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A zeolitic imidazolate framework-8 (ZIF-8) layer was introduced as a surface molecular separator to grant the selective gas-sensing ability to thin-film sensor material composed of SnO2 nanosheets. ZIF-8 possesses a molecular sieving ability, which is in the range of approximately 4.0–4.2 A. Compared to a SnO2 nanosheet gas sensor, a ZIF-8/SnO2 nanosheet gas sensor exhibited a decreased sensor signal response when the gas molecular sizes were large, e.g., C3H6 (4.120 A), 1-C4H8 (5.430 A), and C9H18O (12.011 A). However, the ZIF-8/SnO2 nanosheet sensor signal response to smaller-sized gas molecules, such as C2H4 (3.058 A), was slightly increased due to electron transfer at the ZIF-8 and SnO2 interface. Therefore, the control of gas selectivity based on molecular size was realized by introducing ZIF-8 as a surface molecular separator. These results pave the way for selective gas sensing in various types of applications that depend on gas selectivity.

This study examines the finite $F$-representation type (abbr. FFRT) property of a two-dimensional normal graded ring $R$ in characteristic $p>0$, using notions from the theory of algebraic stacks. Given a graded ring $R$, we consider an orbifold curve $\mathfrak C$, which is a root stack over the smooth curve $C=\text{Proj} R$, such that $R$ is the section ring associated with a line bundle $L$ on $\mathfrak C$. The FFRT property of $R$ is then rephrased with respect to the Frobenius push-forwards $F^e_*(L^i)$ on the orbifold curve $\mathfrak C$. As a result, we see that if the singularity of $R$ is not log terminal, then $R$ has FFRT only in exceptional cases where the characteristic $p$ divides a weight of $\mathfrak C$., 25 pages, exposition on stacks added, to appear in Adv. Math

ZIF-8 membranes are currently attracting attention for the separation of propylene/propane based on the molecular sieve effect. We have recently reported the preparation of ZIF-8 membranes using the counter-diffusion method, which is advantageous in reducing defects in the selective layer. In the present study, ZIF-8 membranes were prepared at the interface of miscible and immiscible pairs of solvents such as water/methanol and water/1-octanol, respectively. ZIF-8 membranes prepared from the immiscible pair of water and 1-octanol showed a propylene permeance of 5.2 × 10−9 mol m−2 s−1 Pa−1 and a propylene/propane permselectivity of 7.2 at 25 °C. As for the ZIF-8 membrane prepared by the initial reaction using the immiscible pair of water/1-octanol and the successive reaction using the miscible pair of water/methanol mixture, the average propylene permeance and average propylene/propane permselectivity increased to 1.2 × 10−8 mol m−2 s−1 Pa−1 and 20 at 25 °C, respectively. The successive reactions in water/1-octanol and water/methanol mixtures successfully decreased the defects in the ZIF-8 selective layer, resulting in high propylene permeance and high permselectivity for propylene/propane. The structure and gas permeation properties were also thoroughly characterized.

In this paper, a powerful and simple method to evaluate quantitatively the influence of the non-ideal contribution of the hydrogen permeation under diffusion control is provided. For this purpose, a Non-Ideality Index (α) is defined as the ratio of the non-ideal permeability term and the overall permeability, this leading to a direct quantification of the non-ideal effect in membrane. The used methodology is described in detail by using experimental data of a real Pd-membrane. From these data, the parameters that characterise permeability as a function of temperature and pressure – i.e., intrinsic permeability (b) and non-ideal factor (a) – are evaluated, highlighting their higher suitability in describing the membrane behaviour with respect to the usual empirical parameters used by the majority of researchers (i.e., pressure exponent and corresponding permeability). It is underlined that the proposed approach is particularly effective for modelling membrane contactors and reactors, where the empirical Sieverts-type law cannot be used because the large difference of pressure and temperature could lead the membrane behaviour to dramatically change even at different locations of the same device.

A uniquely microstructured membrane, a metal–organic framework (MOF) layer within the porous support, was prepared by a counter-diffusion method. The MOF-based membrane prepared from the copper benzene tricarboxylate (Cu-BTC), one of the MOFs, exhibited excellent gas perm-separation properties with an ideal H2/CH4 selectivity of 153.

This study is focused on modeling and simulation of hierarchically structured catalytic media with macro- and meso-pores. The hierarchical structures are expected to enhance the contact between reactants and active catalytic sites. However, heterogeneous simulations of such structures are not computationally feasible for a practical scale, so that a multi-scale approach involving a pseudo-homogeneous approximation is required. This work aims at determining a suitable form for effectiveness factor in the reaction rate and effective diffusivity to be used in a pseudo-homogeneous approximation. To do that, computational fluid dynamics (CFD) simulations of hierarchical structure of particles are carried out in both heterogeneous and homogeneous mode within 240–300 °C and Thiele modulus around 2.4 or less. The analysis is applied to decane oxidation as representative of the oxidation of exhausted gas from Diesel engines. After providing a validation of the analysis on a single catalyst spherical particle, simulations in heterogeneous mode are carried out under isothermal conditions. The results suggest that the effective diffusivity for the pseudo-homogeneous approximation should include porosity and tortuosity of ensemble, which is evaluated considering the particles as dense. Additionally, detailed profile analysis suggests that the analytical expression of the effectiveness factor valid for spherical particles under isothermal conditions could be used in the pseudo-homogeneous approximation. Then, simulations in homogeneous mode are carried out under both isothermal and non-isothermal conditions to confirm the above-cited suggestions. The obtained results demonstrate the suitability of the chosen effectiveness factor and effective diffusivity.

