Isolation,spectroscopic and thermal properties of hydrazinium tris(oxydiacetato)lanthanate(III) hemi(pentahydrate)

Oil-bath reaction of respective metal nitrate with an aqueous mixture of oxydiacetic acid (H₂oda) and hydrazine hydrate led to the formation of crystalline compounds with formula (N₂H₅)₃[Ln(oda)₃]·2.5H₂O (where Ln = La, Ce, Pr, Nd and Sm), which are stable for a week and undergo efflorescence. The resulting complexes were characterized by infrared spectral, thermal (air and nitrogen atmosphere), UV–visible and PXRD studies. From the thermal studies, both in air and nitrogen atmosphere, these compounds show endothermic dehydration below 100 °C to give anhydrous compounds. Next, the anhydrous compounds (in air) undergo endothermic decomposition between 190 and 225 °C to form Ln(Hoda)₃ intermediate, which further show exothermic decomposition to yield respective metal oxide as the end residue. But, in nitrogen atmosphere, the same anhydrous compounds exhibit endo-followed by exothermic decompositions to give respective metal as end product. This is observed as a continuous single step of decomposition in TG. The structure of (N₂H₅)₃[Nd(oda)₃]·2.5H₂O has been determined by single-crystal X-ray analysis. The neodymium atom is coordinated by nine oxygen atoms from three tridentate (O, O, O) oxydiacetate ions with tricapped trigonal prismatic geometry. In addition, both the parent acid and its compounds display strong fluorescent emission due to the ligand, which renders them as fluorescent materials at room temperature.     

Polynomial series expansions for confluent and Gaussian hypergeometric functions

Based on the Hadamard product of power series, polynomial series expansions for confluent hypergeometric functions and for Gaussian hypergeometric functions are introduced and studied. It turns out that the partial sums provide an interesting alternative for the numerical evaluation of the functions and , in particular, if the parameters are also viewed as variables.

     

Riesz-Fejér Inequalities for Harmonic Functions

Potential Analysis - In this article, we prove the Riesz - Fejér inequality for complex-valued harmonic functions in the harmonic Hardy space hp for all p >?1. The result is sharp...     

Characterization and the pre-Schwarzian norm estimate for concave univalent functions

Let Co(α) denote the class of concave univalent functions in the unit disk ${\mathbb{D}}$ . Each function ${f\in Co(\alpha)}$ maps the unit disk ${\mathbb{D}}$ onto the complement of an unbounded convex set. In this paper we find the exact disk of variability for the functional ${(1-|z|^2)\left ( f^{\prime\prime}(z)/f^{\prime}(z)\right), f\in Co(\alpha)}$ . In particular, this gives sharp upper and lower estimates for the pre-Schwarzian norm of concave univalent functions. Next we obtain the set of variability of the functional ${(1-|z|^2)\left(f^{\prime\prime}(z)/f^{\prime}(z)\right), f\in Co(\alpha)}$ whenever f′′(0) is fixed. We also give a characterization for concave functions in terms of Hadamard convolution. In addition to sharp coefficient inequalities, we prove that functions in Co(α) belong to the H ^p space for p < 1/α.     

Harmonic mappings in Bergman spaces

In this paper, we investigate the properties of mappings in harmonic Bergman spaces. First, we discuss the coefficient estimate, the Schwarz-Pick Lemma and the Landau-Bloch theorem for mappings in harmonic Bergman spaces in the unit disk $\mathbb D $ of $\mathbb C $ . Our results are generalizations of the corresponding ones in Chen et al. (Proc Am Math Soc 128:3231–3240, 2000), Chen et al. (J Math Anal Appl 373:102–110, 2011), Chen et al. (Ann Acad Sci Fenn Math 36:567–576, 2011). Then, we study the Schwarz-Pick Lemma and the Landau-Bloch theorem for mappings in harmonic Bergman spaces in the unit ball $\mathbb B ^{n}$ of $\mathbb C ^{n}$ . The obtained results are generalizations of the corresponding ones in Chen and Gauthier (Proc Am Math Soc 139:583–595 2011). At last, we get a characterization for mappings in harmonic Bergman spaces on $\mathbb B ^{n}$ in terms of their complex gradients.     

