The setting of this research is Bishop’s constructive mathematics. Let q be an anticongruence on a semigroup S with apartness. For q we say that it is an rectangular band anticongruence if S/q is a rectangular band. In paper [12] a construction of the maximal rectangular band anticongruence on a semigroup is described. This paper is continuation of that research. Let T be a detachable subsemigr...

We offer a comprehensive theory of pH response of a coupled ISFET sensor to show that the maximum achievable response is given by ΔV/ΔpH = 59 mV/pH × α, where 59 mV/pH is the intrinsic Nernst response and α an amplification factor that depends on the geometrical and electrical properties of the sensor and transducer nodes. While the intrinsic Nernst response of an electrolyte/site-binding inter...

Polyhedral nanostructures are widely used to enable localized surface plasmon resonance (LSPR). In practice, vertices of such structures are almost always truncated due to limitations of nanofabrication processes. This paper studies the effects of vertex truncation of polyhedral nanostructures on the characteristics of LSPR sensing. The optical properties and sensing performance of triangular n...

A rectangular drawing is a plane drawing of a graph in which every face is a rectangle. Rectangular drawings have an application for floorplans, which may have a huge number of faces, so compact code to store the drawings is desired. The most compact code for rectangular drawings needs at most 4 f − 4 bits, where f is the number of inner faces of the drawing. The code stores only the graph stru...

A 3D-dissection (A rectangular solid dissection) is a dissection of a rectangular solid into smaller rectangular solids by planes. In this paper, we propose an O-sequence, a string of representing any 3Ddissection which is dissected by only non-crossing rectangular planes. We also present a necessary and sufficient condition for a given string to be an O-sequence. key words: rectangular solid d...