Structural properties of rutherfordium: An ab-initio study

The structural and electronic properties of rutherfordium, the latest group IV B element, have been evaluated by first principles density functional theory in scalar relativistic formalism with and without spin-orbit coupling and compared with its 5d homologue Hf. It is found that Rf will crystallize in the hexagonal close packed structure as in Hf. However, under pressure, it will have different sequence of phase transitions than Hf: hcp→bcc instead of hcp→ω→bcc. An explanation is offered for this difference in terms of the competition between the band structure and the Ewald energy contributions.     

Nonvanishing of symmetric square -functions of cusp forms inside the critical strip

We shall give a certain nonvanishing result for the symmetric square -function of an elliptic cuspidal Hecke eigenform w.r.t. the full modular group inside the critical strip.

     

Some results on a special case of a general continued fraction of Ramanujan

We derive a new special case C(q) of a general continued fraction recorded by Ramanujan in his Lost Notebook. We give a representation of the continued fraction C(q) as a quotient of Dedekind eta-function and then use it to prove modular identities connecting C(q) with each of the continued fractions \(C(-q)\), \(C(q^{2})\), \(C(q^{3})\), \(C(q^{5})\), \(C(q^{7})\), \(C(q^{11})\), \(C(q^{13})\) and \(C(q^{17})\). We also prove general theorems for the explicit evaluation of the continued fraction C(q) by using Ramanujan’s class invariants.     

Simultaneous Approximation for Generalized Baskakov-Durrmeyer-Type Operators

The present paper deals with the study of a Durrmeyer-type integral modification of certain modified Baskakov operators. Here we study simultaneous approximation properties for these operators by using the iterative combinations. We obtain an asymptotic formula and an error estimation in terms of higher order modulus of continuity for these operators.      

On the impulsive implicit Ψ-Hilfer fractional differential equations with delay

In this paper, we investigate the existence and uniqueness of solutions and derive the Ulam-Hyers-Mittag-Leffler stability results for impulsive implicit Ψ-Hilfer fractional differential equations with time delay. It is demonstrated that the Ulam-Hyers and generalized Ulam-Hyers stability are the specific cases of Ulam-Hyers-Mittag-Leffler stability. Extended version of the Gronwall inequality, abstract Gronwall lemma, and Picard operator theory are the primary devices in our investigation. We provide an example to illustrate the obtained results.     

Analysis of viscoelastic behavior and dynamic mechanical relaxation of copolyester based layered silicate nanocomposites using Havriliak–Negami model

The solid‐state viscoelastic properties are examined for intercalated nanocomposites based on a copolyester and (2‐ethyl‐hexyl)dimethyl hydrogenated‐tallow ammonium montmorillonite. The nanocomposites are prepared via the direct melt intercalation technique using a conventional twin‐screw extruder. Dynamic mechanical thermal analysis of the nanocomposites is conducted using two different test setups. The dynamic mechanical relaxation spectra show an increase in the storage modulus of the nanocomposite over the entire temperature range under study as compared to the pristine polymer (except in the transition region from 70 to 80 °C). These results are analyzed using the empirical Havriliak–Negami (HN) equation. The four temperature independent HN parameters (α, β, E₀, and E_∞) and one temperature dependent parameter (τ, the relaxation time) are determined by solving the HN equation for each temperature over the range of temperatures. The calculated moduli results fit well with the experimental values of the relaxation spectra for the nanocomposites. This study shows that the HN model can be applied to polymer layered silicate nanocomposites, and it can be used to predict their dynamic mechanical properties over a wide range of temperatures and frequencies a priori. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2657–2666, 2004     

Anodic Synthesis of New Benzofuran Derivatives Using Active Methylene Group at Platinum Electrode

A facile and Eco-compatible synthesis of benzofuran derivatives (4a–4h) has been carried out at platinum electrode by electrochemical oxidation of catechol in the presence of active methylene groups. Electro- organic synthesis has been performed in an undivided cell at ambient conditions. The products of electrolysis have been purified and characterized by FTIR, ¹H NMR and ¹³C NMR and mechanism was deduced by voltammetric studies.     

Sustainability of bioplastics: Opportunities and challenges

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Electron-impact fragmentation of triaryl-s-trithianes: A novel skeletal rearrangement involving sulphur-sulphur bond formation

The mass spectral fragmentation of seven substituted 2,4,6-triaryl-s-trithianes has been studied and the fragmentation modes confirmed by deuterium labelling. Triphenyl-s-trithiane shows some interesting features in its mode of cleavage and does not eliminate S, S₂, SH^˙, H₂S or S₂H^˙ from its molecular ion. The prominent radical ions in the mass spectrum are at m/e 180 (52.3%) and m/e 186 (45.2%), corresponding to stilbene and PhCHS₃. Their compositions have been established by deuterium labelling and accurate mass measurements. The formation of stilbene indicates a relationship between pyrolytic and electron-impact studies. The origin of [PhCHS₃]^+˙ suggests that one of the sulphur atoms attaches itself to the other two sulphur atoms in the molecular ion, eliminating a stilbene radical ion. The other important fragmentation corresponds to the monomer radical ion (thiobenzaldehyde) and the thiobenzoyl cation. Among the other substituted triaryl-s-trithianes with substituents such as chloro, methoxy, methylenedioxy and hydroxy groups on the phenyl ring (IV to IX), only the tris-(p-chlorophenyl)-s trithiane shows an insignificant molecular ion. Unlike the triphenyl derivative, the chloro, methoxy and methylenedioxy derivatives show the loss of HS^˙ and/or H₂S from the molecular ion. The spectrum of tris-(p-hydroxyphenyl)-s-trithiane corresponds to the spectrum of p-hydroxythiobenzaldehyde.