Some Inequalities for Derivatives of Trigonometric and Algebraic Polynomials

We investigate inequalities for derivatives of trigonometric and algebraic polynomials in weighted L ^P spaces with weights satisfying the Muckenhoupt A _p condition. The proofs are based on an identity of Balázs and Kilgore [1] for derivatives of trigonometric polynomials. Also an inequality of Brudnyi in terms of rth order moduli of continuity ω_r will be given. We are able to give values to the constants in the inequalities.     

Artificial genetic systems: exploiting the "aromaticity" formalism to improve the tautomeric ratio for isoguanosine derivatives

The tautomerism of 2'-deoxy-7-deaza-isoguanosine (2) was studied and compared to that of 2'-deoxyisoguanosine (1). The fixed (1)N-methyl (8) and O-methyl (4) derivatives were synthesized to represent the pure extremes of each tautomer. The replacement of the imidazole ring in 1 with a pyrrole ring in 2 makes the keto form in the latter more favored by 2 orders of magnitude (K(TAUT) for 2 approximately 10(3), as opposed to K(TAUT) for 1 approximately 10).     

Femtosecond excitation energy transport in triarylamine dendrimers

The search for a model that can be used to describe the optical excitation migration in dendrimers has attracted great attention. In most cases in a dendrimer the conjugation is disrupted at the branching point; however, the excitation is delocalized. The strength of interactions among neighboring chromophores plays a key role in determining the energy migration mechanism. Conversely, having many identical chromophores held tightly together in an ordered macromolecular architecture will allow for many dipoles to be accessible for optical excitation. Therefore, the relative orientation of dipoles will be important in determining the mechanism of energy migration. Here we report the synthesis and photo-physical investigation of triarylamine-based dendrimers. Two important synthetic steps were utilized in the synthesis. First, we employed diphenylmethyl protective groups on the amines to assist in deprotective hydrogenolysis of the larger structures. Second, highly active catalysts for formation of both di- and triarylamines that are based on a 1:1 ratio of P(t-Bu)3 and Pd(dba)2 improved reaction yields of the C-N bond formation and decreased reaction times The energy migration processes in the dendrimers were investigated utilizing ultrafast time-resolved fluorescence anisotropy measurements. The fluorescence anisotropy of all three dendrimers decayed to a residual value within approximately 100 fs. This fluorescence anisotropy decay showed a general trend in decreasing with increasing dendrimer generation. The residual anisotropy value also showed a gradual decrease with an increase in the dendrimer generation. This fast energy depolarization is discussed through a coherent excitonic mechanism among dipoles oriented in different directions. We believe that the formation of coherent domains leads to fast energy migration extending over a large part of the dendrimer.     

Critical surface of the ising model with first-neighbor,second-neighbor,and four-spin interactions

Exact values are obtained for the slopesK ₁ ^c (0, 0)/K ₂,K ₁ ^c (0, 0)/K ₄ of the critical surface of paramagnetic-ferromagnetic transitionsK ₁ ^c (K ₂,K ₄) for the two-dimensional Ising model on a square lattice with first-neighbor, second-neighbor, and four-spin couplingsK ₁,K ₂, andK ₄, respectively. The results are obtained using universality arguments to relate the slopes to known spin-spin correlation functions forK ₂=K ₄=0. The equivalence of different expressions for the slopes in terms of correlation functions yields sum rules for the divergent part of certain sums over the second-neighbor and four-spin energy-energy correlation functions.     

Radical hydroformylation and hydrogenation of cyclopropenes with HCo(CO)4 and HMn(CO)5

The results of a study of the reactions of HCo(CO)₄ and HMn(CO)₅ with a variety of a substituted cyclopropenes are consistent with the formation of the intermediate caged radical pairs; recombination in the cage of the radical pair leads to hydroformylation, and cage escape leads to hydrogenation. Steric factors play an important role in determining rates as well as the stereochemistry of the products.     

Deprotonated and non-deprotonated cobalt(II) complexes of the bis-amide tetradentate ligand N,N′-(dipicolyl)-1,8-naphthylene diamine. Three different modes of coordination by the ligand

The preparation and some properties of the cobalt(II) complexes Co(LH₂)Cl₂·2H₂O, Co(LH₂(NCS)₂ and CoL·H₂O (whereLH₂=N,N-(dipicolyl)-1,8-naphthylenediamine) are reported. On the basis of magnetic moments, visible reflectance and IR data, the structure is proposed to be pseudo-octahedral for Co(LH₂)Cl₂·2 H₂O, pseudo-tetrahedral for Co(LH₂)(NCS)₂ and square planar for CoL·H₂O.

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Deprotonierte und Nicht-deprotonierte Co(II)-Komplexe des vierzähnigen Bisamid-Liganden N,N-(Dipicolyl)-1,8-naphthyldiamin. Drei verschiedene Koordinationstypen

Zusammenfassung Es werden die Darstellung und einige Eigenschaften der Kobalt(II)-Komplexe Co(LH₂)Cl₂·2 H₂O, Co(LH₂)(NCS)₂ und CoL·H₂O [LH₂=N,N-(dipicolyl)-1,8-naphthylendiamin] diskutiert. Auf der Grundlage von magnetischen Momenten, von Daten der sichtbaren Reflektions-und IR-Spektren wird eine pseudooctaedrische Struktur für Co(LH₂)Cl₂·2H₂O, eine pseudotetraedrische für Co(LH₂)(NCS)₂ und eine planar-quadratische für CoL·H₂O vorgeschlagen.

     

Ultrafast fluorescence investigation of excitation energy transfer in different dendritic core branched structures

The mechanism of energy transport in branching structures is suggestively related to the geometry of the multichromophore architecture. In organic conjugated dendrimers, both incoherent (hopping) and coherent energy transfer processes have been observed from different dendritic architectures with different building blocks. In this communication, we report the investigation of three fundamental dendritic architectures (G0) with the same attached chromophores, but with different core atoms, C, N, and P. The synthesis of a phosphorus-containing G0 system with distyrylbenzene chromophores is provided. These three systems provide a comparison by which the relative interaction of branching chromophores can be compared on the basis of their different branching centers. Ultrafast fluorescence anisotropy measurements provide a dual measure of the geometry of the chromophores around the different central units as well as the strength of the interactions among chromophores. The nitrogen-cored system appeared to have both the strongest coupling of chromophore excitation as well as the most planar geometry of the three. Interestingly, the phosphorus system appeared to have the least planar geometry, and its interaction strength was found to be stronger than that observed for the carbon system. These results provide a comparison of the energy migration dynamics of the most common and new dendritic architectures with applications for light emission and light harvesting.