Resolvability in circulant graphs

A set W of the vertices of a connected graph G is called a resolving set for G if for every two distinct vertices u, v ∈ V (G) there is a vertex w ∈ W such that d(u, w) ≠ d(v, w). A resolving set of minimum cardinality is called a metric basis for G and the number of vertices in a metric basis is called the metric dimension of G, denoted by dim(G). For a vertex u of G and a subset S of V (G), the distance between u and S is the number min s∈S d(u, s). A k-partition Π = {S 1 , S 2 , . . . , S k } of V (G) is called a resolving partition if for every two distinct vertices u, v ∈ V (G) there is a set S i in Π such that d(u, Si )≠ d(v, Si ). The minimum k for which there is a resolving k-partition of V (G) is called the partition dimension of G, denoted by pd(G). The circulant graph is a graph with vertex set Zn , an additive group of integers modulo n, and two vertices labeled i and j adjacent if and only if i-j (mod n) ∈ C , where CZn has the property that C =-C and 0 ■ C. The circulant graph is denoted by Xn, Δ where Δ = |C|. In this paper, we study the metric dimension of a family of circulant graphs Xn, 3 with connection set C = {1, n/2 , n-1} and prove that dim(Xn, 3 ) is independent of choice of n by showing that dim(Xn, 3 ) ={3 for all n ≡ 0 (mod 4), 4 for all n ≡ 2 (mod 4). We also study the partition dimension of a family of circulant graphs Xn,4 with connection set C = {±1, ±2} and prove that pd(Xn, 4 ) is independent of choice of n and show that pd(X5,4 ) = 5 and pd(Xn,4 ) ={3 for all odd n ≥ 9, 4 for all even n ≥ 6 and n = 7.     

Quantum Information of the Aharanov–Bohm Ring with Yukawa Interaction in the Presence of Disclination

We investigate quantum information by a theoretical measurement approach of an Aharanov–Bohm (AB) ring with Yukawa interaction in curved space with disclination. We obtained the so-called Shannon entropy through the eigenfunctions of the system. The quantum states considered come from Schrödinger theory with the AB field in the background of curved space. With this entropy, we can explore the quantum information at the position space and reciprocal space. Furthermore, we discussed how the magnetic field, the AB flux, and the topological defect influence the quantum states and the information entropy.     

New Developments on Operator Reverse AM-GM Inequality for Positive Linear Maps

Acta Mathematica Sinica, English Series - In this research article, we shall give some reverse Arithmetic-Geometric mean inequalities for unital positive linear maps on Hilbert space operators...     

Complete Carton-13 Assignments of the Sesquiterpene Lactone 11,13,-Dihydroparthenolide Using 2D-Inadequate

The complete ¹³C NMR resonances for the sesquiterpene lactone 11,13-dihydroparthenolide were established by the application of 2D-INADEQUATE.     

Solvatochromism of 2‐(N,N‐dimethylamino)‐7‐nitrofluorene and the natural dye β‐carotene: application for the determination of solvent dipolarity and polarizability

The effects of solvents on chemical phenomena (rate and equilibrium constants, spectroscopic transitions, etc.) are conveniently described by solvation free‐energy relationships that take into account solvent acidity, basicity and dipolarity/polarizability. The latter can be separated into its components by manipulating the UV–vis spectra of two solvatochromic probes, 2‐(N,N‐dimethylamino)‐7‐nitrofluorene (DMANF) and a di‐(tert‐butyl)‐tetramethyl docosanonaen probe (ttbP9) whose synthesis is laborious and expensive. Recently, we have shown that the natural dye β‐carotene can be conveniently employed instead of ttbP9 for the determination of solvent polarizability (SP) of 76 molecular solvents and four ionic liquids. In the present work, we report the polarizabilities of further 24 solvents. Based on the solvatochromism of β‐carotene and DMANF, we have calculated solvent dipolarity (SD) for 103 protic and aprotic molecular solvents, and ionic liquids. The dependence of SD and SP on the number of carbon atoms in the acyl‐ or alkyl group of several homologous series (alcohols; 2‐alkoxyethanols; carboxylic acid‐ anhydrides, and esters, ionic liquids) is calculated and briefly discussed. Copyright © 2013 John Wiley & Sons, Ltd.     

