Unity, Complexity, dan Intensity Lukisan Karya Yazid

This study discusses how to understand the unity, complexity, and intensity of Yazid's painting using Monroe Beardsley's theory. Yazid is a West Sumatran artist who is quite famous for his naturalist flow and cannot be separated from the concept of natural beauty. This study uses a qualitative method which includes observation, interviews, and literature study. The research was conducted in the cities of Padang, Padang Pariaman and Padangpanjang, West Sumatra. After conducting research, it was found that Unity (unity) in Yazid's paintings as a whole shows how the arrangement of lines, colors, and compositions are produced in a perfect shape so that it looks like a unity. This makes for distinctive strokes and soft colors and object capture. The complexity of Yazid's paintings can be seen in the lighting which is described as similar to what is captured by the five senses so that the object does not look simple. How Yazid tries to present the refraction of light that is shown in each of his paintings. The intensity (seriousness) in Yazid's paintings can be seen in the lighting as the key in each of his works.

Nearly free curves and arrangements: a vector bundle point of view

Over the past forty years many papers have studied logarithmic sheaves associated to reduced divisors, in particular logarithmic bundles associated to plane curves. An interesting family of these curves are the so-called free ones for which the associated logarithmic sheaf is the direct sum of two line bundles. Terao conjectured thirty years ago that when a curve is a finite set of distinct lines (i.e. a line arrangement) its freeness depends solely on its combinatorics, but this has only been proved for sets of up to 12 lines. In looking for a counter-example to Terao’s conjecture, the nearly free curves introduced by Dimca and Sticlaru arise naturally. We prove here that the logarithmic bundle associated to a nearly free curve possesses a minimal non-zero section that vanishes on one single point, P say, called the jumping point, and that this characterises the bundle. We then give a precise description of the behaviour of P. Based on detailed examples we then show that the position of P relative to its corresponding nearly free arrangement of lines may or may not be a combinatorial invariant, depending on the chosen combinatorics.

Coloring and Guarding Arrangements

Combinatorics International audience Given an arrangement of lines in the plane, what is the minimum number c of colors required to color the lines so that no cell of the arrangement is monochromatic? In this paper we give bounds on the number c both for the above question, as well as some of its variations. We redefine these problems as geometric hypergraph coloring problems. If we define $\Hlinecell$ as the hypergraph where vertices are lines and edges represent cells of the arrangement, the answer to the above question is equal to the chromatic number of this hypergraph. We prove that this chromatic number is between Ω(logn/loglogn). and O(n√). Similarly, we give bounds on the minimum size of a subset S of the intersections of the lines in A such that every cell is bounded by at least one of the vertices in S. This may be seen as a problem on guarding cells with vertices when the lines act as obstacles. The problem can also be defined as the minimum vertex cover problem in the hypergraph $\Hvertexcell$, the vertices of which are the line intersections, and the hyperedges are vertices of a cell. Analogously, we consider the problem of touching the lines with a minimum subset of the cells of the arrangement, which we identify as the minimum vertex cover problem in the $\Hcellzone$ hypergraph.

Cubic Partial Cubes from Simplicial Arrangements

We show how to construct a cubic partial cube from any simplicial arrangement of lines or pseudolines in the projective plane. As a consequence, we find nine new infinite families of cubic partial cubes as well as many sporadic examples.