
Arturo Ortiz TapiaBISD · Pathways Learning Center
Arturo Ortiz Tapia
Ph.D.
Math Teacher, High School. Freelance researcher in mathematics and theoretical physics.
About
89
Publications
85,763
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
149
Citations
Introduction
I am working of number theory, mathematical modeling and fractals.
Additional affiliations
June 2006 - October 2011
Education
May 2015 - November 2019
Universidad Abierta y a distancia de México
Field of study
- mathematics
October 1997 - July 2001
October 1994 - September 1996
Publications
Publications (89)
With an empirical approach, this paper compares experimental data to the expected values from a statistical and probabilistic perspective, with the aim to present some insights on the structure of prime pairs in the wake of the Dirichlet's theorem about arithmetic progressions, and on the correlation between first Hardy-Littlewood conjecture, Brun'...
Brief, informal essay about how is mathematics unreasonably effective or ineffective in exploring physical reality or some parts of it.
In this study, we investigate the precision of measuring the internal angles of a presumed regular tetrahedron. Through rigorous numerical analysis, we demonstrate that the observed variation of the percentage error, limited to a maximum of 1.42%, and the Coefficient of Variation (CV), capped at CV " 0.03, can be attributed to the finite methods em...
Divulgation of some of the most important areas of historical and current mathematics
The Paul Erd\H{o}s-Tur\'an inequality is used as a quantitative form of Weyl' s criterion, together with other criteria to asses equidistribution properties on some patterns of sequences that arise from indexation of prime numbers, Jumping Champions (called here and in previous work, "meta-distances" or even md, for short). A statistical meta-analy...
Strong correlations are found between the presence of a subject placed in close proximity both in time and space to a 100mW, 532nm laser source, performing a especially crafted contemplative lucid state with opened eyes (called "Shintergy") that supposedly synchronizes his brain and body in high brain frequencies, and measurements on the intensity...
Starting from an empirical approach, the distribution of twin primes in mod(q) classes is explored. In addition, the model is extended to other prime pairs of the form (, +). Numerical analysis compares experimental data to expected values and leads to the hypothesis that twin primes and other prime pairs thin out in classes with the same cardinali...
In this paper we show that for some constant $c>0$ and for any $A>0$ there exist some $x(A)>0$ such that, If $q\leq (\log x)^{A}$ then we have \begin{align} \Psi_z(x;\mathcal{N}_q(a,b),q) &= \frac{\Theta (z)}{2\phi(q)}x + O\bigg(\frac{x}{e^{c\sqrt{\log x}}}\bigg)\nonumber \end{align}for $x\geq x(A)$ for some $\Theta(z)>0$. In particular for $q\leq...
Starting from an empirical approach, the distribution of twin primes in mod(q) classes is explored. In addition the model is extended to other prime pairs of the form (í µí± í µí± + í µí± §). Numerical analysis compares experimental data to the expected values and leads to the hypothesis that twin primes and other prime pairs thin out in classes...
In this paper we show that for some constant c > 0 and for any A > 0 there exist some x(A) > 0 such that, If q ≤ (log x) A then we have Ψz(x; Nq(a, b), q) = Θ(z) 2φ(q) x + O x e c √ log x for x ≥ x(A). In particular for q ≤ (log x) A for any A > 0 Ψz(x; Nq(a, b), q) ∼ xD(z) 2φ(q) for some constant D(z) > 0 and where φ(q) = #{(a, b) : (p i , p i+z)...
In this paper we show that for some constant c > 0 and for any A > 0, If q ≤ (log x) A then there exist some x(A) > 0 such that for x ≥ x(A) we have Ψz(x, Nq(a, b), q) = Θ(z) 2φ(q) x + O x e c √ log x. In particular for q ≤ (log x) A for any A > 0 Ψz(x; Nq(a, b), q) ∼ xD(z) 2φ(q) for some constant D(z) > 0 and where φ(q) = #{(a, b) : (p i , p i+z)...
Active thermography is an experimental technique used to analyze samples of materials or entire structures without destroying them, by means of a heat source, such as a laser beam of a given power. It is
posed that such experimental procedure can be modeled mathematically through the complete equation of heat transfer. The uncertainty on the assump...
Active thermography is an experimental technique used to analyze samples of materials or entire structures without destroying them, by means of a heat source, such as a laser beam of a given power. It is posed that such experimental procedure can be modeled mathematically through the complete equation of heat transfer. The uncertainty on the assump...
Starting from the first Hardy-Littlewood conjecture some topics will be covered: an empirical approach to the distribution of the twin primes in classes mod(10) and a simplified proof of the Bruns theorem . Finally, it will be explored an approach based on numerical analysis: Monte Carlo Method and Low discrepancy Sequences will be used to prove th...
