This paper studies the spatio-temporal dynamics of a diffusive plant-sulphide model with toxicity delay. More specifically, the effects of discrete delay and distributed delay on the dynamics are explored, respectively. The deep analysis of eigenvalues indicates that both diffusion and delay can induce Hopf bifurcations. The normal form theory is used to set up an exact formula that determines the properties of Hopf bifurcation in a diffusive plant-sulphide model. A sufficiently small discrete delay does not affect the stability and a sufficiently large discrete delay destabilizes the system. Nonetheless, a sufficiently small or large distributed delay does not affect the stability. Both delays cause instability by inducing Hopf bifurcation rather than Turing bifurcation.

Let $X, Y$ be two locally compact Hausdorff spaces and $T:C_0(X)\rightarrow C_0(Y)$ be a standard surjective ɛ-norm-additive map, i.e.

\begin{equation*}\big|\|T(f)+T(g)\|-\|f+g\|\big|\leq \varepsilon,\;{\rm for\;all}\; f, g\in C_0(X).\end{equation*}

Then there exist a homeomorphism $\varphi:Y\rightarrow X$ and a continuous function $\lambda:Y\rightarrow\lbrace\pm1\rbrace$ such that

\begin{equation*}|T(f)(y)-\lambda(y)f(\varphi(y))|\leq\frac{3}{2}\varepsilon,\;{\rm for\;all}\;y\in Y,\;f\in C_0(X).\end{equation*}

The estimate ‘$\frac{3}{2}\varepsilon$’ is optimal. And this result can be regarded as a new nonlinear extension of the Banach–Stone theorem.

This work aims to characterize and study the properties of an Algerian diatomaceous earth (Sig-Mascara) as a catalyst carrier. A commercial product of diatomite was characterized by granulometric analysis, X-ray fluorescence, X-ray diffraction, Fourier-transform infrared spectroscopy, thermogravimetric analysis/differential scanning calorimetry and scanning electron microscopy/energy-dispersive X-ray spectroscopy methods. To purify the diatomite and remove the impurities (iron oxides, clay minerals, quartz and organic matters), the <63 μm fraction of the diatomite was separated out. The 15Ni/Ds-700 catalyst has lower SiO2, Al2O3 and CaO contents compared with the original diatomite. The NiO content of the catalyst is 15 wt.%, indicating successful impregnation. According to the nitrogen sorption–desorption results, the specific surface area of the purified diatomite particles (<63 μm) increased from 26.47 to 46.33 m2 g–1 compared to crude diatomite. The 15Ni/Ds-700 catalyst was applied in the dry reforming of methane to obtain synthesis gas (CO and H2). The results showed that the catalyst was relatively stable during catalytic measurements for 6 h, although the conversion rate value was low (12%).

Turmeric (Curcuma longa L.) is rich in curcuminoids, which are polyphenolic pigments make it one of the most valuable spice and medicinal plant. The rising need for natural colours and the numerous health advantages of curcuminoids are driving up the demand of turmeric. In this study, the effects of genotype and genotype × environment on the colour characteristics of 21 turmeric genotypes were examined in three different production environments namely vertical farming, greenhouse, and field conditions. The pooled analysis of variance revealed highly significant (P < 0.05) differences among genotypes (G), environments (E), and G × E interaction for three colour parameters [L* (lightness index), A* (redness index), B* (yellowness index)]. Among the genotypes, the values ranged from 41.80 to 54.76, 13.92 to 24.83 and 31.72 to 47.67 for L*, A*, B*, respectively. Erode Local (22.34), IISR Pragati (24.56) and IISR Prathiba (26.55) recorded maximum A* value under vertical farming, greenhouse, and field conditions, respectively. Correlation analysis between colour values and curcuminoids revealed a significant positive correlation (r = 0.608–0.735, P < 0.001) between A* value and curcuminoids. Furthermore, stability analysis for A* value revealed 78.87% genotype × environment interaction (GEI) from the first two principal components of GGE biplot. IISR Pragati and Waigon Turmeric are best was most stable for A* value across environments. Our study revealed that colour traits among genotypes vary widely and are strongly impacted by genetic and environmental factors. These findings are crucial for future breeding programs to enhance turmeric's colour, ensuring high-quality, stable products for producers and consumers.

