We analyze the limit of stable solutions to the Ginzburg-Landau (GL) equations when ${\varepsilon }$, the inverse of the GL parameter, goes to zero and in a regime where the applied magnetic field is of order $|\log {\varepsilon } |$ whereas the total energy is of order $|\log {\varepsilon }|^2$. In order to do that, we pass to the limit in the second inner variation of the GL energy. The main difficulty is to understand the convergence of quadratic terms involving derivatives of functions converging only weakly in $H^1$. We use an assumption of convergence of energies, the limiting criticality conditions obtained by Sandier-Serfaty by passing to the limit in the first inner variation, and properties of limiting vorticities to find the limit of all the desired quadratic terms. At last, we investigate the limiting stability condition we have obtained. In the case with magnetic field, we study an example of an admissible limiting vorticity supported on a line in a square ${{\Omega }}=(-L,L)^2$ and show that if L is small enough, this vorticiy satisfies the limiting stability condition, whereas when L is large enough, it stops verifying that condition. In the case without magnetic field, we use a result of Iwaniec-Onninen to prove that every measure in $H^{-1}({{\Omega }})$ satisfying the first-order limiting criticality condition also verifies the second-order limiting stability condition.

The fixed points of the generalized Ricci flow are the Bismut Ricci flat (BRF) metrics, i.e., a generalized metric (g, H) on a manifold M, where g is a Riemannian metric and H a closed 3-form, such that H is g-harmonic and $\operatorname{Rc}(g)=\tfrac{1}{4} H_g^2$. Given two standard Einstein homogeneous spaces $G_i/K$, where each Gi is a compact simple Lie group and K is a closed subgroup of them holding some extra assumption, we consider $M=G_1\times G_2/\Delta K$. Recently, Lauret and Will proved the existence of a BRF metric on any of these spaces. We proved that this metric is always asymptotically stable for the generalized Ricci flow on M among a subset of G-invariant metrics and, if $G_1=G_2$, then it is globally stable.

The obligation of stability generally requires host States to maintain a relatively stable regulatory framework to mitigate political risks facing foreign investments. It has played a significant role in international investment tribunals’ review of host States’ renewable energy transition policies. This paper critically reviews tribunals’ interpretation of the obligation with a particular focus on the Spanish cases involving renewable energy incentive schemes. It canvasses the two ‘dimensions’ adopted by investment tribunals in the interpretation of stability, namely the protection of legitimate expectations and States’ right to regulate for public purposes. Examining the contents of the two dimensions separately, this paper argues that legal stability should be disentangled from the notion of legitimate expectations and be assessed through the reasonableness of regulatory changes per se. It further argues that an intrusive interpretation of legal stability lacks legal and institutional bases; instead, more deferential standards should be adopted in the review of renewable energy transition policies.

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.