Regions of Russia: Clustering Results Based on Economic and Innovation Indexes by V. P. Zavarukhin, T. I. Chinaeva, E. Yu. Churilova

“…When analyzing them, it is advisable to first use cluster analysis methods to obtain homogeneous groups of territories with similar social and economic characteristics, which is confirmed in this study by testing hypotheses about statistically significant differences between the indexes of the third and fourth clusters (differences between the first and second clusters with other clusters and between themselves obvious and do not require any mathematical proof).Conclusion. The leaders in scientific and innovative development are Moscow, St. …”
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Extended summary of ``A mathematical Phenomenon in the Quran of Earth-Shattering Proportions: A Quranic Theory Based on Gematria Determining Quran Primary Statistics (words, verses... by Mohsen Khaleghi Moghadam

“…It proves that the Quran’s miraculous  athematical structure discovered in this study provides unequivocal mathematical proof that the Quran was divinely authored and has been perfectly preserved from the day it was revealed. …”
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A proof of factorization formula for critical percolation by Beliaev, D, Izyurov, K

“…We give mathematical proofs to a number of statements which appeared in the series of papers by Kleban, Simmons and Ziff where they computed the probabilities of several percolation crossing events.…”

18.312 Algebraic Combinatorics, Spring 2009 by Musiker, Gregg

“…Topics were chosen to show the beauty and power of techniques in algebraic combinatorics. Rigorous mathematical proofs are expected.…”
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Massively Parallel Implementations of Theories for Apparent Motion by Grzywacz, Norberto, Yuille, Alan

“…Their effectiveness is demonstrated with mathematical proofs and computer simulations. We discuss relevant psychophysical experiments.…”
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Stochastic processes : theory for applications / by Gallager, Robert G., author

“…"Basic underlying principles and axioms are made clear from the start, and new topics are developed as needed, encouraging and enabling students to develop an instinctive grasp of the fundamentals. Mathematical proofs are made easy for students to understand and remember, helping them quickly learn how to choose and apply the best possible models to real-world situations"--provided by publisher…”

Intuitionism and proof theory : proceedings / by Conference on Intuitionism and Proof Theory (1968 : State University of New York, Buffalo, New York), Kino, A., Myhill, J., Vesley, R. E.

The Role of Representations in Mathematical Reasoning by Jessica Carter

“…This paper discusses the role of representations in mathematical proofs. It is proposed that representations enable us to break a proof down into manageable parts. …”
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An iterative incremental learning algorithm for complex-valued hopfield associative memory by Masuyama, N., Chu, K.L.

“…This paper discusses a complex-valued Hopfield associative memory with an iterative incremental learning algorithm. The mathematical proofs derive that the weight matrix is approximated as a weight matrix by the complex-valued pseudo inverse algorithm. …”
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Computer-Assisted Proving of Combinatorial Conjectures Over Finite Domains: A Case Study of a Chess Conjecture by Predrag Janičić, Filip Marić, Marko Maliković

“…There are several approaches for using computers in deriving mathematical proofs. For their illustration, we provide an in-depth study of using computer support for proving one complex combinatorial conjecture -- correctness of a strategy for the chess KRK endgame. …”
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The Proofchecker by Abrahams, Paul

“…The Proofchecker is a heuristically oriented computer program for checking mathematical proofs, with the checking of textbook proofs as its ultimate goal. …”
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On the Boundedness and Symmetry Properties of the Fractal Sets Generated from Alternated Complex Map by Da Wang, ShuTang Liu

“…In this paper, we improve the previous results by giving the strictly mathematical proofs of the two properties. Some simulations that verify the theoretical proofs are also included.…”
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What if ϕ4 theory in 4 dimensions is non-trivial in the continuum? by Paul Romatschke

“…This tradition is apparently well grounded both in physics arguments and mathematical proofs. Digging into the proofs one finds that they do not actually cover all physically meaningful situations, in particular the case of multi-component fields and non-polynomial action. …”
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Analysis of Recurrent Neural Network and Predictions by Jieun Park, Dokkyun Yi, Sangmin Ji

“…In addition to mathematical proofs, numerical experiments confirmed our claims.…”
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A fundamental flaw in the ++AE authenticated encryption mode by Qahur Al Mahri Hassan, Simpson Leonie, Bartlett Harry, Dawson Ed, Wong Kenneth Koon-Ho

“…We outline the mathematical proofs for the flaw in the ++AE algorithm. …”
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A priori bounds and existence results for singular boundary value problems by Nicholas Fewster-Young

“…The right-hand side of the differential equation is allowed to be unrestricted in the growth of its variables and may depend on the derivative of the solution, which incurs additional difficultly in the mathematical proofs. A new approach is introduced by using a singular differential inequality that ensures that all possible solutions satisfy certain a priori bounds, including their "derivatives", to the singular BVP under consideration. …”
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Proofs as Spatio-Temporal Processes by Petros Stefaneas, Ioannis M. Vandoulakis

“…Finally, we examine certain historical types of styles of mathematical proofs, to elucidate our viewpoint.…”
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Distance-Based Decision Making, Consensus Building, and Preference Aggregation Systems: A Note on the Scale Constraints by İbrahim Gürler, Ozan Çakır, Bora Gündüzyeli

“…We provide necessary mathematical proofs and illustrate our arguments through an abstract physical system, examples, a case study, and a brief computational experiment.…”
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The Multivariate Theory of Functional Connections: Theory, Proofs, and Application in Partial Differential Equations by Carl Leake, Hunter Johnston, Daniele Mortari

“…The reformulation presented in this paper exploits the underlying functional structure presented in the seminal paper on the Theory of Functional Connections to ease the derivation of these interpolating functionals—called constrained expressions—and provides rigorous terminology that lends itself to straightforward derivations of mathematical proofs regarding the properties of these constrained expressions. …”
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A hybrid algorithm based on state-adaptive slime mold model and fractional-order ant system for the travelling salesman problem by Xiaoling Gong, Ziheng Rong, Jian Wang, Kai Zhang, Shengxiang Yang

“…To understand the search behavior of the proposed algorithm, some mathematical proofs of convergence analysis are given. The experimental results validate the efficiency of the hybridization and demonstrate that the proposed algorithm has the competitive ability of finding the better solutions on TSP instances compared with some state-of-the-art algorithms.…”
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