On the number of subgroups of given structure in a finitep-group

Supported in part by the Ministry of Science and Technology of Israel and the Rashi Foundation.     

Structure and mechanical properties of titanium nickelide obtained by synthesis in the combustion regime

A study was made of the structure and mechanical properties of titanium nickelide obtained by synthesis in the combustion regime with subsequent shaping of the final product heated as a result of chemical reaction. It is shown that a nearly aggregate structure is obtained during synthesis, this structure improving the heat resistance of the alloy in the investigated temperature range. At the same time, dispersion hardening significantly improves the strength characteristics of the alloy.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 49–54, October, 1986.     

Integrability, stability, and adiabaticity in nonlinear stimulated Raman adiabatic passage

We study the dynamics of a two-color photoassociation of atoms into diatomic molecules via nonlinear stimulated Raman adiabatic passage process. The system has a famous counterpart in (linear) quantum mechanics, and has been discussed recently in the context of generalizing the quantum adiabatic theorem to nonlinear systems. Here we use another approach to study adiabaticity and stability in the system: we apply methods of classical Hamiltonian dynamics. We find nonlinear dynamical instabilities, cases of complete integrability, and improved conditions of adiabaticity.     

The Cauchy Relations in Linear Elasticity Theory

In linear elasticity, we decompose the elasticity tensor into two irreducible pieces with 15 and 6 independent components, respectively. The vanishing of the piece with 6 independent components corresponds to the Cauchy relations. Thus, for the first time, we recognize the group-theoretical underpinning of the Cauchy relations.     

Characterization of Al(III) complexes with hematein in artistic alum logwood inks

The complexes between Al(III) and hematein, the main coloring matter in alum logwood inks, were characterized by Raman and ²⁷Al NMR (nuclear magnetic resonance) spectroscopies. Raman spectra of the crystallized complexes and of the compounds applied on a paper substrate are presented and assigned based on published data for the parent compounds. These Raman spectra show that the coordination of the hematein to the Al(III) ions takes place in both cases through the carbonyl and hydroxyl groups in the molecule, and that the aromatic rings are also involved in the interaction. The Raman spectra of the pure hematein–Al(III) complexes were found to be consistent with those recorded for a logwood ink prepared following a late 19th century recipe, using logwood chips instead of pure hematein, and applied on a paper substrate. These spectra can be used as references for the noninvasive identification of the compounds in works of art. ²⁷Al solid‐state NMR showed that the coordination of the Al(III) atoms in the crystallized powder is predominantly octahedral, while when applied on a paper substrate the colorant is present mainly as a tetrahedral complex, with an octahedral coordination also present in a smaller proportion. The fact that the predominant coordinations for the complexes in the crystallized material and for the ones present on the paper substrate are different is relevant for the study of the lightfastness and thermal stability of works of art bearing these media. Copyright © 2009 John Wiley & Sons, Ltd.     

Low-energy electron beam source

Experimental results of research into a ferroelectric-plasma-source-assisted hollow anode (HA) discharge as a source of low-energy electron beams are presented. To generate electron beams, the HA auto-bias negative voltage was achieved by the discharge current flowing through the resistor connecting the HA and the grounded electrode. It is shown that this method allows reliable and reproducible generation of low-energy electron beams with electron energy of several hundreds of eV, electron current density up to several A/cm² and pulse duration of several tens of microseconds.     

Lagrangian caps

We establish an h-principle for exact Lagrangian embeddings with concave Legendrian boundary. We prove, in particular, that in the complement of the unit ball B in the standard symplectic ${\mathbb{R}^{2n}, 2n \geq 6}$ R 2 n , 2 n ≥ 6 , there exists an embedded Lagrangian n-disc transversely attached to B along its Legendrian boundary, which is loose in the sense of Murphy (Loose Legendrian embeddings in high dimensional contact manifolds, arXiv:1201.2245, 2013).     

Constructing exact Lagrangian immersions with few double points

We establish, as an application of the results from Eliashberg and Murphy (Lagrangian caps, 2013), an h-principle for exact Lagrangian immersions with transverse self-intersections and the minimal, or near-minimal number of double points. One corollary of our result is that any orientable closed 3-manifold admits an exact Lagrangian immersion into standard symplectic 6-space ${\mathbb{R}^6_{\rm st}}$ with exactly one transverse double point. Our construction also yields a Lagrangian embedding ${S^1 \times S^2 \to \mathbb{R}^6_{\rm st}}$ with vanishing Maslov class.