On three approaches to length-bounded maximum multicommodity flow with unit edge-lengths

The paper presents a comparison between three approaches to solving the length-bounded maximum multicommodity flow problem with unit edge-lengths. Following the first approach, Garg and K?nemann?s, we developed an improved fully polynomial time approximation scheme for this problem. As the second alternative, we considered the well-known greedy approach. The third approach is the one that yields exact solutions by means of a standard LP solver applied to an LP model on the time-expanded network. Computational experiments are carried out on benchmark graphs and the graphs that model software defined satellite networks, to compare the proposed algorithms with an exact linear programming solver. The results of the experiments demonstrate a trade-off between the computing time and the precision of algorithms under consideration.

The Glass Core with an Anti-crack Propagation Structure

The trend of the physical properties of core layer in the PWB (Printed wiring board) is the low CTE (Coefficient of Thermal Expansion) and high modulus reducing the CTE mismatching between semiconductor chip and PWB to reduce the warpage of thin package. To jump up the physical property of the general organic material, thin glass less than 100 micron thickness is evaluated. In order to get the good physical properties, thin glass with the low CTE (3.2 ppm/°C) and high modulus (75GPa) is used for core material. And it is also advantageous in fine via pitch than with a high modulus metal core. But thin glass itself requires special handling to avoid cracks in the process. In order to handling without glass crack, the crack prevention structure was applied and the special insulation material was also laminated on the glass. The insulation layer having the glass fabric is laminated on the both side of thin glass to prevent crack propagation. And this material had no issue in the general PWB production line without any special treatment or Jig for the thin glass. Also the physical properties like CTE and modulus is outstanding. In the comparison of the low CTE organic core and glass core, physical properties of glass core was excellent than that of the organic core. In the final product, unit edge part exposing the thin glass is the weak point. Glass chipping or crack may occur during unit sawing process. But the crack on the sawing cut edge of glass can cause the horizontal crack issue of the glass. After reflow or thermal stress, the glass edge horizontal crack had propagated to the inside of the unit. So some special glass cutting line was added to block the crack propagation in the glass around the unit edge. The glass cutting line has been effective to block horizontal crack propagation into the inside of unit. With this structure and the insulation material, most of reliability test items that are applied in common circuit board were passed through.

Morphology and molecular orientation of thin-film bis(triisopropylsilylethynyl) pentacene

As a modification to the insoluble and herringbone-structured pentacene, bis(triisopropylsilylethynyl) (TIPS) pentacene has two bulky side groups, leading to good solubility in common organic solvents and regular π–π stacking arrangements in the crystalline state. Solution processing of TIPS–pentacene thin films was investigated as a function of various process parameters in this work. Electron diffraction results suggested that TIPS–pentacene molecules tended to align with the acene unit edge on to the substrate, touching down with their bulky side groups. In a TIPS–pentacene polycrystalline film, the long axis of individual crystallite is [2 1 0], while the shorter axis is [1 ¯20]. High-resolution electron microscopy was used to study the local crystal structure and characteristic defects of TIPS–pentacene thin films. Due to the nonaromatic side groups, TIPS–pentacene was found to be significantly more sensitive to the electron beam (critical dose Jc= 0.05 C/cm2at 300 kV) than pentacene itself (Jc= 0.2 C/cm2at 100 kV).

DRAWING WITH FAT EDGES

Traditionally, graph drawing algorithms represent vertices as circles and edges as curves connecting the vertices. We introduce the problem of drawing with "fat" edges, i.e., with edges of variable thickness. The thickness of an edge is often used as a visualization cue, to indicate importance, or to convey some additional information. We present a model for drawing with fat edges and a corresponding efficient polynomial time algorithm that uses the model. We first focus on a restricted class of graphs that occur in VLSI wire routing and then show how to extend the algorithm to general planar graphs. We show how to convert an arbitrary wire routing into a homotopically equivalent routing that maximizes the distance between any two wires, which is a desired property in VLSI design. Among such, we obtain the routing with minimum total wire length. A homotopically equivalent routing that maximizes the distance between any two wires yields a graph drawing which maximizes edge thickness. Our algorithm does not require unit edge thickness but can be applied as well in the presence of different edge weights.

Three-Dimensional Vibration Analysis of a Truncated Quadrangular Pyramid

An analysis is presented for the three-dimensional vibration problem of determining the natural frequencies and the mode shapes of a truncated quadrangular pyramid. For this purpose, the body is transformed into a right quadrangular prism with unit edge lengths by a transformation of variables. With the displacements of the transformed prism assumed in the forms of algebraic polynomials, the dynamical energies of the prism are evaluated, and the frequency equation is derived by the Ritz method. This method is applied to quadrangular pyramids in which the base is clamped and the other sides are free, and the natural frequencies (the eigenvalues of vibration) and the mode shapes are calculated numerically, from which the vibration characteristics arising in the pyramids are studied.

EDGE-EFFECT BIAS IN THE SAMPLING OF SUB-CORTICAL INSECTS

Two general models are presented to describe the relations between the average number of insects bisected by sampling unit boundaries, the per cent edge-effect bias of mean-brood-density estimates, the shape and size of the average individual, and the shape and size of the sampling unit. The two general models, when expanded specifically for sampling late-stage mountain pine beetle broods, gave excellent fit to experimental data. The expanded equations are approximations since individual insects were considered as being rectangular in shape and the angles of the long axes of their orientation relative to the sampling unit boundary were considered to have a uniform frequency distribution. Edge-effect bias was a function of the size and shape of the organism and those of the sampling unit. Edge-effect bias resulting from faulty sampling-unit-area delineation is also considered, and suggestions are made for its reduction in sample surveys of sub-cortical insects.