On an Elliptical Trust-Region Procedure for Ill-Posed Nonlinear Least-Squares Problems

In this paper, we address the stable numerical solution of ill-posed nonlinear least-squares problems with small residual. We propose an elliptical trust-region reformulation of a Levenberg–Marquardt procedure. Thanks to an appropriate choice of the trust-region radius, the proposed procedure guarantees an automatic choice of the free regularization parameters that, together with a suitable stopping criterion, ensures regularizing properties to the method. Specifically, the proposed procedure generates a sequence that even in case of noisy data has the potential to approach a solution of the unperturbed problem. The case of constrained problems is considered, too. The effectiveness of the procedure is shown on several examples of ill-posed least-squares problems.     

A Sharp Upper Bound for the¶Torsional Rigidity of Rods¶by Means of Web Functions

Using web functions, we approximate the Dirichlet integral which represents the torsional rigidity of a cylindrical rod with planar convex cross-section Ω. To this end, we use a suitably defined piercing function, which enables us to obtain bounds for both the approximate and the exact value of the torsional rigidity. When Ω varies, we show that the ratio between these two values is always larger than ¾; we prove that this is a sharp lower bound and that it is not attained. Several extremal cases are also analyzed and studied by numerical methods.     

Wide Oscillation Finite Time Blow Up for Solutions to Nonlinear Fourth Order Differential Equations

We give sufficient conditions for local solutions to some fourth order semilinear ordinary differential equations to blow up in finite time with wide oscillations, a phenomenon not visible for lower order equations. The result is then applied to several classes of semilinear partial differential equations in order to characterize the blow up of solutions including, in particular, its applications to a suspension bridge model. We also give numerical results which describe this oscillating blow up and allow us to suggest several open problems and to formulate some related conjectures.     

A marching-on in time meshless kernel based solver for full-wave electromagnetic simulation

A meshless particle method based on an unconditionally stable time domain numerical scheme, oriented to electromagnetic transient simulations, is presented. The proposed scheme improves the smoothed particle electromagnetics method, already developed by the authors. The time stepping is approached by using the alternating directions implicit finite difference scheme, in a leapfrog way. The proposed formulation is used in order to efficiently overcome the stability relation constraint of explicit schemes. In fact, due to this constraint, large time steps cannot be used with small space steps and vice-versa. The same stability relation holds when the meshless formulation is applied together with an explicit finite difference scheme accounted for the time stepping. The computational tool is assessed and first simulation results are compared and discussed in order to validate the proposed approach.     

Preferential sites for InAsP/InP quantum wire nucleation using molecular dynamics

In this paper, stress fields at the surface of the capping layer of self-assembled InAsP quantum wires grown on an InP (001) substrate have been determined from atomistic models using molecular dynamics and Stillinger-Weber potentials. To carry out these calculations, the quantum wire compositional distribution was extracted from previous works, where the As and P distributions were determined by electron energy loss spectroscopy and high-resolution aberration-corrected Z-contrast imaging. Preferential sites for the nucleation of wires on the surface of the capping layer were studied and compared with (i) previous simulations using finite element analysis to solve anisotropic elastic theory equations and (ii) experimentally measured locations of stacked wires. Preferential nucleation sites of stacked wires were determined by the maximum stress location at the MD model surface in good agreement with experimental results and those derived from finite element analysis. This indicates that MD simulations based on empirical potentials provide a suitable and flexible tool to study strain dependent atom processes.     

A Schiff base expanded porphyrin macrocycle that acts as a versatile binucleating ligand for late first-row transition metals

The coordination chemistry of the Schiff base polypyrrolic octaaza macrocycle 1 toward late first-row transition metals was investigated. Binuclear complexes with the divalent cations Ni(II), Cu(II), and Zn(II) and with the monovalent cation Cu(I) were prepared and characterized. Air oxidation of the Cu(I) ions in the latter complex to their divalent oxidation state resulted in a change in the coordination mode relative to the macrocycle.     

Acetone powder from dormant seeds of Ricinus communis L

The influence of several factors on the hydrolytic activity of lipase, present in the acetone powder from dormant castor seeds (Ricinus communis) was evaluated. The enzyme showed a marked specificity for short-chain substrates. The best reaction conditions were an acid medium, Triton X-100 as the emulsifying agent and a temperature of 30 degrees C. The lipase activity of the acetone powder of different castor oil genotypes showed great variability and storage stability of up to 90%. The toxicology analysis of the acetone powder from genotype Nordestina BRS 149 showed a higher ricin (toxic component) content, a lower 2S albumin (allergenic compound) content, and similar allergenic potential compared with untreated seeds.     

Photochemistry of Hantzsch 1,4-dihydropyridines and pyridines

The photochemistry of some Hantzsch 4-phenyl-1,4-dihydropyridines bearing a substituent on the phenyl ring (the three isomeric chloro derivatives and the 4′-nitro derivative) has been studied. All of these compounds underwent inefficient aromatization to the corresponding pyridines (quantum yield <10⁻⁴ at 366 nm, <10⁻² at 254 nm). This process is scarcely affected by molecular oxygen and is initiated by proton transfer (from C₄-H), probably to the solvent, from the excited singlet. In turn, the thus formed pyridines were photoreactive with comparable or higher efficiency. Thus, the 4-(3′-chlorophenyl) and 4-(4′-chlorophenyl) Hantzsch pyridines underwent positional rearrangement to form two isomers each. The reaction occurs via Dewar benzene--prismane path. In the case of the minor isomer a further 1,3-shift take place at the Dewar benzene level. The 4-(2′-chlorophenyl) derivative underwent C-Cl bond homolysis, which led to cyclization of the phenyl group onto one of the ester groups forming a pyrane ring.     

Mechanism insights into an unexpected isomerisation reaction observed during conversion of N-benzyl piperazinones to corresponding N-benzyl thio-piperazinones

An interesting and surprising rearrangement was observed during the reaction of 4-N-benzyl piperazinone derivatives with Lawesson’s reagent as a thionating agent. Investigation into the possible mechanism responsible for these results is reported herein.