A general 3D flow and transport model in porous media was derived applying an axiomatic continuum modeling approach, which was implemented using the finite element method to numerically simulate, analyze and interpret microbial enhanced oil recovery (MEOR) processes under laboratory conditions at core scale. From the methodological point of view th...
Starting from the first Hardy-Littlewood conjecture some topics will be covered: an empirical approach to the distribution of the twin primes in classes mod(10) and a simplified proof of the Bruns theorem . Finally, it will be explored an approach based on numerical analysis: Monte Carlo Method and Low discrepancy Sequences will be used to prove th...
It is conjectured that there is a converging sequence of some generalized Fibonacci ratios, given the difference between consecutive ratios, such as the Golden Ratio, $\varphi^1$, and the next golden ratio $\varphi^2$. Moreover, the graphic depiction of those ratios show some overlap with the quadratic family, and some numerical evidence suggest th...
The Shannon entropy is used as a basis for applying different lemmas and conjectures concerning the set of gaps between prime numbers G_p , thus estimating several measures of it. The same procedures are applied to artificially created number sets, to compare the size of their entropy against G_p .
A flow and transport model in porous media was implemented in COMSOL Multiphysics to simulate, analyze and interpret Microbial Enhanced Oil Recovery (MEOR) processes at core scale under laboratory conditions. The flow model is biphasic and is based on the oil phase pressure and total velocity formulation. Whereas, the transport model consists of tw...
In this work, a flow and transport model which was implemented using a finite element method to simulate, analyze and interpret MEOR processes at core scale under laboratory conditions is presented. The flow model is based on the oil phase pressure and total velocity formulation, in which the capillary pressure, relative permeabilities, the effects...
Mathematical, Numerical and Computational model for simulating biosurfactant adsorption.
Upon encountering the title of this book, one might wonder what type of differential equations R can solve. It turns out that R can be used to address initial value problems (IVPs), using popular and successful methods such as LSODE (Adams method on its core) and RADAU5 (implicit Runge-Kutta), which enable a wide variety of possible implementations...
Porous media are broadly found in nature and their study is of high relevance in our present lives. In geosciences porous media research is fundamental in applications to aquifers, mineral mines, contaminant transport, soil remediation, waste storage, oil recovery and geothermal energy deposits. Despite their importance, there is as yet no complete...
The quest for common ground in the expression of logical statements--regardless of the given syntax, semantics, or grammar--has taken the best efforts of notable logicians throughout the 20th century. This book gathers a collection of some of the most notable of their works. Its structure is chronological, but it is not merely a book on the history...
Using the S-300 device for wire plasma corona generation and streak, obscure and x-frame cameras for diagnostics, it was possible
to determine the values of several parameters inside helical and toroidal structures formed in z-pinch. We concluded that
the number of particles in the Debye sphere could beN
D
<1, which makes evident the non-ideal cha...
Classes of Solution Functions of Integral Equations
Susceptible to
Some Low Discrepancy Methods.
Fundamental in the numerical solution of any integral equation is the discretization process. Annunziato and Messina describe a heterogeneous process of discretization for the space and temporal variable. Using a contraction theorem invariant to a map, the existence of the solution through their discretization (in space) is proven. Moreover, the un...
Short program to decide which index a prime number has. For example, 5, is the third prime number. 3 is the index of 5.
Continuity can be understood, for example, as moving beyond inequalities with fixed parameters-that render the well-known "true or false" options-into the possibility that the boundaries of the inequalities may be adjusted. This is one of the central issues of this book. The work is a brilliant survey of the different theories concerning cognition,...
In this work, a set of experiments was carried out with the purpose of studying the adsorption mechanisms involved in the interfacial interaction of the asphaltene/mineral system at high asphaltene concentrations. Adsorption isotherms of asphaltenes were obtained by contacting samples of Berea sandstone, Bedford limestone, and a Mexican dolomite ro...
F10.08> P0, Pr[V accepts P0] s.The main theorem we shall see today is the following:Theorem 7.1 (Hastad [Has97])NP ` PCP 1\Gammaffl;12(log; 3) (7.1)where ffl ? 0 is an arbitrarily small constant.We will not prove this from scratch, but assume that we can prove the following weaker version ofthe PCP theorem:Theorem 7.2 There exists a constant ffi ?...
Direct numerical simulations have been performed in this study to visualize the flow behavior of single and multiple square
jets issuing normally into a cross-flow. Three configurations are considered, a single jet located in the centre of the domain,
twin jets in side-by-side (SBS) arrangement in the spanwise direction and triple jets in tandem ar...
Fate of microorganisms in porous media has very important applications in many branches of environmental and petroleum science and engineering, among others; however, concurrently it is a very complex and interacting phenomenon mainly because microorganisms are living. Applying the systematic modeling approach to continuum systems, we derive a mode...
