Synthesis and X-ray Crystal Structures of Two Luminescent Imidazopyridinium Derivatives from the Corresponding N-(aryl)-Pyridine-2-aldimines

Syntheses and X-ray structural characterizations of two new luminescent imidazopyridinium derivatives, 2-(phenyl)-N(3)-(4(methyl)phenyl)-imidazo[1,5a] pyridinium perchlorate (1) and 2-(pyridyl)-N(3)-(4-(chloro)phenyl)-imidazo[1,5a] pyridinium perchlorate (2) are reported. The compounds are prepared in one step from N-(4-(methyl)phenyl) pyridine-2-aldimine and N-(4-(chloro)phenyl) pyridine-2-aldimine respectively in a transformation mediated by Mn(OAc)₂-KMnO₄ mixture. It is found that the molecular structures of the two compounds are similar. In the solid state, 1 forms a three-dimensional network through a series of hydrogen bonds between the cations and anions in the lattice while 2 forms a similar but less extensively linked network. The substitution of hydrogen at the 2-position of the imidazopyridinium ring by phenyl or 2-(pyridyl) affects the nature of their first excited states as detected by changes in their emission and absorption spectra.     

Solvatoemissive dual fluorescence of N-(pyridylmethyl)-3-nitro-1,8-naphthalimides

Solvatoemissive dual fluorescence emission observed in the three positional isomers of N-(n-pyridylmethyl)-3-nitro-1,8-naphthalimide [n?=?2 (1), 3 (2), 4 (3)] are described. Dual fluorescence emission in this class of compounds occurs from the excited states with extended conjugation via π-stacking interactions. The crystal structure of the compound 1 and the chloride salt of 2 were determined. The compound 1 forms dimeric assemblies through π-stacking interactions. Whereas the structure of the chloride salt of 2 is composed of dimeric assemblies of the cationic part which hold cyclic hydrated anionic assemblies through weak C-H^…Cl interactions. Anionic hydrated assemblies between water and chloride ions have cyclic tetrameric structure through O-H^…Cl interactions.     

Cerium Catalyzed Michael Addition of 1,3-Dicarbonyl Compounds Under Microwave Irradiation

Cerium chloride heptahydrate proves to be an efficient catalyst for Michael addition of 1,3-dicarbonyl compounds, through a simple solvent free reaction under microwave irradiations.     

Synthesis, spectroscopy and redox properties of mononuclear manganese(II) and manganese(IV) complexes with N-(aryl)-pyridine-2-aldimine (L) and its amide derivatives. X-ray structural characterization of [Mn(MeL)2(NCS)2] (MeL = N-(4-methylphenyl)-pyridine-2-aldimine)

A series of mononuclear Mn^II and Mn^IV complexes of general formulae [MnL₂(NCS)₂] (1a–1d) and [Mn(L)₂(NCS)₂] (2a–2c) have been prepared where L are Schiff bases obtained by the condensation of pyridine-2-aldehyde with para-alkyl-substituted aniline, and L are the corresponding amide ligands. The room temperature magnetic susceptibility data of (1a–1d) indicate that Mn^II is in a high spin state. The cyclic voltammograms of (1a–1d) exhibit a one-electron quasi-reversible Mn^IIMn^III oxidation. A linear correlation has been found when E⁰[Mn^III/Mn^II] is plotted against Hammett _p parameters. X-ray crystallographic data of (1b) shows that the central Mn^II ion adopts a distorted octahedral geometry with six different Mn–N distances. Upon oxidation of Mn^II complexes (1b–1d) by H₂O₂, the corresponding Mn^IV complexes (2a–2c) were obtained, and the Schiff base ligands were oxidized to the corresponding amides. The lowest energy LMCT bands of these Mn^IV complexes correlate linearly with Hammett _p parameters. The redox behavior of the Mn^IV complexes has been investigated by cyclic voltammetry. E.p.r. spectra of the Mn^II and Mn^IV complexes are also reported.     

Nörlund and Riesz mean of sequences of fuzzy real numbers

In this article we study some properties of the Nörlund and Riesz mean of sequences of fuzzy real numbers. We establish necessary and sufficient conditions for the Nörlund and Riesz means to transform convergent sequences of fuzzy numbers into convergent sequences of fuzzy numbers with limit preserving.     

Effect of two photon absorption on nonlinear pulse propagation in gain medium

The effects of two photon absorption (TPA) and gain dispersion on soliton propagation in amplified medium are investigated. For finite gain bandwidth, the effect of gain dispersion becomes significant along with TPA and is treated as perturbation in fundamental soliton propagation. Including these perturbing effects an analytical expression of integrated intensity is formulated applying a completely new methodology by adopting Rayleigh’s dissipation function in the framework of variational approach. With classical analogy, the Euler–Lagrange equation in non-conservative system is used to solve the problem analytically. In order to justify the analytical prediction a numerical verification is made by split-step beam propagation method following Ginzburg–Landau equation.     

Modular relations for the nonic analogues of the Rogers-Ramanujan functions with applications to partitions

We define the nonic Rogers-Ramanujan-type functions D(q), E(q) and F(q) and establish several modular relations involving these functions, which are analogous to Ramanujan's well known forty identities for the Rogers-Ramanujan functions. We also extract partition theoretic results from some of these relations.     

Matching coefficients in the series expansions of certain q-products and their reciprocals

The Ramanujan Journal - We show that the series expansions of certain q-products have matching coefficients with their reciprocals. Several of the results are associated to Ramanujan’s...     

Ramanujan's Eisenstein series and new hypergeometric-like series for

Using hypergeometric identities and certain representations for Eisenstein series, we uniformly derive several new series representations for 1/π².