Results on L-functions and certain uniqueness questions of Gross

In this paper, we study the value distribution of L-functions in the Selberg class and concentrate on the uniqueness questions of L-functions that share one or two sets with an arbitrary meromorphic function. The results obtained in this paper improve the recent results due to Q.-Q. Yuan, X.-M. Li, and H.-X. Yi [Value distribution of L-functions and uniqueness questions of F. Gross, Lith. Math. J., 58(2):249–262, 2018] and also extend a result due to B.Q. Li [A result on value distribution of L-functions, Proc. Am. Math. Soc., 138(6):2071–2077, 2010].

     

Polarity-Induced Excited-State Intramolecular Proton Transfer (ESIPT) in a Pair of Supramolecular Isomeric Multifunctional Dynamic Metal–Organic Frameworks

A pair of supramolecular isomers of Cd^II-based MOF have been synthesized by utilizing a flexible N,N′-donor linker and a dicarboxylate with ESIPT (excited-state intramolecular proton transfer) fluorophore by varying the reaction media. One of the MOFs has a 3D four-fold interpenetrating framework with guest solvent in the structure that undergoes a solvent-dependent crystalline-to-crystalline structural transformation, which has been extensively studied by powder XRD and IR spectroscopy. The other MOF is structurally rigid in nature and has a two-fold interpenetrating structure without any guest molecules. Both the compounds show moderate CO₂ adsorption and one of them, the MOF with the four-fold interpenetrating structure, also shows moderately high H₂ adsorption. Furthermore, both the compounds show interesting luminescence behavior. In the solid state, the two compounds show single-peak spectra, whereas upon suspension of these compounds in polar solvents, the maxima split into two peaks with a large Stokes shift. On the other hand, in nonpolar solvents, only one emission maximum is observed. This solvatochromic dual-emission phenomenon is due to ESIPT, which has been extensively studied.     

Numerical simulation of shock–vortex interaction in Schardin’s problem

Shock diffraction over a two-dimensional wedge and subsequent shock–vortex interaction have been numerically simulated using the AUSM $+$ + scheme. After the passage of the incident shock over the wedge, the generated tip vortex interacts with a reflected shock. The resulting shock pattern has been captured well. It matches the existing experimental and numerical results reported in the literature. We solve the Navier–Stokes equations using high accuracy schemes and extend the existing results by focussing on the Kelvin–Helmholtz instability generated vortices which follow a spiral path to the vortex core and on their way interact with shock waves embedded within the vortex. Vortex detection algorithms have been used to visualize the spiral structure of the initial vortex and its final breakdown into a turbulent state. Plotting the dilatation field we notice a new source of diverging acoustic waves and a lambda shock at the wedge tip.     

über Kurven vom TYP (m;n) und Beispiele total m-regulärer (k,n)-Kurven

In this paper we are concerned with a special kind of subsets of finite projective planes and give some new examples of totally m-regular (k,n)-arcs.

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Herrn Professor Dr. WERNER BURAU zum 70. Geburtstag     

Nuclear magnetic resonance VI. Some quantitative applications of carbon-13 NMR spectroscopy to phenylindoles

Summary The number of carbons represented by each signal of the phenylindoles1,4, and5 is measured quantitatively by integration of their¹³C NMR spectra, recorded after adding chromium(III) acetylacetonate to the sample solutions as a paramagnetic relaxation agent. Their carbon chemical shifts are assigned unambiguously; the literature assignments of4 are confirmed. By a comparative study of the carbon chemical shifts of1,4, and5, those of2 and3 are also assigned. Theortho carbons of the phenyl group of4 resonate upfield with respect to thepara carbon. Theortho carbons of the 2- and 3-phenyl moieties of1–3 and5, however, are found to absorb downfield from the correspondingpara carbons, probably because of steric and/or electronic effects exerted by their neighbouring phenyl group.

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Kernresonanzspektroskopie, 6. Mitt. Einige quantitative Anwendungen der¹³C-NMR-Spektroskopie auf Phenylindole

Zusammenfassung Die Anzahl der durch jedes Signal der Phenylindole1,4 und5 repräsentierten Kohlenstoffatome wird durch Integration der nach Zusatz von Chrom(III)acetonylacetat als Relaxationsreagens aufgenommenen¹³C-NMR-Spektren bestimmt. Ihre chemischen Verschiebungen werden eindeutig zugeordnet; die Literaturwerte für4 werden bestätigt. Durch eine vergleichende Untersuchung der¹³C-chemischen Verschiebungen von1,4 und5 können jene von2 und3 ebenfalls zugeordnet werden. Dieortho-Kohlenstoffe der Phenylgruppe von4 sind gegenüber denpara-Kohlenstoffatomen zu höherem Feld verschoben. Für die 2- und 3-Phenyl-Substituenten von1–3 und5 kehren sich die Verhältnisse um, wahrscheinlich wegen sterischer und/oder elektronischer Effekte der benachbarten Phenylgruppe.

