Binomial Edge Ideals of Complete Multipartite Graphs

In this article, we prove some results about the binomial edge ideal J _G of a complete r-partite graph G = K _{a 1,…, a r} : (1) characterization of unmixedness of J _G and Cohen–Macaulayness of the residue ring S/J _G , (2) F-purity of S/J _G , and (3) the equality of the symbolic and the ordinary powers of J _G .     

Layered assemblies of a dialuminum-substituted silicotungstate trimer and the reversible interlayer cation-exchange properties

Two polyoxometalate assemblies, TBA(9)[{γ-H(2)SiW(10)O(36)Al(2)(μ-OH)(2)(μ-OH)}(3)] (1; TBA = tetra-n-butylammonium) and TBA(6)Li(3)[{γ-H(2)SiW(10)O(36)Al(2)(μ-OH)(2)(μ-OH)}(3)]·18H(2)O (2), were synthesized by trimerization of a dialuminum-substituted silicotungstate monomer. Both 1 and 2 possessed a layered structure composed of a basal sheet unit [TBA(3){γ-H(2)SiW(10)O(36)Al(2)(μ-OH)(2)(μ-OH)}(3)](6-) and interlayer cations. The interconversion between 1 and 2 reversibly took place through interlayer cation exchange.     

Crystallization efficiencies of inorganic polyphosphate oligomers reacted with magnesium and calcium cations using anion-exchange chromatography with particulate formation-laser scattering detector

A particulate formation-laser scattering detector (PFLSD) was developed and used for evaluating the crystallization efficiency of inorganic polyphosphates (PPs) that reacted with either magnesium or calcium cations. As the solutions for reactive crystallization, 0.5 M ammonium buffer (pH 9.6) containing either 0.15 M MgCl₂ or 0.15 M CaCl₂ (MAP: magnesium ammonium phosphate and HAP: hydroxyapatite solution) were used. In the case of mono- and diphosphate (P1 and P2), the significant dependences of the particulate formation efficiency on various types of both P1/P2 and MAP/HAP reaction solutions were observed with the direct sample injection mode. The PFLSD was hyphenated with the anion-exchange chromatography and the dependence of the particulate formation efficiency on the polymerization degree (n_p) of PP oligomers, separated chromatographically, was evaluated sequentially. The significant suppression of the particulate formation for PP oligomers was clearly confirmed, i.e., the MAP and HAP reaction solutions did not produce the particulates of the PP oligomers having an n_p value of more than 3 and 5, respectively. As the overall tendency, the particulate formation efficiency in the case of the HAP solution was superior to that in the case of the MAP solution.     

An effective method to use ionic liquids as reaction media for asymmetric reduction by Geotrichum candidum

An effective method was developed to use an enzyme in ionic liquids; the asymmetric reduction of ketones by Geotrichum candidum in ionic liquids proceeded smoothly with excellent enantioselectivity when the cell was immobilized on water-absorbing polymer containing water, while the reaction without the polymer did not proceed.     

Novel chiral selectors anchored on polydimethylsiloxane as stationary phases for separation of derivatized amino acid enantiomers by capillary gas chromatography

Six chiral selectors of S-(-)-t-Leu-cyclopropylamide, S-(-)-t-Leu-cyclopentylamide, S-(-)-t-Leu-cyclohexylamide, S-(-)-t-Leu-cycloheptylamide, S-(-)-t-Leu-cyclooctylamide, S-(-)-t-Leu-cyclododecylamide have been prepared and anchored individually through amide bonding to a polydimethylsiloxane functionalized with 2,2,2-trifluoroethyl ester groups by way of nucleophilic displacement reaction. The resulting chiral polysiloxanes have been provided as stationary phases for the separation of amino acid enantiomers by capillary GC. Amino acids were derivatized into N(O)-trifluoroacetyl isopropyl esters. Especially, polydimethylsiloxane anchored with S-(-)-t-Leu-cyclooctylamide was found to be efficient for the separation of aspartic acid (Asp) enantiomers. The method was applied to the estimation of ages from the extent of Asp racemization in human dentines.     

