IA Scholar Query: Structure Theorems for o-Minimal Expansions of Groups.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgSat, 31 Dec 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help14404. Das transhumanistische Menschen- und Körperverständnis in fünf Diskursen
https://scholar.archive.org/work/3twnyfuqyffovbkf2nqpvbe2d4
4. Das transhumanistische Menschenund Körperverständnis in fünf Diskursen 4.1 »Dear Mother Nature« -die »Natur des Menschen« im Transhumanismus 4.1.1 Der Begriff der »Natur des Menschen« in der Debatte um den Transhumanismus »Dear Mother Nature« -das Naturdenken im Transhumanismus »Dear Mother Nature«, schreibt More in seinem Brief an »Mutter Natur« (»A Letter to Mother Nature«). 1 Inspiriert davon, verfasst auch Young eine E-Mail an »Nature«.work_3twnyfuqyffovbkf2nqpvbe2d4Sat, 31 Dec 2022 00:00:00 GMTBooks, Bullets, and Burqas Anatomy of a Crisis – Educational Development, Society, and the State in Afghanistan
https://scholar.archive.org/work/bz7m7745nnanfi4oyckmkmoy5y
When this text, originally conceived in 2007, was published in 2012, it probably still was the most comprehensive analysis of the Afghan education system against the backdrop of the social-political historical context. The analysis covers all relevant related issues such as, i.a. the status of Afghan women and girls, the rejection of central authority by ethnic-tribal groups, the fundamental contradiction between an externally funded rentier state and state sovereignty, intricacies and limitations of capacity building including the competition between humanitarian aid agencies and state authorities. The author argued in favor of customized development solutions instead of a centrally driven one-size-fits-all approach. Moreover, he provided reasons why a military "solution" to the development crisis was all but impossible.Craig C. Naumannwork_bz7m7745nnanfi4oyckmkmoy5yThu, 01 Sep 2022 00:00:00 GMTData-adaptive global full-waveform inversion
https://scholar.archive.org/work/4obvascyqjejzcp5fycvqpqska
We present a novel approach to global-scale full-waveform inversion (FWI) that can reduce computational cost by over an order of magnitude, compared to previously published methods, without sacrificing physical and mathematical rigour. This is based on data-adaptation, and thereby application-oriented specialization, on two complementary levels. On the simulation level, we exploit the approximate azimuthal symmetry of seismic wavefields by implementing wavefield-adapted meshes and discrete adjoints, thereby lowering numerical simulation cost. On the measurement level, we use a quasi-stochastic approach where variable mini-batches of data are used during an iterative misfit minimization in order to promote a parsimonious exploitation of data. In addition to the methodological developments, we present an inversion of long-period (100-200 s) seismic waveforms from 1179 earthquakes for 3-D whole-mantle structure. The computational cost of the 72 iterations in the inversion approximately equals one third of a single iteration using an FWI approach with widely used cubed-sphere-based meshes and non-stochastic gradient optimization. The resulting LOng-Wavelength earth model (LOWE) constitutes the first global FWI constructed entirely from a spherically symmetric initial mantle structure. While mostly serving as a showcase for the method, LOWE contains a wealth of regional-scale structures that compare well to earlier tomographic images. Being conservatively smooth and based on minimal assumptions, it may therefore serve as starting model for future inversions at shorter period or smaller scales.Sölvi Thrastarson, Dirk-Philip van Herwaarden, Lion Krischer, Christian Boehm, Martin van Driel, Michael Afanasiev, Andreas Fichtnerwork_4obvascyqjejzcp5fycvqpqskaThu, 01 Sep 2022 00:00:00 GMTEvolution of channel flow and Darcy law beyond the critical Reynolds number
https://scholar.archive.org/work/7jwthtlejfadvdvbxo2fwn76gy
Channel flow is usually described by Darcy law with the Poiseuille flow profile. However, for incompressible channel flow there is a critical state, characterized by a critical Reynolds number Re_c and a critical wavevector mc, beyond which the channel flow becomes unstable in the linear regime. By obtaining the analytical eigenfunctions of the linearized, incompressible, three dimensional (3D) Navier-Stokes (NS) equation in the channel geometry, i.e., the hydrodynamic modes (HMs), we reduce the full NS equation to a system of coupled autonomous ordinary differential equations (ODEs) by expanding the velocity in terms of the HMs; time becomes the only independent variable. The nonlinear term of the NS equation is converted to a third-rank tensor that couples pairs of the expansion coefficients to effect the time variation on the third. In the linear regime, the value of Re_c is obtained to five significant digit accuracy when compared to the Orszag result. We numerically time evolve the autonomous ODEs at Re>Re_c with a finite set of thermally excited initial HMs to find a fluctuating equilibrium state with a reduced net flow rate, accompanied by vortices. Through the perspective of force balance, interesting features are uncovered in the counter-flow profiles at Re>Re_c.Xiaohui Deng, Ping Shengwork_7jwthtlejfadvdvbxo2fwn76gyMon, 08 Aug 2022 00:00:00 GMTNetwork Influence with Latent Homophily and Measurement Error
