Let us call a lattice path in Z × Z from (0, 0) to (n, 0) using U = (1, k), D = (1,−1), and H = (a, 0) steps and never going below the x-axis a (k, a)-path (of order n). A super (k, a)-path is a (k, a)-path which is permitted to go below the x-axis. We relate the total number of humps in all of the (k, a)paths of order n to the number of super (k, a)-paths, where a hump is defined to be a seque...

Oil droplets loaded with surfactant propel themselves with a velocity up to 6 mm s(-1) when they are placed in an aqueous phase of NaOH solution or buffer solution. The required driving force for such motion is generated on the interface of the droplets by the change in interfacial tension, due to deprotonation of the surfactant. This force induces Marangoni convection, which gives rise to a ci...

The developing legs of Drosophila are subdivided into proximal and distal domains by the activity of the homeodomain proteins Homothorax (Hth) and Distal-less (Dll). The expression domains of Dll and Hth are initially reciprocal. Wingless and Dpp define both domains by activating Dll and by repressing Hth in the distal region of the disc. Wg and Dpp do not act through Dll to repress Hth. Hth fu...

Mathematical analyses of motion perception have established minimum combinations of points and distinct views that are sufficient to recover three-dimensional (3D) structure from two-dimensional (2D) images, using such regularities as rigid motion, fixed axis of rotation, and constant angular velocity. To determine whether human subjects could recover 3D information at these theoretical levels,...

The problem of reflection of water waves by a nearly vertical porous wall has been investigated. A perturbational analysis has been applied for the first order correction to be employed to the corresponding vertical wall problem. The Green's function technique has been used to obtain the solution of the boundary value problem at hand, after utilising a mixed Fourier transform together with an i...

A method to determine the absolute orientation of molecules at liquid interfaces by sum frequency generation (SFG) is reported. It is based on measurements of the orientations of two nonparallel vibrationally active chromophores in the molecule of interest combined with a rotation matrix formulation to obtain the absolute molecular orientation. We chose m-tolunitrile, a planar molecule adsorbed...

PURPOSE In this work, a finite element study is proposed by using the Comsol Multiphysics software to evaluate the effects of microcrack shape, size and direction on the poroelastic behaviors of a single osteon. METHODS This finite element model is established by using the Comsol Multiphysics software, and we just focus on the comparison of the influences of those microcrack geometric paramet...

OBJECTIVES Footwear-generated biomechanical manipulations (e.g., wedge insoles) have been shown to reduce the magnitude of adduction moment about the knee. The theory behind wedged insoles is that a more laterally shifted location of the center of pressure reduces the distance between the ground reaction force and the center of the knee joint, thereby reducing adduction moment during gait. Howe...

High-level ab initio electronic structure calculations, including extrapolations to the complete basis set limit as well as relativistic and diagonal Born-Oppenheimer corrections, resulted in a torsional potential of acetaldehyde in its electronic ground state. This benchmark-quality potential fully reflects the symmetry and internal rotation dynamics of this molecule in the energy range probed...