The well-known Hilbert’s 16th problem has remained unsolved since Hilbert proposed the 23 mathematical problems at the Second International Congress of Mathematics in 1900 [Hilbert, 1902]. Recently, a modern version of the second part of the 16th problem was formulated by Smale [1998], chosen as one of the 18 challenging mathematical problems for the 21st century. To be more specific, consider ...

The second part of Hilbert’s sixteenth problem concerned with the existence and number of the limit cycles for planer polynomial differential equations of degree n. In this article after a brief review on previous studies of a particular class of Hilbert’s sixteenth problem, we will discuss the existence and the stability of limit cycles of this class in the form of fractional differential equa...

The usual methodology employed in analysis after a sequential clinical trial is based on orderings of the possible samples resulting from the design. However, this approach lacks flexibility for use in wider applications. In this paper two estimation techniques not based on orderings are considered and modified to obtain improved accuracy. A bias-adjusted maximum likelihood estimate together wi...

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We have analysed the Constant-Murley (1987) assessment for 25 patients with shoulder pathology. We found the score easy to use, with low inter- and intraobserver errors, but sufficiently imprecise in repeated measurements to give concern in its use for clinical follow-up of patients. We have calculated 95% confidence limits for a single assessment to be within 16 to 20 points in most cases. In ...

Suppose a group G is relatively hyperbolic with respect to a collection P of its subgroups and also acts properly, cocompactly on a CAT (0) (or δ–hyperbolic) space X. The relatively hyperbolic structure provides a relative boundary ∂(G,P). The CAT (0) structure provides a different boundary at infinity ∂X. In this article, we examine the connection between these two spaces at infinity. In parti...

We show that the action of the special conformal transformations of the usual (undeformed) conformal group is the q → 1 scaling limit of the braided adjoint action or R-commutator of q-Minkowski space on itself. We also describe the qdeformed conformal algebra in R-matrix form and its quasi-∗ structure.

We have proposed a new ultra-compact optical demultiplexer based on metal-insulator-metal plasmonic waveguides aperture-coupled to the ring resonators. Our proposed device has high performance, small footprint, and high potential for integration and development to more channels.