Effect of Li2O content on physical and structural properties of vanadyl doped alkali zinc borate glasses

The effect of Li₂O content in vanadyl doped 20ZnO+xLi₂O+(30−x)Na₂O+50B₂O₃ (5≤x≥25) glasses has been studied with respect to their physical and structural properties. The absence of sharp peaks in XRD spectra of these glass samples confirms the amorphous nature. The physical parameters like density, refractive index, ionic concentration and electronic polarizability vary non-linearly with x mol% depending on the diffusivities of alkali ions. EPR and optical absorption spectra reveal that the resonance signals are characteristics of VO²⁺ ions in tetragonally compressed octahedral site. Spin-Hamiltonian, crystal field, tetragonal field and bonding parameters are found to be in good agreement with the other reported glass systems. The tetragonal distortion (g_⊥-g_∥) and Dt reveals that their values vary non-linearly with Li₂O content and reaches a minimum at x=10 mol%. An anomaly of character has been observed in all the properties of vanadyl doped glass systems, which gives a clear indication of mixed alkali effect.     

Substrate-dependent structure, microstructure, composition and properties of nanostructured TiN films

Titanium nitride films of a thickness of ∼1.5 μm were deposited on amorphous and crystalline substrates by DC reactive magnetron sputtering at ambient temperature with 100% nitrogen in the sputter gas. The growth of nanostructured, i.e. crystalline nano-grain sized, films at ambient temperature is demonstrated. The microstructure of the films grown on crystalline substrates reveals a larger grain size/crystallite size than that of the films deposited on amorphous substrates. Specular reflectance measurements on films deposited on different substrates indicate that the position of the Ti-N 2s band at 2.33 eV is substrate-dependent, indicating substrate-mediated stoichiometry. This clearly demonstrates that not only structure and microstructure, but also chemical composition of the films is substrate-influenced. The films deposited on amorphous substrates display lower hardness and modulus values than the films deposited on crystalline substrates, with the highest value of hardness being 19 GPa on a lanthanum aluminate substrate.     

Tunable optofluidic aperture configured by a liquid-core/liquid-cladding structure

Miniaturized and tunable optical components, such as the waveguide, lens, and prism, have been of great interest for lab-on-chip systems. This Letter reports an optofluidic aperture stop formed by the liquid-core/liquid-cladding flow. The aperture size can be tuned accordingly by adjusting the flow rates. Manipulation of the aperture size allows control of the amount of light passing through the corresponding optical system as well as the angular aperture on the image side. This optofluidic aperture enables lab-on-chip optical systems to have a greater flexibility and more functionalities.     

The large rank of a finite semigroup using prime subsets

The large rank of a finite semigroup \(\Gamma \) , denoted by \(r_5(\Gamma )\) , is the least number \(n\) such that every subset of \(\Gamma \) with \(n\) elements generates \(\Gamma \) . Howie and Ribeiro showed that \(r_5(\Gamma ) = |V| + 1\) , where \(V\) is a largest proper subsemigroup of \(\Gamma \) . This work considers the complementary concept of subsemigroups, called prime subsets, and gives an alternative approach to find the large rank of a finite semigroup. In this connection, the paper provides a shorter proof of Howie and Ribeiro’s result about the large rank of Brandt semigroups. Further, this work obtains the large rank of the semigroup of order-preserving singular selfmaps.     

Wandering Subspaces of the Bergman Space and the Dirichlet Space Over {{\mathbb{D}^{n}}}

Doubly commuting invariant subspaces of the Bergman space and the Dirichlet space over the unit polydisc \({\mathbb{D}^n}\) (with \({n \geq 2}\) ) are investigated. We show that for any non-empty subset \({\alpha=\{\alpha_1,\ldots,\alpha_k\}}\) of \({\{1,\ldots,n\}}\) and doubly commuting invariant subspace \({\mathcal{S}}\) of the Bergman space or the Dirichlet space over \({\mathbb{D}^n}\) , restriction of the multiplication operator tuple on \({\mathcal{S}, M_{\alpha}|_\mathcal{S}:=(M_{z_{\alpha_1}}|_\mathcal{S},\ldots, M_{z_{\alpha_k}}|_\mathcal{S})}\) , always possesses generating wandering subspace of the form $$\bigcap_{i=1}^k(\mathcal{S}\ominus z_{\alpha_i}\mathcal{S})$$ .     

Maximal Contractive Tuples

Maximality of a contractive tuple of operators is considered. A characterization for a contractive tuple to be maximal is obtained. The notion of maximality for a submodule of the Drury–Arveson module on the \(d\) -dimensional unit ball \({\mathbb {B}}_d\) is defined. For \(d=1\) , it is shown that every submodule of the Hardy module over the unit disc is maximal. But for \(d\ge 2\) we prove that any homogeneous submodule or submodule generated by polynomials is not maximal. A characterization of maximal submodules is obtained.     

Asymptotic Behavior of Positive Harmonic Functions in Certain Unbounded Domains

We derive asymptotic estimates at infinity for positive harmonic functions in a large class of non-smooth unbounded domains. These include domains whose sections, after rescaling, resemble a Lipschitz cylinder or a Lipschitz cone, e.g., various paraboloids and horns.     

A unified approach to the integrals of Mellin–Barnes–Hecke type

In this paper, we provide a unified approach to a family of integrals of Mellin–Barnes type using distribution theory and Fourier transforms. Interesting features arise in many of the cases which call for the application of pull-backs of distributions via smooth submersive maps defined by Hörmander. We derive by this method the integrals of Hecke and Sonine related to various types of Bessel functions which have found applications in analytic and algebraic number theory.     

A simple efficient sequential one-pot intermolecular aza-Michael addition and intramolecular Buchwald–Hartwig α-arylation of amines: synthesis of functionalized tetrahydroisoquinolines

An efficient one-pot sequential intermolecular aza-Michael addition and Pd-catalyzed intramolecular Buchwald–Hartwig α-arylation of secondary amines have been investigated, for the synthesis of tetrahydroisoquinolines. This method is simple and furnished products in very good yield and also successfully applied for the synthesis of novel aza-spirotricylcic ethers.