In this note we give the formula for Bellman function associated with problem considered by B. Davis (Duke Math J 43:697–704, 1976) in 1976. article estimates of type ?Sf?p ? Cp?f?p, p ? 2, were dyadic square operator S, and found sharp values constants Cp. However, along one can consider a more subtle characteristic above estimate. This quantity is called problem. It has never been proved that...

We compare the Fresnel diffraction pattern of a thin circular disk with that of a square obstacle, specifically evaluating the on-axis field strength. Photographs of the diffraction patterns reveal some curious features for the square obstacle. Second, the precise electric and magnetic fields behind a conducting circular disk are evaluated without invoking the Fresnel approximation and contrast...

The analysis of scalar dispersion in turbulent flows is relevant for a broad range of applications, including investigation of hazardous releases, bio-terrorism and control of air quality. In the last 50 years, experimental and numerical investigations of canonical flows, such as turbulent boundary layers (Fackrell & Robins 1982) or grid-generated turbulence (Livescu et al. 2000), have enhanced...

Results for time-dependent, viscous, incompressible flows were investigated using the lattice-Boltzmann (BGK) automata. The decay of a synthetic turbulent flow field and the time evolution of an initial vortex were simulated for validation purposes. The focal point was the investigation of the instationary flow around a square obstacle in a twodimensional channel for a range of Reynolds numbers...

Topological spin textures on artificial pinning landscape may show unique static and dynamic properties. Here, we computationally that the helicity of frustrated skyrmions an square-grid obstacle pattern can be switched by a current pulse. The is formed defect lines with enhanced perpendicular magnetic anisotropy, which could protect skyrmion from being annihilated at sample edge. It found driv...

In this paper, the heat transfer to the fluid, passing through the double forward facing step (FFS) channel with square obstacle is enhanced by Taguchi’s S/N ratio analysis. Flow through the forward facing step channel has a wide range of applications in thermal systems due to its flow separation and subsequent reattachment, which in turn enhances the heat transfer. Flow separation and reattach...

In this paper, recurrent neural network is used for path planning in the joint space of the robot with obstacle in the workspace of the robot. To design the neural network, first a performance index has been defined as sum of square of error tracking of final executor. Then, obstacle avoidance scheme is presented based on its space coordinate and its minimum distance between the obstacle and ea...