     

Absorption Spectrophotometric,NMR and Quantum Chemical Investigations of Ground State Non-Covalent Interactions between Fullerenes and a Designed Trihomocalix[6]arene in Solution

Ground state non-covalent interactions between a newly designed macrocyclic 1,3,5-trihomo calix[6]arene receptor, designated as 1, and the C₆₀ and C₇₀ fullerenes have been studied in toluene solutions. It was observed that the absorbances of both C₆₀ and C₇₀ solutions increased upon the addition of increasing concentrations of compound 1. Job’s method of continuous variation established 1:1 stoichiometry for these fullerene-1 complexes. The binding constant (K) data reveal that compound 1 binds to C₇₀ more strongly compared to C₆₀, i.e., K_C60-1 = 230 dm³·mol^-1K_{C60\mbox{-}\boldsymbol{1}} = 230~\mathrm{dm}^{3}{\cdot}\mathrm{mol}^{-1} and K_C70-1 = 517 dm³·mol^-1K_{C70\mbox{-}\boldsymbol{1}}= 517~\mathrm{dm}^{3}{\cdot}\mathrm{mol}^{-1}. Proton NMR analysis provides very good support for strong binding between C₇₀ and 1. Estimations of the solvent reorganization energy (R _S ) suggest that the C₇₀-1 complex is stabilized more than the corresponding C₆₀-1 complex, with R_S(C60-1) = -1.970 eVR_{S(C60\mbox{-}\boldsymbol{1})} = -1.970~\mathrm{eV} and R_S(C70-1) = -2.300 eVR_{S(C70\mbox{-}\boldsymbol{1})}= -2.300~\mathrm{eV}. Molecular mechanics force field method calculations established that the binding pattern of C₇₀ towards 1 occurs in the side-on rather than end-on orientation, and that the C₇₀-1 complex gains 5.23 kJ⋅mol⁻¹ of extra stabilization energy with this side-on geometrical arrangement.     

Experimental and theoretical investigations of solvation dynamics of ionic fluids: appropriateness of dielectric theory and the role of DC conductivity

An analysis is provided of the subnanosecond dynamic solvation of ionic liquids in particular and ionic solutions in general. It is our hypothesis that solvation relaxation in ionic fluids, in the nonglassy and nonsupercooled regimes, can be understood rather simply in terms of the dielectric spectra of the solvent. This idea is suggested by the comparison of imidazolium ionic liquids with their pure organic counterpart, butylimidazole (J. Phys. Chem. B 2004, 108, 10245-10255). It is borne out by a calculation of the solvation correlation time from frequency dependent dielectric data for the ionic liquid, ethylammonium nitrate, and for the electrolyte solution of methanol and sodium perchlorate. Very good agreement is obtained between these theoretically calculated solvation relaxation functions and those obtained from fluorescence upconversion spectroscopy. Our comparisons suggest that translational motion of ions may not be the predominant factor in short-time solvation of ionic fluids and that many tools and ideas about solvation dynamics in polar solvents can be adapted to ionic fluids.     

Synthesis, structure, and electrochemical properties of a family of 2-(arylazo)phenolate complexes of ruthenium with unusual C-C coupling and N=N cleavage

Reaction of 2-(4'-R-phenylazo)-4-methylphenols (R = OCH3, CH3, H, Cl, and NO2) with [Ru(dmso)(4)Cl2]affords a family of five ruthenium(III) complexes, containing a 2-(arylazo)phenolate ligand forming a six-membered chelate ring and a tetradentate ligand formed from two 2-(arylazo)phenols via an unusual C-C coupling linking the two ortho carbons of the phenyl rings in the arylazo fragment. A similar reaction with 2-(2'-methylphenylazo)-4-methylphenol with [Ru(dmso)(4)Cl2] has afforded a similar complex, in which one 2-(2'-methylphenylazo)-4-methylphenolate ligand is coordinated forming a six-membered chelate ring, and the other two ligands have undergone the C-C coupling reaction, and the coupled species is coordinated as a tetradentate ligand forming a five-membered N,O-chelate ring, a nine-membered N,N-chelate ring, and another five-membered chelate ring. Reaction of 2-(2',6'-dimethylphenylazo)-4-methylphenol with [Ru(dmso)(4)Cl2] has afforded a complex in which two 2-(2',6'-dimethylphenylazo)-4-methylphenols are coordinated as bidentate N,O-donors forming five- and six-membered chelate rings, while the third one has undergone cleavage across the N=N bond, and the phenolate fragment, thus generated, remains coordinated to the metal center in the iminosemiquinonate form. Structures of four selected complexes have been determined by X-ray crystallography. The first six complexes are one-electron paramagnetic and show rhombic ESR spectra. The last complex is diamagnetic and shows characteristic 1H NMR signals. All the complexes show intense charge-transfer transitions in the visible region and a Ru(III)-Ru(IV) oxidation on the positive side of SCE and a Ru(III)-Ru(II) reduction on the negative side.     

Assessing the roles of the constituents of ionic liquids in dynamic solvation: Comparison of an ionic liquid in micellar and bulk form

Dynamic solvation of the dye, coumarin 153, is compared in an ionic liquid that forms micelles in water against the bulk solvent. This provides the unprecedented opportunity of investigating the behavior of the ionic liquid in two globally different configurations. It is proposed that the imidazolium moiety is in both cases responsible for the majority of the solvation, which manifests itself in the first 100 ps. Exploiting the use of ionic liquids capable of accommodating specific structures thus provides a deeper insight into how solutes interact with these fascinating and interesting solvents (at least those that are imidazolium based) that are gaining ever increasing interest in the scientific community.     

Anion Selectivity of Metalloporphyrins in Membranes

Lipophilic Co(III) and Mn(III) complexes of 5,10,15,20-tetrakis[4-(hexyloxycarbonyl)phenyl]porphyrin act as positively charged carriers for anions and induce anion selectivities in membranes clearly deviating from the sequence of classical anion exchangers. Different anion selectivities are observed for the Co(III) and Mn(III) porphyrins.