Relative position of four subspaces in a Hilbert space

We study the relative position of several subspaces in a separable infinite-dimensional Hilbert space. In finite-dimensional case, Gelfand and Ponomarev gave a complete classification of indecomposable systems of four subspaces. We construct exotic examples of indecomposable systems of four subspaces in infinite-dimensional Hilbert spaces. We extend their Coxeter functors and defect using Fredholm index. The relative position of subspaces has close connections with strongly irreducible operators and transitive lattices. There exists a relation between the defect and the Jones index in a type II₁ factor setting.     

Amplitude modulation of submillimeter wave gyrotron output

Amplitude modulation of gyrotron by a small modulation of the anode voltage is calculated using an energy transfer formula. Experimental measurements using a submillimeter wave gyrotron are in good agreement. One hundred percent modulation of the output at frequencies up to several hundred kilohertz has been achieved with anode modulation levels of only a few percent. Numerical calculations lend further support to the experimental results.     

Bistable Optical Devices Using Laser Diodes Coupled to Interference Filters

A bistable optical device was demonstrated by using the longitudinal mode hopping of the laser diode and the narrow transmission spectrum of an interference filter. The device is capable of converting changes in the wavelength of the laser diode into changes in intensity by transmitting it through the filter. Exclusive OR operation was observed with the use of triple signal outputs. In addition, an optical switch-off phenomenon was confirmed by directly injecting a pulse 500 ps wide into an external dye laser.     

Investigation of the influence of cell density of human fibroblasts cryopreserved inside collagen sponges at various cooling rates

The influence of cell density of cells cryopreserved inside a collagen matrix at various cooling rates was investigated. Human fibroblasts were three-dimensionally cultured for 2 days in a collagen sponge (20 mm in diameter and 1 mm in thickness) as an extracellular matrix to imitate biological tissue (artificial tissue). Different cell densities for the artificial tissue were used, from 10(5) to 10(7) cells/cm(3). Four artificial tissues were first stacked in a test chamber, frozen at a cooling rate of 0.3 to 50 degrees C/min in a solution of Dulbecco's Modified Eagle Medium, 20% fetal bovine serum and 10% dimethylsulfoxide, kept frozen below -185 degrees C for 2 hours, and then finally thawed. Membrane integrity of fibroblasts using a trypan blue exclusion assay was evaluated as an index for post-thaw cellular viability. Results show that with increasing cell density, the post-thaw membrane integrity decreased. Therefore, in the cryopreservation of biological tissue, it seems high cell density is one factor which causes a decline in viability.     

Rapid and Efficient Copper‐Catalyzed Finkelstein Reaction of (Hetero)Aromatics under Continuous‐Flow Conditions

A general, rapid, and efficient method for the copper‐catalyzed Finkelstein reaction of (hetero)aromatics has been developed using continuous flow to generate a variety of aryl iodides. The described method can tolerate a broad spectrum of functional groups, including N‐H and O‐H groups. Additionally, in lieu of isolation, the aryl iodide solutions were used in two distinct multistep continuous‐flow processes (amidation and Mg–I exchange/nucleophilic addition) to demonstrate the flexibility of this method.     

Trapping Nanostructures on Surfaces through Weak Interactions

The assembly of imidazole‐functionalized phenanthroline‐strapped zinc porphyrins (ZnPorphen) with alkyl or polyethylene glycol (PEG) side chains was studied in solution and by AFM after casting on highly oriented pyrolytic graphite (HOPG) or mica. The nature of the solvent and its evaporation time influenced the morphology of the objects observed. On HOPG, short rods of about 100 nm were observed after fast evaporation of solutions of the alkyl derivatives in CHCl₃, THF, or pyridine, whereas islands of aligned rows of longer wires were obtained from methylcyclohexane (MCH). Slow evaporation of MCH led to a three‐dimensional assembly. The PEG porphyrin assembled into short wires on HOPG or fibers on mica after slow evaporation of solutions in THF. This study shows the role of surface–molecule interactions in the interfacial assembly of ZnPorphen derivatives and contributes to understanding the parameters that control their noncovalent assembly into molecular wires on a surface.     

Air/water two-phase flow test tunnel for airfoil studies

A test tunnel for the study of airfoil performances under air/water two-phase flow condition has been designed and constructed. This facility will serve for a better understanding of the flow phenomena and characteristics of hydraulic machinery under gas/ liquid two-phase flow operating conditions. At the test section of the tunnel, a two-dimensional isolated airfoil or a cascade of airfoils is installed in a two-phase inlet flow with a uniform velocity (up to 10 m/s) and void fraction (up to 12%) distribution. The details of the tunnel structure and the measuring systems are described and the basic characteristics of the constructed tunnel are also given. As an example of the test results, void fraction distribution around a test airfoil is shown.Dedicated to the 60th Birthday of Professor Klaus Gersten