The known facts about solvability of equations over groups are considered from a more general point of view. A generalized version of the theorem about solvability of unimodular equations over torsion-free groups is proved. In a special case, this generalized version become a multivariable variant of this theorem. For unimodular (ordinary and generalized) equations over torsion free groups, we ...

This paper presents algorithms for computing stable Lagrangian invariant subspaces of a Hamiltonian matrix and a symplectic pencil, respectively, having purely imaginary and unimodular eigenvalues. The problems often arise in solving continuousor discrete-time H∞-optimal control, linear-quadratic control and filtering theory, etc. The main approach of our algorithms is to determine an isotropic...

We show that the cosmological constant appears as a Lagrange multiplier if nature is described by a canonical noncommutative spacetime. It is thus an arbitrary parameter unrelated to the action and thus to vacuum fluctuations. The noncommutative algebra restricts general coordinate transformations to four-volume preserving non-commutative coordinate transformations. The noncommutative gravitati...

The reliability of Integrated circuits mainly depends on the VLSI Design Automation techniques. The main problem faced in these techniques is the Physical Design Implementation. The size and performance parameters of an integrated circuit mainly rely on the three main domains of Physical Design which are Placement, Partitioning, and Routing. In this paper, the problem domain is expressed in Uni...

In this paper we discuss a possibility to extend unimodular transformations to non-perfectly nested loops. The main idea behind this extension is to convert a non-perfectly nested loop into a perfectly nested one by moving code into to innermost loop and properly guarding it to avoid multiple execution. This form of the loop can be viewed as an intermediate form for the transformation. Having o...

The classical Hausdorff-Young inequality for locally compact abelian groups states that, for 1 ≤ p ≤ 2, the L-norm of a function dominates the L-norm of its Fourier transform, where 1/p + 1/q = 1. By using the theory of non-commutative L-spaces and by reinterpreting the Fourier transform, R. Kunze (1958) [resp. M. Terp (1980)] extended this inequality to unimodular [resp. non-unimodular] groups...

We find all convex lattice polygons in the plane (up to equivalence) with at most one interior lattice point. A lattice point in the plane is a point with integer coordinates. A lattice segment is a line segment whose endpoints are lattice points. A lattice polygon is a simple polygon whose vertices are lattice points. In 1980, Arkinstall [1] proved that, up to lattice equivalence (defined belo...

Hermite normal form and Smith normal form are canonic forms of integral matrices with respect to congruence produced by multiplication with right unimodular matrix resp. by multiplication with left and right unimodular matrix simultaneously. This lower-diagonal resp. diagonal form has many applications in various elds. Unfortunately, the computation of them is extremely resource consuming. The ...

By an eigenvalue comparison-technique[16], the expected return probability of the delayed random walk on the finite clusters of critical Bernoulli bond percolation on the two-dimensional Euclidean lattice is estimated. The results are generalised to invariant percolations on unimodular graphs with almost surely finite clusters. A similar method has been used elsewhere[17] to derive bounds for i...