https://scholar.archive.org/work/xcg6pw54jfcsrkprkugvw67jta
Modeling social influence on outcomes of network-connected individuals is a central research question in several scientific disciplines. However, network influence cannot be identified from observational data because it is confounded with unobserved homophily. We propose a latent homophily-adjusted Spatial Autoregressive model (SAR) for networked responses to identify the causal contagion effects. The latent homophily is estimated from the spectral embedding of the network's adjacency matrix. We further develop maximum likelihood estimators for the parameters of the SAR model when covariates are measured with error. The bias-corrected MLE enjoys statistical consistency and asymptotic normality properties. We combine the estimated latent homophily with the bias corrected MLE in the SAR model to estimate network influence. Our simulations show that the methods perform well in finite samples. Applying our methodology to a data-set of female criminal offenders in a therapeutic community (TC), we provide causal estimates of network influence on graduation from the TC.Subhadeep Paul, Shanjukta Nath, Keith Warrenwork_xcg6pw54jfcsrkprkugvw67jtaMon, 08 Aug 2022 00:00:00 GMTPhase Transition of Parabolic Ginzburg–Landau Equation with Potentials of High-Dimensional Wells
https://scholar.archive.org/work/hnd3hy7rtza6pds6irz5efolje
In this work, we study the co-dimensional one interface limit and geometric motions of parabolic Ginzburg--Landau systems with potentials of high-dimensional wells. The main result generalizes the one by Lin et al. (Comm. Pure Appl. Math., 65(6):833-888, 2012) to a dynamical case. In particular combining modulated energy methods and weak convergence methods, we derive the limiting harmonic heat flows in the inner and outer bulk regions segregated by the sharp interface, and a non-standard boundary condition for them. These results are valid provided that the initial datum of the system is well-prepared under natural energy assumptions.Yuning Liuwork_hnd3hy7rtza6pds6irz5efoljeMon, 08 Aug 2022 00:00:00 GMTCardinality Minimization, Constraints, and Regularization: A Survey
https://scholar.archive.org/work/qbruvpkhpbd23ldgdligzqbyiu
We survey optimization problems that involve the cardinality of variable vectors in constraints or the objective function. We provide a unified viewpoint on the general problem classes and models, and give concrete examples from diverse application fields such as signal and image processing, portfolio selection, or machine learning. The paper discusses general-purpose modeling techniques and broadly applicable as well as problem-specific exact and heuristic solution approaches. While our perspective is that of mathematical optimization, a main goal of this work is to reach out to and build bridges between the different communities in which cardinality optimization problems are frequently encountered. In particular, we highlight that modern mixed-integer programming, which is often regarded as impractical due to commonly unsatisfactory behavior of black-box solvers applied to generic problem formulations, can in fact produce provably high-quality or even optimal solutions for cardinality optimization problems, even in large-scale real-world settings. Achieving such performance typically draws on the merits of problem-specific knowledge that may stem from different fields of application and, e.g., shed light on structural properties of a model or its solutions, or lead to the development of efficient heuristics; we also provide some illustrative examples.Andreas M. Tillmann, Daniel Bienstock, Andrea Lodi, Alexandra Schwartzwork_qbruvpkhpbd23ldgdligzqbyiuMon, 08 Aug 2022 00:00:00 GMTConformal field theory for particle physicists
https://scholar.archive.org/work/thnfxef4jfdmpfn2d4uzz62mka
