First eigenvalue of submanifolds in Euclidean space by Kairen Cai

“…We give some estimates of the first eigenvalue of the Laplacian for compact and non-compact submanifold immersed in the Euclidean space by using the square length of the second fundamental form of the submanifold merely. …”
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Submanifolds of Euclidean space with parallel mean curvature vector by Tahsin Ghazal, Sharief Deshmukh

“…The object of the paper is to study some compact submanifolds in the Euclidean space Rn whose mean curvature vector is parallel in the normal bundle. …”
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Null Curve Evolution in Four-Dimensional Pseudo-Euclidean Spaces by José del Amor, Ángel Giménez, Pascual Lucas

“…This Lie bracket will be employed to study integrability properties of evolution equations for null curves in a pseudo-Euclidean space. In particular, a geometric recursion operator generating infinitely many local symmetries for the null localized induction equation is provided.…”
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Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space by Fred Brackx, Nele De Schepper, Frank Sommen

“…A new method for constructing Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space is presented. In earlier research, we only dealt with scalar-valued weight functions. …”
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Complete Self-Shrinking Solutions for Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space by Ruiwei Xu, Linfen Cao

“…Let f(x) be a smooth strictly convex solution of det(∂2f/∂xi∂xj)=exp(1/2)∑i=1nxi(∂f/∂xi)-f defined on a domain Ω⊂Rn; then the graph M∇f of ∇f is a space-like self-shrinker of mean curvature flow in Pseudo-Euclidean space Rn2n with the indefinite metric ∑dxidyi. …”
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Quaternionic Curves Which Lie on the Special Planes in 4−Dimensional Euclidean Space E4 by İlim Kişi, Sezgin Büyükkütük, Günay Öztürk

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Harigeeta: Cic Mechanism with Euclidean Steiner Tree for Service Latency Prediction in Delay-Sensitive Cloud Services by Rahul Kumar Sharma, Sarvpal Singh

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Combining and congruence evaluation of phylogenetic signals from different genes based on geometric approach by V. M. Efimov, V. Yu. Kovaleva, Yu. N. Litvinov

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A quasi-linear parabolic system of chemotaxis by Takasi Senba, Takasi Suzuki

“…In the case where the domain is a bounded domain of two-dimensional Euclidean space, it is shown that some solutions to Keller-Segel system blow up in finite time. …”
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Cycle-based formulations in Distance Geometry by Liberti, Leo, Iommazzo, Gabriele, Lavor, Carlile, Maculan, Nelson

“…The distance geometry problem asks to find a realization of a given simple edge-weighted graph in a Euclidean space of given dimension $K$, where the edges are realized as straight segments of lengths equal (or as close as possible) to the edge weights. …”
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Properties of solutions of optimization problems for set functions by Slawomir Dorosiewicz

“…This case of optimal problems can be transformed to standard mixed problems of mathematical programming in Euclidean space. It makes possible the applications of various algorithms for these optimization problems for finding conditional extrema of set functions.…”
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Fourier transforms of Dini-Lipschitz functions on Vilenkin groups by M. S. Younis

“…In [4] we proved some theorems on the Fourier Transforms of functions satisfying conditions related to the Dini-Lipschitz conditions on the n-dimensional Euclidean space Rn and the torus group Tn. In this paper we extend those theorems for functions with Fourier series on Vilenkin groups.…”
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A note on convex functions by Yu-Ru Syau

“…In this paper, we give two weak conditions for a lower semi-continuous function on the n-dimensional Euclidean space Rn to be a convex function. We also present some results for convex functions, strictly convex functions, and quasi-convex functions.…”
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Hamiltonian and Lagrangian BRST Quantization in Riemann Manifold II by Vipul Kumar Pandey

“…We have previously developed the BRST quantization on the hypersurface VN−1 embedded in N-dimensional Euclidean space RN in both Hamiltonian and Lagrangian formulation. …”
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Fractional Derivative Regularization in QFT by Vasily E. Tarasov

“…The regularization procedure is demonstrated for scalar massless fields in φ4-theory on n-dimensional pseudo-Euclidean space-time.…”
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Lightlike Hypersurfaces and Canal Hypersurfaces of Lorentzian Surfaces by Jianguo Sun, Donghe Pei

“…The lightlike hypersurfaces in semi-Euclidean space are of special interest in Relativity Theory. …”
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Sums of distances between points of a sphere by Glyn Harman

“…Given N points on a unit sphere in k+1 dimensional Euclidean space, we obtain an upper bound for the sum of all the distances they determine which improves upon earlier work by K. …”
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Pick’s Theorem in Two-Dimensional Subspace of R3 by Lin Si

“…In the Euclidean space R3, denote the set of all points with integer coordinate by Z3. …”
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Adjoint curves of special Smarandache curves with respect to Bishop frame by Esra Damar

“…In this paper, adjoint curves generated by means of integral curves of special Smarandache curves with respect to the Bishop frame in three-dimensional Euclidean space were introduced. Relations between the main curve and the Bishop apparatus of these adjoint curves were obtained. …”
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