Intelligent reversible watermarking technique in medical images using GA and PSO

The advances in recording, editing, and broadcasting multimedia contents in digital form motivate to protect these digital contents from illegal use, such as duplication, manipulation, and redistribution. However, watermarking algorithms are designed to satisfy requirements of applications, as different applications have different concerns. We intend to design a watermarking algorithm for applications which require high embedding capacity and imperceptibility, to maintain the integrity of the host signal as well as embedded information. Reversible watermarking is a promising technique which satisfies our requirements. In this paper, we concentrate on improving the watermark capacity and reducing the perceptual degradation of an image. We investigated the Luo's [1] additive interpolation-error expansion algorithm and enhanced it by incorporating with two intelligent techniques: genetic algorithm (GA), and particle swarm optimization (PSO). Genetic algorithm is applied to exploit the correlation of image pixel values to obtain better estimation of neighboring pixel values, which results in optimal balance between information storage capacity and imperceptibility. Particle swarm optimization (intelligent technique) is also applied for the same purpose. Experimental results show that PSO and GA nearly give the same results, but GA outperforms the PSO. Experimental results also reveal that the proposed strategy outperforms the state of art works in terms of perceptual quality and watermarking payload.     

Aggregation and microenvironmental properties of gemini and conventional mixed surfactants systems: A fluorometric study

Aggregation behavior of cationic gemini (hexanediyl-1,5-bis(dimethylcettylammonium bromide) (16-5-16)) surfactant with conventional single chain surfactants cetyltrimethylammonium bromide (CTAB) and tetradecyltrimethylammonium bromide (TTAB) were studied with the help of fluorescence measurements. Fluorescence probe is a proficient technique for examining the surfactant-surfactant interaction and aggregation. The micelle aggregation number (N _agg) was measured using steady-state fluorescence quenching method. The micelle aggregation numbers of binary combinations fall between those of constituent surfactants. The micropolarity (I ₁/I ₃), binding constant (K _sv) and dielectric constant (D _exp) of mixed systems were determined from the ratio of peaks intensity in the pyrene fluorescence spectrum. The I ₁/I ₃ values were found to be more than >1, showing more polar environment around pyrene in the mixed micelle as compared to the pure micelles.     

The Smart 2-(2-Fluorobenzoyl)-N-(2-Methoxyphenyl)Hydrazinecarbothioamide Functionalized as Ni(II) Sensor in Micromolar Concentration Level and its Application in Live Cell Imaging

In recent years, fluorescent probes for the detection of environmentally and biologically important metal cations have received extensive attention for designing and development of fluorescent chemosensors. Herein, we report the photophysical results of 2-(2-fluorobenzoyl)-N-(2-methoxyphenyl) hydrazinecarbothioamide (4) functionalized as Ni (II) sensor in micromolar concentration level. Through fluorescence titration at 488 nm, we were confirmed that ligand 4 showed the remarkable emission by complexation between 4 and Ni (II) while it appeared no emission in case of the competitive ions (Cr³⁺, Fe²⁺, Co²⁺, Ba²⁺, Cu²⁺, Ca²⁺, Na⁺, K⁺, Cu⁺, Cs⁺). Furthermore, ligand 4 exhibited no toxicity with precise cell permeability toward normal living cells using L929 cell lines in bio imaging experiment investigated through confocal fluorescence microscope. The non-toxic behavior of ligand 4 (assessed by MTT assay) and its ability to track the Ni²⁺ in living cells suggest its possibility to use in biological system as nickel sensor.

Magnetic structure of the Sm5Ge4-type Tb2Ti3Ge4

The orthorhombic Sm₅Ge₄-type Tb₂Ti₃Ge₄ shows square modulated non-collinear magnetic ordering with wave vector K=[±1/3, 1/2, 1/2] at 2 K. The terbium magnetic moments lie in the bc plane and magnetic moment value of 7.5(2) μ_B/Tb is obtained at 2 K.     

Nonclassicality of two-mode nonorthogonal states

Nonclassical features of Schrödinger cat state with two-mode superposition state based on two coherent states π out of phase by fixing the relative phase equal to average photon number are discussed. Study of two-mode quadrature squeezing, oscillatory and sub-Poissonian photon statistics show that nonclassicality exists for these states. However, it is observed that the considered states do not violates the Cauchy–Schwarz inequality. Furthermore, simultaneously existence of quadrature squeezing and sub-Poissonian photon statistics shows that these states have more nonclassical features than that of famous even and odd coherent states.