This is a set of introductory lecture notes on conformal field theory. Unlike most existing reviews on the subject, CFT is presented here from the perspective of a unitary quantum field theory in Minkowski space-time. It begins with a non-perturbative formulation of quantum field theory (Wightman axioms), and then gradually focuses on the implications of scale and special conformal symmetry, all the way to the modern conformal bootstrap. This approach includes topics often left out, such as subtleties of conformal transformations in Minkowski space-time, the construction of Wightman functions and time-ordered correlators both in position- and momentum-space, unitarity bounds derived from the spectral representation, and the appearance of UV and IR divergences.Marc Gilliozwork_thnfxef4jfdmpfn2d4uzz62mkaMon, 08 Aug 2022 00:00:00 GMTA variational study of two-nucleon systems with lattice QCD
https://scholar.archive.org/work/e2vzgz6f2rdbzgc62ocfdeigne
The low-energy spectrum and scattering of two-nucleon systems are studied with lattice quantum chromodynamics using a variational approach. A wide range of interpolating operators are used: dibaryon operators built from products of plane-wave nucleons, hexaquark operators built from six localized quarks, and quasi-local operators inspired by two-nucleon bound-state wavefunctions in low-energy effective theories. Sparsening techniques are used to compute the timeslice-to-all quark propagators required to form correlation-function matrices using products of these operators. Projection of these matrices onto irreducible representations of the cubic group, including spin-orbit coupling, is detailed. Variational methods are applied to constrain the low-energy spectra of two-nucleon systems in a single finite volume with quark masses corresponding to a pion mass of 806 MeV. Results for S- and D-wave phase shifts in the isospin singlet and triplet channels are obtained under the assumption that partial-wave mixing is negligible. Tests of interpolating-operator dependence are used to investigate the reliability of the energy spectra obtained and highlight both the strengths and weaknesses of variational methods. These studies and comparisons to previous studies using the same gauge-field ensemble demonstrate that interpolating-operator dependence can lead to significant effects on the two-nucleon energy spectra obtained using both variational and non-variational methods, including missing energy levels and other discrepancies. While this study is inconclusive regarding the presence of two-nucleon bound states at this quark mass, it provides robust upper bounds on two-nucleon energy levels that can be improved in future calculations using additional interpolating operators and is therefore a step toward reliable nuclear spectroscopy from the underlying Standard Model of particle physics.Saman Amarasinghe, Riyadh Baghdadi, Zohreh Davoudi, William Detmold, Marc Illa, Assumpta Parreno, Andrew V. Pochinsky, Phiala E. Shanahan, Michael L. Wagmanwork_e2vzgz6f2rdbzgc62ocfdeigneMon, 08 Aug 2022 00:00:00 GMTOnline Matching Frameworks under Stochastic Rewards, Product Ranking, and Unknown Patience
https://scholar.archive.org/work/5oxp63w7jfe4zgc2h5gs6noxre
We study generalizations of online bipartite matching in which each arriving vertex (customer) views a ranked list of offline vertices (products) and matches to (purchases) the first one they deem acceptable. The number of products that the customer has patience to view can be stochastic and dependent on the products seen. We develop a framework that views the interaction with each customer as an abstract resource consumption process, and derive new results for these online matching problems under the adversarial, non-stationary, and IID arrival models, assuming we can (approximately) solve the product ranking problem for each single customer. To that end, we show new results for product ranking under two cascade-click models: an optimal algorithm when each item has its own hazard rate for making the customer depart, and a 1/2-approximate algorithm when the customer has a general item-independent patience distribution. We also present a constant-factor 0.027-approximate algorithm in a new model where items are not initially available and arrive over time. Finally, we present three negative results of interest: one formalizing the notion of a stochasticity gap exhibited by existing approaches to this problem, an example showing the analysis of SimpleGreedy in existing work to be tight, and another one for the single-customer problem in which any constant-factor approximation is impossible when compared to a benchmark that knows the realization of the patience in advance.Brian Brubach, Nathaniel Grammel, Will Ma, Aravind Srinivasanwork_5oxp63w7jfe4zgc2h5gs6noxreMon, 08 Aug 2022 00:00:00 GMTEffective Dynamics of Extended Fermi Gases in the High-Density Regime
https://scholar.archive.org/work/3tke2my4ubhe5lcz6vxobor3y4
