Relevant bibliographies by topics / Higher-Dimensional Mathematics

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Higher-Dimensional Mathematics'

Author: Grafiati
Published: 2 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Higher-Dimensional Mathematics"

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Baez, John C., and Martin Neuchl. "Higher Dimensional Algebra." Advances in Mathematics 121, no. 2 (1996): 196–244. http://dx.doi.org/10.1006/aima.1996.0052.

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Shonkwiler, Clayton, and David Shea Vela-Vick. "Higher-dimensional linking integrals." Proceedings of the American Mathematical Society 139, no. 04 (2011): 1511. http://dx.doi.org/10.1090/s0002-9939-2010-10603-2.

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Rogers, James T. "Higher dimensional aposyndetic decompositions." Proceedings of the American Mathematical Society 131, no. 10 (2003): 3285–88. http://dx.doi.org/10.1090/s0002-9939-03-06888-6.

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Kim, Gwang-Il. "Higher dimensional PH curves." Proceedings of the Japan Academy, Series A, Mathematical Sciences 78, no. 10 (2002): 185–87. http://dx.doi.org/10.3792/pjaa.78.185.

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Borwein, Jonathan M., O.-Yeat Chan, and R. E. Crandall. "Higher-Dimensional Box Integrals." Experimental Mathematics 19, no. 4 (2010): 431–46. http://dx.doi.org/10.1080/10586458.2010.10390634.

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Schwartzman, Sol. "Higher Dimensional Asymptotic Cycles." Canadian Journal of Mathematics 55, no. 3 (2003): 636–48. http://dx.doi.org/10.4153/cjm-2003-026-0.

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AbstractGiven a p-dimensional oriented foliation of an n-dimensional compact manifold Mn and a transversal invariant measure τ, Sullivan has defined an element of Hp(Mn; R). This generalized the notion of a μ-asymptotic cycle, which was originally defined for actions of the real line on compact spaces preserving an invariant measure μ. In this one-dimensional case there was a natural 1—1 correspondence between transversal invariant measures τ and invariant measures μ when one had a smooth flow without stationary points.For what we call an oriented action of a connected Lie group on a compact m
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Gomi, Kiyonori, and Yuji Terashima. "Higher-dimensional parallel transports." Mathematical Research Letters 8, no. 1 (2001): 25–33. http://dx.doi.org/10.4310/mrl.2001.v8.n1.a4.

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Banerjee, Deveena R., Sara Chari, and Adriana Salerno. "Higher-dimensional origami constructions." Involve, a Journal of Mathematics 16, no. 2 (2023): 297–312. http://dx.doi.org/10.2140/involve.2023.16.297.

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Barja, Miguel Ángel, Rita Pardini, and Lidia Stoppino. "Higher-dimensional Clifford–Severi equalities." Communications in Contemporary Mathematics 22, no. 08 (2019): 1950079. http://dx.doi.org/10.1142/s0219199719500792.

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Let [Formula: see text] be a smooth complex projective variety, [Formula: see text] a morphism to an abelian variety such that [Formula: see text] injects into [Formula: see text] and let [Formula: see text] be a line bundle on [Formula: see text]; denote by [Formula: see text] the minimum of [Formula: see text] for [Formula: see text]. The so-called Clifford–Severi inequalities have been proven in [M. A. Barja, Generalized Clifford–Severi inequality and the volume of irregular varieties, Duke Math. J. 164(3) (2015) 541–568; M. A. Barja, R. Pardini and L. Stoppino, Linear systems on irregular
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Knibbeler, Vincent, Sara Lombardo, and Jan A. Sanders. "Higher-Dimensional Automorphic Lie Algebras." Foundations of Computational Mathematics 17, no. 4 (2016): 987–1035. http://dx.doi.org/10.1007/s10208-016-9312-1.

