Formalization of the “Twin Paradox” for Non-uniformly Accelerated Motions

The use of hyperbolic numbers for studying space-time geometry and trigonometry is extended for demonstrating the Frenet’s formulas in space-time. By means of this introduction the twin paradox for non-uniformly accelerated motions is formalized in a straightforward way.     

The Spectrum of the Cubic Oscillator

We prove the simplicity and analyticity of the eigenvalues of the cubic oscillator Hamiltonian, $$\begin{array}{ll}H(\beta)=-\frac{d^2}{dx^2}+x^2+i\sqrt{\beta}x^3\end{array}$$ , for β in the cut plane ${\mathcal{C}_c:=\mathcal{C}\backslash \mathcal{R}_-}$ . Moreover, we prove that the spectrum consists of the perturbative eigenvalues {E _n (β)} _{n ≥ 0} labeled by the constant number n of nodes of the corresponding eigenfunctions. In addition, for all ${\beta \in \mathcal{C}_c, E_n(\beta)}$ can be computed as the Stieltjes-Padé sum of its perturbation series at β = 0. This also gives an alternative proof of the fact that the spectrum of H(β) is real when β is a positive number. This way, the main results on the repulsive PT-symmetric and on the attractive quartic oscillators are extended to the cubic case.     

Exsolution of Nickel Nanoparticles from Mixed-Valence Metal Oxides: A Quantitative Evaluation by Magnetic Measurements

A fast and accurate experimental method is demonstrated to assess the fraction of exsolved metallic nanoparticles using magnetic measurements. As a benchmark, nanometric metallic nickel exsolved from (La_1−xSr_x)(Cr_1−yNi_y)O_3−δ is used for its high relevance as a solid oxide fuel cell component. The method is based on the difference in the magnetic response of the exsolved metallic nickel (ferromagnetic) and Sr-doped lanthanum chromite ceramic matrix (paramagnetic). The exsolved nickel results in coherent nanoparticles pinned on the surface of the Sr-doped lanthanum chromite ceramic matrix, as evidenced by electron microscopy analyses. The results obtained indicate the procedure as a fast and sensitive method to study the exsolution of ferromagnetic nanoparticles.     

Onn-th commutators with nilpotent or regular values in rings

Then-th commutator for a,b in a ringR is defined inductively as follows: [a,b]₁=[a,b]=ab−ba and[a,b] _n=[[a,b]₋₁,b]. We characterize the ringsR without non-zero nil right ideals in which[a,b] _nis nilpotent or regular for alla,b∈R. We also examine the case whereR is a semiprime ring with involution in which[t ₁, t₂]_nis nilpotent or regular for all tracest ₁,t₂∈R.     

Nearest-neighbor configuration in (GaIn)(NAs) probed by x-ray absorption spectroscopy

Ga(1-x)In(x)N(y)As(1-y) is a promising material system for the fabrication of inexpensive "last-mile" optoelectronic components. However, details of its atomic arrangement and the relationship to observed optical properties is not fully known. Particularly, a blueshift of emission wavelength is observed after annealing. In this work, we use x-ray absorption fine structure to study the chemical environment around N atoms in the material before and after annealing. We find that as-grown molecular beam epitaxy material consists of a nearly random distribution of atoms, while postannealed material shows segregation of In toward N. Ab initio simulations show that this short-range ordering creates a more thermodynamically stable alloy and is responsible for blueshifting the emission.     

Exterior products of forms and the cohomology ring of a complex space

In recent publications, we have defined complexes of differential forms on analytic spaces which are resolutions of the constant sheaf. These complexes were used to prove the existence of a mixed Hodge structure on the cohomology of analytic spaces which possess kählerian hypercoverings, in particular, projective algebraic varieties. We define an exterior product on these forms, which induces the cup product on the cohomology of analytic spaces. The main difficulty is to prove that this exterior product is functorial with respect to morphisms of analytic spaces. This exterior product can be used to prove that the cup product is compatible with the mixed Hodge structure on the cohomology.     

Effect of Bohm potential on a charged gas

Bohm’s interpretation of Quantum Mechanics leads to the derivation of a Quantum Kinetic Equation (QKE): in the present work, propagation of waves in charged quantum gases is investigated starting from this QKE. Dispersion relations are derived for fully and weakly degenerate fermions and bosons (for the latter above critical temperature) and the differences discussed. Use of a kinetic equation permits investigation of “Landau-type” damping: it is found that the presence of damping in fermion gases is dependent upon the degree of degeneracy, whereas it is always present in boson gases. In fully degenerate fermions a phenomenon appears that is akin to the “zero sound” propagation.     

A Highly Warped Heptagon‐Containing sp2 Carbon Scaffold via Vinylnaphthyl π‐Extension

A new strategy is demonstrated for the synthesis of warped, negatively curved, all‐sp²‐carbon π‐scaffolds. Multifold C?C coupling reactions are used to transform a polyaromatic borinic acid into a saddle‐shaped polyaromatic hydrocarbon ( 2 ) bearing two heptagonal rings. Notably, this Schwarzite substructure is synthesized in only two steps from an unfunctionalized alkene. A highly warped structure of 2 was revealed by X‐ray crystallographic studies and pronounced flexibility of this π‐scaffold was ascertained by experimental and computational studies. Compound 2 exhibits excellent solubility, visible range absorption and fluorescence, and readily undergoes two reversible one‐electron oxidations at mild potentials.