Pole-zero analysis and synthesis of discrete system bifurcation

A scalar z-transform approach provides a preliminary background of theory for discrete system limit cycles/orbits and local stability. Then orbit bifurcation/biconfluence is expressed in terms of pole-zero introduction/cancellation, and pole discontinuities of the perturbed system discerned from pole loci. Finally, necessary conditions viewed from the pole-zero approach are related to bisectrix intersection and gradient properties. Thereby a new insight into bifurcation of maps is presented.     

PICOSECOND FLUORESCENCE OF R3230AC MAMMARY CARCINOMA MITOCHONDRIA AFTER TREATMENT WITH HEMATOPORPHYRIN DERIVATIVE and PHOTOFRIN® II in vivo

Hematoporphyrin derivative (HPD) and other porphyrin samples were excited by 20-ps 532-nm laser pulses. Fluorescence was detected using a low-jitter streak camera. Data were fitted to a sum of exponential decay times on the order of picoseconds. Fluorescence of porphyrins in aqueous solution show various behaviors depending on the hydrophobicity of the porphyrins. The most hydrophilic porphyrins show long decays only (greater than 500 ps). Porphyrins intermediate in hydrophobicity have intensity-dependent fast decays. The most hydrophobic have fast decays (less than 20 ps). Picosecond fluorescences of mitochondria prepared from rat tumors treated in vivo with HPD or Photofrin II show an increase in the ratio of fast to slow decays when compared to the injected porphyrins. These results are consistent with the concentration of the more hydrophobic porphyrins in mitochondria in photosensitization treatment. Thus picosecond fluorescence studies of porphyrins may provide a means to obtain photoproperties which differentiate between effective and ineffective in vivo photosensitizers.     

Structure-property relationships in polycaprolactone-polyurethanes

The structure-property relationships of polycaprolactone-based segmented polyurethanes were studied using differential scanning calorimetry (DSC), small-angle x-ray scattering (SAXS), wide-angle x-ray diffraction (WAXD), dynamic mechanical, and stress-strain testing. The materials studied varied in hard-segment type [4,4′-diphenylmethane diisocyanate/butanediol (MDI/BD) or 4,4′-dicyclohexyl methane diisocyanate/butanediol (H₁₂MDI/BD)], soft-segment molecular weight (830 or 2000 MW polycaprolactone), hard-segment content (23–77% by weight), and thermal history. The materials with aromatic (MDI/BD) hard segments had semicrystalline hard-segment domains, while the materials with aliphatic (H₁₂MDI/BD) hard segment had mostly amorphous domains. Materials with the shorter polycaprolactone soft segment (830 MW) exhibited thermal and mechanical behavior which indicated a considerable degree of hard- and soft-segment compatibility. The materials which contained a 2000-MW polycaprolactone soft segment exhibited better-defined microphase separation. SAXS was used to characterize the microphase structure of each system. The effects of hard-segment content and soft-segment molecular weight were similar for the aromatic (MDI) and aliphatic (H₁₂MDI) hard-segment-based block copolymers. Changing the hard segment from aromatic to aliphatic gave materials with larger interfacial area and slightly higher tensile strength. A range of morphologies between isolated hard domains in a rubbery matrix and isolated rubbery domains in a hard matrix was observed.     

A generalization of Lagrange's method of undetermined multipliers using zero-zone functionals

A unifying zero-zone function concept extends the Lagrange method of undetermined multipliers to treat both equality and inequality subsidiary conditions. The mathematical formulation is general for restrained function extremization in algebra.     

CPN−1 coupled to gauge fields: Mean field theory and monte carlo results

We define a two parameter lattice field theory which interpolates between the O (2N) Heisenberg model, pure U(1) gauge theory, and a lattice version of the CP^N?1 model. The phase diagram in space-time dimension d=4 is obtained by Monte Carlo simulation on a 4⁴ lattice, and the nature of the phases is discussed in mean field approximation.     

Convex polyhedra of doubly stochastic matrices—IV

Basic geometrical properties of general convex polyhedra of doubly stochastic matrices are investigated. The faces of such polyhedra are characterized, and their dimensions and facets are determined. A connection between bounded faces of doubly stochastic polyhedra and faces of transportation polytopes is established, and it is shown that there exists an absolute bound for the number of extreme points of d-dimensional bounded faces of these polyhedra.     

Computer controlled techniques for high emission density mapping of thermionic cathodes

Some of the techniques commonly used (e.g. SLEEP and thermionic emission microscope) for measuring emission or work function uniformity of thermionic cathode surfaces require the use of very low or near zero current densities, thus the cathode is characterized at current densities and temperatures much lower than that of a normally operating cathode. The system reported on here uses a high voltage pulse technique and is capable of measuring emission densities in the range 1 to 80 A/cm² at normal cathode operating temperatures. The cathode surface is scanned with an anode having a 0.025 mm aperture whose position is controlled by computer operated stepping motors. The current through the aperture to a collector electrode is measured using a sample-and-hold amplifier. Pulsing and sampling are computer synchronized with the scanning, and data for each pulse are accumulated and can be processed and displayed in several ways using the computer, including a detailed “three-dimensional” map of either the electron emission density or work function variations. The entire surface of the cathode or any portion of it can be mapped in steps as small as 0.001 mm (1μm), but typically steps of 5–100 μm were used. Measurements are presented illustrating the uniformity or nonuniformity of the electron emission densities and work functions for type-B and type-M cathodes.     

Differential cross-sections for pp → π−π+, K−K+ between 0.8 and 2.4 GeV/c

We present measurements from a spark chamber experiment of the differential cross-sections for $\text{p}$p → π^?π⁺, K^?K⁺ at 20 momenta in the range 0.8–2.4 GeV/c (c.m. energy 2.02 to 2.57 GeV). The c.m. angular range was $\text{?0.95 <}\text{cos}\text{θ}{}^1\text{< 0.95}$. There are about 2000π^?π⁺ events and about 300 K^?K⁺ events at each momentum.