AN IDENTITY ON SYMMETRIC POLYNOMIALS by Đặng Tuấn Hiệp, Lê Văn Vĩnh

“…In the proof of the identity, we propose two different proofs. …”
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Nouvelle économie du développement et essais cliniques randomisés : une mise en perspective d’un outil de preuve et de gouvernement by Agnès Labrousse

“…Whereas this technique of proof is largely consolidated now, the embeddedness of this novel instrument in a wider epistemological framework (type of inference, relationship to theory, modes of generalization and relation to historical specificity) remains often fragmentary, leading to some blank spots and limits. …”
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Synchronization of the Fractional-Order Brushless DC Motors Chaotic System by Shiyun Shen, Ping Zhou

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The Principle of Mathematical Induction: Applications in Physical Optics by Joseph Ivin Thomas

“…The bare rudiments of the principle of mathematical induction as a method of proof date back to ancient times. In the contemporary university milieu, the demonstrative scheme is taught as part of a course in discrete mathematics, set theory, number theory, graph theory, group theory, game theory, linear algebra, logic, and combinatorics. …”
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Nonuniform Continuity of the Osmosis K(2, 2) Equation by Aiyong Chen, Yong Ding, Wentao Huang

“…We show that the solution map is not uniformly continuous by using the theory of Himonas and Misiolek. The proof relies on a construction of smooth periodic travelling waves with small amplitude.…”
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On Some Basic Theorems of Continuous Module Homomorphisms between Random Normed Modules by Guo Tiexin

“…Then, for the future development of the theory of module homomorphisms on complete random inner product modules, we give a proof with better readability of the known orthogonal decomposition theorem and Riesz representation theorem in complete random inner product modules under two kinds of topologies. …”
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A Dynamic Electro-Elastic Viscoplastic Contact Problem with an Internal Variable by Ahmed Hamidat, Hakim Bagua

“…We present both the mechanical and variational formulations of the problem, establishing the existence and uniqueness of the solution. Our proof relies on the theory of variational equations and fixed-point arguments. …”
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Bifurcation Problems for Generalized Beam Equations by Fosheng Wang

“…We investigate a class of bifurcation problems for generalized beam equations and prove that the one-parameter family of problems have exactly two bifurcation points via a unified, elementary approach. The proof of the main results relies heavily on calculus facts rather than such complicated arguments as Lyapunov-Schmidt reduction technique or Morse index theory from nonlinear functional analysis.…”
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Solvability of Nonlocal Fractional Boundary Value Problems by Zhongmin Huang, Chengmin Hou

“…This paper is devoted to introduce a new approach to investigate the existence of solutions for a three-point boundary value problem of fractional difference equations as fllows: , , and = We present an existence result at resonance case. The proof relies on coincidence degree theory.…”
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The five gradients inequality for non quadratic costs by Caillet, Thibault

“…We give a proof of the “five gradients inequality” of Optimal Transportation Theory for general costs of the form $c(x,y)=h(x-y)$ where $h$ is a $C^1$ strictly convex radially symmetric function.…”
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Refinement of a Previous Hypothesis of the Lyapunov Analysis of Isotropic Turbulence by Nicola de Divitiis

“…There, the analytical expression of the structure function of the longitudinal velocity difference Δur is derived through a statistical analysis of the Fourier transformed Navier-Stokes equations and by means of considerations regarding the scales of the velocity fluctuations, which arise from the Kolmogorov theory. Due to these latter considerations, this Lyapunov analysis seems to need some of the results of the Kolmogorov theory. …”
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A Novel Approach for Cyclic Decompositions of Balanced Complete Bipartite Graphs into Infinite Graph Classes by A. El-Mesady, Omar Bazighifan, S. S. Askar

“…Graph theory is considered an attractive field for finding the proof techniques in discrete mathematics. …”
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On the existence of generalised syzygies in the planar three-body problem by Tsygvintsev, Alexei

“…Assuming that the motion is bounded and collision-free, we provide a simple sufficient condition for the existence of such configurations. Our proof is elementary and uses only basic tools from the Sturm–Liouville theory.…”
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Existence of Global Solutions for Nonlinear Magnetohydrodynamics with Finite Larmor Radius Corrections by Fariha Elsrrawi, Harumi Hattori

“…We show the existence of global solutions by the energy methods. Our techniques of proof are based on the existence of local solution by semigroups theory and a priori estimate.…”
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Stability of the Levi-Civita tensors and an Alon–Tarsi type theorem by Yeliussizov, Damir

“…The proof uses the connection of Tao’s slice rank with semistable tensors. …”
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The Unity of Space in Kant’s Pre-Critical Philosophy by Dai Heide

“…I contend, then, that this theory is not abandoned at all. Rather, like Kant’s 1763 proof of the existence of God, it is epistemically demoted: it is Kant’s preferred view, but one that falls short of the demanding epistemic standards of the critical philosophy.…”
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Variational Analysis of a Dynamic Contact Problem with Wear and Damage Involving Viscoelastic Materials with Long-Term Memory by Ahmed Hamidat, Hakim Bagua, Adel Aissaoui

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Automorphisms of Regular Wreath Product 𝑝-Groups by Jeffrey M. Riedl

“…We also present a short new proof, based on representation theory, for determining the order of the automorphism group Aut(𝑃), where 𝑃 is the regular wreath product of a finite cyclic 𝑝-group by an arbitrary finite 𝑝-group.…”
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A note on one-parameter groups of automorphisms by A. B. Thaheem, Noor Mohammad

“…The purpose of this note is to provide a simple and short proof of the central decomposition result: αt=βt on Mp and a αt=β−t on M(1−p) for a central projection p∈M, without using the theory of spectral subspaces.…”
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TIE‐GCM ROPE ‐ Dimensionality Reduction: Part I by Piyush M. Mehta, Richard J. Licata

“…We recently demonstrated a proof‐of‐concept for developing what we call a reduced order probabilistic emulator (ROPE) for the thermosphere using the thermosphere ionosphere electrodynamics ‐ general circulation model (TIE‐GCM). …”
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