The absence of efficient dual pairs of spanning trees in planar graphs

A spanning tree T in a finite planar connected graph G determines a dual spanning tree T* in the dual graph G such that T and T* do not intersect. We show that it is not always possible to find T in G, such that the diameters of T and T* are both within a uniform multiplicative constant (independent of G) of the diameters of their ambient graphs.Comment: 7 pages, 3 figure

Program to design, fabricate, test, and deliver a thermal control-mixing control device for the George C. Marshall Space Flight Center

The development and testing of a temperature sensor and pulse duration modulation (PDM) diverter valve for a thermal control-mixing control device are described. The temperature sensor selected for use uses a fluidic pin amplifier in conjunction with an expansion device. This device can sense changes of less than 0.25 F with greater than 15:1 signal to noise ratio when operating with a typical Freon pump supplied pressure. The pressure sensitivity of the sensor is approximately 0.0019 F/kPa. The valve which was selected was tested and performed with 100% flow diversion. In addition, the valve operates with a flow efficiency of at least 95%, with the possibility of attaining 100% if the vent flow of the PDM can be channeled through the last stage of the diverter valve. A temperature sensor which utilized an orifice bridge circuit and proportional-vortex combination mixing valve were also evaluated, but the concepts were rejected due to various problems

Homologous non-isotopic symplectic tori in a K3-surface

For each member of an infinite family of homology classes in the K3-surface E(2), we construct infinitely many non-isotopic symplectic tori representing this homology class. This family has an infinite subset of primitive classes. We also explain how these tori can be non-isotopically embedded as homologous symplectic submanifolds in many other symplectic 4-manifolds including the elliptic surfaces E(n) for n>2.Comment: 15 pages, 9 figures; v2: extended the main theorem, gave a second construction of symplectic tori, added a figure, added/updated references, minor changes in figure

Holographic and ultrasonic detection of bond flaws in aluminum panels reinforced with boron-epoxy

An experimental investigation was made of the application of holographic interferometry to the nondestructive detection of unbonded areas (flaws) in bonded panels. Flaw detection results were compared with results obtained with an ultrasonic flaw detector. Holography, with panel deformation accomplished by a reduction in ambient pressure, is less sensitive for flaws beneath 5 and 10 plies of boron-epoxy than the ultrasonic method, though it does have its operational advantages. A process for the manufacture of bonded panels which incorporate known unbonded areas was also developed. The unbonded areas were formed without the use of foreign materials, which makes the method suitable for the construction of reference standards for bonded panels whenever needed for the proper setup of ultrasonic flaw-detection instruments

Graphics of Thermodynamics

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