The constraint nondegeneracy condition is one of the most relevant and useful constraint qualifications in nonlinear semidefinite programming. It can be characterized in terms of any fixed ...orthonormal basis of the, let us say,
ℓ
-dimensional kernel of the constraint matrix, by the linear independence of a set of
ℓ
(
ℓ
+
1
)
/
2
derivative vectors. We show that this linear independence requirement can be equivalently formulated in a smaller set, of
ℓ
derivative vectors, by considering all orthonormal bases of the kernel instead. This allows us to identify that not all bases are relevant for a constraint qualification to be defined, giving rise to a strictly weaker variant of nondegeneracy related to the global convergence of an external penalty method. We use some of these ideas to revisit an approach of Forsgren (Math Program 88, 105–128, 2000) for exploiting the sparsity structure of a transformation of the constraints to define a constraint qualification, which led us to develop another relaxed notion of nondegeneracy using a simpler transformation. If the zeros of the derivatives of the constraint function at a given point are considered, instead of the zeros of the function itself in a neighborhood of that point, we obtain an even weaker constraint qualification that connects Forsgren’s condition and ours.
We synthesized DyMnO3 nanoparticles with particle sizes of about 7.5a15.3 nm in the pores of mesoporous silica and investigated their crystal structure and magnetic properties. As the particle size ...decreased, the lattice constants of the DyMnO3 nanoparticles deviated from those of the bulk crystal, and the JahnaTeller distortion in the nanoparticle systems decreased. In addition, the estimated lattice strain increased with decreasing particle size. The DyMnO3 nanoparticles showed superparamagnetic behavior. The blocking temperature and the coercive field increased with decreasing particle size, and this behavior was contrary to the usual magnetic size effects. It is deduced that these unique size dependences of the magnetic properties for the DyMnO3 nanoparticles were derived from the changes in lattice constants and lattice strain. The anisotropic lattice deformation in the crystal structure of the nanoparticles induces an enhancement of the magnetic anisotropy, which results in the increase in blocking temperature and coercive field with decreasing particle size.
We examine the surface size- and shape-effects of soliton annihilation and soliton nucleation in chiral magnet CrNb3S6. We measure magnetization (M) curves of submillimeter-sized single crystals with ...an equal length along the c-axis (Lc = 10 μm) but with different cross sections in the ab-plane (Sab = 0.120–0.014 mm2). We find a ferromagnetic type of magnetizing (FMM) with a convex curve (d2M/dH2 < 0) near zero field (H = 0) and a major jump in M near the forced ferromagnetic state, which are more conspicuous, compared with earlier samples with submillimeter Lc K. Tsuruta et al. J. Phys. Soc. Jpn. 85, 013707 (2016). A new finding is that the major jump in M occurs at lower fields in samples with the smaller Sab. We further perform numerical simulation of the magnetization process with the Landau–Lifshitz–Gilbert equation of the Langevin-type. Based on the numerical results, we attribute the FMM at small fields to rapid annihilation of soliton assisted by the reduction of Dzyaloshinskii-Moriya interaction near the surfaces. We also discuss possible penetration processes of chiral soliton through the ac-(bc-)plane as well as ab-plane, and its relation to the major jump in M. Our experimental and calculated results will contribute to understanding of the effects of topological metastability in chiral magnets.
The constant rank constraint qualification, introduced by Janin in 1984 for nonlinear programming, has been extensively used for sensitivity analysis, global convergence of first- and second-order ...algorithms, and for computing the directional derivative of the value function. In this paper we discuss naive extensions of constant rank-type constraint qualifications to second-order cone programming and semidefinite programming, which are based on the Approximate-Karush–Kuhn–Tucker necessary optimality condition and on the application of the reduction approach. Our definitions are strictly weaker than Robinson’s constraint qualification, and an application to the global convergence of an augmented Lagrangian algorithm is obtained.
The chiral magnet CrNb3S6 with its solitonic objects has novel magnetic and transport properties, in which the spin-orbit coupling (SOC) plays a central role. Aiming to address the possible existence ...of orbital moments driven by SOC, we perform soft x-ray magnetic circular dichroism spectroscopy at the Cr L2,3 edges with in-plane magnetization. The dichroic signals provide direct experimental evidence that the Cr orbital magnetic moment is not quenched and is coupled antiparallel to the spin counterpart. Application of the orbital sum rule reveals that the magnitude of the Cr orbital moment is about 1% of the total magnetization. These findings are consistent with the first-principles electronic structure calculations that utilize the Cr 2p core radial function to define the Cr local 3d quantities. The distinct roles of the atomic SOC among the Cr 3d and Nb 4d states are discussed.
The ceramic YBa2Cu4O8 superconductor composed of submicron grains is considered a random Josephson-coupled network containing the so-called π junctions and shows successive phase transitions. With ...decreasing temperature, first the intragrain superconductive transition occurs inside each grain at Tc1 and then the chiral-glass transition occurs among the grains at Tc2 (< Tc1). The third transition at Tc3 (< Tc2) is the intergrain superconducting transition. We measured the nonlinear susceptibility and resistivity of the ceramic YBa2Cu4O8 superconductor to determine the field dependences of the transition temperatures Tc2 and Tc3. The phase diagram of the intergrain ordering is discussed in light of the result predicted by Kawamura.
The exogenous application of plant hormones and their analogues has been exploited to improve crop performance in the field. Protodioscin is a saponin whose steroidal moiety has some similarities to ...plant steroidal hormones, brassinosteroids. To test the possibility that protodioscin acts as an agonist or antagonist of brassinosteroids or other plant growth regulators, we compared responses of the weed species Bidens pilosa L. to treatment with protodioscin, brassinosteroids, auxins (IAA) and abscisic acid (ABA). Seeds were germinated and grown in agar containing protodioscin, dioscin, brassinolides, IAA and ABA. Root apex respiratory activity was measured with an oxygen electrode. Malondialdehyde (MDA) and antioxidant enzymes activities were assessed. Protodioscin at 48-240 μm inhibited growth of B. pilosa seedlings. The steroidal hormone 24-epibrassinolide (0.1-5 μm) also inhibited growth of primary roots, but brassicasterol was inactive. IAA at higher concentrations (0.5-10.0 μm) strongly inhibited primary root length and fresh weight of stems. ABA inhibited all parameters of seedling growth and also seed germination. Respiratory activity of primary roots (KCN-sensitive and KCN-insensitive) was activated by protodioscin. IAA and ABA reduced KCN-insensitive respiration. The content of MDA in primary roots increased only after protodioscin treatment. All assayed compounds increased APx and POD activity, with 24-epibrassinolide being most active. The activity of CAT was stimulated by protodioscin and 24-epibrassinolide. The results revealed that protodioscin was toxic to B. pilosa through a mechanism not related to plant growth regulator signalling. Protodioscin caused a disturbance in mitochondrial respiratory activity, which could be related to overproduction of ROS and consequent cell membrane damage.
The well known constant rank constraint qualification Math. Program. Study 21:110–126, 1984 introduced by Janin for nonlinear programming has been recently extended to a conic context by exploiting ...the eigenvector structure of the problem. In this paper we propose a more general and geometric approach for defining a new extension of this condition to the conic context. The main advantage of our approach is that we are able to recast the strong second-order properties of the constant rank condition in a conic context. In particular, we obtain a second-order necessary optimality condition that is stronger than the classical one obtained under Robinson’s constraint qualification, in the sense that it holds for every Lagrange multiplier, even though our condition is independent of Robinson’s condition.
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