A simple route to 9-fluorenylidenes by domino Suzuki/Heck coupling reactions

A palladium catalyzed domino intermolecular Suzuki followed by intramolecular Heck coupling is described. This strategy afforded a novel and convenient synthesis of various 9-fluorenylidene derivatives in one-pot under relatively mild reaction condition.     

Synthesis and characterization of sol-gel derived Mn2+ doped In2S3 nanocrystallites embedded in a silica matrix

Mn²⁺ doped In₂S₃–SiO₂ nanocomposite thin films were synthesized by sol-gel technique. The films were annealed in air at different temperatures (473–623 K) and characterized by optical, microstructural and electron spin resonance (ESR) study. Optical transmittance study revealed the manifestation of quantum size effect while ESR indicated the presence of manganese in indium sulphide as dispersed dopant rather than manganese cluster.     

Plasmon energy, bulk modulus, electronic polarisability of AIBIIIC2VI and AIIBIVC2V ternary chalcopyrite semiconductors

A simple relation between the bulk modulus, plasmon energy, electronic polarisability are given for ternary chalcopyrite semiconductors. Bulk modulus has been evaluated from plasmon energy by proposing a linear relation between them. From bulk modulus electronic polarisability has been evaluated. The estimated values are in good agreement with the experimental values and earlier researchers.     

Triterpenoid Constituents of Borreria Articularis

The chloroform extract of the aerial parts and roots of Borreria articularis yielded a new triterpene, 3α‐acetoxy‐oleana‐12‐en‐29‐oic acid along with β‐amyrin. The structures were established by means of spectral as well as chemical studies.     

Characterizations of symmetrized polydisc

Let Γ_n, n ≥ 2, denote the symmetrized polydisc in ?ⁿ, and Γ₁ be the closed unit disc in ?. We provide some characterizations of elements in Γ_n. In particular, an element (s₁,..., s_n?1, p) ∈ ?ⁿ is in Γ_n if and only if \({s_j} = {\beta _j} + \overline {{\beta _{n - j}}}p\), j = 1,..., n ? 1, for some (β₁,..., β_n?1) ∈ Γ_n?1, and |p| ≤ 1.     

Local polynomial convexity of the union of two totally-real surfaces at their intersection

We consider the following question: Let S ₁ and S ₂ be two smooth, totally-real surfaces in ${\mathbb{C}^2}$ that contain the origin. If the union of their tangent planes is locally polynomially convex at the origin, then is ${S_1\cup S_2}$ locally polynomially convex at the origin? If T ₀ S ₁ ?? T ₀ S ₂?=?{0}, then it is a folk result that the answer is yes. We discuss an obstruction to the presumed proof, and provide a different approach. When ${dim_\mathbb{R}(T_0S_1\cap T_0S_2)=1}$ , we present a geometric condition under which no consistent answer to the above question exists. We then discuss conditions under which we can expect local polynomial convexity.     

Nonlinear response properties of atomic hydrogen under quantum plasma environment: A time-dependent variation perturbation study on hyperpolarizability and two-photon excitations

Pilot calculations on the frequency-dependent nonlinear response property, viz. the electric dipole hyperpolarizability of atomic hydrogen under quantum plasma environment, have been performed using an external oscillatory electric field. Fourth-order perturbation theory within a variational scheme is adopted to obtain the hyperpolarizability within and beyond normal dispersion region. Two-photon absorption from the ground state is explicitly obtained from the pole positions of nonlinear response of the system and studied up to principal quantum number n = 4 . Ground and perturbed wave functions of appropriate symmetries are represented by linear combination of Slater-type orbitals. Exponential cosine-screened Coulomb potential is used to simulate the quantum plasma environment. With respect to plasma strength, the nonlinear response properties are considerably enhanced. Results are compared with those under classical plasma environment represented by screened Coulomb potential. Departure from Coulomb potential results in lifting of the accidental degeneracy in the respective two-photon excited states beyond n = 2 . For free hydrogen atom, the transition energies and the radial density profiles of the respective two-photon excited states match exactly with those obtained from analytical wave functions.     

Cyclic DNA codes over the ring $$\mathbb {F}_2+u\mathbb {F}_2+v\mathbb {F}_2+uv\mathbb {F}_2+v^2\mathbb {F}_2+uv^2\mathbb {F}_2$$

We study the structure of cyclic DNA codes of odd length over the finite commutative ring \(R=\mathbb {F}_2+u\mathbb {F}_2+v\mathbb {F}_2+uv\mathbb {F}_2 + v^2\mathbb {F}_2+uv^2\mathbb {F}_2,~u^2=0, v^3=v\), which plays an important role in genetics, bioengineering and DNA computing. A direct link between the elements of the ring R and 64 codons used in the amino acids of living organisms is established by introducing a Gray map from R to \(R_1=\mathbb {F}_2+u\mathbb {F}_2 ~(u^2=0)\). The reversible and the reversible-complement codes over R are investigated. We also discuss the binary image of the cyclic DNA codes over R. Among others, some examples of DNA codes obtained via Gray map are provided.