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Dissertations / Theses on the topic "Higher-Dimensional Mathematics"

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Durkee, Mark N. "New approaches to higher-dimensional general relativity." Thesis, University of Cambridge, 2011. https://www.repository.cam.ac.uk/handle/1810/240580.

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This thesis considers various aspects of general relativity in more than four spacetime dimensions. Firstly, I review the generalization to higher dimensions of the algebraic classification of the Weyl tensor and the Newman-Penrose formalism. In four dimensions, these techniques have proved useful for studying many aspects of general relativity, and it is hoped that their higher dimensional generalizations will prove equally useful in the future. Unfortunately, many calculations using the Newman-Penrose formalism can be unnecessarily complicated. To address this, I describe new work introducin
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Chandrasekhar, Karthik. "BOUNDING THE NUMBER OF COMPATIBLE SIMPLICES IN HIGHER DIMENSIONAL TOURNAMENTS." UKnowledge, 2019. https://uknowledge.uky.edu/math_etds/63.

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A tournament graph G is a vertex set V of size n, together with a directed edge set E ⊂ V × V such that (i, j) ∈ E if and only if (j, i) ∉ E for all distinct i, j ∈ V and (i, i) ∉ E for all i ∈ V. We explore the following generalization: For a fixed k we orient every k-subset of V by assigning it an orientation. That is, every facet of the (k − 1)-skeleton of the (n − 1)-dimensional simplex on V is given an orientation. In this dissertation we bound the number of compatible k-simplices, that is we bound the number of k-simplices such that its (k − 1)-faces with the already-specified orientatio
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Ramasu, Pako. "Internal monoid actions in a cartesian closed category and higher-dimensional group automorphisms." Doctoral thesis, University of Cape Town, 2015. http://hdl.handle.net/11427/20248.

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The notion of cat¹-group which was introduced by Loday is equivalent to the notions of crossed module and of internal category in the category of groups. This notion of cat¹-groups and their morphisms admits natural generalization to catⁿ-groups, which give rise to n-fold categories in the category of groups. There is also a characterization of catⁿ-groups in terms of crossed n-cubes which was given by Ellis and Steiner. The category Catⁿ (Groups) of internal n-fold categories in the category of groups is a cartesian closed category, however given an object X in Catⁿ (Groups), calculating corr
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Godazgar, Mohammad Mahdi. "Aspects of higher dimensional Einstein theory and M-theory." Thesis, University of Cambridge, 2012. https://www.repository.cam.ac.uk/handle/1810/245148.

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This thesis contains two main themes. The first is Einstein's theory of general relativity in higher dimensions, while the second is M-theory. The first part of the thesis concerns the use of classification techniques based on the Weyl curvature in an attempt to systematically study higher dimensional general relativity and its solutions. After a review of the various classification schemes, the application of these schemes to the study of higher dimensional solutions is explained. The first application of the tensor approach that is discussed is the systematic classification of higher dimensi
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Metzner, Norman. "Twistor theory of higher-dimensional black holes." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:0c275046-2d6f-4860-9bb3-5d5e5048cd5a.

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The correspondence of stationary, axisymmetric, asymptotically flat space-times and bundles over a reduced twistor space has been established in four dimensions. The main impediment for an application of this correspondence to examples in higher dimensions is the lack of a higher-dimensional equivalent of the Ernst poten- tial. This thesis will propose such a generalized Ernst potential, point out where the rod structure of the space-time can be found in the twistor picture and thereby provide a procedure for generating solutions to the Einstein field equations in higher dimensions from the ro
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Griffiths, Rhiannon Cerys. "Slices of Globular Operads for Higher Categories." Case Western Reserve University School of Graduate Studies / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=case1623155240596704.

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Belayneh, Sirak. "The identity of zeros of higher and lower dimensional filter banks and the construction of multidimensional nonseparable wavelets." Fairfax, VA : George Mason University, 2008. http://hdl.handle.net/1920/3417.

