This paper examines the effect of curved boundary continuity on finite element simulations. Quartic C0 continuous and G1 continuous meshes with curved boundaries are created from CAD geometry. These C0 continuous and G1 continuous surface triangles are constructed using Bézier triangles and triangular Gregory patches respectively. Curved tetrahedra are constructed using a shape blending with te...

We solve the monomer-dimer problem on a nonbipartite lattice, a simple quartic lattice with cylindrical boundary conditions, with a single monomer residing on the boundary. Due to the nonbipartite nature of the lattice, the well-known method of solving single-monomer problems with a Temperley bijection cannot be used. In this paper, we derive the solution by mapping the problem onto one of clos...

For a fixed prime p ≡ 1 (mod 4), we define the corresponding quartic residue graph and determine the number of triangles contained in such a graph. Our computation requires us to compute the number of pairs of consecutive quartic residues modulo p via the evaluation of certain quartic Jacobi sums.

We prove that a nodal quartic threefold X containing no planes is Q-factorial provided that it has not more than 12 singular points, with the exception of a quartic with exactly 12 sin-gularities containing a quadric surface. We give some geometrical constructions related to the latter quartic.

In this paper we present an approximation method of quadric surface using quartic spline. Our method is based on the approximation of quadratic rational Bézier patch using quartic Bézier patch. We show that our approximation method yields G (tangent plane) continuous quartic spline surface. We illustrate our results by the approximation of helicoid-like surface.

Collocation methods based on quartic splines are presented for second-order two-point boundary value problems. In order to obtain a uniquely solvable linear system for the degrees of freedom of the quartic spline collocation approximation, in addition to the boundary conditions specified by the problem, extra boundary or near-boundary conditions are introduced. Non-optimal (fourth-order) and op...

and Applied Analysis 3 is called a quadratic functional equation. In particular, every solution of the quadratic functional equation is said to be a quadratic mapping. A generalized Hyers-Ulam stability problem for the quadratic functional equation was proved by Skof 7 for mappings f : X → Y , where X is a normed space and Y is a Banach space. Cholewa 8 noticed that the theorem of Skof is still...

Two birational projective varieties in $$\mathbb {P}^n$$ are Cremona Equivalent if there is a modification of mapping one onto the other. The minimal degree $$X\subset \mathbb integer among all degrees that to X. Equivalence and well understood for subvarieties codimension at least 2 while both general very subtle questions divisors. In this note, I compute quartic surfaces {P}^3$$ . This allow...

We construct infinite families of elliptic curves with given torsion group structures over quartic number fields. In a 2006 paper, the first two authors and Park determined all of the group structures which occur infinitely often as the torsion of elliptic curves over quartic number fields. Our result presents explicit examples of their theoretical result. This paper also presents an efficient ...