arXiv subjects
Publications and source records attributed to Masood Aryapoor.
The main point of this paper is to present a class of equations over integers that one can check if they have a solution by checking a set of inequalities. The prototype of such equations is the equations appearing in the well-known Gale-Ryser theorem.
Latin squares are interesting combinatorial objects with many applications. When working with Latin squares, one is sometimes led to deal with partial Latin squares, a generalization of Latin squares. One of the problems regarding partial Latin square and with applications to Latin squares is whether a partial Latin square with a given set of conditions exists. The goal of this article is to introduce some problems of this kind and answer some existence questions regarding partial Latin squares
The pasch configuration and Steiner triple systems
A characterization of multiplicative (and additive) arithmetical functions is given. Using this characterization, we show that the group of multiplicative arithmetical functions is isomorphic to the group of additive arithmetical functions.
By simulating an ergodic Markov chain whose stationary distribution is uniform over the space of nxn Latin squares, Mark T. Jacobson and Peter Matthews [4], have discussed elegant methods by which they generate Latin squares with a uniform distribution (approximately). The central issue is the construction of "moves" that connect the squares. Most of their lengthy paper is to prove that the associated graph is indeed connected. We give a short proof of this fact by using the concepts of Latin bitrades.
We study the self-dual Yang-Mills equations in split signature. We give a special solution, called the basic split instanton, and describe the ADHM construction in the split signature. Moreover a split version of t'Hooft ansatz is described.
A version of the Penrose transform is introduced in the split signature. It relates the cohomological data with supports on the open subsets of the complex 3-projective space and kernel of differential operators on the (real) Grassmannian of 2-planes in the Euclidean 4-space. As an example we derive a cohomological interpretation of the so-called X-ray transform. Furthermore, a cohomological realization of the so-called "minimal" representation of SL(4,R) is given. We also present the split Penrose transform in split instanton backgrounds.
In this paper we study some properties of the field of rational pseudo-differential operators on a field and some other related rings. As an application we reconstruct the Kac co-cycle on the Lie algebra of differential operators on a circle.
Non-commutative Henselian rings are defined and it is shown that a local ring which is complete and separated in the topology defined by its maximal ideal is Henselian provided that it is almost commutative.