An Organotin(IV) Carboxylate Based on Amide Carboxylic Acid: Synthesis,Crystal Structure,and Characterizations

An organotin carboxylate based on amide carboxylic acid (Ph₃Sn)(L)·C₇H₈ (complex 1 ) (HL = 3‐(1,3‐dioxo‐1H,3H‐benzo[de]isoquinolin‐2‐yl)propanoic acid) has been synthesized and characterized by elemental analyses (IR, ¹H, ¹³C, and ¹¹⁹Sn NMR), UV–visible spectroscopies, and X‐ray crystallography diffraction analysis. Complex 1 is a monomeric triphenyltin carboxylate. Ligand HL in complex 1 adopts unidentate coordination mode. Intermolecular hydrogen bonds and C H···π interactions help complex 1 to build fascinating one‐dimensional and two‐dimensional structures, which are discussed in detail.     

Stepwise fusion of porphyrin β,β'-pyrrolic positions to imidazole rings

A strategy for the stepwise annulation of pyrrolic rings of a porphyrin to imidazole rings is presented. Mono(imidazole), Janus and corner bis(imidazole), T-shaped tris(imidazole), and tetrakis(imidazole) porphyrins have been synthesized and characterized.     

On S-duo rings

A unital left R-module R M is said to have property (S) if every surjective endomorphism of R M is an automorphism, the ring R is called left (right) S-ring if every left (right) R-module with property (S) is Noetherian, R is called S-ring if it is both a left and a right S-ring. In this note we show that a duo ring is a left S-ring if and only if it is left Artinian left principal ideal ring. To do this we shall construct on every non distributive Artinian local ring with radical square zero a non-finitely generated module with property (S). And we give an example of left duo left Artinian left principal ideal ring which is not a left S-ring, showing the necessity of the ring to be duo in the above result.     

On the exponential behaviour of stochastic evolution equations for non-Newtonian fluids

We investigate the exponential long-time behaviour of the stochastic evolution equations describing the motion of a non-Newtonian fluids excited by multiplicative noise. Some results on the exponential convergence in mean square and with probability one of the weak probabilistic solution to the stationary solutions are given. We also prove an interesting result related to the stabilization of these stochastic evolution equations.     

Luminescence properties of pHEMA-TiO2 gels based hybrids materials

Photoluminescence (PL) of photochromic pHEMA-TiO₂ gels-based hybrids was studied by means of time- and energy-resolved spectroscopy at temperatures between 300 K and 10 K. The PL band at 485 nm is assigned to S0←T1 transition of methoxyphenol (organic molecule added to the commercial monomer hydroxyethyl methacrylate, HEMA and used as an inhibitor of spontaneous polymerisation) in the polymer environment, while the PL band at 600 nm is assigned to the self-trapped exciton onto octahedral TiO₆ site of the inorganic component. The mechanisms of the excited states population are discussed. In particular it is shown that both singlet-triplet energy transfer in methoxyphenol and methoxyphenol–TiO₂ charge transfer are strongly affected by the material composition and temperature. The hypothesis about the photoexcited holes annihilation with the trapped electrons is confirmed to be one of main mechanisms limiting the Ti³⁺ centres concentration.     

Graph operations characterizing rank-width

Graph complexity measures such as tree-width, clique-width and rank-width are important because they yield Fixed Parameter Tractable algorithms. These algorithms are based on hierarchical decompositions of the considered graphs, and on boundedness conditions on the graph operations that, more or less explicitly, recombine the components of decompositions into larger graphs. Rank-width is defined in a combinatorial way, based on a tree, and not in terms of graph operations. We define operations on graphs that characterize rank-width and help for the construction of Fixed Parameter Tractable algorithms, especially for problems specified in monadic second-order logic.     

An Analytical Study of Boundary Layer Flows on a Continuous Stretching Surface

In this paper the momentum and heat transfer characteristics for a self-similarity boundary layer on exponentially stretching surface modeled by a system of nonlinear differential equations is studied. The system is solved using the Homotopy Analysis Method (HAM), which yields an analytic solution in the form of a rapidly convergent infinite series with easily computable terms. Homotopy analysis method contains the auxiliary parameter ℏ, which provides us with a simple way to adjust and control the convergence region of solution series. By suitable choice of the auxiliary parameter ℏ, reasonable solutions for large modulus can be obtained.     

Semiparametric estimation of the link function in binary-choice single-index models

We propose a new, easy to implement, semiparametric estimator for binary-choice single-index models which uses parametric information in the form of a known link (probability) function and nonparametrically corrects it. Asymptotic properties are derived and the finite sample performance of the proposed estimator is compared to those of the parametric probit and semiparametric single-index model estimators of Ichimura (J Econ 58:71–120, 1993) and Klein and Spady (Econometrica 61:387–421, 1993). Results indicate that if the parametric start is correct, the proposed estimator achieves significant bias reduction and efficiency gains compared to Ichimura (1993) and Klein and Spady (1993). Interestingly, the proposed estimator still achieves significant bias reduction and efficiency gains even if the parametric start is not correct.     

Asymptotic behavior of solutions of stochastic evolution equations for second grade fluids

In this Note we show that under suitable conditions on the data we can construct a sequence of solutions of the stochastic second grade fluid that converges to the probabilistic strong solution of the stochastic Navier–Stokes equations when the stress modulus α tends to zero.     

Uniqueness results for Stokes cascade systems and application to insensitizing controls

This Note is devoted to some insensitizing control problems for the Stokes system with a reduced number of controls. We give some ε-insensitization results with external unidirectional forces in different geometric configurations. We also provide a negative result of insensitization for the Stokes system in some 2-D manifold without boundary with one scalar control.