The row–column multiplication of high dimensional rhotrices

This paper presents the row–column multiplication of rhotrices that are of high dimension. This is an extension of the same multiplication carried out on rhotrices of dimension three, considered to be the base rhotrices.     

Conversion of a rhotrix to a ‘coupled matrix’

In this note, a method of converting a rhotrix to a special form of matrix termed a ‘coupled matrix’ is proposed. The special matrix can be used to solve various problems involving n?×?n and (n?–?1)?×?(n?–?1) matrices simultaneously.     

Interactions between photodegradation components

ABSTRACT: BACKGROUND: The interactions of p-cresol photocatalytic degradation components were studied by response surface methodology. The study was designed by central composite design using the irradiation time, pH, the amount of photocatalyst and the p-cresol concentration as variables. The design was performed to obtain photodegradation % as actual responses. The actual responses were fitted with linear, two factor interactions, cubic and [left-to-right mark] quadratic model to select an appropriate model. The selected model was validated by analysis of variance which provided evidences such as high F-value (845.09), very low P-value (<.0.0001), non-significant lack of fit, the coefficient of R-squared (R2 = 0.999), adjusted R-squared (Radj2 = 0.998), predicted R-squared (Rpred2 = 0.994) and the adequate precision (95.94). RESULTS: From the validated model demonstrated that the component had interaction with irradiation time under 180 min of the time while the interaction with pH was above pH 9. Moreover, photocatalyst and p-cresol had interaction at minimal amount of photocatalyst (< 0.8 g/L) and 100 mg/L p-cresol. CONCLUSION: These variables are interdependent and should be simultaneously considered during the photodegradation process, which is one of the advantages of the response surface methodology over the traditional laboratory method.     

Green Regioselective Azidolysis of Epoxides Catalyzed by Multi‐Site Phase‐Transfer Catalyst

A facile synthesis of 1,2‐azidoalcohols from their epoxides using α,α',α”‐N‐hexakis(triethylammoniummethylene chloride)‐melamine as a multi‐site phase‐transfer catalyst in water was developed. By this eco‐friendly and highly atom‐economic method, a variety of 1,2‐azidoalcohols was obtained in high yields with excellent regioselectivity and in short reaction times. Application of this six‐site PTC in the ring opening of epoxides by cyanide, acetate and chloride anions was also studied. The catalyst can be recovered after completion of the reaction and can be recycled without affecting the catalytic property.     

Impacts of zeolite nanoparticles on substrate properties of thin film nanocomposite membranes for engineered osmosis

In this work, microporous substrates modified by zeolite nanoparticles were prepared and used for composite membrane making with the aim of reducing internal concentration polarization (ICP) effect of membranes during engineered osmosis applications. Nanocomposite substrates were fabricated via phase inversion technique by embedding nanostructured zeolite (clinoptilolite) in the range of 0–0.6 wt% into matrix of polyethersulfone (PES) substrate. Of all the substrates prepared, the PES0.4 substrate (with 0.4 wt% zeolite) exhibited unique characteristics, i.e., increased surface porosity, lower structural parameter (S) (from 0.78 to 0.48 mm), and enhanced water flux. The thin film nanocomposite (TFN) membrane made of this optimized substrate was also reported to exhibit higher water flux compared to the control composite membrane during forward osmosis (FO) and pressure-retarded osmosis (PRO) test, without compromising reverse solute flux. The water flux of such TFN membrane was 43% higher than the control TFC membrane (1.93 L/m² h bar) with salt rejection recorded at 94.7%. An increment in water flux is ascribed to the reduction in structural parameter, leading to reduced ICP effect.     

