We determine the automorphism group of modular curve $X_0^*(N)$, obtained as quotient $X_0(N)$ by its Atkin-Lehner involutions, for all square-free values $N$.

Let C ⊆ P be an unramified nonspecial real space curve having many real branches and few ovals. We show that C is a rational normal curve if n is even, and that C is anM -curve having no ovals if n is odd.

For each integer n, an n-folding curve is obtained by folding n times a strip of paper in two, possibly up or down, and unfolding it with right angles. Generalizing the usual notion of infinite folding curve, we define complete folding curves as the curves without endpoint which are unions of increasing sequences of n-folding curves for n integer. We prove that there exists a standard way to ex...

Given an odd surjective Galois representation ̺ : GQ → PGL2(F3) and a positive integer N, there exists a twisted modular curve X(N, 3)̺ defined over Q whose rational points classify the quadratic Q-curves of degree N realizing ̺. The paper gives a method to provide an explicit plane quartic model for this curve in the genus-three case N= 5.

The research mainly focuses on the fatigue strength characteristics of 6061-T6 aluminum alloy fillet welds under different vibration frequencies. Firstly, by introducing Stress Life Curve (S-N Curve) and Probability (P-S-N Curve), external stress effects main load-bearing points in environment welded joints are analyzed. Subsequently, a test control system is designed to analyze relationship be...

Precise quantification of plant nitrogen (N) nutrition status is essential for crop N management. The concept of critical N concentration (Nc) has been widely used for assessment of plant N status. This study aimed to develop a new winter wheat Nc dilution curve based on leaf area duration (LAD). Four field experiments were performed on different cultivars with different N fertilization modes i...

The geometric intersection number of a curve on a surface is the minimal number of selfintersections of any homotopic curve, i.e., of any curve obtained by continuous deformation. Given a curve c represented by a closed walk of length at most ` on a combinatorial surface of complexity n we describe simple algorithms to (1) compute the geometric intersection number of c in O(n+ `2) time, (2) con...