Some observations on HC-128

In this paper, we study HC-128 in detail from cryptanalytic point of view. First, we use linear approximation of the addition modulo 2 ⁿ of three n-bit integers to identify linear approximations of g ₁, g ₂, the feedback functions of HC-128. This, in turn, shows that the process of keystream output generation of HC-128 can be well approximated by linear functions. In this direction, we show that the ??least significant bit?? based distinguisher (presented by the designer himself) of HC-128 works for the complete 32-bit word. Using the above linear approximations of g ₁, g ₂, we present a new distinguisher for HC-128 which is slightly weaker than Wu??s distinguisher. Finally, in the line of Dunkelman??s observation, we also study how HC-128 keystream words leak secret state information of the cipher due to the properties of the functions h ₁, h ₂ and present improved results.     

Idempotents in the neighbourhood of Patterson-Wiedemann functions having Walsh spectra zeros

In this paper we study the neighbourhood of 15-variable Patterson-Wiedemann (PW) functions, i.e., the functions that differ by a small Hamming distance from the PW functions in terms of truth table representation. We exploit the idempotent structure of the PW functions and interpret them as Rotation Symmetric Boolean Functions (RSBFs). We present techniques to modify these RSBFs to introduce zeros in the Walsh spectra of the modified functions with minimum reduction in nonlinearity. Our technique demonstrates 15-variable balanced and 1-resilient functions with currently best known nonlinearities 16272 and 16264 respectively. In the process, we find functions for which the autocorrelation spectra and algebraic immunity parameters are best known till date.     

On stochastic games,II

In this paper, we consider positive stochastic games, when the state and action spaces are all infinite. We prove that, under certain conditions, the positive stochastic game has a value and that the maximizing player has an -optimal stationary strategy and the minimizing player has an optimal stationary strategy.The authors are grateful to Professor David Blackwell and the referee for some useful comments.     

Continuum states from time-dependent density functional theory

Linear response time-dependent density functional theory is used to study low-lying electronic continuum states of targets that can bind an extra electron. Exact formulas to extract scattering amplitudes from the susceptibility are derived in one dimension. A single-pole approximation for scattering phase shifts in three dimensions is shown to be more accurate than static exchange for singlet electron-He(+) scattering.     

Synthesis of homochiral bis (oxazolinyl) pyridine type ligands for asymmetric cyclopropanation reactions

Homochiral bis(oxazolinyl)pyridine type ligands were synthesized from (S)-valine and converted into their Cu(II) complexes. Reduction of these Cu(II) complexes into Cu(I) with diazoesters was studied by uv-vis and epr spectroscopy. The enantioselective cyclopropanation reaction was carried out using styrene as a model substrate.     

Switching behaviour of a nonlinear Mach-Zehnder interferometer

In the present paper, a detailed investigation on the switching behaviour of a nonlinear Mach-Zehnder interferometer (NMZI) has been carried out using beam propagation method (BPM). A thorough investigation on input vs. output characteristic has been carried out by varying different parameters like length of the arms, refractive index of the linear/nonlinear arm, wavelength of the input beams and nonlinear coefficient of the material of the nonlinear arm. The input vs. output characteristic has also been investigated by shifting the balance point of the NMZI. The present paper provides a physically intuitive understanding of the effect of change in different parameters of the NMZI on its switching behaviour.     

Nature of halogen-centered intermolecular interactions in crystal growth and design: Fluorine-centered interactions in dimers in crystalline hexafluoropropylene as a prototype

The wide occurrence of halogen-centered noncovalent interactions in crystal growth and design prompted this study, which includes a mini review of recent advances in the field. Particular emphasis is placed on providing compelling theoretical evidence of the formation of these interactions between sites of positive electrostatic potential, as well as between sites of negative electrostatic potential, localized on the electrostatic surfaces of the bound fluorine atoms in a prototypical system, hexafluoropropylene (C₃F₆), upon its interaction with another same molecule to form (C₃F₆)₂ dimers. The existence of σ- and π-hole interactions is shown for the stable dimers. Even so, weakly bound interactions locally responsible in holding the molecular fragments together cannot and should not be overlooked since they are partly responsible for determining the overall geometry of the crystal. The results of combined quantum theory of atoms in molecules, molecular electrostatic surface potential, and reduced density gradient noncovalent interaction analyses showed that these latter interactions do indeed play a role in the stability and growth of crystalline C₃F₆ itself and the (C₃F₆)₂ dimers. A symmetry adapted perturbation theory energy decomposition analysis leads to the conclusion that a great majority of the (C₃F₆)₂ dimers examined are the consequence of dispersion (and electrostatics), with nonnegligible contribution from polarization, which together competes with an exchange repulsion component to determine the equilibrium geometries. In a few structures of the (C₃F₆)₂ dimer, the fluorine is found to serve as a six-center five-bond donor/acceptor, as found for carbon in other systems (Malischewski and Seppelt, Angew. Chem. Int. Ed. 2017, 56, 368). © 2019 Wiley Periodicals, Inc.     

Influence of Cavity Decay on Phase Distribution and Rabi Flopping in Cavity QED

The quantum mechanical phase distribution and the quantum oscillations of population are studied for a cavity field togetherwith a driven classical field. The atom is sent through the cavity and driven by a classical field. Also the time evolution of the system including decay is obtained. The graph showing the Rabi oscillations for this system is changed into a bit pattern from the system without decay. The phase probability function is also affected due to the presence of cavity decay.     

Solvent- and Substrate-Induced Chiroptical Inversion in Amphiphilic,Biocompatible Glycoconjugate Supramolecules: Shape-Persistent Gelation,Self-Healing,and Antibacterial Activity

We have shown solvent- and substrate-dependent chiral inversion of a few glycoconjugate supramolecules. (Z)-F-Gluco, in which d -glucosamine has been attached chemically to Cbz-protected l -phenylalanine at the C terminus, forms a self-healing hydrogel through intertwining of the nanofibers wherein the gelators undergo lamellar packing in the β-sheet secondary structures with a single chiral handedness. Dihybrid (Z)-F-gluco nanocomposite gel was prepared by in-situ formation of silver nanoparticles AgNPs in the gel; this enhances the mechanical properties of the composite gel through physical crosslinking without altering the packing pattern. In contrast, (Z)-L-gluco bearing an l -leucine moiety does not form a hydrogel but an organogel. Interestingly, the chiral handedness of the aggregates of (Z)-L-gluco can be reversed by choosing suitable solvents. In addition to self-healing behavior, (Z)-L-gluco gel revealed shape persistency. Further, (Z)-F-gluco hydrogel is benign, nontoxic, non-immunogenic, and non-allergenic in animal cells. AgNP-loaded (Z)-F-gluco hydrogel showed antibacterial activity against both Gram-positive and Gram-negative bacteria.