A flexible coordination polymer crystal providing reversible structural and magnetic conversions

Structural flexibility is a remarkable characteristic of coordination polymers and significant for the attainment of environmental responsivity. We have prepared a 2D cyanide-bridged MnIICrIII coordination polymer, [Mn(NNdmenH)(H2O)][Cr(CN)6].H2O (1; NNdmen = N,N-dimethylethylenediamine), with sophisticatedly arranged removable water coligands. The compound clearly showed a reversible single-crystal-to-single-crystal transformation between the 2D sheet and a 3D pillared-sheet framework of dehydrated [Mn(NNdmenH)][Cr(CN)6] (1a). The structural change was reversible and accompanied with generation/cleavage of CN-Mn bonds between 2D sheets by dehydration/hydration. Compounds 1 and 1a also exhibited a ferrimagnetic ordering at 35.2 and 60.4 K, respectively, and the magnetic characteristics were reversibly converted by guest adsorption/desorption. In addition, the dehydrated 1a demonstrated a size-selective solvent adsorption linking chemi- and physisorption processes and shrinkage/expansion of its framework. The flexible magnetic framework incorporating removable coligands delivered multifunctions with chemical response.     

On an extremal problem of Selberg II

Let m_p be the minimum of the product under the conditions that and . In our previous paper [J. Kaneko, On an extremal problem of Selberg, J. Approx. Theory 142 (2006) 129–137], we showed that the following estimates hold. provided p255. In this note, we prove that the limit of as p→∞ exists and is expressed by the (unique) solution of some simultaneous transcendental equations. By using this expression we obtain numerically.     

RBM band shift-evidenced dispersion mechanism of single-wall carbon nanotube bundles with NaDDBS

The dispersion process of single-wall carbon nanotube (SWNT) by using sodium dodecylbenzene sulfonate (NaDDBS) was studied by means of surface tension measurements, ultraviolet-visible (UV-Vis) spectroscopy, scanning electron microscopy (SEM), and transmission electron spectroscopy (TEM). The critical micelle concentration (CMC) and the concentration where the surface tension begins to drop increase by the presence of SWNT. The isotherm of NaDDBS amount adsorbed on SWNT shows the plateau region at 0.2-6 mM and the saturated region above 40 mM. The external surface of SWNT bundle is fully covered with adsorbed NaDDBS at the plateau region, showing that SWNTs can be dispersed with the bundle form. On the other hand, SWNTs are dispersed in individual tubes at the saturated region, where the adsorption amount corresponds to coating of individual tube surfaces with NaDDBS. This dispersion state was confirmed by SEM and TEM observations. The effect of the dispersion state of SWNTs on radial breathing mode in Raman spectrum gave inherent peak shifts, being the in situ evidences on the step-wise dispersion mechanism of the SWNT bundle to the individual tubes.     

Formation of fractal porous silica by hydrolysis of TEOS in a bicontinuous microemulsion

Mesoporous silica particles have been prepared by hydrolysis of TEOS (Si(OC₂H₅)₄) in bicontinuous microemulsions containing polyoxyethylene (POE) dodecylether, isooctane and water. TEOS was dissolved in a continuous water phase and hydrolyzed by the dispersed water at around the phase inversion temperature (60°C). Undulating solid materials with layered mesostructures were produced from middle-phase microemulsions in the three phase region (o/w=0.2–0.7). On the other hand, the solids obtained from the lower aqueous phase in the three phase region were found to have a heterogeneous disordered structure. Measurements of the fractal dimensions were performed in the macropore region using a box-counting method for the outline of the SEM texture. We found that the macropore size distribution in the particles prepared from the middle-phase microemulsion follows the fractal rule with a dimension of 1.7. From the results of nitrogen adsorption/desorption curves on the silica, a steep increase in the adsorption amounts was observed at a relative pressure below 0.2, and adsorption/desorption hysteresis was also observed at a relative pressure between 0.3 and 0.5. These studies suggest that the silica synthesized in the bicontinuous microemulsion mesostructure has a very broad size range from micro to macropores with a fractal distribution.     

Straight-Line Embeddings of Two Rooted Trees in the Plane

We prove the following theorem: Let T ₁ and T ₂ be two disjoint rooted trees with roots v ₁ and v ₂ , respectively, and let P be a set of |T₁ T₂| points in the plane in general position containing two specified points p ₁ and p ₂ . Then the union T ₁ $\cup$ T ₂ can be straight-line embedded onto P such that v ₁ and v ₂ correspond to p ₁ and p ₂ , respectively. Moreover, we give a O(n ² log n) time algorithm for finding such an embedding, where n is the number of vertices contained in T ₁ $\cup$ T ₂ . Received July 3, 1997, and in revised form February 25, 1998.     

Negative pion transfer process in a hydrogen-containing gas mixture

Annihilation γ-rays of π⁰ and pionic X-rays were measured in the gas mixtures of H₂+Z and CH₄+Z systems (Z=He, Ne, Ar and Kr). Pion capture probability of hydrogen atom was obtained from the annihilation γ-ray counts and the capture probability of Z atom was obtained from the pionic X-ray intensities. Transfer rates were determined from the data based on a combined large mesomolecular model. The transfer rates obtained were smaller than the systematics of the Russian group. Difference in the transfer rate between the gas and the liquid phases was found by a comparison of the present results with our previous ones.     

Electrostatic Retention Mechanism of 2,2'-Dihydroxyazobenzene-Metal chelates on Octadecylsilanized Silica Stationary Phase

The chelating agent 2,2'-dihydroxyazobenzene (DHAB), as shown in Fig. 1, was superior to the determination of trace metal ions by HPLC with ion-pair partition mode. Among the DHAB-metal chelates, only the cationic DHAB-aluminium 1:lchelate,[AIL]⁺, is fluorescent. Thus this chelate is expected to be applicable for selective and sensitive determination of aluminium ion by HPLC. However, the retention behavior of[AlL]⁺ on octadecylsilanized silica stationary phase was not well understood. The interaction between[A1L]⁺ and octadecylsilanized silica stationary phase has been investigated.     

On packing 3‐vertex paths in a graph

Let G be a connected graph and let eb(G) and λ(G) denote the number of end‐blocks and the maximum number of disjoint 3‐vertex paths Λ in G. We prove the following theorems on claw‐free graphs: (t1) if G is claw‐free and eb(G) ≤ 2 (and in particular, G is 2‐connected) then λ(G) = ⌊| V(G)|/3⌋; (t2) if G is claw‐free and eb(G) ≥ 2 then λ(G) ≥ ⌊(| V(G) | − eb(G) + 2)/3 ⌋; and (t3) if G is claw‐free and Δ^*‐free then λ(G) = ⌊| V(G) |/3⌋ (here Δ^* is a graph obtained from a triangle Δ by attaching to each vertex a new dangling edge). We also give the following sufficient condition for a graph to have a Λ‐factor: Let n and p be integers, 1 ≤ p ≤ n − 2, G a 2‐connected graph, and |V(G)| = 3n. Suppose that G − S has a Λ‐factor for every S ⊆ V(G) such that |S| = 3p and both V(G) − S and S induce connected subgraphs in G. Then G has a Λ‐factor. © 2001 John Wiley & Sons, Inc. J Graph Theory 36: 175–197, 2001