In this article we characterize the ideal unimodular singularities in terms of their invariants. On the basis of this characterization we give an implementation of a classifier for ideal unimodular singularities in the computer algebra system SINGULAR.

Abstract Let $(\xi _j)_{j\ge 1} $ be a non-stationary Markov chain with phase space $X$ and let $\mathfrak {g}_j:\,X\mapsto \textrm {SL}(m,{\mathbb {R}})$ sequence of functions on values in the unimodular group. Set $g_j=\mathfrak {g}_j(\xi _j)$ denote by $S_n=g_n\ldots g_1$, product matrices $g_j$. We provide sufficient conditions for exponential growth norm $\|S_n\|$ when is not supposed to s...

Unimodular gravity is classically equivalent to General Relativity. This equivalence extends to actions which are functions of the curvature scalar. At the quantum level, the dynamics could differ. Most importantly, the cosmological constant is not a coupling in the unimodular action, providing a new vantage point from which to address the cosmological constant fine-tuning problem. Here, a quan...

Unimodular transformation has been proposed as a powerful techniques for loop parallelization in imperative language programs. In this paper, we propose to apply unimodular transformation to functional language programs. In particular, we propose a method of applying unimodular transformation to monolithic arrays such as Haskell array comprehensions. Using our method, a compiler can deduce a sa...

Unimodular/Phase-only sequence having impulse like aperiodic auto-correlation function plays a central role in the applications of RADAR, SONAR, Cryptography, and Wireless (CDMA) Communication Systems. In this paper, we propose fast iterative algorithm to design phase-only sequences arbitrary lengths by minimizing Integrated Side-lobe Level (ISL) metric, which is very closely related property s...

We consider totally unimodular multistage stochastic programs, that is, multistage stochastic programs whose extensive-form constraint matrices are totally unimodular. We establish several sufficient conditions and identify examples that have arisen in the literature.

The Lapped Orthogonal Transform (LOT) [ I ] is a popular transform and has found many applications in signal processing. Its extension, BiOrthogonal Lapped Transform (BOLT), has been investigated in detail in [2]. In this paper, we will study Lapped Unimodular Transform (LUT). All of these three transforms are first-order matrices with FIR inverses. We will show that like LOT and BOLT, all LUTs...

We characterize the class of integral square matrices M having the property that for every integral vector q the linear complementarity problem with data M; q has only integral basic solutions. These matrices, called principally unimodular matrices, are those for which every principal nonsingular submatrix is unimodular. As a consequence , we show that if M is rank-symmetric and principally uni...