Mathematics Commons^™

A Pedagogic Analysis Of Linear Algebra Courses, Andrew Taylor

Mathematics & Statistics ETDs

This project is concerned with investigating the question, "Do our applied linear algebra courses (at the University of New Mexico) adequately prepare STEM students for future work in their respective fields?" In order to explore this, surveys were issued to three groups (sections) of students (among two different instructors) at the conclusion of their applied linear algebra course, as well as STEM professors/instructors from a variety of STEM fields. Students were surveyed regarding their perceived mastery of given topics/ideas from the course and professors/instructors were surveyed about the level of mastery they felt was necessary (referred to as ``desired mastery") …

Implications Of The Modifiable Areal Unit Problem For Wildfire Analyses, Timothy P. Nagle-Mcnaughton, Xi Gong, Jose A. Constantine

Geography and Environmental Studies Faculty Publications

Wildfires pose a danger to both ecologies and communities. To this end, many large-scale analyses of wildfire patterns and behavior rely on the aggregation of point data to polygons, typically those based on distinct disparate ecological areas. However, the sizes, shapes, andorientations of the polygons to which data are aggregated are not neutral factors in the resulting analysis. The influence of the aggregation polygons on calculated results is known as the modifiable areal unit problem (MAUP), which is well-documented in the spatial statistics literature. Despite the documentation of the MAUP, relatively few wildfire studies consider the effects of the MAUP …

Re-Reading Wilczek’S Remark On “Lost In Math”: The Perils Of Postempirical Science And Their Resolution, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Sabine Hossenfelder’s recent book “Lost in Math” has attracted numerous responses, including by notable physicists such as Frank Wilczek. In this article we focus on Wilczek’s remark on that book, in particular on the perils of postempirical science. We also discuss shortly multiverse hypothesis from philosophical perspective. In last section, we offer a resolution from the perspective of Neutrosophic Logic on this problem of classical tension between mathematics and experience approach to physics, which seems to cause the stagnation of modern physics.

Recent Experimental Findings Supporting Smarandache’S Hypothesis And Quantum Sorites Paradoxes And Subquantum Kinetic Model Of Electron, Victor Christianto, Robert N. Boyd, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Smarandache Hypothesis states that there is no speed limit of anything, including light and particles. While the idea is quite simple and based on known hypothesis of quantum mechanics, called Einstein-Podolski-Rosen paradox, in reality such a superluminal physics seems still hard to accept by majority of physicists. Here we review some experiments to support superluminal physics and also findings to explain Smarandache Quantum Paradoxes and Quantum Sorites Paradox. We also touch briefly on new experiment on magneton, supporting SubQuantum Kinetic Model of Electron.

Conclusion & Significance: Multiexperimental findings assessment allows one to verify conjectures by two of us (FS & …

New Foundation In The Sciences: Physics Without Sweeping Infinities Under The Rug, Florentin Smarandache, Victor Christianto, Robert Neil Boyd

Branch Mathematics and Statistics Faculty and Staff Publications

It is widely known among the Frontiers of physics, that “sweeping under the rug” practice has been quite the norm rather than exception. In other words, the leading paradigms have strong tendency to be hailed as the only game in town. For example, renormalization group theory was hailed as cure in order to solve infinity problem in QED theory. For instance, a quote from Richard Feynman goes as follows: “What the three Nobel Prize winners did, in the words of Feynman, was "to get rid of the infinities in the calculations. The infinities are still there, but now they can …

Optimal Relaxation Weights For Multigrid Reduction In Time (Mgrit), Masumi Sugiyama

Mathematics & Statistics ETDs

Based on current trends in computer architectures, faster compute speeds must come from increased parallelism rather than increased clock speeds, which are stagnate. This situation has created the well-known bottleneck for sequential time-integration, where each individual time-value (i.e., time-step) is computed sequentially. One approach to alleviate this and achieve parallelism in time is with multigrid. In this work, we consider the scheme known as multigrid-reduction-in-time (MGRIT), but note that there exist other parallel-in-time methods such as parareal and the parallel full approximation scheme in space and time (PFASST). MGRIT is a full multi-level method applied to the time dimension and …