Multiphase fluid flow models in porous media are frequent in many important applications of Earth Sciences, such as in groundwater contamination, subsurface remediation and reservoir modeling. The aim of the present work is to implement in COMSOL Multiphysics a multiphase fluid flow model in porous media, also known in the oil reservoir engineering...
An array of numerical simulations of the equation of transport were performed using the adsorption isotherm equation proposed by Zhu and Gu, a linear isotherm and a simple cubic polynomial. The COMSOL implementation, was in 1D, where the solutes are injected from one face of a homogeneous, isotropic core (small sample of reservoir rock); the concen...
Theory and problems addressed for High School (bachelor, secondary school, preparatory, pre-university) students. Some elementary calculus and probability is introduced.
This column on computer game history, from the perspective of the gaming industry, complements the column from the last issue on the history of virtual worlds. I met Daniel Pargman, then a graduate student studying multiplayer games, exactly ten years ago. He told me that one day there would be a research field dedicated to online games, and he pla...
A prime number (or a prime) is a natural number that has exactly two (distinct) natural number divisors, which are 1 and the prime number itself. Infinitude of prime numbers exists, as demonstrated by Euclid in about 300 BC [1].
The problem of modeling the distribution of prime numbers is a popular subject of investigation for number theorists. When looking at individual numbers, the primes seem to be randomly distributed, but the “global” distribution of primes follows well-defined laws [1, 2]. Let: d=Pi+1-Pi, i ∈ N (21.1) be the distance between consecutive prime numbers...
A review of Internet Phone Services Simplified by Jim Doherty and Neil Anderson. The authors present a simplified handbook for making your own decisions about VoIP, how to install it at home, and how to deal with troubleshooting.
A review of "The Linux Enterprise Cluster" by Karl Kopper. The author gathers almost all of the information necessary to build and administer a high-availability cluster based on Linux and its related free software. Two main ideas are emphasized in the text: First, a high-availability cluster is one that should act like a single unified computing r...
A review of "High-Performance Computing: Paradigm and Infrastructure," Laurence T. Yang and Minyi Guo, eds.
Let a quantified inequality constraint over the reals be a formula in the first-order predicate language over the structure of the real numbers, where the allowed predicate symbols areand
A review of Internet Effectively: A Beginner's Guide to the World Wide Web by Tyrone Adams and Sharon Scollard.
Peter Naur's radical view of some aspects of modern psychology and historical philosophy, with regard to the inner workings of the human mind, is presented in a perfectly understandable, and a daringly new, way. Whether we should agree with his views or not is another matter. Naur mainly challenges the views of behaviorism and cognitivism, and I ha...
A review of "Inescapable Data: Harnessing the Power of Convergence" by Chris Stakutis and John Webster.
A review of Computer Viruses and Malware by John Aycock
A brief travel through several of the most important disciplines of mathematics, showing the connection between the theory and its applications.
A review of High Performance Linux Clusters with Oscar, Rocks, openMosix & MPI by Joseph D. Sloan.
A review of Field-Based Coordination for Pervasive Multiagent Systems by Marco Mamei and Franco Zambonelli.
The feasibility of stabilizing a Z-pinch by means of an axial shear flow has been studied theoretically, numerically and experimentally. Since the results of the MHD stability analysis can depend on the equilibria that are being considered, we start by analysing families of self-consistent equilibria with sheared flow, which could represent feasibl...
In several z-pinch devices there has been observation of regular structures, which appear systematically when repeating the experiments. The fact that very identifiable, recurrent, geometrical structures appear in z-pinches, which are relatively long lived, has motivated the analysis of the experimental data from the point of view of self-organizat...
Program to calculate numerical integrals (quadratures) using trapezoid, middle point, Simpson and Monte Carlo. With the last one there is a visualization.
Program that at last is expected to do correctly Gram_Schmidt Orthogonalization for me
'Program for generating the fibonacci numbers,
' the number phi and the number pi from the number phi.
Makes visualization of 3 dimensional mathematical objects in a computer screen, using different geometrical properties for projecting a 3D object onto a 2D space, including rendering depth.
make numerical quadratures, treating the integrals as if they were an ordinary differential equation, with initial and boundary conditions.
! Program that at last is expected to do correctly Gram_Schmidt
! Orthogonalization for me (Fortran 90)
Some patterns in prime numbers, connected with other areas of mathematics and physics (the figures are in "figpri2.doc"
program to make evident the difference in programing a polynom (for example, x*x*x as opposite to x to the 3rd power)
program to calculate the apothem, the area and the sum of areas of succesive polygons (each time smaller but with the same number of sides), knowing only the [size of the] initial side
Brief historic account of the last 100 years (from 1895 to 1995) about mathematical developments, and speculations about the future of its applications.
solves algebraic trinomials of the form x^2+mx+n (if you multiply a*n, then it can even solve trinomials of the form ax^2+mx+n) warning!, a,m,n must be integers
Inspired by the quasi-random integration developed by Halton, Hammersley and Wozniakowski, and the concept of measurable function used in Lebesgue integration, the possibility of using distances between chains of patterns of the distances between primes (meta-distances or meta-chains) as a pool of quasi-random numbers for multivariable integration...