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Thesis (Ph.D.)--George Mason University, 2008.<br>Vita: p. 160. Thesis director: Edward J. Wegman. Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Information Technology. Title from PDF t.p. (viewed Mar. 9, 2009). Includes bibliographical references (p. 151-159). Also issued in print.
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Whitley, Michael Aaron. "Grid stabilization for the one-dimensional advection equation using biased finite differnces of odd orders and orders higher than twenty-two." Thesis, Kansas State University, 2013. http://hdl.handle.net/2097/16285.

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Master of Science<br>Department of Mathematics<br>Nathan Albin<br>This work utilizes finite differences to approximate the first derivative of non-periodic smooth functions. Math literature indicates that stabilizing Partial Differential Equation solvers based on high order finite difference approximations of spatial derivatives of a non-periodic function becomes problematic near a boundary. Hagstrom and Hagstrom have discovered a method of introducing additional grid points near a boundary, which has proven to be effective in stabilizing Partial Differential Equation solvers. Hagstrom and
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Moreno, Agustin. "Algebraic Torsion in Higher-Dimensional Contact Manifolds." Doctoral thesis, Humboldt-Universität zu Berlin, 2019. http://dx.doi.org/10.18452/19849.

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Wir konstruieren Beispiele von Kontaktmannigfaltigkeiten in jeder ungeraden Dimension, welche endliche nicht-triviale algebraische Torsion (im Sinne von Latschev-Wendl) aufweisen, somit straff sind und keine starke symplektische Füllung haben. Wir beweisen, dass Giroux Torsion algebraische 1-Torsion in jeder ungeraden Dimension impliziert, womit eine Vermutung von Massot-Niederkrüger-Wendl bewiesen wird. Wir konstruieren unendlich viele nicht diffeomorphe Beispiele von 5-dimensionalen Kontaktmannigfaltigkeiten, welche straff sind, keine starke symplektische Füllung zulassen und keine Giroux
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Markowsky, Peter [Verfasser], and Christoph [Akademischer Betreuer] Schnörr. "Model-based Stochastical Segmentation of Higher-dimensional Data / Peter Markowsky ; Betreuer: Christoph Schnörr." Heidelberg : Universitätsbibliothek Heidelberg, 2019. http://d-nb.info/1200918843/34.

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Books on the topic "Higher-Dimensional Mathematics"

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Cavicchioli, Alberto. Higher-dimensional generalized manifolds: Surgery and constructions. European Mathematical Society, 2016.

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H, Hubbard John. Differential Equations: A Dynamical Systems Approach: Higher-Dimensional Systems. Springer New York, 1995.

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J, Kovacs Sandor, ed. Classification of higher dimensional algebraic varieties. Birkhäuser, 2010.

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1945-, Kauffman Louis H., and Sandin Daniel J, eds. Hypercomplex iterations: Distance estimation and higher dimensional fractals. World Scientific, 2002.

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Makkai, Mihály. Models, logics, and higher-dimensional categories: A tribute to the work of Mihaly Makkai. American Mathematical Society, 2011.

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Steiner, Rudolf. The fourth dimension: Sacred geometry, alchemy, and mathematics : listeners' notes of lectures on higher-dimensional space and of questions and answers on mathematical topics. Anthroposophic Press, 2001.

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Fonseca, Carlos M. da. A panorama of mathematics: Pure and applied : Conference on Mathematics and Its Applications, November 14-17, 2014, Kuwait University, Safat, Kuwait. American Mathematical Society, 2016.

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Glovackaya, Alevtina. Computational model. INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1013723.

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The textbook covers the basics of classical numerical methods of computational mathematics used for solving linear and nonlinear equations and systems; interpolation and approximation of functions; numerical integration and differentiation; solutions of ordinary differential equations by methods of one-dimensional and multidimensional optimization. Meets the requirements of the Federal state educational standards of higher education of the latest generation. It is intended for students of higher educational institutions studying in the discipline "Numerical methods".
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Watson, N. A. Introduction to heat potential theory. American Mathematical Society, 2012.

