We show that each hereditary interval algebra has a countable density and not conversely. Moreover, we show that, for an interval algebra, having countable density and being subal-gebra of the interval algebra over the real line are equivalent statements. 1. Introduction. Boolean algebras that are generated by subchains, that is, subsets that are linearly ordered under the Boolean partial order...

Let I = [a, b] be a real compact interval and f : I → I a continuous function. Define Kc([a, b]) the class of all non empty compact subinterval of [a, b] and let f̄ the natural extension of f to Kc([a, b]), that is to say, f̄(J) = f(J) for all J ∈ I([a, b]). Also, let Fc([a, b]) the class of all fuzzy-intervals with support contained in [a, b] and consider f̂ the Zadeh’s extension of f to Fc([a, b...

Microscopes and various forms of interferometers have been used for decades in optical metrology objects that are typically larger than the wavelength light ?. Metrology sub-wavelength objects, however, was deemed impossible due to diffraction limit. We report measurement physical size with deeply accuracy by analyzing pattern coherent scattered deep learning enabled analysis. With a 633 nm las...

we have designed a new type of optical channel drop filter (cdf) based on two dimensionaltriangular lattice photonic crystals. cdf operation is based on coupling to the photonic crystalwaveguide. the proposed structure is optimized to work as a cdf for obtaining the cdfcharacteristics and band structure of the filter the finite difference time domain (fdtd) method andplane wave expansion (pwe) ...

Pulse oximetry measures the relative concentration of arterial oxygenated hemoglobin and reduced hemoglobin. This paper presents the design of a pulse oximeter, which measures the presence of a third substance, carboxyhemoglobin (HbCO), by unfiltered LEDs at 660 nm, 810 nm, and 940 nm. Background information is given on the theory of pulse oximetry. Theoretical approximations and calculations w...

waveguides with low confinement loss, low chromatic dispersion, and low nonlinear effects are used in optical communication systems. optical fibers can also be employed in such systems. besides optical fibers, photonic crystal fibers are also highly suitable transmission media for optical communication systems. in this paper, we introduce two new designs of index-guiding photonic crystal fiber ...

in this article, we suggested a novel design of polarization splitter based on coupler waveguide on inp substrate at 1.55mm wavelength. photonic crystal structure is consisted of two dimensional (2d) air holes embedded in inp/ingaasp material with an effective refractive index of 3.2634 which is arranged in a hexagonal lattice. the photonic band gap (pbg) of this structure is determined using t...