Vibrational spectra and structures of H2O-NO, HDO-NO, and D2O-NO complexes. An IR matrix isolation and DFT study

The IR spectra of H2O+NO, HDO+NO, and D2O+NO, isolated in solid neon at low temperature have been investigated. Concentration effects and detailed vibrational analysis of deuterated and partially deuterated species allowed identification of three 1:1 HDO-NO species, two 1:1 D2O-NO species, and only one 1:1 H2O-NO complex. From comparison between the experimental spectra and the results of DFT calculations, it appeared that two different types of weakly bound complexes between water and nitric oxide can be formed in a neon matrix. The first species is a 1:1 complex where bonding occurs between water hydrogen and nitric oxide nitrogen, in which OH-N and OD-N intermolecular bonds are engaged. For this complex only DOD-NO, HOD-NO, and DOH-NO isotopic species have been experimentally detected and no IR bands of HOH-NO were observed. This result could be explained by the fact that the dissociation energy of HOH-NO is lower than those of DOD-NO, HOD-NO and DOH-NO. For the second detected 1:1 H2O-NO complex and its isotopic variants, the H2O-NO potential surface was explored systematically at the B3LYP level, but no stable species corresponding to the complex could be calculated. The structure of the second observed 1:1 H2O-NO complex results from columbic attractions between water and nitric oxide and could be stabilized only in matrix, probably by interaction between NO, water and (Ne)n.     

Frequency polygons for continuous random fields

We study the frequency polygon investigated by Scott (J Am Stat Assoc 80: 348–354, 1985) as a nonparametric density estimate for a continuous and stationary real random field \({\left( X_{\mathbf{t}},\mathbf{t}\in\mathbb{R}^{N}\right)}\). We establish the asymptotic expressions for the integrated pointwise squared bias and the integrated pointwise squared variance of the estimate when the field is observed over a rectangular domain of \({\mathbb{R}^{N}}\). Under mild mixing conditions, we show that the estimate achieves the same rate of convergence to zero of the integrated mean squared error as kernel estimators and it can also attain the optimal uniform strong rate of convergence \({\left(\widehat{\mathbf{T}}^{-1} \log \widehat{\mathbf{T}}\right)^{1/3}}\) for appropriate choices of the bin widths.     

Isometric Equivalence of Integration Operators

We are interested in the isometric equivalence problem for the Cesàro operator C(f) (z) = \frac1z ò₀^zf(x) \frac11-xd x{C(f) (z) =\frac{1}{z} \int_{0}^{z}f(\xi) \frac{1}{1-\xi}d \xi} and an operator T_g(f)(z)=\frac1zò₀^zf(x) g^￠(x) d x{T_{g}(f)(z)=\frac{1}{z}\int_{0}^{z}f(\xi) g^{\prime}(\xi) d \xi}, where g is an analytic function on the disc, on the Hardy and Bergman spaces. Then we generalize this to the isometric equivalence problem of two operators T_g1{T_{g_{1}}} and T_g2{T_{g_{2}}} on the Hardy space and Bergman space. We show that the operators T_g1{T_{g_{1}}} and T_g2{T_{g_{2}}} satisfy T_g1U₁=U₂T_g2{T_{g_{1}}U_{1}=U_{2}T_{g_{2}}} on H ^p , 1 ≤ p < ∞, p ≠ 2 if and only if g₂(z) = lg₁(e^iqz){g_{2}(z) =\lambda g_{1}(e^{i\theta}z) }, where λ is a modulus one constant and U _i , i = 1, 2 are surjective isometries of the Hardy Space. This is analogous to the Campbell-Wright result on isometrically equivalence of composition operators on the Hardy space.     

Bounded-degree polyhedronization of point sets

In 1994 Grünbaum showed that, given a point set S in ${\mathbb{R}}^3$, it is always possible to construct a polyhedron whose vertices are exactly S. Such a polyhedron is called a polyhedronization of S. Agarwal et al. extended this work in 2008 by showing that there always exists a polyhedronization that can be decomposed into a union of tetrahedra (tetrahedralizable). In the same work they introduced the notion of a serpentine polyhedronization for which the dual of its tetrahedralization is a chain. In this work we present a randomized algorithm running in $O(n{\log }^{6}n)$ expected time which constructs a serpentine polyhedronization that has vertices with degree at most 7, answering an open question by Agarwal et al.     

Kinetic study on effect of novel cationic dimeric surfactants for the cleavage of carboxylate ester

Kinetic study has been performed to understand the reactivity of novel cationic gemini surfactants viz. alkanediyl‐α,ω‐bis(hydroxyethylmethylhexadecylammonium bromide) C₁₆‐s‐C₁₆ MEA, 2Br^? (where s = 4, 6) in the cleavage of p‐nitrophenyl benzoate (PNPB). Novel cationic gemini C₁₆‐s‐C₁₆ MEA, 2Br^? surfactants are efficient in promoting PNPB cleavage in presence of butane 2,3‐dione monoximate and N‐phenylbenzohydroxamate ions. Model calculation revealed that the higher catalytic effect of ethanol moiety of gemini surfactants (C₁₆H₃₃N⁺ C₂H₄OH CH₃ (CH₂)_S N⁺ C₂H₄OH CH₃C₁₆H₃₃, 2Br^?, s = 4, 6) is due to their higher binding capacity toward substrate. This is in line with finding that binding constants for novel series of cationic gemini surfactants are higher than conventional cationic gemini (C₁₆H₃₃N⁺(CH₃)₂(CH₂)_SN⁺(CH₃)₂C₁₆H₃₃, 2Br^?, s = 10, 12), cetyldimethylethanolammonium bromide and zwitterionic surfactants, i.e. C_nH_2n+1N⁺Me₂ (CH₂)₃ SO₃^? (n = 10; SB3‐10). The fitting of kinetic data was analyzed by the pseudophase model. Copyright © 2013 John Wiley & Sons, Ltd.     

