(the prime indicates differentiation with respect to x). P(x) and Q(x) (positive downward) are the live load per unit length and the dead load of the roadway, cable, and hangers per unit length. E and / (assumed constants) are the modulus of elasticity and moment of inertia of the roadway and H (constant) is the horizontal dead-load tension in the cable. The term h (constant), the induced live-...

The uniform box product was introduced by Scott Williams in 2001, but very little was done with it until the recent (2010 and 2012) [B1], [H1] dissertations of Jocelyn Bell and Jeffrey Hankins. Their results had to do with two questions that Williams posed a decade earlier: whether the uniform box product of compact spaces is normal, and whether it is paracompact. Hankins answered the latter qu...

Given the prevalence of the use of rhetorical relations in the generation of text (Itovy, 1989; Moore and Paris, 1988; Scott and Souza, 1990), it is surprising how little work has actually been done on the grammatical realization of these relations. Most systems, based on Mann and Thompson's formulation of Rhetorical Structure Theory (Mann and Thompson, 1988), have adopted simplified solutions ...

The electrical potential differences were measured at various points in an organic phase of a water-oil-water liquid membrane system in which self-oscillations of an electrical potential difference occurred across a three-phases-liquid membrane by using an H-shaped cell. The electrical potential difference oscillated in the direction through the two aqueous phases, but not in its vertical direc...

In this paper, we propose an intra mode bit skip algorithm for H.264 intra 4×4 mode to reduce the mode representation burden. The proposed algorithm enhances the “adaptive intra mode bit skip (AIMBS)” in literature by considering the bit skip for more modes rather than only DC mode. In this work, the correlation between vertical and horizontal differences of reference pixels and encoded modes a...

Bipedal running can easily result in a fall due to poor availability of the ground reaction force at the boundary of the flight and support phases. We propose methods to decompose and synthesize a running gait pattern into vertical, horizontal and rotational components so that time-dependent ground friction limits are satisfied. We also extend previously proposed boundary condition, the diverge...

In the recent paper [12] we have proved that the only stable C minimal surfaces in the first Heisenberg group Hn which are graphs over some plane and have empty characteristic locus must be vertical planes. This result represents a sub-Riemannian version of the celebrated theorem of Bernstein. In this paper we extend the result in [12] to C complete embedded minimal surfaces in H with empty cha...