Enhancing the impact resistance performance of carbon fiber-reinforced polymer (CFRP) laminates stands as a prominent research focus among various nations. Existing studies have shown tendency towards arbitrary selection inter-ply helix angle values in CFRP laminates, which is accompanied by limited number samples representing chosen angles. However, existing relatively random spiral between an...

Consider a quadratic cone K in the 3-dimensional projective space PG(3,q) over finite field of order q, where q is prime power. Let E (respectively, T, S) denote set all lines that are external tangent, secant) with respect to K. We characterize minimum size blocking sets line A, A one E, S, E∪T, E∪S and T∪S.

Consider a quadratic cone K in the 3-dimensional projective space PG(3,q) over finite field of order q, where q is prime power. Let E (respectively, T, S) denote set all lines that are external tangent, secant) with respect to K. We characterize minimum size blocking sets line A, A one E, S, E∪T, E∪S and T∪S.

Cones of tangent vectors (generated by families of control variations) are the principal analytical tool for obtaining necessary and sufficient conditions for optimality and nonlinear controllability. Unlike the classical Pontryagin cone, it is known that in general high-order variational cones may fail to be convex. For control variations that converge in L to the reference control, this was s...

We give a solution to the weak Schottky problem for genus five Jacobians with vanishing theta null, answering question of Grushevsky and Salvati Manni. More precisely, we show that if principally polarized abelian variety dimension has null quadric tangent cone rank at most three, then it is in Jacobian locus, up extra irreducible components. employ degeneration argument, together study ramific...

Fix a prime power q and integers m ≥ 2, σ > 0, x > 0, g ≥ 0, d ≥ mσ + 1 such that q ≥ (δ − 1)δ3, where δ := d3 + 3dx + 4x + 2g − 2. Let C ⊂ P be a smooth degree x curve defined over Fq such that h(P,IC(σ − 1)) = h(C,OC (σ − 2)) = 0 and pa(C) = g. Here we prove the existence of a degree d surface X ⊆ P3 defined over Fq, such that Sing(X) = C and X has ordinary multiplicity m along C, i.e. for ev...

We investigate the relationships between the Lipschitz outer geometry and the embedded topological type of a hypersurface germ in (Cn, 0). It is well known that the Lipschitz outer geometry of a complex plane curve germ determines and is determined by its embedded topological type. We prove that this does not remain true in higher dimensions. Namely, we give two normal hypersurface germs (X1, 0...

The geometry of circles in the plane is inextricably tied with the group of Möbius transformations, which take circles to circles. This geometry can be seen in a more symmetric after transforming the plane to the sphere, by stereographic projection. Interpretations will be discussed for Voronoi diagrams, Delaunay triangulations,etc. from this point of view. Fortune’s algorithm for constructing ...

The aim of this paper is to derive convergence results for projected line-search methods on the real-algebraic variety M≤k of real m× n matrices of rank at most k. Such methods extend Riemannian optimization methods, which are successfully used on the smooth manifold Mk of rank-k matrices, to its closure by taking steps along gradient-related directions in the tangent cone, and afterwards proje...