On Bernstein Algebras Satisfying Chain Conditions

Our aim in this article is to study Noetherian and Artinian Bernstein algebras. We show that for Bernstein algebras which are either Jordan or nuclear, each of the Noetherian and Artinian conditions implies finite dimensionality. This result fails for general Noetherian or Artinian Bernstein algebras. We also investigate the relationships between the three finiteness conditions: Noetherian, Artinian, and finitely generated. Especially, we prove that Noetherian Bernstein algebras are finitely generated.     

Design,Synthesis, Molecular Modeling Study,and Antimicrobial Activity of Some Novel Pyrano[2,3‐b]pyridine and Pyrrolo[2,3‐b]pyrano[2.3‐d]pyridine Derivatives

Novel derivatives of pyrano[2,3‐b]pyridine and pyrrolo[2,3‐b]pyrano[2.3‐d]pyridine were prepared, and their structures were elucidated by spectral and elemental analyses. The newly prepared candidates were evaluated for their antimicrobial activity against Candida sp., Aspergillus multi, Aspergillus niger, Escherichia coli, and Staphylococcus aureus. All the tested compounds revealed potent to moderate activity toward all tested microorganisms; especially, candidate 10 showed comparable antifungal activity as that showed by the standard drug ketoconazole toward Candida sp., and ethyl 4‐methyl‐1,7,8,9‐tetrahydropyrano[2,3‐b]pyrrolo[2,3‐d]pyridine‐3‐carboxylate ( 12 ) was the most active compound against all the tested bacteria. Furthermore, the newly synthesized compounds are subjected to molecular docking study for the inhibition of the enzyme L‐glutamine: D‐fructose‐6‐phosphate amidotransferase [GlcN‐6‐P], which is a new target for antimicrobials to explain action mode of these target compounds as leads for discovering other antimicrobial agents.     

Synthesis of Bimetallic Copper‐Rich Nanoclusters Encapsulating a Linear Palladium Dihydride Unit

The structurally precise Cu‐rich hydride nanoclusters [PdCu₁₄H₂(dtc/dtp)₆(C≡CPh)₆] (dtc: di‐butyldithiocarbamate ( 1 ); dtp: di‐isopropyl dithiophosphate ( 2 )) were synthesized from the reaction of polyhydrido copper clusters [Cu₂₈H₁₅(S₂CNⁿBu₂)₁₂]⁺ or [Cu₂₀H₁₁{S₂P(OⁱPr)₂}₉] with phenyl acetylene in the presence of Pd(PPh₃)₂Cl₂. Their structures and compositions were determined by single‐crystal X‐ray diffraction and the results supported by ESI‐mass spectrometry. Hydride positions in 1 were confirmed by single‐crystal neutron diffraction. Each hydride is connected to one Pd⁰ and four Cu^I atoms in slightly distorted trigonalbipyramidal geometry. The anatomies of clusters 1 and 2 are very similar and DFT calculations allow rationalizing the interactions between the encapsulated [PdH₂]^2? unit and its Cu₁₄ bicapped icosahedral cage. As a result, Pd has the highest coordination number (14) so far recorded.     

Activation and Photoinduced Release of Alkynes on a Biomimetic Tungsten Center: The Photochemical Behavior of the W−S-Phoz System

The synthesis and structural determination of four tungsten alkyne complexes coordinated by the bio-inspired S,N-donor ligand 2-(4′,4′-dimethyloxazoline-2′-yl)thiophenolate (S-Phoz) is presented. A previously established protocol that involved the reaction of the respective alkyne with the bis-carbonyl precursor [W(CO)₂(S-Phoz)₂] was used for the complexes [W(CO)(C₂R₂)(S-Phoz)₂] (R=H, 1 a ; Me, 1 b ; Ph, 1 c ). Oxidation with pyridine-N-oxide gave the corresponding W-oxo species [WO(C₂R₂)(S-Phoz)₂] (R=H, 2 a ; Me, 2 b ; Ph, 2 c ). All W-oxo-alkyne complexes ( 2 a , b , c ) were found to be capable of alkyne release upon light irradiation to afford five-coordinate [WO(S-Phoz)₂] ( 3 ). The photoinduced release of the alkyne ligand was studied in detail by in situ ¹H NMR measurements, which revealed correlation of the photodissociation rate constant ( 2 b>2 a>2 c ) with the elongation of the alkyne C≡C bond in the molecular structures. Oxidation of [WO(S-Phoz)₂] ( 3 ) with pyridine-N-oxide yielded [WO₂(S-Phoz)₂] ( 4 ), which shows highly fluxional behavior in solution. Variable-temperature ¹H NMR spectroscopy revealed three isomeric forms with respect to the ligand arrangement versus each other. Furthermore, compound 4 rearranges to tetranuclear oxo compound [W₄O₄(μ-O)₆(S-Phoz)₄] ( 5 ) and dinuclear [{WO(μ-O)(S-Phoz)}₂] ( 6 ) over time. The latter two were identified by single-crystal X-ray diffraction analyses.