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editor, Donagi Ron, Douglas, Michael (Michael R.), editor, Kamenova Ljudmila 1978 editor, and Roček M. (Martin) editor, eds. String-Math 2013: Conference, June 17-21, 2013, Simons Center for Geometry and Physics, Stony Brook, NY. American Mathematical Society, 2014.

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Book chapters on the topic "Higher-Dimensional Mathematics"

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Arrigo, Daniel. "Higher Dimensional Problems." In Synthesis Lectures on Mathematics & Statistics. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-22087-6_7.

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Dougherty, Steven T. "Higher Dimensional Finite Geometry." In Springer Undergraduate Mathematics Series. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-56395-0_6.

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Lang, Serge. "Equidimensional higher dimensional theory." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0093848.

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Rosenthal, Daniel, David Rosenthal, and Peter Rosenthal. "Some Higher Dimensional Spaces." In Undergraduate Texts in Mathematics. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-00632-7_14.

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Lang, Serge. "Higher Dimensional Diophantine Problem." In Springer Collected Works in Mathematics. Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4614-8710-4_7.

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Koschorke, Ulrich. "Higher order homotopy invariants for higher dimensional link maps." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/bfb0074427.

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Eckmann, Beno. "Aspherical Manifolds and Higher-Dimensional Knots." In Springer Collected Works in Mathematics. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-37339-8_50.

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Reider, Igor. "Toward abel-jacobi theory for higher dimensional varieties." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0083345.

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Rieffel, Marc A. ""Vector bundles" over higher dimensional "non-commutative tori"." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/bfb0074902.

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Scheucher, Manfred. "A SAT Attack on Higher Dimensional Erdős–Szekeres Numbers." In Trends in Mathematics. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-83823-2_17.

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Conference papers on the topic "Higher-Dimensional Mathematics"

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Dzhus, Anna, Victor Greshta, Tetiana Pulina, and Gennadii Snizhnoi. "EVALUATION AND PREDICTION OF RESISTANCE OF PLATE-LIKE HEAT EXCHANGERS MADE OF 06KhN28MDT ALLOY (ANALOGOUS TO AISI904L STEEL) TO CREVICE CORROSION IN RECYCLED WATER OF ENTERPRISES." In SGEM International Multidisciplinary Scientific GeoConference 24. STEF92 Technology, 2024. https://doi.org/10.5593/sgem2024/6.1/s24.09.

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The article develops one-dimensional linear regression mathematical models that establish the relationship between the activation potentials Ecrev, repassivation Erep, and corrosion Ecor of the 06KhN28MDT alloy used in the production of plate-like heat exchangers and its chemical composition and structure components in model recycled water. It has been found that the limiting potential Elim of the alloy shifted in the positive direction with an increase in the content of Cr, Mo, Si, S, the volume of titanium sulphides Vs, and a decrease in Mn. It has been found that its positive effect on Elim
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Salano, Loretta, Ilaria Dagna, Mattia Vallerio, and Flavio Manenti. "Development and Integration of a Co-Current Hollow Fiber Membrane Unit for Gas Separation in Process Simulators Using CAPE-OPEN Standards." In The 35th European Symposium on Computer Aided Process Engineering. PSE Press, 2025. https://doi.org/10.69997/sct.182712.

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Process simulation is essential for optimizing chemical processes, offering a cost-effective alternative to the experimental approach. This study presents a co-current hollow fibre membrane model for CO2 separation, integrated into Aspen HYSYS� using the CAPE-OPEN standard. A one-dimensional boundary value problem (BVP) is solved through the shooting method, ensuring accuracy for complex gas separation processes. The unit is implemented in C++, facilitating interoperability, error handling, and optimization of key performance indicators like energy consumption and separation efficiency. Approp
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De Almeida, R., and H. R. Malonek. "On a Higher Dimensional Analogue of the Joukowski Transformation." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2991005.

