On the direct construction of recursive MDS matrices

MDS matrices allow to build optimal linear diffusion layers in the design of block ciphers and hash functions. There has been a lot of study in designing efficient MDS matrices suitable for software and/or hardware implementations. In particular recursive MDS matrices are considered for resource constrained environments. Such matrices can be expressed as a power of simple companion matrices, i.e., an MDS matrix \(M = C_g^k\) for some companion matrix corresponding to a monic polynomial \(g(X) \in \mathbb {F}_q[X]\) of degree k. In this paper, we first show that for a monic polynomial g(X) of degree \(k\ge 2\), the matrix \(M = C_g^k\) is MDS if and only if g(X) has no nonzero multiple of degree \(\le 2k-1\) and weight \(\le k\). This characterization answers the issues raised by Augot et al. in FSE-2014 paper to some extent. We then revisit the algorithm given by Augot et al. to find all recursive MDS matrices that can be obtained from a class of BCH codes (which are also MDS) and propose an improved algorithm. We identify exactly what candidates in this class of BCH codes yield recursive MDS matrices. So the computation can be confined to only those potential candidate polynomials, and thus greatly reducing the complexity. As a consequence we are able to provide formulae for the number of such recursive MDS matrices, whereas in FSE-2014 paper, the same numbers are provided by exhaustively searching for some small parameter choices. We also present a few ideas making the search faster for finding efficient recursive MDS matrices in this class. Using our approach, it is possible to exhaustively search this class for larger parameter choices which was not possible earlier. We also present our search results for the case \(k=8\) and \(q=2^{16}\).     

Elucidation of the electronic structure of semiconducting single-walled carbon nanotubes by electroabsorption spectroscopy

We report benchmark calculations of electroabsorption in semiconducting single-walled carbon nanotubes that provide motivation to perform electroabsorption measurement on these systems. We show that electroabsorption can detect the continuum bands in different energy manifolds. Direct determination of the binding energies of excitons in higher manifolds thereby becomes possible. We also find that electroabsorption can provide evidence for Fano-type coupling between the second exciton and the lowest continuum band states.     

Indium trichloride catalyzed efficient one-pot synthesis of highly substituted furans

A one-pot synthesis of the substituted furans 3 could be achieved in good yields by reacting but-2-ene-1,4-diones 1 with acetoacetates 2 in the presence of a catalytic amount of InCl₃ (20 mol %) using i-PrOH as solvent at 80-90 °C for 4-8 h. InCl₃ was observed to give the optimum results among the various Lewis acids examined.     

A one-pot synthesis of a paramagnetic high-nuclearity nickel(II) cluster: an octadecanuclear Ni(II)16Na(I)2 metal aggregate

An unusual Ni(II)(16)Na(I)(2) cluster which features formate as a bridging clamp between two octanuclear nickel cages is reported; preliminary magnetic studies exhibit paramagnetic low-lying states resulting from dominating antiferromagnetic interactions between the nickel(II) centers.     

A Remarkable Fluorescence Quenching Based Amplification in ATP Detection through Signal Transduction in Self-Assembled Multivalent Aggregates

Signal transduction is essential for the survival of living organisms, because it allows them to respond to the changes in external environments. In artificial systems, signal transduction has been exploited for the highly sensitive detection of analytes. Herein, a remarkable signal transduction, upon ATP binding, in the multivalent fibrillar nanoaggregates of anthracene conjugated imidazolium receptors is reported. The aggregates of one particular amphiphilic receptor sensed ATP in high pm concentrations with one ATP molecule essentially quenching the emission of thousands of receptors. A cooperative merging of the multivalent binding and signal transduction led to this superquenching and translated to an outstanding enhancement of more than a millionfold in the sensitivity of ATP detection by the nanoaggregates; in comparison to the “molecular” imidazolium receptors. Furthermore, an exceptional selectivity to ATP over other nucleotides was demonstrated.     

Improving hydrothermal performance of double-tube heat exchanger with modified twisted tape inserts using hybrid nanofluid

Journal of Thermal Analysis and Calorimetry - The experimental studies on Al2O3?+?TiO2 hybrid nanofluid flowing under the turbulent condition in a double-tube heat exchanger with...     

π-Hydrogen bonding wins over conventional hydrogen bonding interaction: a jet-cooled study of indole···furan heterodimer

In this study, we have explored the conformational landscape of the indole···furan dimer in a supersonic jet by using resonant two-photon ionization (R2PI) and IR-UV double-resonance spectroscopic techniques combined with dispersion-corrected density functional theory (DFT) calculations. Only one conformer of the dimer has been observed in the experiment. DFT/B97-D level calculation shows that N-H···π hydrogen-bonded conformer (T') is energetically more stable than the N-H···O hydrogen-bonded conformer (HB). Natural bond orbital (NBO) calculation also shows that the hydrogen-bonding interaction in the HB conformer is very weak. Finally, the structure of the observed dimer has been determined to be tilted T-shaped N-H···π hydrogen-bonded (T') from very excellent agreement between experimental and theoretical N-H stretch frequency. The most significant finding of this study is the first-time observation of a N-H···π bound conformer of a dimer, which wins over a conventional hydrogen-bonded conformer of the dimer.