frequently in practical life. We need to transfer materials from production centers to consumption centers to secure the areas’ need for the transported material or allocate machines or people to do a specific job at the lowest cost, or in the shortest time. We know that the cost factors Time is one of the most important factors that decision-makers care about because it plays an “important” role in many of the practical and scientific issues that we face in our daily lives, and we need careful study to enable us …

On Refined Neutrosophic Finite P-Group, Sunday Adesina Adebisi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The neutrosophic automorphisms of a neutrosophic groups G (I) , denoted by Aut(G (I)) is a neu-trosophic group under the usual mapping composition. It is a permutation of G (I) which is also a neutrosophic homomorphism. Moreover, suppose that X1 = X(G (I)) is the neutrosophic group of inner neutrosophic auto-morphisms of a neutrosophic group G (I) and Xn the neutrosophic group of inner neutrosophic automorphisms of Xn-1. In this paper, we show that if any neutrosophic group of the sequence G (I), X1, X2, … is the identity, then G (I) is nilpotent.

Neutrosophic Treatment Of The Modified Simplex Algorithm To Find The Optimal Solution For Linear Models, Florentin Smarandache, Maissam Ahmad Jdid

Branch Mathematics and Statistics Faculty and Staff Publications

Science is the basis for managing the affairs of life and human activities, and living without knowledge is a form of wandering and a kind of loss. Using scientific methods helps us understand the foundations of choice, decision-making, and adopting the right solutions when solutions abound and options are numerous. Operational research is considered the best that scientific development has provided because its methods depend on the application of scientific methods in solving complex issues and the optimal use of available resources in various fields, private and governmental work in peace and war, in politics and economics, in planning and …

Development Of Some New Hybrid Structures Of Hypersoft Set With Possibility-Degree Settings, Atiqe Ur Ur Rahman, Florentin Smarandache, Muhammad Saeed, Khuram Ali Khan

Branch Mathematics and Statistics Faculty and Staff Publications

The concept of a hypersoft membership function is introduced in the extension of a soft set known as a hypersoft set, permitting it to handle complicated and uncertain information in a more powerful and flexible manner. Many academics have already become fascinated with this new area of study, leading to the development of a number of hybrid structures. This chapter develops some new hybrid hypersoft set structures by taking into account multiple fuzzy set-like settings and possibility degree-based settings collectively. Additionally, numerical examples are included to clarify the concept of these structures. Researchers can utilize this work to better understand …

Generalized Plithogenic Whole Hypersoft Set, Pfhss-Matrix, Operators And Applications As Covid-19 Data Structures, Shazia Rana, Muhammad Saeed, Madiha Qayyum, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This article is a preliminary draft for initiating and commencing a new pioneer dimension of expression. To deal with higher-dimensional data or information flowing in this modern era of information technology and artificial intelligence, some innovative super algebraic structures are essential to be formulated. In this paper, we have introduced such matrices that have multiple layers and clusters of layers to portray multi-dimensional data or massively dispersed information of the plithogenic universe made up of numerous subjects their attributes, and sub-attributes. For grasping that field of parallel information, events, and realities flowing from the micro to the macro level of …