The Effect of Maturity and Extraction Solvents on Bioactive Compounds and Antioxidant Activity of Mulberry (Morus alba) Fruits and Leaves

Cultivation location, maturity levels, and extraction solvents could affect the bioactive compounds and biological activities of mulberry (Morus alba Linnaeus). The lack of study on Malaysia-grown mulberry causes its underutilization. This study investigated the bioactive compound content and the antioxidant activity of Sabah-grown mulberry at two different maturity stages (fruits: red mature and black fully ripe; leaves: young and mature) extracted using 70% (v/v) methanol, 60% (v/v) ethanol, and 65% (v/v) acetone. Analyses showed that mulberry fruits demonstrated maturity-dependent increment (except UHPLC-DAD quantification), while the leaves revealed maturity-dependent reduction. Principal component analysis (PCA) displayed 65% (v/v) acetone black fully ripe fruits as the best phenolics and antioxidant sources. However, the 60% (v/v) ethanol black fully ripe fruits contained 20.08–68.43% higher total anthocyanins. Meanwhile, the 65% (v/v) acetone and 70% (v/v) methanol red mature fruits were higher in chlorogenic acid (27.53–47.12%) and rutin (31.42–35.92%) than other fruit extracts, respectively. For leaves, 65% (v/v) acetone young leaves were the best phenolics and antioxidant sources. However, the 60% (v/v) ethanol young leaves possessed greater chlorogenic acid (19.56–74.11%) than other leaf extracts. Overall, Malaysia-grown mulberry is rich in phenolics and antioxidants, suggesting its potential application in food and pharmaceutical products.     

Hypercrosslinked Additives for Ageless Gas‐Separation Membranes

The loss of internal pores, a process known as physical aging, inhibits the long‐term use of the most promising gas‐separation polymers. Previously we reported that a porous aromatic framework (PAF‐1) could form a remarkable nanocomposite with gas‐separation polymers to stop aging. However, PAF‐1 synthesis is very onerous both from a reagent and reaction‐condition perspective, making it difficult to scale‐up. We now reveal a highly dispersible and scalable additive based on α,α′‐dichloro‐p‐xylene (p‐DCX), that inhibits aging more effectively, and crucially almost doubles gas‐transport selectivity. These synergistic effects are related to the intimately mixed nanocomposite that is formed though the high dispersibility of p‐DCX in the gas‐separation polymer. This reduces particle‐size effects and the internal free volume is almost unchanged over time. This study shows this inexpensive and scalable polymer additive delivers exceptional gas‐transport performance and selectivity.     

Investigation of Poly(ether-b-amide)/Nanosilica Membranes for CO2/CH4Separation

The results of molecular dynamics （MD） simulations on transport process of CO2 and CH4 gases in poly（ether-b- amide） （PEBAX）/nanosilica membranes are discussed. The diffusion coefficients for CH4 and CO2 gases at 6 cases with different amounts of nanosilica loading in the simulation boxes are presented. The results show that diffusion coefficients for CO2 gas in all cases are larger than those for the CH4 one. Moreover 10% nanosilica loading case shows maximum effects on diffusion coefficients and improves them by more than 68% and 157% for CO2 and CH4 gases, respectively. Additionally, the results of 3-D Cartesian trajectories and displacements curves are presented and the jumping attempt of CO2 is significantly more than that of CH4. Due to the rubbery state of PEBAX membranes in ambient temperature, the results confirm that channel lifetimes are very short and then back diffusion is not observed for this polymer.     

Pressure boundary condition for the time‐dependent incompressible Navier–Stokes equations

In Gresho and Sani (Int. J. Numer. Methods Fluids 1987; 7 :1111–1145; Incompressible Flow and the Finite Element Method, vol. 2. Wiley: New York, 2000) was proposed an important hypothesis regarding the pressure Poisson equation (PPE) for incompressible flow: Stated there but not proven was a so‐called equivalence theorem (assertion) that stated/asserted that if the Navier–Stokes momentum equation is solved simultaneously with the PPE whose boundary condition (BC) is the Neumann condition obtained by applying the normal component of the momentum equation on the boundary on which the normal component of velocity is specified as a Dirichlet BC, the solution (u, p) would be exactly the same as if the ‘primitive’ equations, in which the PPE plus Neumann BC is replaced by the usual divergence‐free constraint (? · u = 0), were solved instead. This issue is explored in sufficient detail in this paper so as to actually prove the theorem for at least some situations. Additionally, like the original/primitive equations that require no BC for the pressure, the new results establish the same thing when the PPE approach is employed. Copyright © 2005 John Wiley & Sons, Ltd.