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.     

Optimizing specimen collection for processing in clinical testing laboratories

We study the logistics of specimen collection for a clinical testing laboratory that serves sites dispersed in an urban area. The specimens that accumulate at the customer sites throughout the working day are transported to the laboratory for processing. The problem is to construct and schedule a series of tours to collect the accumulated specimens from the sites throughout the day. Two hierarchical objectives are considered: (i) maximizing the amount of specimens processed by the next morning, and (ii) minimizing the daily transportation cost. We show that the problem is NP-hard and formulate a linear Mixed Integer Programming (MIP) model to solve the bicriteria problem in two levels. We characterize properties of optimal solutions and develop a heuristic approach based on solving the MIP model with additional constraints that seeks for feasible solutions with specific characteristics. To evaluate the performance of this approach, we provide an upper bounding scheme on the daily processed amount, and develop two relaxed MIP models to generate lower bounds on the daily transportation cost. The effectiveness of the proposed solution approach is evaluated using realistic problem instances. Insights on key problem parameters and their effects on the solutions are extracted by further experiments.     

Empirical analysis of self-adaptive differential evolution

Differential evolution (DE) is generally considered as a reliable, accurate, robust and fast optimization technique. DE has been successfully applied to solve a wide range of numerical optimization problems. However, the user is required to set the values of the control parameters of DE for each problem. Such parameter tuning is a time consuming task. In this paper, a self-adaptive DE (SDE) algorithm which eliminates the need for manual tuning of control parameters is empirically analyzed. The performance of SDE is investigated and compared with other well-known approaches. The experiments conducted show that SDE generally outperform other DE algorithms in all the benchmark functions. Moreover, the performance of SDE using the ring neighborhood topology is investigated.     

Synthesis of some new triamide derivatives via Ugi five-component reaction in aqueous solution

Triamide derivatives have been synthesized in good yields in a novel, one-pot, five-component, and efficient process by the reaction of Z-oxazolone, water, primary amines, aldehydes, isocyanides, in the presence of catalytic amount of KAl(SO₄)₂·12H₂O (alum) as a non-toxic, reusable, inexpensive, and easily available reagent via Ugi reaction in aqueous solution.     

Minimal integer automaton behind crystal plasticity

Power law fluctuations and scale-free spatial patterns are known to characterize steady state plastic flow in crystalline materials. In this Letter we study the emergence of correlations in a simple Frenkel-Kontorova-type model of 2D plasticity which is largely free of arbitrariness, amenable to analytical study, and is capable of generating critical exponents matching experiments. Our main observation concerns the possibility to reduce continuum plasticity to an integer-valued automaton revealing inherent discreteness of the plastic flow.     

Galangin/β-Cyclodextrin Inclusion Complex as a Drug-Delivery System for Improved Solubility and Biocompatibility in Breast Cancer Treatment

The purpose of this study was to evaluate the potential of a newly modified cyclodextrin derivative, water-soluble β-cyclodextrin–epichlorohydrin (β-CD), as an effective drug carrier to enhance the poor solubility and bioavailability of galangin (GAL), a poorly water-soluble model drug. In this regard, inclusion complexes of GAL/β-CDP were prepared. UV-VIS spectrophotometry, Fourier-transform infrared spectroscopy (FTIR), X-ray crystallography (XRD), zeta potential analysis, particle size analysis, field emission scanning electron microscopy (FESEM), and transmission electron microscopy (TEM) were applied to characterize the synthesized GAL/β-CD. Michigan Cancer Foundation-7 (MCF-7; human breast cancer cells) and rat embryo fibroblast (REF; normal cells) were employed to examine the in vitro cytotoxic effects of GAL/β-CD using various parameters. The dye-based tests of MTT and crystal violet clearly exhibited that GAL/β-CD-treated cells had a reduced proliferation rate, an influence that was not found in the normal cell line. The cells’ death was found to follow apoptotic mechanisms, as revealed by the dye-based test of acridine orange/ethidium bromide (AO/EtBr), with the involvement of the mitochondria via caspase-3-mediated events, as manifested by the Rh 123 test. We also included a mouse model to examine possible in vivo toxic effects of GAL/β-CD. It appears that the inclusion complex does not have a significant influence on normal cells, as indicated by serum levels of kidney and liver enzymatic markers, as well as thymic and splenic mass indices. A similar conclusion was reached on the histological level, as manifested by the absence of pathological alterations in the liver, kidney, thymus, spleen, heart, and lung.     

Cyclo[2]benzimidazole: luminescence turn-on sensing of anions

Cyclo[2]benzimidazole is a new host for anions that turns on its luminescence up to 150 fold upon binding. Photoexcited cyclo[2]benzimidazole undergoes an efficient non-radiative deactivation through an excited-state intramolecular proton-transfer (ESIPT) mechanism. Upon binding an anion, the ESIPT pathway is blocked, resulting in an increase in the luminescence efficiency.     

A novel single source precursor: [bis(N,N-diethyl-N'-naphthoyl-selenoureato)palladium(II)] for palladium selenide thin films and nanoparticles

We describe for the first time the use of a single source precursor to deposit thin films and nanocrystals of palladium selenide.     

Synthesis and structural characterization of trivalent amino acid derived chiral phosphorus compounds

Reaction of the N-toluenesulfonyl derivatives of (S)-alanine, phenylalanine, and valine (4-6) with PhPCl(2) gave in high yield the 4-methyl, benzyl, and isopropyl derivatives (7-9) of 2-phenyl-1-p-toluenesulfonyl-1,3,2-oxazaphospholidin-5-one. The ratios of the (2S,4S)/(2R,4S) diastereomers (cis/trans isomers) were 1:1, 2:1, and 10:1 for the methyl, benzyl, and isopropyl derivatives 7a,b, 8a,b, and 9a,b, respectively. For 7a,b, both isomers could be crystallized, but for the others only the major isomers were isolable. The X-ray crystal structure of 9a shows that the isopropyl and phenyl groups are mutually cis and that the tolyl moiety is oriented s-trans to both the isopropyl and phenyl groups. Reaction of 6 with Cl(2)PCH(2)CH(2)PCl(2) (10) gave a 56:38:7 mixture of the cis/cis, cis/trans, and trans/trans diphosphorus heterocycles 11a-c. The major isomer could be crystallized and isolated free of the other diastereomers. Reaction of 6 with EtPCl(2) gave a 6:1 mixture of cis/trans isomers of the ethyl-substituted heterocycles 12a,b as an inseparable oil but allowed confirmation of the structure of 11a. Slow epimerization at phosphorus may occur by inversion but more likely by ring opening/closure, since 7b, 9a, and 11a give rise upon standing in solution to mixtures containing starting material and 7a, 9b, and 11b, respectively, along with the free amino acid derivatives 4 and 6. The NMR spectra, and in particular the coupling constants between the alpha-hydrogen atom of the amino acid moiety and phosphorus, were used to establish the identities of the cis and trans isomers. Reaction of 9a with (THF)W(CO)(5) gave the phosphorus-ligated adduct (9a)W(CO)(5) (13), and the IR spectrum of this complex shows that 9a is a strongly electron-withdrawing ligand. The geometry of the sulfonamide moiety is discussed in detail, as are the (1)H NMR coupling constants. The data are consistent with the presence of little steric interaction between the cis isopropyl and phosphorus substituent in 9a, 11a, and 12a and orientation of the tolyl moiety s-cis to the isopropyl group in 9b, 12b, and 13.