From Cymatics To Sound Therapy: Their Role In Spirituality And Consciousness Research, Victor Christianto, Kasan Susilo, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Sound is one of the types of waves that can be felt by the sense of hearing (ears). In physics, the definition of sound is something that is produced from objects that vibrate. Objects that produce sound are called sound sources. The sound source that vibrates will vibrate the molecules into the air around it. Sound is mechanical compression or longitudinal waves that propagate through the medium. This medium or intermediate agent can be liquid, solid, gas. So, sound waves can propagate for example in water, coal, or air. Most sounds are a combination of various vibratory signals composed of …

A Remark On How A Consciousness Model And Entanglement Can Lead Us To Quantum Communication, Victor Christianto, Robert N. Boyd, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In a recent paper, we describe how a model of quantum communication based on combining consciousness experiment and entanglement can serve as impetus to stop 5G-caused diseases. Therefore, in this paper we will discuss how entanglement can be explained in terms of quantum theory. This short review may be considered as an effort to bring QM into real problem solving, i.e. telecommunication.

On Three Possible Applications Of Neutrosophic Logic In Applied Sciences, Including Matter Creation, Victor Christianto, Robert N. Boyd, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In the same spirit with the theme of last issue of this SGJ journal (“Ongoing creation”), this paper shortly reviews a plausible mechanism from Aether to become ordinary matter from the perspective of Neutrosophic Logic. We also discuss two other possible applications of Neutrosophic Logic, including a resolution of conflicting paradigms in medicine. We hope that some ideas as outlined herein will be proved useful in the near future.

On Newtonian Dynamics With A Variable Earth Mass: Geodetic Evidence And Its Implications On Pioneer Spacecraft Anomaly And Lageos Satellite, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Around 3 decades ago, Jayant Narlikar & Halton Arp argued on possible variable mass hypothesis cosmology (VMH). In the meantime, the Earth expansion problem has attracted great interest, and recent study gives geodetic evidence that the Earth has been expanding, at least over the recent several decades. Therefore, in the present article discusses some interesting effects related to varying G, but here we argue that instead of varying G we can think of varying mass (M). Among other things we discuss receding planets from the Sun, calculation of Pioneer spacecraft anomaly as proposed by B.G. Sidharth, and also possible slight …

On Cellular Automata Representation Of Submicroscopic Physics: From Static Space To Zuse’S Calculating Space Hypothesis, Victor Christianto, Volodymyr Krasnoholovets, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In some recent papers (G. ‘t Hooft and others), it has been argued that quantum mechanics can arise from classical cellular automata. Nonetheless, G. Shpenkov has proved that the classical wave equation makes it possible to derive a periodic table of elements, which is very close to Mendeleyev’s one, and describe also other phenomena related to the structure of molecules. Hence the classical wave equation complements Schrödinger’s equation, which implies the appearance of a cellular automaton molecular model starting from classical wave equation. The other studies show that the microworld is constituted as a tessellation of primary topological balls. The …

A Harmless Wireless Quantum Alternative To Cell Phones Based On Quantum Noise, Florentin Smarandache, Robert Neil Boyd, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

In the meantime we know that 4G and 5G technologies cause many harms to human health. Therefore, here we submit a harmless wireless quantum alternative to cell phones. It is our hope that this alternative

“A Thousand Words”: How Shannon Entropy Perspective Provides Link Among Exponential Data Growth, Average Temperature Of The Earth, Declining Earth Magnetic Field, And Global Consciousness, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The sunspot data seems to indicate that the Sun is likely to enter Maunder Minimum, then it will mean that low Sun activity may cause low temperature in Earth. If this happens then it will cause a phenomenon which is called by some climatology experts as “The Little Ice Age” for the next 20-30 years, starting from the next few years. Therefore, the Earth climate in the coming years tend to be cooler than before. This phenomenon then causes us to ask: what can we do as human being in Earth to postpone or avoid the worsening situation in terms …

One-Note-Samba Approach To Cosmology, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

Inspired by One Note Samba, a standard jazz repertoire, we present an outline of Bose-Einstein Condensate Cosmology. Although this approach seems awkward and a bit off the wall at first glance, it is not impossible to connect altogether BEC, Scalar Field Cosmology and Feshbach Resonance with Ermakov-Pinney equation. We also briefly discuss possible link with our previous paper which describes Newtonian Universe with Vortex in terms of Ermakov equation.

