Fast oxygen ion migration in Cu–In–oxide bulk and its utilization for effective CO2 conversion at lower temperature

Efficient activation of CO₂ at low temperature was achieved by reverse water–gas shift via chemical looping (RWGS-CL) by virtue of fast oxygen ion migration in a Cu–In structured oxide, even at lower temperatures. Results show that a novel Cu–In₂O₃ structured oxide can show a remarkably higher CO₂ splitting rate than ever reported. Various analyses revealed that RWGS-CL on Cu–In₂O₃ is derived from redox between Cu–In₂O₃ and Cu–In alloy. Key factors for high CO₂ splitting rate were fast migration of oxide ions in the alloy and the preferential oxidation of the interface of alloy–In₂O₃ in the bulk of the particles. The findings reported herein can open up new avenues to achieve effective CO₂ conversion at lower temperatures.

Efficient activation of CO₂ at low temperature was achieved by reverse water–gas shift via chemical looping (RWGS-CL) by virtue of fast oxygen ion migration in a Cu–In structured oxide, even at lower temperatures.     

Modeling the adsorption of U(VI) onto animal chitin using coupled mass transfer and surface complexation

This paper reports the development of a treatment system, using animal chitin as a passive biosorbent, for removing U(VI) from aqueous waste streams. An integral part of this system is a model that provides for the optimization of the treatment system through simulation of U(VI) removal efficiency based on the characteristics of the influent waste stream. The model accounts for changing solution matrix conditions through the coupling of surface complexation and mass transfer models. Complexation of U(VI) by chitin surface sites was modeled using FITEQL. Application of FITEQL in the “forward” mode provided the sorbed and aqueous phase concentrations needed for the mass transfer model. The mass transfer model was derived for both batch and continuously stirred tank reactor (CSTR) configurations using Fick's Law, reactor mass balances and rate law expressions. The coupled model was successfully validated using CSTR data at pH 6.5 and rate constants determined from batch sorption experiments. The CSTR configuration yields a steady-state, eighty percent U(VI) removal for 1 μM influent U(VI) with a solution-phase pH of 6.5 and 3.9 g l⁻¹ chitin.     

Superconvergence of the iterated collocation methods for Hammerstein equations

In this paper, we analyse the iterated collocation method for Hammerstein equations with smooth and weakly singular kernels. The paper expands the study which began in [16] concerning the superconvergence of the iterated Galerkin method for Hammerstein equations. We obtain in this paper a similar superconvergence result for the iterated collocation method for Hammerstein equations. We also discuss the discrete collocation method for weakly singular Hammerstein equations. Some discrete collocation methods for Hammerstein equations with smooth kernels were given previously in [3, 18].     

On an extremal problem of Selberg

We consider the minimum value m_p of the product under the conditions that and . This problem stems from estimation of the Selberg integral appeared in the study of integral-valued entire functions [A. Selberg, Über einen Satz von A. Gelfond, Arch. Math. Naturvid. 44 (1941) 159–170]. We give upper and lower estimates of m_p : . This, in particular, slightly improves the earlier lower estimate given by Selberg: logm_p>p·0.31654924….     

Vertices of Degree 5 in a Contraction Critically 5-connected Graph

An edge of a k-connected graph is said to be k-contractible if the contraction of the edge results in a k-connected graph. A k-connected graph with no k-contractible edge is said to be contraction critically k-connected. We prove that a contraction critically 5-connected graph on n vertices has at least n/5 vertices of degree 5. We also show that, for a graph G and an integer k greater than 4, there exists a contraction critically k-connected graph which has G as its induced subgraph.     

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.     

A mixed version of Menger's theorem

An(a, b)-n-fan means a union ofn internally disjoint paths. Menger's theorem states that a graphG has an(a, b)-n-fan if and only ifG isn-connected betweena andb. We show thatG contains edge-disjoint(a, b)-n-fans if and only if for anyk withk0min{n–1, |V(G)|–2} and for any subsetX ofV(G)-{a, b} with cardinalityk, G-X is (n-k)-edge-connected betweena andb.     

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.     

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