Area-efficient algorithms for straight-line tree drawings

We investigate several straight-line drawing problems for bounded-degree trees in the integer grid without edge crossings under various types of drawings: (1) upward drawings whose edges are drawn as vertically monotone chains, a sequence of line segments, from a parent to its children, (2) order-preserving drawings which preserve the left-to-right order of the children of each vertex, and (3) orthogonal straight-line drawings in which each edge is represented as a single vertical or horizontal segment.

Main contribution of this paper is a unified framework to reduce the upper bound on area for the straight-line drawing problems from O(nlogn) (Crescenzi et al., 1992) to O(nloglogn). This is the first solution of an open problem stated by Garg et al. (1993). We also show that any binary tree admits a small area drawing satisfying any given aspect ratio in the orthogonal straight-line drawing type.

Our results are briefly summarized as follows. Let T be a bounded-degree tree with n vertices. Firstly, we show that T admits an upward straight-line drawing with area O(nloglogn). If T is binary, we can obtain an O(nloglogn)-area upward orthogonal drawing in which each edge is drawn as a chain of at most two orthogonal segments and which has O(n/logn) bends in total. Secondly, we present O(nloglogn)-area (respectively, -volume) orthogonal straight-line drawing algorithms for binary trees with arbitrary aspect ratios in 2-dimension (respectively, 3-dimension). Finally, we present some experimental results which shows the area requirements, in practice, for (order-preserving) upward drawing are much smaller than theoretical bounds obtained through analysis.     

Methods to enhance tolerances of Chlorella KR-1 to toxic compounds in flue gas

Possible methods to minimize the toxic effects of SO _x and NO _x on the growth of a highly CO₂ tolerant and fast-growing microalga, Chlorella sp. KR-1, were investigated. Maintaining the pH of the culturing media at an adequate value was quite important to enhancing the tolerances of the microalgae to SO _x and NO _x . Controlling the pH by adding an alkaline solution, using a low flow rate of gas fed to the culture, and using a high concentration of inoculating cells were effective methods to maintaining the proper pH of the culture. Controlling the pH was the most effective method but could be applied only for some specific microalgae.     

Complex of cobalt(II) bromide with hexa­methyl­phospho­ric tri­amide

The title compound, di­bromo­bis­[tris­(di­methyl­amino)­phos­phine oxide]­cobalt(II), [CoBr₂(C₆H₁₈N₃OP)₂], displays tetrahedral coordination about cobalt. The mol­ecule has twofold crystallographic site symmetry. The short P—N bonds and the planarity of the di­methyl­amino groups indicate the importance of dπ–pπ interactions. One of the NMe₂ groups has an irregular conformation about the P—N bond and deviates from planarity. It is ascribed to the steric hindrance induced by coordination at the O atom of hexa­methyl­phospho­ric tri­amide.     

Photoelastic experimental hybrid method for fracture mechanics of anisotropic materials

In this paper, the isotropic and anisotropic photoelastic experimental hybrid methods for fracture mechanics are developed. Using the photoelastic experimental hybrid method, it is demonstrated that one can precisely obtain stress intensity factors and separate the stress components of isotropic and anisotropic plate problems from the only isochromatics.     

Superparamagnetic behavior of iron oxides supported on porous silica gels

Spinel iron oxide (Fe₃O₄-γ-Fe₂O₃) particles were supported on microbeads of silica gel by the calcination of the silica gel base adsorbing citric acid and Fe³⁺ ions. The X-ray diffraction patterns and the⁵⁷Fe Mössbauer spectra measured for the spinel iron oxide indicated that the particle size of the oxide was regulated by the mean pore diameter (4–82 nm) of the silica gel support employed. In the case of α-Fe₂O₃ particles prepared by using the same silica gel beads, it was revealed by the Mössbauer spectra and the electron micrographs that there were relatively large particles of the oxide on the surface of the beads, in addition to the particles in the silica gel micropores.     

Synthesis and characterization of organosoluble copolyimides based on 2,2‐Bis[4‐(4‐aminophenoxy)phenyl]propane, 2,2‐Bis[4‐(4‐aminophenoxy)phenyl]hexafluoropropane and a pair of commercial aromatic dianhydrides

Organosoluble homopolyimides (PIs) and copolyimides (CoPIs) were synthesized from 2,2‐bis[4‐(4‐aminophenoxy)phenyl]propane (BAPP) or 2,2‐bis[4‐(4‐aminophenoxy)phenyl]hexafluoropropane (6FBAPP) and six kinds of commercial aromatic dianhydrides (PMDA, II _a ; BTDA, II _b ; BPDA, II _c ; ODPA, II _d ; DSDA, II _e ; 6FDA, II _f ). Although BAPP and II _d∼f could prepare three kinds of soluble PIs ( III‐A _d∼f ), likewise 6FBAPP and II _c∼f could prepare four PIs ( III‐B _c∼f ), the insoluble PIs were synthesized from these two diamines and other dianhydrides. However, soluble CoPIs could be prepared by alternative copolycondensation from a pair of dianhydrides of soluble PIs and insoluble PIs in certain molar ratios (m₁/m₂). The ratios of m₁/m₂ of BAPP/PMDA series CoPIs ( IV _{m1(d–f)/m2a} ) ranged from 3–5, but ratios of 6FBAPP/PMDA series CoPIs ( V _{m1(c∼f)/m2a} ) decreased to 2–3. The m₁/m₂ of the BAPP/BTDA and 6FBAPP/BTDA series CoPIs were 2, while the BAPP/BPDA series were between 1–2. Composition, solubility, tensile properties and thermal properties of these CoPIs synthesized via a two‐stage thermal cyclodehydration were determined and were compared with their corresponding PIs. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 3954–3961, 2000