We consider a characteristic initial value problem, with data given on future null cone, for the Einstein (massless) scalar field system positive cosmological constant, in Bondi coordinates. prove that, small data, this has unique global classical solution which is causally geodesically complete to and decays polynomially radius exponentially time, approaching de Sitter solution.

We offer an alternative way of evalating the relative importance of the state coordinates of a nonlinear control system. Our approach is based on making changes of state coordinates to bring the controllability and observability functions into input normal form. These changes of coordinates are done degree by degree and the resulting normal form is unique through terms of degree seven. 1 The Pr...

This paper shows the coordinates influence on singularity of a three degree-of-freedom structure, namely, three-Universal-Prismatic-Spherical (3-UPS) parallel manipulator. Rotational coordinates, which are chosen to define the orientation of the platform, affect the singularity of the manipulator. Euler parameters, which don't have any inherent geometrical singularity are utilized, however they...

Multiple-access interference (MAI) and time-varying multipath effects are the two most significant factors limiting the performance of code-division multiple-access (CDMA) systems. While multipath effects are exploited in existing CDMA systems to combat fading, they are often considered a nuisance to MAI suppression. We propose an integrated framework based on canonical multipath-Doppler coordi...

Constraints are found on the spatial variation of finite-time Lyapunov exponents of two- and three-dimensional systems of ordinary differential equations. In a chaotic system, finite-time Lyapunov exponents describe the average rate of separation, along characteristic directions, of neighboring trajectories. The solution of the equations is a coordinate transformation that takes initial conditi...

We consider the center-focus problem for analytic families of planar vector fields having a monodromic singularity with characteristic directions. give method to compute center conditions family provided there is an inverse integrating factor whose expression in polar coordinates has exceptional divisor first blow-up as isolated zero-set. Some non-trivial examples are analyzed.

In an earlier work, the authors have determined all possible weights n for which there exists a vanishing sum ζ1 + · · · + ζn = 0 of m th roots of unity ζi in characteristic 0. In this paper, the same problem is studied in finite fields of characteristic p. For given m and p, results are obtained on integers n0 such that all integers n ≥ n0 are in the “weight set” Wp(m). The main result (1.3) i...

This paper presents new explicit formulae for the point doubling, tripling and addition for ordinary Weierstraß elliptic curves with a point of order 3 and their equivalent Hessian curves over finite fields of characteristic three. The cost of basic point operations is lower than that of all previously proposed ones. The new doubling, mixed addition and tripling formulae in projective coordinat...

This paper proposes new explicit formulae for the point doubling, tripling and addition on ordinary Weierstrass elliptic curves with a point of order 3 over finite fields of characteristic three. The cost of basic point operations is lower than that of all previously proposed ones. The new doubling, mixed addition and tripling formulae in projective coordinates require 3M + 2C, 8M + 1C + 1D and...

We study the extension generated by the x-coordinates of the petorsion points of an elliptic curve over a function field of characteristic p. If S → C is a non-isotrivial elliptic surface in characteristic p with a pe-torsion section, then for pe > 11 our results imply restrictions on the genus, the gonality, and the p-rank of the base curve C, whereas for pe ≤ 11 such a surface can be construc...