Improved Protocols of Secure Quantum Communication Using W States

Recently, Hwang et al. (Eur. Phys. J. D 61:785, 2011) and Yuan et al. (Int. J. Theor. Phys. 50:2403, 2011) have proposed two efficient protocols of secure quantum communication using 3-qubit and 4-qubit symmetric W state respectively. These two dense coding based protocols are generalized and their efficiencies are considerably improved. Simple bounds on the qubit efficiency of deterministic secure quantum communication (DSQC) and quantum secure direct communication (QSDC) protocols are obtained and it is shown that dense coding is not essential for designing of maximally efficient DSQC and QSDC protocols. This fact is used to design maximally efficient protocols of DSQC and QSDC using 3-qubit and 4-qubit W states.     

The Pseudo-differential Operator hμ,a on Hankel Invariant Spaces

Using Hankel transform the symbol 'a' is defined and the pseudo-differential operator (p.d.o.) h_μ,a associated with the Bessel operator d ²/dx ² + (1 ? 4μ ²)/4x ² in terms of this symbol is defined. It is shown that the operator h_μ,a is a continuous linear map of a Hankel invariant space into itself. A special pseudo-differential operator called the Hankel potential is defined and some of its properties are investigated.     

Pseudo-differential operators involving Watson transform

A class of pseudo-differential operators (p.d.o.'s) associated with the general Fourier kernel studied by Hardy and Titchmarsh is defined. A symbol class T ^m is introduced. It is shown that the p.d.o.'s associated with the symbol are continuous linear mappings of the Braaksma and Schuitman space T(λ,μ) into itself. An integral representation of p.d.o. is obtained. Some special forms of the symbol are considered. It is shown that these p.d.o.'s and their products are bounded in certain Sobolev type space.     

Geometrical Model for Phenylthallium Dihalides

The geometry of the phenylthallium dihalides, PhTlX₂(X=F, Cl or Br) which has heitherto been unknown, has been proposed on the basis of several qualitative aspects and quantitative arguments. These molecules have a planar structure with C_2v symmetry and the ring geometry has been assumed to be the same as that of benzene. The ring-substituent bond length has been taken to be 2.218 A° in all the three molecules, and the Tl-F, Tl-Cl and Tl-Br bond lengths in respective molecules have been estimated to be 1.878, 2.366 and 2.520 A°. The remaining parameter inter-bond angle, F-Tl-F has been taken to be 116° in PhTlF₂, whereas, angles Cl-Tl-Cl and Br-Tl-Br in respective molecules have been taken to be 120°, as expected in the case of a pure sp² hybridization.     

Subweakly Biased Pairs and Jungck Contractions with Applications

The existence of common fixed point results for a weakly biased pair under Jungck contraction is established. We define a new class of subweakly biased pair which properly contains the classes of C _q -commuting, pointwise R-subweakly commuting and R-subweakly commuting maps and establish common fixed point results for this class of maps. As applications several invariant best approximation results are proved which unify, extend, and complement the well-known results.     

A fluorescent di-zinc(II) complex of bis-calix[4]arene conjugate as chemosensing-ensemble for the selective recognition of ATP

A triethylene glycol di-imine locked triazole linked bis-calix[4]arene conjugate L has been synthesised and characterised. Conjugate L exhibits high fluorescence enhancement towards Zn²⁺ among the 13 metal ions studied down to a lower detection limit of ～12 ppb. The absorption and visual colour change experiments differentiated the Zn²⁺ from the other metal ions studied. The isolated zinc complex, [Zn₂L] has been used as a chemo-sensing ensemble for the recognition of anions based on their binding affinities towards Zn²⁺. [Zn₂L] was found to be sensitive and selective towards phosphate-bearing species and in particular to adenosine triphosphate (ATP^2 ? ) among the other 20 anions studied as observed based on the changes occurred in the fluorescence intensity. The selectivity of the ATP^2 ?  has been shown on the basis of the changes observed in the emission and absorption spectral studies. The lowest detectable concentration for ATP^2 ?  with the chemo-sensing ensemble [Zn₂L] is 348 ppb in methanol. The fluorescence quenching by the phosphate-based anions has been modelled by molecular mechanics studies and found that the anions possessing two or more phosphate moieties can only bridge between the two zinc centres, and hence those possessing only one phosphate moiety (H₂PO₄^?  and AMP^2 ? ) are ineffective.