On. the synthesis of distributed resistive structures

A spanning tree model for the Heegaard Floer homology of a branched double-cover

“…We wrote code in Mathematica to do this (cf. a related program by Ciprian Manolescu [11]). To input a given example into the program, one begins with a marked diagram of a knot and enters in by hand the white and black graphs, the crossing incidence numbers µ, and the coloring matrix.…”

“…Treating each case in turn, we obtain the following concise result. Define ψ(x, c) = ±1, according as x(c) lies to the right / left of the oriented overstrand at c, and collect these values into a vector(11)…”

Synthesis of Geometrical Shape of the Distributed Resistive Microelectronic Structures for Maximum Robustness

“…Our method for designing a resistive distributed structure as to obtain a specific transfer characteristic follows two steps [1], [2]: i) first, the positions of the conductive segments on a standard domain (upper complex half-plane) is determined, as to obtain the desired transfer characteristics and to obey the constraints imposed by the distributed nature of the structure; ii) starting from these results, a particular geometry of the distributed domain can be chosen (from an infinite possible variety), as to obtain the most favorable production conditions and and to fulfill several other second order effects important for production and usage. For production that means high robustness, so trimming would not be needed; for usage the second order effects can refer to the most favorable positions and dimensions of the conductive terminals on the structure's boundary, the most advantageous electric, magnetic or thermic field pattern in the distributed domain as to avoid crowding and stress and so on.…”