Some generalizations of Chirka's extension theorem

In this paper, we generalize Chirka's theorem on the extension of functions holomorphic in a neighbourhood of - where is the open unit disc in and is the graph of a continuous valued function on - to higher dimensions, for certain classes of graphs 1$">. In particular, we show that Chirka's extension theorem generalizes to configurations in 1$">, involving graphs of (non-holomorphic) polynomial maps with small coefficients.

     

Vectorial Approach to Fast Correlation Attacks

A new, vectorial approach to fast correlation attacks on binary memoryless combiners is proposed. Instead of individual input sequences or their linear combinations, the new attack is targeting subsets of input sequences as a whole thus exploiting the full correlation between the chosen subset and the output sequence. In particular, the set of all the input sequences can be chosen as the target. The attack is based on a novel iterative probabilistic algorithm which is also applicable to general memoryless combiners over finite fields or finite rings. To illustrate the effectiveness of the introduced approach, experimental results obtained for random balanced combining functions are presentedMost of this work was done while he was with Rome CryptoDesign Center, Gemplus, Italy     

On the Motion of a Dynamic System with Minimal Dissipation

The motion of a holonomic scleronomic non-conservative mechanicalsystem with minimal dissipation is considered. As applicationsof the theory several problems are studied in detail.     

Polynomial approximation, local polynomial convexity, and degenerate CR singularities

We begin with the following question: given a closed disc and a complex-valued function , is the uniform algebra on generated by z and F equal to ? When F∈C¹(D), this question is complicated by the presence of points in the surface that have complex tangents. Such points are called CR singularities. Let p∈S be a CR singularity at which the order of contact of the tangent plane with S is greater than 2; i.e. a degenerate CR singularity. We provide sufficient conditions for S to be locally polynomially convex at the degenerate singularity p. This is useful because it is essential to know whether S is locally polynomially convex at a CR singularity in order to answer the initial question. To this end, we also present a general theorem on the uniform algebra generated by z and F, which we use in our investigations. This result may be of independent interest because it is applicable even to non-smooth, complex-valued F.     

Cu‐Based Nanoparticles as Emerging Environmental Catalysts

This account provides an overview of current research activities on nanoparticles containing the earth‐abundant and inexpensive element copper (Cu) and Cu‐based nanoparticles, especially in the field of environmental catalysis. The different synthetic strategies with possible modification of the chemical/ physical properties of these nanoparticles using such strategies and/or conditions to improve catalytic activity are presented. The design and development of support and/or bimetallic systems (e. g., alloys, intermetallic, etc.) are also included. Herein, we report synthetic approaches of Cu and Cu‐based nanoparticles (monometallic copper, bimetallic copper and copper (II) oxide nanoparticles/nanostructures) and impregnation of such nanoparticles onto support material (e. g., Co₃O₄ nanostructure), along with their applications as environmental catalyst for various oxidation and reduction reactions. Finally, this account provides necessary advances and perspectives of Cu‐based nanoparticles in the environmental catalysis.     

Direct Hydrogenation of Nitroaromatics at Room Temperature Catalyzed by Magnetically Recoverable Cu@Fe2O3 Nanoparticles

Metal embedded in metal oxide nanoparticles are active as catalyst in plethora of industrially important reactions. Herein, embedded Cu@Fe₂O₃ nanoparticles was synthesized via a one step hydrothermal strategy which selectively catalyzes the hydrogenation of diverse nitroaromatics in H₂O at room temperature. The remarkable catalytic performance is due to the successful hybridization of metallic Cu and Fe₂O₃ which in turn allows easy electroflipping between various oxidation states of Cu and Fe. Azo- and azoxy-compounds are not formed during the catalyzed process. This evidently establish that the hydrogenation of nitroaromatics proceeds via direct route with >99% selectivity to the corresponding anilines.