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.     

Vibration characteristics of FGM circular cylindrical shells filled with fluid using wave propagation approach

The vibration characteristics of a functionally graded material circular cylindrical shell filled with fluid are examined with a wave propagation approach. The shell is filled with an incompressible non-viscous fluid. Axial modal dependence is approximated by exponential functions. A theoretical study of shell vibration frequencies is analyzed for simply supported-simply supported, clamped-simply supported, and clamped-clamped boundary conditions with the fluid effect. The validity and the accuracy of the present method are confirmed by comparing the present results with those available in the literature. Good agreement is observed between the two sets of results.     

Physical vapor deposition of SnS:PbS-dithiocarbamate chalcogenide semiconductor thin films: elucidation of optoelectronic and electrochemical features

Abstract

This work reports the first investigation on the physical vapor deposition of thin films of tin sulfide doped lead sulfide (SnS:PbS). In-situ synthesis route using diethyldithiocarbamate (DTC) ligand was adopted for SnS-DTC, PbS-DTC and SnS:PbS-DTC complex formation. PbS-DTC and SnS:PbS-DTC expressed an average crystallite size of 30.98 and 29.74?nm, respectively shown by X-ray diffraction (XRD) analysis. A face centered cubic geometry was revealed from XRD. Ultraviolet visible spectrophotometry expressed a direct and indirect band gap of 3.4 and 3.2?eV, respectively for SnS:PbS-DTC. A smooth morphology with presence of larger agglomerated particles was disclosed by scanning electron microscopy for SnS:PbS-DTC thin films with 615?nm thickness. SnS:PbS-DTC thin films expressed remarkable electrochemical behavior explored via cyclic voltammetry, linear sweep voltammetry and chronoamperometry showing an improvement in the photo-current response upon potential bias increment. The results of the current research indicated the potential of SnS:PbS-DTC thin films for utilization in different types of photovoltaic devices.     

Determination of the surface parameters for aspheric aphakic lenses

Two methods are proposed for aspherical surface evaluation — scanning and interferometry. Each of these methods enables the determination of the radius of curvature at the lens vertex, the asphericity, astigmatism, rotation asymmetry, surface topography and the deviation of the surface from following the theoretically stated shape. While the scanning technique is low cost and simple, the interferometric technique (which needs optical arrangements) gives more information about the surface quality. These methods, combined with a computer, establish powerful instruments for controlling lens production.     

Abelian varieties and the general Hodge conjecture

We investigate the relationship between the usual and general Hodgeconjectures for abelian varieties. For certain abelian varieties A, weshow that the usual Hodge conjecture for all powers of A implies thegeneral Hodge conjecture for A.     

Double sequential fission in the reaction (16.7 MeV/u) U + Au observed with mica detectors

One of the main advantages of using dielectric track detectors in the study of heavy ion interactions is the possibility of observing each multi-prong event individually with complete kinematical details. It is thus possible to analyze even those reaction channels that have very low branching ratios. In the study of reactions induced by 16.7 MeV/u uranium ions incident on natural gold targets, we have observed 18 four-pronged events in a total detector area of 24 cm². Using a polynomial range-energy relationship, empirically fitted to the observed data of binary and ternary events, it was possible to perform kinematical analysis of 10 out of 18 events. The masses and relative velocities of the reaction products, determined in this analysis were compared with theoretical prediction based on double sequential fission process. An agreement within one standard deviation with respect to theoretical values has been found for eight analysed events.     

Spin-2—on-line low temperature nuclear orientation facility at YASNAPP-2 complex in Jinr Dubna

The Spin-2 facility built at YASNAPP-2 experimental complex of the Joint Institute of Nuclear Research is described. The basic parameters of SPIN-2 and YASNAPP-2 are discussed.