Let ${\mathcal {R}} \subset \mathbb {P}^1_{\mathbb {C}}$ be a finite subset of markings. Let G be an almost simple simply-connected algebraic group over $\mathbb {C}$. Let $K_G$ denote the compact real form of G. Suppose for each lasso l around the marked point, a conjugacy class $C_l$ in $K_G$ is prescribed. The aim of this paper is to give verifiable criteria for the existence of an irreducible homomorphism of $\pi _{1}(\mathbb P^1_{\mathbb {C}} \,{\backslash}\, {\mathcal {R}})$ into $K_G$ such that the image of l lies in $C_l$.

This paper is focused on the stability of real-time hybrid aeroelastic simulation systems for flexible wings. In a hybrid aeroelastic simulation, a coupled aeroelastic system is ‘broken down’ into an aerodynamic simulation subsystem and a structural vibration testing subsystem. The coupling between structural dynamics and aerodynamics is achieved by real-time communication between the two subsystems. Real-time hybrid aeroelastic simulations can address the limitations associated with conventional aeroelastic testing performed within a wind tunnel or with pure computational aeroelastic simulation. However, as the coupling between structural dynamics and aerodynamics is completed through the real-time actuation and sensor measurement, their delays may inherently impact the performance of hybrid simulation system and subsequently alter the measured aeroelastic stability characteristics of the flexible wings. This study aims to quantify the impact of actuation and sensor measurement delays on the measured aeroelastic stability, e.g. the flutter boundary, of flexible wings during real-time hybrid simulations, especially when different aerodynamic models are implemented.

Analytical data from aqueous dissolution studies of minerals, mineral systems, and naturally equilibrated solutions such as surface waters and groundwaters provide the basic ingredients necessary to calculate comparative solubility (or activity) products (CKs) and comparative free energies of formation (CΔGf0) of possible minerals or hypothetical minerals. Using a thermodynamic approach, quasi-thermodynamic values are obtained which can help in understanding the relative stabilities of different but similar materials and changes in reacting systems. Illite equilibrated solutions demonstrated that: 1) there is a 5 kcal spread in comparative free energies of formation of the five illites used, 2) the comparative stabilities remain about the same when highly simplified but similar hypothetical mineral formulas are considered, and 3) some of these illites are probably not the most stable phase in a closed chemical system at standard temperature and pressure.

A “mineral index system” composed of common rock-forming minerals, products of chemical weathering and perhaps hypothetical minerals is proposed, which offers a means of studying naturally equilibrated solutions. Such a system can show changes with respect to CΔGf0 of these minerals at a particular site through time or in relationship to spatial distribution and geologic changes through synchronous sampling at different sites.

There are many results in the literature where superstablity-like independence notions, without any categoricity assumptions, have been used to show the existence of larger models. In this paper we show that stability is enough to construct larger models for small cardinals assuming a mild locality condition for Galois types.Theorem 0.1.

Suppose $\lambda <2^{\aleph _0}$. Let ${\mathbf {K}}$ be an abstract elementary class with $\lambda \geq {\operatorname {LS}}({\mathbf {K}})$. Assume ${\mathbf {K}}$ has amalgamation in $\lambda $, no maximal model in $\lambda $, and is stable in $\lambda $. If ${\mathbf {K}}$ is $(<\lambda ^+, \lambda )$-local, then ${\mathbf {K}}$ has a model of cardinality $\lambda ^{++}$.

The set theoretic assumption that $\lambda <2^{\aleph _0}$ and model theoretic assumption of stability in $\lambda $ can be weakened to the model theoretic assumptions that $|{\mathbf {S}}^{na}(M)|< 2^{\aleph _0}$ for every $M \in {\mathbf {K}}_\lambda $ and stability for $\lambda $-algebraic types in $\lambda $. This is a significant improvement of Theorem 0.1, as the result holds on some unstable abstract elementary classes.