Coefficient characterizations and sections for some univalent functions

Let (α) denote the class of locally univalent normalized analytic functions f in the unit disk |z| < 1 satisfying the condition $Re\left( {1 + \frac{{zf''(z)}} {{f'(z)}}} \right) < 1 + \frac{\alpha } {2}for|z| < 1 $ and for some 0 < α ≤ 1. We firstly prove sharp coefficient bounds for the moduli of the Taylor coefficients a _n of f ∈ (α). Secondly, we determine the sharp bound for the Fekete-Szegö functional for functions in (α) with complex parameter λ. Thirdly, we present a convolution characterization for functions f belonging to (α) and as a consequence we obtain a number of sufficient coefficient conditions for f to belong to (α). Finally, we discuss the close-to-convexity and starlikeness of partial sums of f ∈ (α). In particular, each partial sum s _n (z) of f ∈ (1) is starlike in the disk |z| ≤ 1/2 for n ≥ 11. Moreover, for f ∈ (1), we also have Re(s′ _n (z)) > 0 in |z| ≤ 1/2 for n ≥ 11.     

Highly efficient organic indolocarbazole dye in different acceptor units for optoelectronic applications—a first principle study

A series of novel organic dyes (ICZA1, ICZA2, ICZA3, ICZA4) with D-π-A structural configuration incorporating indolo[3,2,1-jk]carbazole moiety as donor (D) unit, thiophene as π-linker and 2-cyanoacrylic acid as acceptor unit were investigated using density functional theory (DFT) and time-dependent DFT (TD-DFT) methods. Indolo[3,2,1-jk]carbazole-based D-π-A dyes composed of different acceptor groups were designed. By modulating acceptor unit, the efficiency of D-π-A dye-based dye-sensitized solar cells (DSSCs) can be further improved. In the present work, four novel push-pull organic dyes only differing in electron acceptor, have been designed based on the experimental literature value of IC-2. In order to further improve the light harvesting capability of indolo[3,2,1-jk]carbazole dyes, the acceptor influence on the dye performance were examined. The NLO property of the designed dye molecules can be derived as polarizability and hyperpolarizability. The calculated value of ICZA2 dye is the best candidate for NLO properties. Furthermore, the designed organic dyes exhibit good photovoltaic performance of charge transfer characteristics, driving force of electron injection, dye regeneration, global reactivity, and light harvesting efficiency (LHE). From the calculated value of ICZA4 dye, it has been identified as a good candidate for DSSCs applications. Finally, it is concluded that the both ICZA2 and ICZA4 dyes theoretically agrees well with the experimental value of IC-2 dye. Hence, the dyes ICZA2 and ICZA4 can serve as an excellent electron withdrawing groups for NLO and DSSCs applications.     

Geometric Properties of Generalized Hypergeometric Functions

Let denote the generalized hypergeometric function where no denominator parameter can be zero or a negative integer and (a,n) denotes the ascending factorial notation. Ponnusamy and Vuorinen raised the problem of finding conditions on the parameters a_j > 0, b_j > 0 so that the function is univalent in . The main aim of this paper is to discuss this problem in detail for the case q = 2.     

Stereoselective synthesis of 3-spiro-α-methylene-γ-butyrolactone oxindoles from Morita-Baylis-Hillman adducts of isatin

A concise stereoselective synthesis of 3-spiro-α-methylene-γ-butyrolactone oxindoles from Morita-Baylis-Hillman adducts of isatin in excellent yield has been achieved following a three-step reaction sequences viz. (1) Isomerisation of the Morita-Baylis-Hillman adducts of isatin with trimethyl orthoformate and montmorillonite K10 clay catalyst, (2) a second Morita-Baylis-Hillman reaction with formaldehyde, and (3) an acid catalysed lactonization. The structure and stereochemistry of the products were assigned by X-ray crystallographic and NMR spectroscopic studies. Formation and mechanism of the minor product spirofuran oxindoles and a one-pot base promoted second Morita-Baylis-Hillman adduct formation-lactonization reaction have also been achieved.