Bulk Spectrum And K-Theory For Infinite-Area Topological Quasicrystals [Dataset], Terry A. Loring

Math and Statistics Datasets

Archived here are files, data and program files, that are supplementary the following article, expected to be published in 2019:

* Terry A. Loring. Bulk Spectrum and K-theory for Infinite-Area Topological Quascrystal. Journal of Mathematical Physics, (2019 est.).

The files, in Matlab format, allow the user to create approximate eigenvalues for a topological Hamilontian on a round patch of a quasicrystal. The data files describe pathes of the Ammann-Bennkeer tiling. One of the data files is really large. Read the file README.txt first (available via the main download button), so see if you can avoid downloading the largest file.

Recommended …

A Deep Learning Approach To Uncertainty Quantification, Mst Afroja Akter

Mathematics & Statistics ETDs

In this thesis we consider ordinary differential equations (ODEs) with random parameters. We focus on Monte Carlo (MC) sampling for computing the statistics of some quantities of interest (QoIs) given by the solution of the ODE problems. We use the 4th order accurate Runge-Kutta (RK4) method as the deterministic ODE solver. We then develop a hybrid MC sampling method that combines RK4 with neural network models to efficiently compute the statistics of QoIs within a desired accuracy. We present several numerical examples to verify the accuracy and efficiency of the proposed hybrid method compared to classical MC sampling. The hybrid …

L^{\Infty}-Estimates Of The Solution Of The Navier-Stokes Equations For Periodic Initial Data, Santosh Pathak

Mathematics & Statistics ETDs

In this doctoral dissertation, we consider the Cauchy problem for the 3D incompressible Navier-Stokes equations. Here, we are interested in a smooth periodic solution of the problem which happens to be a special case of a paper by Otto Kreiss and Jens Lorenz. More precisely, we will look into a special case of their paper by two approaches. In the first approach, we will try to follow the similar techniques as in the original paper for smooth periodic solution. Because of the involvement of the Fourier expansion in the process, we encounter with some intriguing factors in the periodic case …

A Hybrid Plithogenic Decision-Making Approach With Quality Function Deployment For Selecting Supply Chain Sustainability Metrics, Florentin Smarandache, Mohamed Abdel-Basset, Rehab Mohamed, Abd El-Nasser H. Zaied

Branch Mathematics and Statistics Faculty and Staff Publications

Supply chain sustainability has become one of the most attractive decision management topics. There are many articles that have focused on this field presenting many different points of view. This research is centred on the evaluation of supply chain sustainability based on two critical dimensions. The first is the importance of evaluation metrics based on economic, environmental and social aspects, and the second is the degree of difficulty of information gathering. This paper aims to increase the accuracy of the evaluation. The proposed method is a combination of quality function deployment (QFD) with plithogenic aggregation operations. The aggregation operation is …

Direct Detection Of Relic Neutrino Background Remains Impossible: A Review Of More Recent Arguments, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The existence of big bang relic neutrinos—exact analogues of the big bang relic photons comprising the cosmic microwave background radiation—is a basic prediction of standard cosmology. The standard big bang theory predicts the existence of 1087 neutrinos per flavour in the visible universe. This is an enormous abundance unrivalled by any other known form of matter, falling second only to the cosmic microwave background (CMB) photon. Yet, unlike the CMB photon which boasts its first (serendipitous) detection in the 1960s and which has since been observed and its properties measured to a high degree of accuracy in a series of …

Extension Of Soft Set To Hypersoft Set, And Then To Plithogenic Hypersoft Set, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we generalize the soft set tothe hypersoft set by transforming the function F into a multi-attribute function. Then we introduce the hybrids of Crisp, Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Hypersoft Set.

An Approach To Determining Customer Satisfaction In Traditional Serbian Restaurants, Florentin Smarandache, Dragisa Stanujkic, Darjan Karabasevic, Edmundas Kazimieras Zavadskas, Fausto Cavallaro

Branch Mathematics and Statistics Faculty and Staff Publications

The aim of this paper is to make a proposal for an easy–to–use approach to the evaluation of customer satisfaction in restaurants. In order to provide a reliable way to collect respondents’ real attitudes, an approach based on the use of smaller number of evaluation criteria and interactive questionnaire created in a spreadsheet file is proposed in this paper, whereby an easy-to-understand and simple-touse procedure is proposed for determining weights of criteria. In addition to the said, the proposed approach applies the simplified SERVQUAL-based approach, for which reason a simplified version of the Weighted Sum Method based on the decision …

From Big Science To “Deep Science”, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

The Standard Model of particle physics has accomplished a great deal including the discovery of Higgs boson in 2012. However, since the supersymmetric extension of the Standard Model has not been successful so far, some physicists are asking what alternative deeper theory could be beyond the Standard Model? This article discusses the relationship between mathematics and physical reality and explores the ways to go from Big Science to “Deep Science”.