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Afgani, Rizal, Abednego Wiliardy, and Bobby Eka Gunara. "Special class of higher dimensional stationary manifold." In THE 5TH INTERNATIONAL CONFERENCE ON MATHEMATICS AND NATURAL SCIENCES. AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4930627.

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Hidayat, Alam A., Bobby E. Gunara, and Fiki T. Akbar. "The Penrose inequality in higher dimensional spherically symmetric spacetimes." In THE 5TH INTERNATIONAL CONFERENCE ON MATHEMATICS AND NATURAL SCIENCES. AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4930625.

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Mulyanto, Fiki Taufik Akbar, and Bobby Eka Gunara. "Maxwell-Higgs equation on higher dimensional static curved spacetimes." In THE 5TH INTERNATIONAL CONFERENCE ON MATHEMATICS AND NATURAL SCIENCES. AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4930630.

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Rasyida, A. N., and H. S. Ramadhan. "Compactification of higher dimensional spacetime with Maxwell field." In INTERNATIONAL SYMPOSIUM ON CURRENT PROGRESS IN MATHEMATICS AND SCIENCES 2016 (ISCPMS 2016): Proceedings of the 2nd International Symposium on Current Progress in Mathematics and Sciences 2016. Author(s), 2017. http://dx.doi.org/10.1063/1.4991117.

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Lamine, M. S., and M. G. Edwards. "Higher Dimensional Upwind Schemes for Flow in Porous Media on Unstructured Grids." In 11th European Conference on the Mathematics of Oil Recovery. EAGE Publications BV, 2008. http://dx.doi.org/10.3997/2214-4609.20146379.

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Bučková, Z., P. Pólvora, M. Ehrhardt, and M. Günther. "Implementation of alternating direction explicit methods for higher dimensional Black-Scholes equations." In APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 8th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’16. Author(s), 2016. http://dx.doi.org/10.1063/1.4964961.

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Shang, Jielin, Hongmei Pei, and Simin Wang. "Three-dimensional Simulation Function of MATLAB in the Teaching Practice of Higher Mathematics." In 2016 International Conference on Education, E-learning and Management Technology. Atlantis Press, 2016. http://dx.doi.org/10.2991/iceemt-16.2016.61.

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Reports on the topic "Higher-Dimensional Mathematics"

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Semerikov, Serhiy, Illia Teplytskyi, Yuliia Yechkalo, Oksana Markova, Vladimir Soloviev, and Arnold Kiv. Computer Simulation of Neural Networks Using Spreadsheets: Dr. Anderson, Welcome Back. [б. в.], 2019. http://dx.doi.org/10.31812/123456789/3178.

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The authors of the given article continue the series presented by the 2018 paper “Computer Simulation of Neural Networks Using Spreadsheets: The Dawn of the Age of Camelot”. This time, they consider mathematical informatics as the basis of higher engineering education fundamentalization. Mathematical informatics deals with smart simulation, information security, long-term data storage and big data management, artificial intelligence systems, etc. The authors suggest studying basic principles of mathematical informatics by applying cloud-oriented means of various levels including those traditio
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Meni, Mackenzie, Ryan White, Michael Mayo, and Kevin Pilkiewicz. Entropy-based guidance of deep neural networks for accelerated convergence and improved performance. Engineer Research and Development Center (U.S.), 2025. https://doi.org/10.21079/11681/49805.

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Neural networks have dramatically increased our capacity to learn from large, high-dimensional datasets across innumerable disciplines. However, their decisions are not easily interpretable, their computational costs are high, and building and training them are not straightforward processes. To add structure to these efforts, we derive new mathematical results to efficiently measure the changes in entropy as fully-connected and convolutional neural networks process data. By measuring the change in entropy as networks process data effectively, patterns critical to a well-performing network can
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