Our main goal in this paper is to construct the first explicit fundamental domain of the Picard modular group acting on the complex hyperbolic space CH . The complex hyperbolic space is a Hermitian symmetric space, its bounded realization is the unit ball in C equipped with the Bergman metric. The Picard modular group is a discontinuous holomorphic automorphism subgroup of SU(2, 1) with Gaussia...

We investigate several infinite families of purely cubic complex congruence function fields with small fundamental units. Specifically, we compute the fundamental units of fields K of unit rank 1 and characteristic not equal to 3 where the generator of K over Fq(t) is a cube root of D = (M3 − F )/E3 with E3 dividing M3 − F and F dividing M2. We also characterize all purely cubic complex functio...

By using the generalized Chua’s chaotic oscillator as fundamental unit, a complex network displaying the small-world property is synchronized. Authors resort to existing information about that long-range connection in a network increases the data flow from one unit to another to achieve synchronization under a small fixed coupling strength. Computer simulations are provided to show this chaos s...

Complementing recent advances made in the field of structural health monitoring and damage detection, the concept of a wireless sensing network with distributed computational power is proposed. The fundamental building block of the proposed sensing network is a wireless sensing unit capable of acquiring measurement data, interrogating the data and transmitting the data in real time. The computa...

This paper presents a method for determining the possible instantaneous motions of a sliding object during multiple contact pushing. The approach consists of two components: a kinematic analysis considering kinematic motion constraints, and a force analysis considering force constraints on the motion. A new representation of the support friction of a sliding object is presented, and the results...

We prove the following: there are infinitely many finite-covolume (resp. cocompact) Coxeter groups acting on hyperbolic space Hn for every n ≤ 19 (resp. n ≤ 6). When n = 7 or 8, they may be taken to be nonarithmetic. Furthermore, for 2 ≤ n ≤ 19, with the possible exceptions n = 16 and 17, the number of essentially distinct Coxeter groups in Hn with noncompact fundamental domain of volume ≤ V gr...

Charge neutrality and stoichiometry impose severe restrictions on the mechanisms of epitaxial growth of complex oxides. The fundamental question arises of what is the minimum growth unit when sample thickness is reduced beyond the size of the unit cell. We have investigated the growth mechanism of YBa2Cu3O7 cuprate superconductor, using a consistent approach based on the growth of noninteger nu...

We show that a particular parameter plays a vital role in the resolution of S-unit equations, at the stage where LLL-reduction is applied. We define the notion of optimal system of fundamental S-units (with respect to this parameter), and prove that such a system exists and can be effectively constructed. Applying our results and methods, one can obtain much better bounds for the solutions of S...

The spurious regression phenomenon in least squares occurs for a wide range of data generating processes, such as driftless unit roots, unit roots with drift, long memory, trend and brokentrend stationarity. Indeed, spurious regressions have played a fundamental role in the building of modern time series econometrics and have revolutionized many of the procedures used in applied macroeconomics....

The fundamental unit of rapid, physiological color change in vertebrates is the dermal chromatophore unit. This unit, comprised of cellular associations between different chromatophore types, is relatively conserved across the fish, amphibian, and reptilian species capable of physiological color change and numerous attempts have been made to understand the nature of the four major chromatophore...