Simple PTAS's for families of graphs excluding a minor

We show that very simple algorithms based on local search are polynomial-time approximation schemes for Maximum Independent Set, Minimum Vertex Cover and Minimum Dominating Set, when the input graphs have a fixed forbidden minor.Comment: To appear in Discrete Applied Mathematic

Spectral methods in general relativistic astrophysics

We present spectral methods developed in our group to solve three-dimensional partial differential equations. The emphasis is put on equations arising from astrophysical problems in the framework of general relativity.Comment: 51 pages, elsart (Elsevier Preprint), 19 PostScript figures, submitted to Journal of Computational & Applied Mathematic

CONTROL SYSTEM IS AN APPLIED MATHEMATIC

This paper presents developments and applications of Control Systems (CS) as an Applied Mathematic (AM). Several characteristics of CS can be linked to human behavior. CS can "think" in the sense that they can replace to some extent, human operation. CS can distinguish between open-loop and closed-loop CS and it is a concept or principle that seems to fundamental in nature and not necessarily peculiar to engineering. In human social and political organizations, for example, a leader remains the leader only as long as she is successful in realizing the desires of the group. CS theory can be discussed from four viewpoints as: an intellectual discipline within science and the philosophy of science, a part of engineering, with industrial applications and Social Systems (SS) of the present and the future. In global communication, developed countries and developing countries should build several attractive and sound symbiosis bridges, to prevent loss of universe balances. CS applications have social impacts not only in developed countries but also in developing countries. A new work force strategy without denying the existing of CS is established by retooling the work forces, thus the challenges of social impacts could be answers wisely and would be bright opportunities to improve human standards of living.  Keywords: control  system,   applied  mathematic,  Social  System,   social  impacts,  human standards of living Pada makalah ini dibahas perkembangan dan aplikasi Sistem Kendali sebagai bagian dari Matematika Terapan. Sistem Kendali dapat dihubungkan dengan perilaku manusia. Sistem Kendali dapat “berpikir” sehingga sampai tahap tertentu dapat menggantikan manusia. Sistem kendali merupakan konsep atau prinsip yang secara mendasar berlaku dalam seluruh aspek kehidupan manusia, bukan hanya berlaku dalam bidang teknik. Dalam organisasi politik, misalnya, seorang pemimpin hanya dapat bertahan jika ia mampu mewujudkan harapan kelompoknya. Teori Sistem Kendali dapat dibahas dari beberapa sudut pandang yaitu: sebagai suatu cabang ilmu, bagian dari teknik yang diterapkan dalam industri dan sistem sosial pada masa kini dan masa depan. Aplikasi sistem kendali mempunyai dampak sosial terhadap negara maju dan negara berkembang sehingga perlu dibangun kerjasama yang saling menguntungkan untuk menjaga keseimbangan dunia.Sistem Kendali dapat dilengkapi dengan strategi baru untuk mengatasi dampak sosial teknologi dan meningkatkan standard kehidupan manusia.Kata kunci: sistem kendali, matematika terapan, sistem sosial, dampak sosia

Alternating sign matrices and tournaments

We settle a question of Bressoud concerning the existence of an explicit bijection from a class of oriented square-ice graphs to a class of tournaments. We give an algorithm constructing such a bijection.Comment: 18 pages, LaTeX; minor corrections. To appear in FoataFest proceedings issue of Advances in Applied Mathematic

Exact meromorphic stationary solutions of the real cubic Swift-Hohenberg equation

We show that all meromorphic solutions of the stationary reduction of the real cubic Swift-Hohenberg equation are elliptic or degenerate elliptic. We then obtain them all explicitly by the subequation method, and one of them appears to be a new elliptic solution.Comment: 15 pages, 3 figures, to appear, Studies in Applied Mathematic