In this work, we aim to prove the theta dichotomy conjecture for dual dual pairs of type ( ̃ Sp(W ),O(V )) with dim(V ) odd. The crux of the proof relies on the analysis the reducibility of a certain a degenerate principal series representation of the group ̃ Sp(W ′) having double the rank of ̃ Sp(W ). This analysis is carried out by way of a normalized standard intertwining operator which is al...

The sphere S contains a simple family of constant mean curvature (CMC) hypersurfaces of the form Λp,q a ≡ S p(a)×Sq( √ 1− a) for p+ q+1 = n and a ∈ (0, 1) called the generalized Clifford hypersurfaces. This paper demonstrates that new, topologically non-trivial CMC hypersurfaces resembling a pair of neighbouring generalized Clifford tori connected to each other by small catenoidal bridges at a ...

A psychological refractory period (PRP) approach and the locus of slack logic were applied to examine the novel question of whether spatial translation processes can begin before the central bottleneck when effector or noneffector stimuli are processed from an egocentric (viewer-centered) perspective. In single tasks, trials requiring spatial translations were considerably slower than trials wi...

In this paper, flip bifurcations of homoclinic orbits in conservative reversible systems are analysed. In such systems, orbit-flip and inclination-flip bifurcations occur simultaneously. It is shown that multi-pulses either do not bifurcate at all at flip bifurcation points or else bifurcate simultaneously to both sides of the bifurcation point. An application to a fifth-order model of water wa...

We present a review of the development of long-period fiber grating devices for application in optical communication. The recent studies on the realization of long-period gratings in optical planar waveguides are also highlighted.

There is considerable lay discussion that children with attention deficit hyperactivity disorder (ADHD) have increased difficulty with multitasking, but there are few experimental data. In the current study, we examine the simultaneous processing of two stimulus-response tasks using the Psychological Refractory Period (PRP) effect. We hypothesized that children with ADHD would show a greater PR...

We establish a link between von Neumann–Morgenstern stable set and the Nash solution in a general n-player utility set. The stable set-solution is defined with respect to a dominance relation: payoff vector u dominates v if one player prefers u even with one period delay. We show that a stable set exists and, if the utility set has a smooth surface, any stable set converges to the Nash bargaini...