Physics Beyond Catching A Mouse In The Dark: From Big Science To Deep Science, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The Higgs particle has been detected a few years ago, that is what newspapers tell us. For many physicists, the Standard Model of particle physics has accomplished all the jobs. Or to put it simply: The game is over. Is it true? Then some physicists began to ask: can go beyond the Standard Model? Because the supersymmetric extension of the Standard Model has failed. If you feel that theoretical physics is becoming boring, you are not alone. Fortunately, there is good news: a new generation of physicists are doing table-top experiments in their basements. Can we expect new results later?2 …

Remark On Creatio Ex Nihilo, Intelligent Design And Emergence Philosophy Approaches To Origin Of The Universe, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

It is known that the Big Bang theory was based on the concept of creation ex nihilo, after ancient Greek philosophers. In this paper, we will make few remark on the concept of creatio ex nihilo (as a commentary to a recent paper by Kalachanis, Athanasios Anastasiou, Ioannis Kostikas, Efstratios Theodossious and Мilan S. Dimitrijevi), as well as two other approaches, i.e. Intelligent Design and Emergence Theory by Clayton/Yong. As continuation of our recent paper to appear in forthcoming issue of J. Asia Mathematika, we argue that beside the above three approaches, a new concept called creatio ex-rotatione offers a …

Numerical Solution For Solving Procedure For 3d Motions Near Libration Points In The Circular Restricted Three Body Problem (Cr3bp), Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In a recent paper in Astrophysics and Space Science Vol. 364 no. 11 (2019), S. Ershkov & D. Leschenko presented a new solving procedure for Euler-Poisson equations for solving momentum equations of the CR3BP near libration points for uniformly rotating planets having inclined orbits in the solar system with respect to the orbit of the Earth. The system of equations of the CR3BP has been explored with regard to the existence of an analytic way of presentation of the approximated solution in the vicinity of libration points. A new and elegant ansatz has been suggested in their publication whereby, in …

Towards Helmholtz’S Electron Vortex From Kolmogorov’S Theory Of Turbulence And A New Model Of Origination Of Charge And Matter, Victor Christianto, Florentin Smarandache, Robert N. Boyd

Branch Mathematics and Statistics Faculty and Staff Publications

In the present paper we discuss: a) how Hilbert’s unification program failed completely, and b) we outline a new electron model based on Helmholtz’s electron vortex and Kolmogorov theory of turbulence. Novelty aspect: we discuss among other things, electron capture event, and von Karman vortex street. We also discuss a new model of origination of charge and matter. This paper is a sequel to a preceding paper on similar theme.

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.

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 …

An Approach To Determining Customer Satisfaction In Traditional Serbian Restaurants, Florentin Smarandache, Dragisa Stanujkic, Darjan Karabasevic, Edmundas Kazimieras Zavadskas, F. Cavallaro

Branch Mathematics and Statistics Faculty and Staff Publications

The aim of this paper is to make a proposal for an easy–to–use approach to the evaluation of customer satisfaction in restaurants. In order to provide a reliable way to collect respondents’ real attitudes, an approach based on the use of smaller number of evaluation criteria and interactive questionnaire created in a spreadsheet file is proposed in this paper, whereby an easy-to-understand and simple-touse procedure is proposed for determining weights of criteria. In addition to the said, the proposed approach applies the simplified SERVQUAL-based approach, for which reason a simplified version of the Weighted Sum Method based on the decision …

Nidus Idearum. Scilogs, Vii: Superluminal Physics - Second Edition, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

My lab[oratory] is a virtual facility with non-controlled conditions in which I mostly perform scientific meditation and chats: a nest of ideas (nidus idearum, in Latin). I called the jottings herein scilogs (truncations of the words scientific, and gr. Λόγος – appealing rather to its original meanings "ground", "opinion", "expectation"), combining the welly of both science and informal (via internet) talks (in English, French, and Romanian). * In this seventh book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, referring to different scientific topics – email messages to research colleagues, or …