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.     

Selective and periodic inventory routing problem for waste vegetable oil collection

We consider a biodiesel production company that collects waste vegetable oil from source points that generate waste in large amounts. The company uses the collected waste as raw material for biodiesel production. The manager of this company needs to decide which of the present source points to include in the collection program, which of them to visit on each day, which periodic routing schedule to repeat over an infinite horizon and how many vehicles to operate such that the total collection, inventory and purchasing costs are minimized while the production requirements and operational constraints are met. For this selective and periodic inventory routing problem, we propose two different formulations, compare them and apply the better performing one on a real-world problem with 36 scenarios. We generate lower bounds using a partial linear relaxation model, and observe that the solutions obtained through our model are within 3.28% of optimality on the average. Several insights regarding the customer selection, routing and purchasing decisions are acquired with sensitivity analysis.     

Ultra-Sensitive Fluorimetric Method for the First Estimation of Vonoprazan in Real Human Plasma and Content Uniformity Test

Journal of Fluorescence - Vonoprazan (VON) has been approved recently via US-FDA in 2015 as the first in class of potassium competitive acid blocker group. VON is used for management of...     

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.     

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.     

Reactivity of the Cu2O(1 0 0) surface: Insights from first principles calculations

We present a summary of results of systematic first principles calculations of the electronic and geometric structures of the Cu₂O(1 0 0) surface and the process of CO oxidation on this surface (energetics and pathways of adsorption, diffusion and reactions of CO and O₂ on the surface). The (p, T) phase diagram of the Cu₂O(1 0 0) in equilibrium of with gas phase O₂ built using the ab initio thermodynamics approach suggests that the O-terminated surface is preferred over the Cu-terminated one within the entire ranges of pressures and temperatures in which the compound exists. Metastable Cu-terminated Cu₂O(1 0 0) is found to undergo a surface reconstruction in agreement with experiment. We find CO to oxidize spontaneously on the O-terminated Cu₂O(1 0 0) surface by consuming surface O atoms. Our calculations also show that the surface O-vacancies left in the course of the CO oxidation can be easily filled with dissociative adsorption of the gas phase O₂ molecules, which are usually present in reaction environment.     

Iterative approximation of fixed points of Prešić operators on partial metric spaces

We study the convergence of the Pre?i? type k‐step iterative method for a class of operators satisfying Pre?i? type contractive conditions on the setting of partial metric spaces. Some examples are presented to illustrate our obtained results. As applications of the presented convergence theorems, we derive global attractivity results for a class of matrix difference equations. Numerical experiments are also presented to illustrate the theoretical findings.     

Transfer of radioactivity from soil to vegetation in Rechna Doab, Pakistan

In Rechna Doab, samples of the most common vegetation, perennial grass Desmostachya bipinnata (dab), were collected along with soil samples from 29 sites. Natural radioactivity of 22?Ra, 232Th/22?Ac and ??K was measured by using high purity germanium-based gamma ray spectrometer. Activity concentration levels of 22?Ra, 232Th/22?Ac and ??K in soil were found to be 46.8 ± 6.2 (36.0-57.6), 61.4 ± 5.9 (48.2-73.2) and 644.8 ± 73.9 (537.7-868.4) Bq kg?1 (dry mass), respectively, and those in vegetation were 2.74 ± 1.70 (1.00-6.39), 2.24 ± 0.59 (1.56-2.61) and 172.72±113.37 (53.14-469.24) Bq kg?1 (dry mass), respectively. The measured values of the activity concentration in vegetation are comparable with some other international data. Calculated soil to vegetation transfer factors of 22?Ra, 22?Ac and ??K were 0.06 ± 0.03 (0.02-0.14), 0.04 ± 0.01 (0.03-0.04) and 0.26 ± 0.16 (0.09-0.69). The mean outdoor absorbed dose rate in air for the area under study was determined as 8.22 nGy h?1 and the mean indoor absorbed dose rate in air was 11.52 nGy h?1. The total annual effective dose to the general public from the vegetation was found to be (0.02-0.16) mSv, which is below the recommended limit value of 1 mSv y?1 for the general public. The dab vegetation under study was found to be radiologically safe for the population and environment.