We study the quantum evolution of many-body Fermi gases in three dimensions, in arbitrarily large domains. We consider both particles with non-relativistic and with relativistic dispersion. We focus on the high-density regime, in the semiclassical scaling, and we consider a class of initial data describing zero-temperature states. In the non-relativistic case we prove that, as the density goes to infinity, the many-body evolution of the reduced one-particle density matrix converges to the solution of the time-dependent Hartree equation, for short macroscopic times. In the case of relativistic dispersion, we show convergence of the many-body evolution to the relativistic Hartree equation for all macroscopic times. With respect to previous work, the rate of convergence does not depend on the total number of particles, but only on the density: in particular, our result allows us to study the quantum dynamics of extensive many-body Fermi gases.Luca Fresta, Marcello Porta, Benjamin Schleinwork_3tke2my4ubhe5lcz6vxobor3y4Mon, 08 Aug 2022 00:00:00 GMTAnother proof of the corona theorem
https://scholar.archive.org/work/5odlszxjsnhnfb4u5trttztsym
Let H^∞(Δ) be the uniform algebra of bounded analytic functions on the open unit disc Δ, and let 𝔐(H^∞) be the maximal ideal space of H^∞(Δ). By regarding Δ as an open subset of 𝔐(H^∞), the corona problem asks whether Δ is dense in 𝔐(H^∞), which was solved affirmatively by L. Carleson. Extending the cluster value theorem to the case of finitely many functions, we provide a direct proof of the corona theorem: Let ϕ be a homomorphism in 𝔐(H^∞), and let f_1, f_2, ..., f_N be functions in H^∞(Δ). Then there is a sequence {ζ_j} in Δ satisfyingf_k(ζ_j) →ϕ(f_k) for k=1, 2, ..., N. On the other hand, the corona problem remains unsolved in many general settings, for instance, certain plane domains, polydiscs and balls, our approach is so natural that it may be possible to deal with such cases from another point of view.Jun-ichi Tanakawork_5odlszxjsnhnfb4u5trttztsymMon, 08 Aug 2022 00:00:00 GMTThe hadronic running of the electromagnetic coupling and the electroweak mixing angle from lattice QCD
https://scholar.archive.org/work/6fkaj7u4mfcvhobeacdl2gamyy
We compute the hadronic running of the electromagnetic and weak couplings in lattice QCD with N_f=2+1 flavors of 𝒪(a) improved Wilson fermions. Using two different discretizations of the vector current, we compute the quark-connected and -disconnected contributions to the hadronic vacuum polarization (HVP) functions Π̅^γγ and Π̅^γ Z for Euclidean squared momenta Q^2≤ 7 GeV^2. Gauge field ensembles at four values of the lattice spacing and several values of the pion mass, including its physical value, are used to extrapolate the results to the physical point. The ability to perform an exact flavor decomposition allows us to present the most precise determination to date of the SU(3)-flavor-suppressed HVP function Π̅^08 that enters the running of sin^2θ_W. Our results for Π̅^γγ, Π̅^γ Z and Π̅^08 are presented in terms of rational functions for continuous values of Q^2 below 7 GeV^2. We observe a tension of up to 3.5 standard deviation between our lattice results for Δα^(5)_had(-Q^2) and estimates based on the R-ratio for space-like momenta in the range 3–7 GeV^2. The tension is, however, strongly diminished when translating our result to the Z pole, by employing the Euclidean split technique and perturbative QCD, which yields Δα^(5)_had(M_Z^2)=0.027 73(15) and agrees with results based on the R-ratio within the quoted uncertainties.Marco Cè, Antoine Gérardin, Georg von Hippel, Harvey B. Meyer, Kohtaroh Miura, Konstantin Ottnad, Andreas Risch, Teseo San José, Jonas Wilhelm, Hartmut Wittigwork_6fkaj7u4mfcvhobeacdl2gamyyMon, 08 Aug 2022 00:00:00 GMT2D Percolation as a Conformal Field Theory
https://scholar.archive.org/work/og6i5im5e5e4pm3ztviieososq
Fitting percolation into the conformal field theory framework requires showing that connection probabilities have a conformally invariant scaling limit. For critical site percolation on the triangular lattice, we prove that the probability that n vertices belong to the same open cluster has a well-defined scaling limit for every n ≥ 2. Moreover, the limiting functions P_n(x_1,...,x_n) transform covariantly under Möbius transformations of the plane as well as under local conformal maps, i.e., they behave like correlation functions of primary operators in conformal field theory. In particular, they are invariant under translations, rotations and inversions, and P_n(sx_1,...,sx_n)=s^-5n/48P_n(x_1,...,x_n) for any s>0. This implies that the ratio P_3(x_1,x_2,x_3)/√(P_2(x_1,x_2)P_2(x_1,x_3)P_2(x_2,x_3)) is independent of x_1,x_2,x_3, which confirms a prediction of the physics literature. We also define a site-diluted spin model