Boundedness of solutions of matrix nonlinear volterra difference equations by Michael I. Gil', Rigoberto Medina

“…Nonlinear discrete-time Volterra equations in a Euclidean space are considered. Conditions for the boundedness of solutions are established by virtue of recent estimates for the norm of the resolvent of Volterra operators. …”
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On Linear Difference Equations for Which the Global Periodicity Implies the Existence of an Equilibrium by István Győri, László Horváth

“…This result is extended for higher order linear inhomogeneous system in a real or complex Euclidean space. The work was highly motivated by the early works of Smith (1934, 1941) and the papers of Kister (1961) and Bas (2011).…”
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Estimation of the Value at Risk Using the Stochastic Approach of Taylor Formula by Vini Yves Bernadin Loyara, Remi Guillaume Bagré, Diakarya Barro

“…A higher dimensional extension of the Taylor–Young formula is used for this estimation in a Euclidean space. Moreover, a time-varying and conditional copula is used for the modeling of the VaR.…”
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On CR-Lightlike Product of an Indefinite Kaehler Manifold by Rakesh Kumar, Jasleen Kaur, R. K. Nagaich

“…Mixed foliate CR-lightlike submanifold of indefinite complex space form has also been discussed and showed that the indefinite Kaehler manifold becomes the complex semi-Euclidean space.…”
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Study of Differential Equations on Warped Product Semi-Invariant Submanifolds of the Generalized Sasakian Space Forms by Ibrahim Al-Dayel

“…More precisely, by analyzing Bochner’s formula on these inequalities, we demonstrate that, under certain conditions, the base of these submanifolds is isometric to Euclidean space. We also look at the effects of certain differential equations on warped product semi-invariant product submanifolds and show that the base is isometric to a special type of warped product under some geometric conditions.…”
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Linear algebra and differential geometry on abstract Hilbert space by Alexey A. Kryukov

“…However, while n-dimensional spaces in applications are always realized as the Euclidean space Rn, Hilbert spaces admit various useful realizations as spaces of functions. …”
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Weyl-Euler-Lagrange Equations of Motion on Flat Manifold by Zeki Kasap

“…Furthermore, a flat manifold is one Euclidean space in terms of distances. Weyl introduced a metric with a conformal transformation for unified theory in 1918. …”
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Small sets in convex geometry and formal independence over ZFC by Menachem Kojman

“…To each closed subset S of a finite-dimensional Euclidean space corresponds a σ-ideal of sets 𝒥 (S) which is σ-generated over S by the convex subsets of S. …”
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Noether Symmetries of the Area-Minimizing Lagrangian by Adnan Aslam, Asghar Qadir

“…It is shown that the Lie algebra of Noether symmetries for the Lagrangian minimizing an (n-1)-area enclosing a constant n-volume in a Euclidean space is so(n)⊕sℝn and in a space of constant curvature the Lie algebra is so(n). …”
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The Euclidean model of space and time, and the wave nature of matter by Radovan Machotka

“…The EMST offers a unified description of all particles of matter as waves moving through four-dimensional Euclidean space at the speed of light. Unlike the usual description in three dimensions, where the group and phase velocities of a particle differ, in four-dimensional space the wave and the associated particle can be treated as a single object. …”
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Lax Triples for Integrable Surfaces in Three-Dimensional Space by Jan L. Cieśliński, Artur Kobus

“…., Lax representations consisting of three linear equations) associated with families of surfaces immersed in three-dimensional Euclidean space E3. We begin with a natural integrable deformation of the principal chiral model. …”
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A note on surfaces with prescribed oriented Euclidean Gauss map by Ricardo Sa Earp, Eric Toubiana

“…We present another proof of a theorem due to Hoffman and Osserman in Euclidean space concerning the determination of a conformal immersion by its Gauss map. …”
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Global well-posedness of 2D incompressible Navier–Stokes–Darcy flow in a type of generalized time-dependent porosity media by Linlin Tan, Bianru Cheng

“…This study investigates the global well-posedness of a coupled Navier–Stokes–Darcy model incorporating the Beavers–Joseph–Saffman–Jones interface boundary condition in two-dimensional Euclidean space. We establish the existence of global strong solutions for the system in both linear and nonlinear cases where porosity depends on pressure. …”
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SOME ITERATIVE METHODS FOR QUASI-EQUILIBRIUM PROBLEMS by Jean Jacques Strodiot, Nguyễn Thị Thu Vân, Nguyễn Văn Hiền

“…In this paper we present two new extensions of Korpelevich's extragraclient method for solving the scalar Quasi-Equilibrium Problem (QEP) in Euclidean space. In both extensions we replace the second orthogonal projection in the correction step of the extragradient method by an Armijo linesearch adapted to (QEP). …”
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Translational and great Darboux cyclides by Lubbes, Niels

“…A surface that is the pointwise sum of circles in Euclidean space is either coplanar or contains no more than 2 circles through a general point. …”
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The maximal operator in weighted variable spaces Lp(⋅) by Vakhtang Kokilashvili, Natasha Samko, Stefan Samko

“…We study the boundedness of the maximal operator in the weighted spaces Lp(⋅)(ρ) over a bounded open set Ω in the Euclidean space ℝn or a Carleson curve Γ in a complex plane. …”
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Numerical Characterization of DNA Sequence Based on Dinucleotides by Xingqin Qi, Edgar Fuller, Qin Wu, Cun-Quan Zhang

“…Alignment methods and graphical techniques (where each sequence is represented by a curve in high-dimension Euclidean space) have been used popularly for a long time. …”
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Graphing, homotopy groups of spheres, and spaces of long links and knots by Robin Koytcheff

“…We study homotopy groups of spaces of long links in Euclidean space of codimension at least three. With multiple components, they admit split injections from homotopy groups of spheres. …”
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Quantitative spectral inequalities for the anisotropic Shubin operators and applications to null-controllability by Alphonse, Paul, Seelmann, Albrecht

“…We prove quantitative spectral inequalities for the (anisotropic) Shubin operators on the whole Euclidean space, thus relating for functions from spectral subspaces associated to finite energy intervals their $L^2$-norm on the whole space to the $L^2$-norm on a suitable subset. …”
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Anatomy of the Higgs Boson Decay into Two Photons in the Unitary Gauge by Athanasios Dedes, Kristaq Suxho

“…The result for the amplitude agrees with the “famous” one obtained using dimensional regularisation (DR) in the limit d → 4 , where d is the number of spatial dimensions in Euclidean space. At the exact equality d = 4 , a three-sphere surface term appears that renders the Ward Identities and the equivalence theorem inconsistent. …”
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