Questions
Questions (15)
We have made almost 400 laser experiments where the measurements are done through a photocell, registering voltage variations corresponding to variations in the intensity of the laser beam. When the raw data was plotted, we noticed a "raining" effect, meaning that there was a general line and often from that line came straight down several data points (see for example the Figure attached to this explanation, which includes a base line and the experimental line)
Upon close examination, it was found that the "raining" effect was because Arduino, the laptop, or combination of both, registered the same time stamp for different data. The parsing frequency is 1/100 per second or 100 registers per second. The time stamps do have a resolution of 1/1000th second (for example, 11:09:06.676 -> 332, where the three last digits before the arrow represent tenths, hundredths and milliseconds, but still we get the said "raining" phenomenon).
Here is the question: how to properly calculate statistics with data (time series) repeated in the same time stamp?
Up to now, the descriptive statistics of the data were performed "as is", but later we wondered if the "raining" effect should be removed. The way I came with to remove the rain was to calculate the median of data within the same time stamp (sort of inspired by what it is done in quantum calculations), and then we would have graphics without rain, but then I realized that this entailed that all statistics should be recalculated to account for this modification. So, the choices I am facing, which are the motivation of this question are:
- Keep using both the graphics and data as they were (no "raining" removed).
- Use the statistics with all the original data and the graphics with raining removed for better visualization of the difference between base lines and experimental lines.
- Recalculate all the statistics, once the raining has been removed.
To me, either option 0) or 2) would be consistent in the way of handling data, but I do not discard 1), but the point remains on whether removing the "raining" and substitute it with the median across the subset of points would be a good idea, at least for the graphical representation for the data.
Some recent events point that IBM got a 27 qubit computer (https://www.ibm.com/blogs/research/2020/09/ibm-quantum-roadmap/), and maybe 10 years from now one with one million qubits (see same source). Speculations aside, the fact is that quantum entanglement does proves a remarkable advancement in cryptography, among many other applications.
On the other hand let us recapitulate that the Riemann hypothesis (RH) is still out there, unsolved, and that its proof (or disproof) might lead to an understanding on how to factorize much faster than now. We know that today's internet security is based on prime cryptography, and hence its very close connection to a proof of the RE, even if that proof is only existential (the tools for proving it may show a way for faster factorization, and hence to decrypt in way that can't be done now).
It seems that quantum cryptography might arrive much faster than the solution to the RE, and hence the question. As concerns of cryptography, RE would appear that it has lost its most important motivation to be researched, at least commercially speaking. Thus, RE would remain as a pure mathematical problem ( a very tough one, though), connected, perhaps, with many other mathematical statements that are assumed true, if RE is proven true. So, the question is:
Is RE still relevant for some foreseeable practical applications, other that cryptography?
Suppose one has a 1-D, homogeneous heat equation
rm*Cp*T_t = -lm*T_xx
(with rm being the density of the material, Cp is the heat capacity coefficient; lm is the thermal conductivity of the material being studied) , with Robin boundary conditions that depend both on time and space. For example, suppose that the boundary condition includes a heat source, convection and radiation:
q0 + hconv(Tenv-T(x,t)) + sigma*em*(Tenv^4-T(x,t)^4)
where q0 is a heat source, hconv is the convection constant, Tenv is it environment temperature, sigma is the Stefan-Boltzmann constant, em is the emissivity and T(x,t) is the function of temperature to be solved for, meaning that it is the same function to be solved for in the heat equation.
I would say that it is not the case that this partial differential equation can be solved using separation of variables. Or can't it? The point being, I do not have a mathematical or physical argument to actually be convinced that such is the case, or not.
I am interested in the names of the mathematicians authors of the theorem that says that given a sufficiently long cord, in a confined environment, it will knot with probability 1, in the audio of this video(https://www.youtube.com/watch?v=UkmQNbvlK8s) I could not grasp them correctly. I am also interested in the source paper, where the proof of such theorem is given.
Thanks!
I just received an invitation to publish a paper on the journal "Quarterly Physics Review" (www.journals.ke-i.org/index.php/qpr), and I would like to know if this is a serious journal. I am asking this, because a couple of years ago I had a bad experience with another journal, which later I found it among the list of "predator journals". If anyone could give me a hint on this, I would be grateful.