whose n-point correlation functions C_n can be expressed in terms of percolation connection probabilities and, as a consequence, have a well-defined scaling limit with the same properties as the functions P_n. In particular, C_2(x_1,x_2)=P_2(x_1,x_2). We prove that the magnetization field associated with this spin model has a well-defined scaling limit in an appropriate space of distributions. The limiting field transforms covariantly under Möbius transformations with exponent (scaling dimension) 5/48. A heuristic analysis of the four-point function of the magnetization field reveals the presence of an additional conformal field of scaling dimension 5/4, which counts the number of percolation four-arm events and can be identified with the so-called "four-leg operator" of conformal field theory.Federico Camiawork_og6i5im5e5e4pm3ztviieososqSun, 07 Aug 2022 00:00:00 GMTData-Driven Discovery of Molecular Photoswitches with Multioutput Gaussian Processes
https://scholar.archive.org/work/7fyig6ugsvf6dbxwmijziel67m
Photoswitchable molecules display two or more isomeric forms that may be accessed using light. Separating the electronic absorption bands of these isomers is key to selectively addressing a specific isomer and achieving high photostationary states whilst overall red-shifting the absorption bands serves to limit material damage due to UV-exposure and increases penetration depth in photopharmacological applications. Engineering these properties into a system through synthetic design however, remains a challenge. Here, we present a data-driven discovery pipeline for molecular photoswitches underpinned by dataset curation and multitask learning with Gaussian processes. In the prediction of electronic transition wavelengths, we demonstrate that a multioutput Gaussian process (MOGP) trained using labels from four photoswitch transition wavelengths yields the strongest predictive performance relative to single-task models as well as operationally outperforming time-dependent density functional theory (TD-DFT) in terms of the wall-clock time for prediction. We validate our proposed approach experimentally by screening a library of commercially available photoswitchable molecules. Through this screen, we identified several motifs that displayed separated electronic absorption bands of their isomers, exhibited red-shifted absorptions, and are suited for information transfer and photopharmacological applications. Our curated dataset, code, as well as all models are made available at https://github.com/Ryan-Rhys/The-Photoswitch-DatasetRyan-Rhys Griffiths, Jake L. Greenfield, Aditya R. Thawani, Arian R. Jamasb, Henry B. Moss, Anthony Bourached, Penelope Jones, William McCorkindale, Alexander A. Aldrick, Matthew J. Fuchter Alpha A. Leework_7fyig6ugsvf6dbxwmijziel67mSun, 07 Aug 2022 00:00:00 GMTClassical groups and Haar integration
https://scholar.archive.org/work/ctqxr7ssrfgmbpf3oz6e4wyf4y
This is an introduction to the closed subgroups G⊂ U_N, with all needed preliminaries included. We discuss the basic theory, and we perform some probability computations, in the finite case. In the general case, we explain how the Weingarten integration formula works, and we present some basic N→∞ applications.Teo Banicawork_ctqxr7ssrfgmbpf3oz6e4wyf4ySun, 07 Aug 2022 00:00:00 GMTThe smallest bimolecular mass action reaction networks admitting Andronov-Hopf bifurcation
https://scholar.archive.org/work/medcouptyzbd5o2ghca3fj45rm
We address the question of which small, bimolecular, mass action chemical reaction networks (CRNs) are capable of Andronov--Hopf bifurcation (from here on abbreviated to "Hopf bifurcation"). It is easily shown that any such network must have at least three species and at least four irreversible reactions, and one example of such a network was previously known due to Wilhelm. In this paper, we develop both theory and computational tools to fully classify three-species, four-reaction, bimolecular CRNs, according to whether they admit or forbid Hopf bifurcation. We show that there are, up to a natural equivalence, 86 minimal networks which admit nondegenerate Hopf bifurcation. Amongst these, we are able to decide which admit supercritical and subcritical bifurcations. Indeed, there are 25 networks which admit both supercritical and subcritical bifurcations, and we can confirm that all 25 admit a nondegenerate Bautin bifurcation. A total of 31 networks can admit more than one nondegenerate periodic orbit. Moreover, 29 of these networks admit the coexistence of a stable equilibrium with a stable periodic orbit. Thus, fairly complex behaviours are not very rare in these small, bimolecular networks. Finally, we can use previously developed theory to predict the occurrence of Hopf bifurcation in larger networks which include the networks we find here as subnetworks in an appropriate sense.Murad Banaji, Balázs Boroswork_medcouptyzbd5o2ghca3fj45rmSun, 07 Aug 2022 00:00:00 GMTQuantum error mitigation via matrix product operators
