The Synthesis of Some Fused Pyrazolo‐1,4‐Naphthoquinones

New fused pyrazolo‐1,4‐naphthoquinones were prepared from the reaction of hydrazines with 6‐(4‐methyl‐3‐pentenyl)‐1,4‐naphthoquinone. The reaction was extended to hydroxylamine to afford the corresponding isoxazolo‐1,4‐napthoquinone compound.     

An easy route to pentacyclic terpenylquinones

Cyclisation of terpenylnaphthohydroquinone derivatives or terpenylquinone cycloadducts, obtained from methyl myrcecommunate, was performed in the presence of HI, I₂ or BF₃·OEt₂ and provides efficient synthetic strategies for the preparation of pentacyclic terpenylquinones.     

Local Estimates for Minimizers of Some Convex Integral Functional of the Gradient and the Strong Maximum Principle

We consider a class of convex integral functionals with lagrangeans depending only on the gradient and satisfying a generalized symmetry assumption, which includes as a particular case the rotational symmetry. Adapting the method by A. Cellina we obtain a kind of local estimates for minimizers in the respective variational problems, which is applied then to deduce some versions of the Strong Maximum Principle in the variational setting.     

One-pot methodology for conversion of o-halogen nitrobenzenes to benzofuroxans

Reaction of o-halonitrobenzenes with sodium azide under reflux of DMF/H₂O gives benzofuroxans in one step in moderate to good yields. This is a faster methodology compared to the conventional procedure involving the preparation and subsequent pyrolysis of o-nitrophenyl azides. For comparison, the reaction was also performed under phase-transfer catalysis.     

Realization of 2D convolutional codes of rate \frac{1}{n} by separable Roesser models

In this paper, two-dimensional convolutional codes constituted by sequences in $(\mathbb F ^n)^{\mathbb{Z }^{2}}$ where $\mathbb F $ is a finite field, are considered. In particular, we restrict to codes with rate $\frac{1}{n}$ and we investigate the problem of minimal dimension for realizations of such codes by separable Roesser models. The encoders which allow to obtain such minimal realizations, called R-minimal encoders, are characterized.     

L 2-Harmonic 1-Forms on Submanifolds with Finite Total Curvature

Let $x:M^{m}\to\bar{M}$ , m≥3, be an isometric immersion of a complete noncompact manifold M in a complete simply connected manifold $\bar{M}$ with sectional curvature satisfying $-k^{2}\leq K_{\bar{M}}\leq0$ , for some constant k. Assume that the immersion has finite total curvature in the sense that the traceless second fundamental form has finite L ^m -norm. If $K_{\bar{M}}\not\equiv0$ , assume further that the first eigenvalue of the Laplacian of M is bounded from below by a suitable constant. We prove that the space of the L ² harmonic 1-forms on M has finite dimension. Moreover, there exists a constant Λ>0, explicitly computed, such that if the total curvature is bounded from above by Λ then there are no nontrivial L ²-harmonic 1-forms on M.     

On the optimal control of a class of non-Newtonian fluids

We consider optimal control problems of systems governed by stationary, incompressible generalized Navier–Stokes equations with shear dependent viscosity in a two-dimensional or three-dimensional domain. We study a general class of viscosity functions with shear-thinning and shear-thickening behavior. We prove an existence result for such class of optimal control problems.