arXiv research

The paper studies curves of constant-ratio in pseudo-Galilean space.

In this paper, we study generalized constant ratio surfaces in the Euclidean 4-space. We also obtain a classifications of constant slope surfaces.

In this paper, we study generalized constant ratio (GCR) hypersurfaces in Euclidean spaces. We mainly focus on the hypersurfaces in $\mathbb E^4$. First, we deal with $δ(2)$-ideal GCR hypersurfaces. Then, we study on hypersurfaces with constant (first) mean curvature. Finally, we obtain the complete classification of G…

A twisted curve in Euclidean 3-space E^3 can be considered as a curve whose position vector can be written as linear combination of its Frenet vectors. In the present study we study the twisted curves of constant ratio in E^3 and characterize such curves in terms of their curvature functions. Further, we obtain some re…

A hypersurface in a Euclidean space $\mathbb{E}^{n+1}$ is said to be a generalized constant ratio (GCR) hypersurface if the tangential part of its position vector is one of its principle directions. In this work, we move the study of generalized constant ratio hypersurfaces started in \cite% {YuFu2014GCRS} into the Min…

Study finds all helical surfaces with a constant ratio of principal curvatures.

Study surfaces with constant ratio of principal curvatures in Euclidean and isotropic geometries.

This research solves Plateau's problem for CRPC surfaces.

The study finds parametrizations for surfaces of revolution with a linear curvature ratio.

Given a Riemannian manifold $N^n$ and ${\cal Z}\in \mathfrak{X}(N)$, an isometric immersion $f\colon M^m\to N^n$ is said to have the \emph{constant ratio property with respect to ${\cal Z}$} either if the tangent component ${\cal Z}^T_f$ of ${\cal Z}$ vanishes identically or if ${\cal Z}^T_f$ vanishes nowhere and the r…

Study of deep linear neural networks with proportional width and depth.

The study characterizes loxodromes on specific rotational surfaces in 3D space.

Paper analyzes adversarial training's performance in binary classification.

Active search is a learning paradigm for actively identifying as many members of a given class as possible. A critical target scenario is high-throughput screening for scientific discovery, such as drug or materials discovery. In this paper, we approach this problem in Bayesian decision framework. We first derive the B…

The paper analyzes how over-parameterization affects reinforcement learning performance.