The q-Poincaré group of [1] is shown to have the structure of a semidirect product and coproduct B>⊳ ̃ SOq(1, 3) where B is a braided-quantum group structure on the q-Minkowski space of 4-momentum with braided-coproduct ∆p = p⊗ 1+1⊗p. Here the necessary B is not a usual kind of quantum group, but one with braid statistics. Similar braided-vectors and covectors V (R), V (R) exist for a general R...

Let (X, 36, m) be a probability space and let x be any invertible measure-preserving transformation of X. Given A, Bs 08, the Poincare return time sequence is the sequence of whole numbers n(A,B) = (neZ: m(A n zB) > 0). There is also a related point return time sequence, given for xeX and A €08 by n(x,A) = (neZ: xxsA). A Poincare return time sequence is the democratic version of the point retur...

We use braided groups to introduce a theory of ∗-structures on general inhomogeneous quantum groups, which we formulate as quasi-∗ Hopf algebras. This allows the construction of the tensor product of unitary representations up to a quantum cocycle isomorphism, which is a novel feature of the inhomogeneous case. Examples include q-Poincaré quantum group enveloping algebras in R-matrix form appro...

We study the noncommutative Poincare duality between Poisson homology and cohomology of unimodular algebras, show that Kontsevich's deformation quantization as well Koszul preserve corresponding duality. As a corollary, Batalin-Vilkovisky algebra structures naturally arise in these cases are all isomorphic.

In this paper, the existence of limit cycles for the specific bilinear systems is explored. Based on the BellmanGronwall inequality approach, not only the exponentially stable limit cycles phenomenon of such systems can be certified but also the oscillation behaviors of such systems can be correctly predicted. Finally, a numerical example is provided to illustrate the feasibility and effectiven...

BACKGROUND Atrial fibrillation (AFib) is one of the prominent causes of stroke, and its risk increases with age. We need to detect AFib correctly as early as possible to avoid medical disaster because it is likely to proceed into a more serious form in short time. If we can make a portable AFib monitoring system, it will be helpful to many old people because we cannot predict when a patient wil...

There has been extensive work on the existence of periodic solutions for nonlinear second order autonomous differantial equations, but little work regarding the third order problems. The popular Poincare-Bendixon theorem applies well to the former but not the latter (see [2] and [3]). We give a necessary condition for the existence of periodic solutions for the third order autonomous system...

We estabish an analog of the Poincare-Cauchy separation theorem for normal matrices in terms of majorization. The result is applied to obtain new information on the geometry of the roots of a complex polynomial and of its derivative. We prove the old conjectures of de Bruijn-Springer and Schoenberg about these roots.

A candidate supergravity solution of intersecting D7-branes with a fivedimensional intersecting domain (an I5-brane) is presented. This displays an enhanced Poincare symmetry and supersymmetry away from the brane cores. We also explore the possibility of a relation between the intersection region of D7-branes and conifolds through F-theory.

A nonlinear Poincare sphere method for measuring polarization-mode dispersion (PMD) using the four-wave mixing (FWM) effect in single-mode optical fibers is presented. This method is based on the FWM-power transfer function on the polarization states of the input signals. Average PMD can be obtained by using this method with measurements in just a narrow optical bandwidth.