Attenuation of shock waves propagating over arrayed baffle plates

The paper reports results of shock tube experiments of the attenuation of shock waves propagating over arrayed baffle plates, which is motivated to simulate shock wave attenuation created accidentally at the acoustic delay line in synchrotron radiation factory upon the rupture of a metal membrane separating the acceleration ring at high vacuum and atmospheric test chambers. Experiments were carried out, by using double exposure holographic interferometry with double path arrangement, in a 100 mm×180 mm shock tube equipped with a test section of 180 mm×1100 mm view field. Two baffle plate arrangements were tested: Oblique and staggered baffle plates; and vertical symmetric ones. Pressures were measured along the shock tube sidewall at individual compartments for shock Mach numbers ranging from 1.2 to 3.0 in air. The results were compared with a numerical simulation. The rate of shock attenuation over these baffle plates was compared for vertical and oblique baffle plates. Shock wave attenuation is more pronounced in the oblique baffle plate arrangements than in the vertical ones. PACS 47.40.Nm; 42.40.Kw Communicated by C. Needham     

Overpressure generation and repetition of collapsing microbubbles induced by shock wave reflection in a narrow gap

This paper reports the summary of experiments performed to successive generate small-scale underwater shock waves by means of shock-induced collapse of microbubbles confined in a narrow gap. The project is motivated to develop a method for efficient inactivation of marine bacteria contained in ship ballast water by high impulsive pressure loading. The shock wave–air bubbles interaction was visualized by shadowgraph; the images were recorded by ImaCon200, and simultaneous pressure measurements were performed by using an optical fiber pressure transducer with higher temporal resolution. Attaching small air bubbles on a single nylon fiber and placing it in a confined space, we demonstrated sequential generation of impulsive high pressures at the successive collapses of small bubbles at incident and reflected shock loadings. The values of the very short impulsive pressures that occurred repeatedly for a relatively long term are found high enough to inactivate marine bacteria.     

Experimental study of underwater rock drilling using a pulsed Ho:YAG laser-induced jets

This paper is primarily an assessment of laser-induced water jets for boring rock surfaces. It also reports the result of preliminary experiments of pulsed Ho:YAG laser-induced jets applied to drill a submerged rock specimen. The irradiation of pulsed Ho:YAG laser beams at 3 Hz inside a thin metal tube produces intermittent water vapor bubbles which result in liquid jet discharge from the exit of the metal tube. The laser-induced water jets are visualized by shadowgraphs and images are recorded by a high-speed digital video camera. High stagnation pressures were eventually generated by the jet impingements. Simultaneously shock waves of about 22.7 MPa were generated at bubble collapse, which effectively cracked the surface of the rock specimens. Repeated exposures of these laser-induced jets against submerged rock specimens have a potential to practically bore holes on rock surfaces.     

Diffuse holographic interferometric observation of shock wave reflection from a skewed wedge

The pattern of shock wave reflection over a wedge is, in general, either a regular reflection or a Mach reflection, depending on wedge angles, shock wave Mach numbers, and specific heat ratios of gases. However, regular and Mach reflections can coexist, in particular, over a three-dimensional wedge surface, whose inclination angles locally vary normal to the direction of shock propagation. This paper reports a result of diffuse double exposure holographic interferometric observations of shock wave reflections over a skewed wedge surface placed in a 100 × 180 mm shock tube. The wedge consists of a straight generating line whose local inclination angle varies continuously from 30° to 60°. Painting its surface with fluorescent spray paint and irradiating its surface with a collimated object beam at a time interval of a few microseconds, we succeeded in visualizing three-dimensional shock reflection over the skewed wedge surface. Experiments were performed at shock Mach numbers, 1.55, 2.02, and 2.53 in air. From reconstructed holographic images, we estimated critical transition angles at these shock wave Mach numbers and found that these were very close to those over straight wedges. This is attributable to the flow three-dimensionality.