Search results for " solution"
showing 10 items of 3084 documents
Response determination of linear dynamical systems with singular matrices: A polynomial matrix theory approach
2017
Abstract An approach is developed based on polynomial matrix theory for formulating the equations of motion and for determining the response of multi-degree-of-freedom (MDOF) linear dynamical systems with singular matrices and subject to linear constraints. This system modeling may appear for reasons such as utilizing redundant DOFs, and can be advantageous from a computational cost perspective, especially for complex (multi-body) systems. The herein developed approach can be construed as an alternative to the recently proposed methodology by Udwadia and coworkers, and has the significant advantage that it circumvents the use of pseudoinverses in determining the system response. In fact, ba…
Heats and Entropies of Reaction of Transition Metal Ions with Ethylenediamine
1960
THE heats of formation of complexes between ligands and metal ions are very important to further the ligand field-theory and check its implications. Until now, only the heats of hydration of the first transition group ions have been used for this purpose1 as the thermochemical data on the complexes formed by ligands other than water are very incomplete. The transition metal complexes of ethylenediamine, which have a very nearly octahedral configuration, could also be fruitfully studied in terms of ligand field-theory. Unfortunately only the thermal data on nickel (II), copper (II) and zinc (II) complexes are known2, and so the formation constants have been used instead of the values of enth…
Multiplicity of ground states for the scalar curvature equation
2019
We study existence and multiplicity of radial ground states for the scalar curvature equation $$\begin{aligned} \Delta u+ K(|x|)\, u^{\frac{n+2}{n-2}}=0, \quad x\in {{\mathbb {R}}}^n, \quad n>2, \end{aligned}$$when the function $$K:{{\mathbb {R}}}^+\rightarrow {{\mathbb {R}}}^+$$ is bounded above and below by two positive constants, i.e. $$0 0$$, it is decreasing in (0, 1) and increasing in $$(1,+\infty )$$. Chen and Lin (Commun Partial Differ Equ 24:785–799, 1999) had shown the existence of a large number of bubble tower solutions if K is a sufficiently small perturbation of a positive constant. Our main purpose is to improve such a result by considering a non-perturbative situation: we ar…
Multiplicity of Radial Ground States for the Scalar Curvature Equation Without Reciprocal Symmetry
2022
AbstractWe study existence and multiplicity of positive ground states for the scalar curvature equation $$\begin{aligned} \varDelta u+ K(|x|)\, u^{\frac{n+2}{n-2}}=0, \quad x\in {{\mathbb {R}}}^n\,, \quad n>2, \end{aligned}$$ Δ u + K ( | x | ) u n + 2 n - 2 = 0 , x ∈ R n , n > 2 , when the function $$K:{{\mathbb {R}}}^+\rightarrow {{\mathbb {R}}}^+$$ K : R + → R + is bounded above and below by two positive constants, i.e. $$0<\underline{K} \le K(r) \le \overline{K}$$ 0 < K ̲ ≤ K ( r ) ≤ K ¯ for every $$r > 0$$ r > 0 , it is decreasing in $$(0,{{{\mathcal {R}}}})$$ ( 0 , R ) and increasing in $$({{{\mathcal {R}}}},+\infty )$$ ( R , + ∞ ) for a certain $${{{\mathcal {R}}}}&g…
Infinitely many periodic solutions for a second-order nonautonomous system
2003
The existence of infinitely many solutions for a second-order nonautonoumous system was investigated. Some multiplicity results for problem (P) under very different assumptions on the potential G were established. It was shown that infinitely many solutions follow from a variational principle by B. Ricceri.
Composition and clues to the origin of refractory metal nuggets extracted from chondritic meteorites
2014
Refractory metal nuggets (RMNs) contain elements, such as Os, Ir, Mo, and Ru, which are predicted to condense from a cooling gas of solar composition simultaneously with CAI-minerals. Berg et al. (2009) identified a large number of RMNs in acid-resistant residues of the Murchison meteorite and suggested that they are pristine condensates. In extending the work of these authors, we have improved the chemical extraction process to enrich the concentration of RMNs in the residue sample and prepared three additional RMN-rich residues from the chondritic meteorites Murchison, Allende, and Leoville. The results show that, while their origin is clearly solar, the compositions in detail of RMNs fro…
Spin crossover in solid solution
1980
Abstract The temperature dependent high spin (HS) ⇌ low spin (LS) transition, otherwise called spin crossover, has been well established for many first-row transition metal complexes, particularly for complexes of iron(II) [1]. The phenomenon has been observed mostly in the crystalline state, but also in solution. The spin crossover characteristics have been found to depend on various chemical influences, such as ligand substitution, the nature of the non-coordinating anion and the crystallizing solvent. It has been shown by 57Fe Mossbauer spectroscopy that the spin crossover behaviour in the solid solutions of [FexZn1−x(2-pic)3] Cl2·EtOH (2-pic = 2-picolylamine) is also susceptible to meta…
Synergistic effects of multiwalled carbon nanotubes and Al on the electrochemical hydrogen storage properties of Mg2Ni-type alloy prepared by mechani…
2012
Abstract Mg 2− x Al x Ni ( x = 0, 0.25) electrode alloys with and without multiwalled carbon nanotubes (MWCNTs) have been prepared by mechanical alloying (MA) under argon atmosphere at room temperature using a planetary high-energy ball mill. The microstructures of synthesized alloys are characterized by XRD, SEM and TEM. XRD analysis results indicate that Al substitution results in the formation of AlNi-type solid solution that can interstitially dissolve hydrogen atoms. In contrast, the addition of MWCNTs hardly affects the XRD patterns. SEM observations show that after co-milling with 5 wt. % MWCNTs, the particle sizes of both Mg 2 Ni and Mg 1.75 Al 0.25 Ni milled alloys are decreased e…
Deformations of the seventh order Peregrine breather solutions of the NLS equation with twelve parameters.
2013
We study the solutions of the one dimensional focusing NLS equation. Here we construct new deformations of the Peregrine breather of order 7 with 12 real parameters. We obtain new families of quasi-rational solutions of the NLS equation. With this method, we construct new patterns of different types of rogue waves. We recover triangular configurations as well as rings isolated. As already seen in the previous studies, one sees appearing for certain values of the parameters, new configurations of concentric rings.
Deformations of third order Peregrine breather solutions of the NLS equation with four parameters
2013
In this paper, we give new solutions of the focusing NLS equation as a quotient of two determinants. This formulation gives in the case of the order 3, new deformations of the Peregrine breather with four parameters. This gives a very efficient procedure to construct families of quasi-rational solutions of the NLS equation and to describe the apparition of multi rogue waves. With this method, we construct the analytical expressions of deformations of the Peregrine breather of order N=3 depending on $4$ real parameters and plot different types of rogue waves.