We synthesized and characterized for the first time an ampholytic ion-recognition linear copolymer of [3-(methacryloylamino)propyl]trimethylammonium chloride (MAPTAC), acrylic acid (AA), and benzo[18]crown-6-acrylamide (BCAm). In this copolymer, the MAPTAC unit has a positive charge. The AA unit has a negative charge that depends on the pH. The crown receptor of the BCAm unit forms a complex with specific ions such as Ba2+ because of the high complex formation constant which behaved like a fixed positive charge. Thus, the copolymers behaved as an ion-recognition polyampholytes and shrank at a pH equal to the isoelectric point (IEP), which shifted to a higher pH when the BCAm complexed with a cation. At that time, the BCAm also became hydrophilic with water of hydration accompanied by the cation. As a result of the combination of these two effects, we found that the reverse behaviors of swelling and shrinking occurred at different pHs in response to the same ion signal.

We present two applications of a characteristic p analog of multiplier ideals, which is a generalization of the test ideal in the theory of tight closure. Namely, we give alternative proofs to Smith's result on base-point-freeness of adjoint bundles in characteristic p > 0 and results on uniform behavior of symbolic powers in a regular local ring due to Ein, Lazarsfeld and Smith, and Hochster and Huneke.

We give a quick new proof of Wahl's vanishing theorem for rational surface singularities, using prime characteristic technique. Our method also gives a criterion for F-rationality in dimension 2.

The notions of F -rational and F -regular rings are defined via tight closure, which is a closure operation for ideals in a commutative ring of positive characteristic. The geometric significance of these notions has persisted, and K. E. Smith proved that F -rational rings have rational singularities. We now ask about the converse implication. The answer to this question is yes and no. For a fixed positive characteristic, there is a rational singularity which is not F -rational, so the answer is no. In this paper, however, we aim to show that the answer is yes in the following sense: If a ring of characteristic zero has rational singularity, then its modulo p reduction is F -rational for almost all characteristic p . This result leads us to the correspondence of F -regular rings and log terminal singularities.

LetR be a two-dimensional normal graded ring over a field of characteristicp>0. We want to describe the tight closure of (O) in the local cohomology moduleH R+ 2 (R) using the graded module structure ofH R+ 2 (R). For this purpose we explore the condition that the Frobenius mapF: [H R+ 2 (R)]n→[H R+ 2 (R)]pninduced on graded pieces ofH R+ 2 (R) is injective. This problem is treated geometrically as follows: There exists an ample fractional divisorD onX=Proj (R) such thatR=R (X, D)= ⊕ n≥0H0(X O X (n D)). Then the above map is identified with the induced Frobenius on the cohomology groups Our interest is the casen0 is defined via tight closure and is expected to characterize rational singularities. We ask if a modulop reduction of a rational signularity in characteristic 0 isF-rational forp≫0. Our result answers to this question affirmatively and also sheds light to behavior ofF-rationality in smallp.

In this paper, using the notion of the tight integral closure, we will give a criterion for F-rationality of Rees algebras of m-primary ideals in a Cohen–Macaulay local ring. As its application, we prove the following results: (1) In dimension two, if A is F-rational and I is integrally closed, then the Rees algebra R(I) is F-rational. On the other hand, in higher dimensions, we construct many examples of Cohen–Macaulay, normal Rees algebras which are not F rational. (2) If both A and R(I) are F-rational, then so is the extended Rees algebra R′(I). (3) If R(I) is F-rational and a(G(I))≠−1, then A is F-rational.On the other hand, using resolution of singularities, we will prove that a two-dimensional rational singularity always admits F-rational Rees algebras. In particular, this theorem gives another way than that devised by Watanabe (1997, J. Pure Appl. Algebra122, 323–328) to construct counterexamples to the Boutot-type theorem for F-rational rings.

When a noise source is located in a very large room as compared to the wavelength concerned, the integral equation method to calculate the sound field is not applicable because of limitations in computer capacity. In this case, an approximate approach based on Kirchhoff's diffraction formula becomes more practical. This formula requires the velocity potential and its normal derivative at the aperture, which are unknown. These unknowns may be assumed to consist of the direct wave from the source and the diffused ones. The latter are assumed to be plane waves with the same amplitude but random phase. The relation between the amplitude of the direct wave and the reflected ones is determined by geometrical acoustics. Thus the radiated sound field can be readily evaluated from the aperture by Kirchhoff's formula. The numerical results for a scale model of a reverberation chamber with a rectangular aperture are shown with measurements. The agreement between the calculations and the measurements is satisfactory.