Three-dimensional electromagnetic simulation of monolithic radial transmission lines for Z-pinch

The electromagnetic simulation of the monolithic radial transmission lines for future Z-pinch was performed. Focusing on the difference in the maximum transmitted power efficiency between the electromagnetic simulation and the circuit simulation, the monolithic radial transmission lines with different impedance profile (exponential, Gaussian, hyperbolic) were compared. The power efficiency for the exponential line is higher than that for the Gaussian lines and the hyperbolic line, which is similar to that from the circuit simulation. However, all the power efficiencies obtained with the electromagnetic simulation are about 15% lower than those obtained with the circuit simulation, indicating the existence of considerable non-TEM modes and a non-ignorable error in the circuit simulation based on the quasi-TEM mode approximation. In consideration of several monolithic radial transmission lines being stacked together and the flat electrodes required by the stacked lines, the hyperbolic line was compared with the exponential line with several wide radial slots cut on the flat electrodes. While the hyperbolic line has a little bit lower transmitted power efficiency than that of the exponential line, it is much easier in fabrication. For this reason, the hyperbolic line was recommended as the best choice.

Transitivity for the modular group

Let Γ be a Fuchsian group of the first kind acting on the upper half plane H+. Let be a Ford fundamental region for Γ in H+. Let ξ be a real number (a limit point) and let L( = Lξ) = {ξ + iy|0 ≤ y < 1}. L can be broken into successive intervals each one of which can be mapped by an element of Γ into . Since L is a hyperbolic line (h-line), this gives us a set of h-arcs in which we will call the image.

Evaluation of standard curves in the graded hemagglutination-inhibition method applied to quantitation of human immunoglobulins.

For accurate quantitation of human immunoglobulins A and B by graded hemagglutination inhibition, I have established standard curves. For IgA, plotting the inner diameter of the ring formed by sedimented erythrocytes vs the log of the antigen concentrations gives a straight line. Plotting the same parameters for IgG gives a hyperbolic line. These ratios between antigen concentration and ring diameter were constant for at least one year. Both undiluted and 10,000-fold diluted human serum may be quantitated by this method, depending only on immunoglobulin concentrations. Precision (CV) of the system, assessed in 35 patients’ sera over the period of one year, ranged from 0.5 to 15.2% (mean 10%) for IgA and from 1.4 to 14.9% (mean 7.3%) for IgG.

Evaluation of standard curves in the graded hemagglutination-inhibition method applied to quantitation of human immunoglobulins.

For accurate quantitation of human immunoglobulins A and B by graded hemagglutination inhibition, I have established standard curves. For IgA, plotting the inner diameter of the ring formed by sedimented erythrocytes vs the log of the antigen concentrations gives a straight line. Plotting the same parameters for IgG gives a hyperbolic line. These ratios between antigen concentration and ring diameter were constant for at least one year. Both undiluted and 10,000-fold diluted human serum may be quantitated by this method, depending only on immunoglobulin concentrations. Precision (CV) of the system, assessed in 35 patients’ sera over the period of one year, ranged from 0.5 to 15.2% (mean 10%) for IgA and from 1.4 to 14.9% (mean 7.3%) for IgG.