We give sufficient conditions for the tautness of a transversely homogenous foliation defined on compact manifold, by computing its base-like cohomology. As an application, we prove that if is non-unimodular then either ambient closure leaves or total space associated principal bundle fiber over S 1 .

In this paper, we mainly study the embedding problem of unimodular row vectors, focusing on avoiding identification polynomial zeros. We investigate existence minimal syzygy module ZLP matrix and demonstrate that has structural properties are similar to fundamental solution system homogeneous linear equations found in algebra. Finally, provide several methods for vectors certain cases.

We show that on an n = 24m+ 8k-dimensional even unimodular lattice, if the shortest vector length is ≥ 2m, then as the number of vectors of length 2m decreases, the secrecy gain increases. We will also prove a similar result on general unimodular lattices. Furthermore, assuming the conjecture by Belfiore and Solé, we will calculate the difference between inverses of secrecy gains as the number ...

We prove that for the Activated Random Walks model on transitive unimodular graphs, if there is fixation, then every particle eventually fixates, almost surely. We deduce that the critical density is at most 1. Our methods apply for much more general processes on unimodular graphs. Roughly put, our result apply whenever the path of each particle has an automorphism invariant distribution and is...

A Golay Complementary Sequence (CS) has Peak-to-Average-Power-Ratio (PAPR) ≤ 2.0 for its one-dimensional continuous Discrete Fourier Transform (DFT) spectrum. Davis and Jedwab showed that all known length 2m CS, (GDJ CS), originate from certain quadratic cosets of Reed-Muller (1,m). These can be generated using the Rudin-Shapiro construction. This paper shows that GDJ CS have PAPR ≤ 2.0 under a...

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...