An n × n complex matrix is full ray-nonsingular if it has no zero entries and every matrix obtained by changing the magnitudes of its entries is nonsingular. It is shown that a 5×5 full ray-nonsingular matrix does not exist. This, combined with earlier results, shows that there exists an n× n full ray-nonsingular matrix if and only if n ≤ 4.

The primary goal of this note is to prove that every abstract nonsingular curve can be realized as an open subset of a (unique) nonsingular projective curve. Note that this encapsulates two facts in one: that every nonsingular abstract curve is quasiprojective, and that it can be “compactified” into a projective curve without introducing singularities. We start from the definitions and state th...

A block graph is a graph in which every block is a complete graph (clique). Let G be a block graph and let A(G) be its (0,1)-adjacency matrix. Graph G is called nonsingular (singular) if A(G) is nonsingular (singular). Characterizing nonsingular block graphs, other than trees, is an interesting open problem. In this article, we give some classes of nonsingular and singular block graphs and rela...

We give an affirmative answer to a 1976 question of M. Rosen: every abelian group is isomorphic to the class group of an elliptic Dedekind domain R. We can choose R to be the integral closure of a PID in a separable quadratic field extension. In particular, this yields new and – we feel – simpler proofs of theorems of L. Claborn and C.R. Leedham-Green. Luther Claborn received his PhD from U. Mi...

In one-loop string effective action, we study a generality of non-singular cosmological solutions found in the isotropic and homogeneous case. We discuss Bianchi I and IX type spacetimes. We find that nonsingular solutions still exist in Bianchi I model around nonsingular flat Friedmann solutions. On the other hand, we cannot find any nonsingular solutions in Bianchi IX model. Non-existence of ...

New type of nonsingular oscillating solutions for the Universe described by cos-mological equations of gauge theories of gravity is presented. Advantages of these solutions with respect to existing nonsingular solutions within framework of general relativity and gauge gravity are discussed. It is shown in particular that these solutions have nonzero measure and stable on contraction stage unlik...

If V is a nonsingular real algebraic set we say Ht(V;Z2) * s algebraic if it is generated by nonsingular algebraic subsets of V. Let V be a 3-dimensional nonsingular real algebraic set. Then, we prove that any immersed surface in V can be isotoped to an algebraic subset if and only if Ht (V: Z 2 ) / = 1,2 are algebraic. This isotopy above carries the natural stratification of the immersed surfa...

in this note we introduce the notion of weak mccoy rings as a generalization of mccoy rings, and investigate their properties. also we show that, if is a semi-commutative ring, then is weak mccoy if and only if is weak mccoy.