Activity expressions are presented for a six end-member, regular solution, site-mixing model for chlorites. The end members are ideal 14-Å chlorites for which experimental stability data are lacking. Estimates were made of the standard state 25°C and 1 bar molar 3rd law entropies, volumes, and the Maier-Kelley heat capacity coefficients. Experimental stability data from the literature for 14-Å chlorites were used with different sets of exchange energies, for cations on adjacent sites, to compute estimates of the standard state chemical potentials of the end members at 25°C and 1 bar. More experimental data are needed for an adequate definition of the exchange energies and the standard state chemical potentials. The model was applied to diagenesis in clastic reservoirs. Aqueous activity ratios of Mg2+:Fe2+ were computed as an equilibrium function of the corresponding molar ratios in authigenic chlorites. The aqueous activity ratio was independent of the chlorite Al content at a constant molar ratio of Mg2+:Fe2+ in the chlorite. The model predicts a wide range of molar Mg2+:Fe2+ ratios in authigenic chlorites in equilibrium with reservoir fluids. Trends in these molar ratios should be independent of the Al content in the chlorites. The model can be applied directly to 7-Å chlorites when experimental data become available to estimate the various thermodynamic parameters of the 7-Å end members.

High-Mg chlorites from Vermont and Quebec and high-Fe chlorites from Michigan and New Mexico were equilibrated at room temperature in the near-neutral pH range. Gibbsite, kaolinite, and hematite of known stability were added to the samples to control unmeasurable variables at calculable levels. Equilibrium solution compositions were obtained from undersaturation and from supersaturation. Other indicators of equilibrium were good agreement between successive analyses over a long period of time, between duplicate samples, between independent systems, and between independent measures of equilibrium. All four chlorites were stable relative to brucite and, with a few exceptions, relative to talc under the conditions of study. When in equilibrium with gibbsite, the pH − ½Mg2+ value of the chlorites ranged from 6.3 to 6.5, at a pH4SiO4 value of 4.0. These values are in good agreement with prior estimates of chlorite stability. The calculated standard free energy of formation of the chlorites is dependent upon solution Fe2+ calculated from the sample Eh and assumed equilibrium with hematite, with the assumption that the Fe2+-Fe3+ couple is at the same Eh as the sample.

Chemical activity diagrarns, prepared to illustrate the properties expected if mixed-layer mont-morillonite/illite is regarded as a solid solution, are compared to those derived from a treatment of these materials as a mixture of two phases. If the system is a solid solution, the coexisting aqueous solution should range from higher dissolved silica contents in the presence of kaolinite and a montmorillonite end member to lower dissolved silica in the presence of kaolinite and an illitic end member. Silica concentration in the aqueous solution might vary by a factor of as much as six. If the system is two phase, the silica content of a solution in equilibrium with kaolinite and both phases would be fixed at a given T and P, as would a solution equilibrated with both phases and K-feldspar. In the absence of a third phase, silica in equilibrium with both phases should be nearly constant, but increase with increasing ratio of K+/H+ in solution. Available data on coexisting aqueous solutions apparently are more nearly consistent with two phases than with a solid solution.

The Nriagu polymer model of 2:1 layer type clay minerals develops from the premise that clay minerals are condensation copolymers of solid hydroxides. In the Mattigod-Sposito formulation of the model, standard state chemical potentials (standard Gibbs energies of formation from the elements) of 2:1 clay minerals are predicted quantitatively with a linear correlation equation relating the standard Gibbs energy of the polymerization reaction (ΔGor) to the half-cell layer charge of the clay mineral and to the valence and ionic radius of the exchangeable cation. It is now shown that this correlation equation can be derived from two basic assumptions: (1) that the standard Gibbs energy change for the transfer of a cation in a pure hydroxide solid to a hydroxide component in the tetrahedral or octahedral sheet of a 2:1 clay mineral is independent of the nature of the cation and (2) that the difference between ΔGor for the polymerization reaction to form a 2:1 clay mineral and ΔGor for the same reaction to form the zero layer-charge analog of the clay mineral is proportional to the number of interlayer exchangeable cations per unit cell of the clay mineral and to the radius of its exchangeable cation. Both of these assumptions can be tested experimentally, independent of the polymer model.