https://scholar.archive.org/work/g756f2ajn5fyba5ucncp2kf4n4
In the era of noisy intermediate-scale quantum (NISQ) devices, the number of controllable hardware qubits is insufficient to implement quantum error correction (QEC). As an alternative, quantum error mitigation (QEM) can suppress errors in measurement results via repeated experiments and postprocessing of data. Typical techniques for error mitigation, e.g., the quasi-probability decomposition method, ignore correlated errors between different gates. Here, we introduce a QEM method based on the matrix product operator (MPO) representation of a quantum circuit that can characterize the noise channel with polynomial complexity. Our technique is demonstrated on a depth=20 fully parallel quantum circuit of up to N_q=20 qubits undergoing local and global noise. The circuit error is reduced by several times with only a small bond dimension D^' = 1 for the noise channel. The MPO representation increases the accuracy of modeling noise without consuming more experimental resources, which improves the QEM performance and broadens its scope of application. Our method is hopeful of being applied to circuits in higher dimensions with more qubits and deeper depth.Yuchen Guo, Shuo Yangwork_g756f2ajn5fyba5ucncp2kf4n4Sun, 07 Aug 2022 00:00:00 GMTMaximizing Fair Content Spread via Edge Suggestion in Social Networks
https://scholar.archive.org/work/g3q3qqxhdrh7fbnaky7u637oby
Content spread inequity is a potential unfairness issue in online social networks, disparately impacting minority groups. In this paper, we view friendship suggestion, a common feature in social network platforms, as an opportunity to achieve an equitable spread of content. In particular, we propose to suggest a subset of potential edges (currently not existing in the network but likely to be accepted) that maximizes content spread while achieving fairness. Instead of re-engineering the existing systems, our proposal builds a fairness wrapper on top of the existing friendship suggestion components. We prove the problem is NP-hard and inapproximable in polynomial time unless P = NP. Therefore, allowing relaxation of the fairness constraint, we propose an algorithm based on LP-relaxation and randomized rounding with fixed approximation ratios on fairness and content spread. We provide multiple optimizations, further improving the performance of our algorithm in practice. Besides, we propose a scalable algorithm that dynamically adds subsets of nodes, chosen via iterative sampling, and solves smaller problems corresponding to these nodes. Besides theoretical analysis, we conduct comprehensive experiments on real and synthetic data sets. Across different settings, our algorithms found solutions with nearzero unfairness while significantly increasing the content spread. Our scalable algorithm could process a graph with half a million nodes on a single machine, reducing the unfairness to around 0.0004 while lifting content spread by 43%.Ian P. Swift, Sana Ebrahimi, Azade Nova, Abolfazl Asudehwork_g3q3qqxhdrh7fbnaky7u637obySat, 06 Aug 2022 00:00:00 GMTMathematical proof and epistemological obstacles: Assumptions of the methodological teaching proposal of the Fedathi sequence
https://scholar.archive.org/work/rmqryr3wpfbopa6sxnony5kiya
The Multimedia Research Laboratory, inserted in the Federal University of Ceará has the Multimedia Mathematics Education Group, in which they study the mathematics teaching with the methodological contribution of the Fedathi sequence (FS). In one of the study meetings, the members raised the issue of how a class in the light of the FS could be, which would address mathematical proof. To this end, the mathematical object used to illustrate the answer to this question was the ordering in the set of rational numbers, aiming at the didactic session in the mathematics undergraduate course. Thus, this research aimed to develop a model of mathematical proof approach based on the FS methodological proposal, attempting to solve the issue raised. To make this work possible, the FS research methodology was used, with a qualitative bias. Regarding the results, it was possible to develop the model with the purpose of performing mathematical proof using the FS as a teaching methodology, considering that this way of mediating knowledge is not a transmission of content, but rather, a way of providing learning.Carlos Henrique Delmiro Araújo, Daniel Brandão Menezeswork_rmqryr3wpfbopa6sxnony5kiyaSat, 06 Aug 2022 00:00:00 GMT