Circular chromatic index of graphs of maximum degree 3

This paper proves that if G is a graph (parallel edges allowed) of maximum degree 3, then χ′_c(G) ≤ 11/3 provided that G does not contain H₁ or H₂ as a subgraph, where H₁ and H₂ are obtained by subdividing one edge of K (the graph with three parallel edges between two vertices) and K₄, respectively. As χ′_c(H₁) = χ′_c(H₂) = 4, our result implies that there is no graph G with 11/3 < χ′_c(G) < 4. It also implies that if G is a 2‐edge connected cubic graph, then χ′_c(G) ≤ 11/3. © 2005 Wiley Periodicals, Inc. J Graph Theory 49: 325–335, 2005     

One-dimensional backreacting holographic <Emphasis Type="Italic">p</Emphasis>-wave superconductors

We analytically and numerically study the properties of one-dimensional holographic p-wave superconductors in the presence of backreaction. We employ the Sturm–Liouville eigenvalue problem for the analytical calculation and the shooting method for the numerical investigations. We apply the \(\hbox {AdS}_{{3}}\)/\(\hbox {CFT}_{{2}}\) correspondence and determine the relation between the critical temperature \(T_{c}\) and the chemical potential \(\mu \) for different values of the mass m of a charged spin-1 field \(\rho _{\mu }\) and backreacting parameters. We observe that the data of both analytical and numerical studies are in good agreement. We find that increasing the backreaction and the mass parameter causes the greater values for \({T_{c}}/{\mu }\). Thus, it makes the condensation harder to form. In addition, the analytical and numerical approaches show that the value of the critical exponent \( \beta \) is 1 / 2, which is the same as in the mean field theory. Moreover, both methods confirm the existence of a second order phase transition.     

Affinity of two novel five-coordinated anticancer Pt(II) complexes to human and bovine serum albumins: a spectroscopic approach

The interactions of two organoplatinum complexes, [Pt(C^N)Cl(dppa)], 1, and [Pt(C^N)Cl(dppm)], 2 (C^N = N(1), C(2')-chelated, deprotonated 2-phenylpyridine, dppa = bis(diphenylphosphino)amine, dppm = bis(diphenylphosphino)methane), as antitumor agents, with bovine serum albumin (BSA) and human serum albumin (HSA) have been studied by fluorescence and UV-vis absorption spectroscopic techniques at pH 7.40. The quenching constants and binding parameters (binding constants and number of binding sites) were determined by fluorescence quenching method. The obtained results revealed that there is a strong binding interaction between the ligands and proteins. The calculated thermodynamic parameters (ΔG, ΔH, and ΔS) confirmed that the binding reaction is mainly entropy-driven, and hydrophobic forces played a major role in the reaction. The displacement experiment shows that these Pt complexes can bind to the subdomain IIA (site I) of albumin. Moreover, synchronous fluorescence spectroscopy studies revealed some changes in the local polarity around the tryptophan residues. Finally, the distance, r, between donor (serum albumin) and acceptor (Pt complexes) was obtained according to F?rster theory of nonradiation energy transfer.     

Lattice Boltzmann simulation of particles agglomeration and rheology in a particulate flow

The dynamics and rheology of particles in a Newtonian fluid subjected to shear are simulated using Lattice Boltzmann Method. A computationally-efficient Smoothed Profile Method is used to resolve fluid-solid interactions, and the Lennard-Jones inter-particle potential is implemented to account for inter-particle forces. The use of a bi-periodic computational domain with Lees-Edward boundary conditions allows simulation for systems consisting of a large number of particles under shear. The method is validated for single and dual particle problems and an analysis is performed for multi-particle problems under a range of shear rates and particle fractions. The introduction of particle-particle interactions, which are physically important in many engineering processes, is found to have a considerable impact on the dynamics, agglomeration and rheology. The total stress exhibits high unsteadiness primarily due to the solid component contribution, at higher particle fractions. The simulations underscore the complex interplay between shear, interparticle forces and agglomeration and the complex dependencies of the rheological properties.     

Maximality of linear continuous logic

The linear compactness theorem is a variant of the compactness theorem holding for linear formulas. We show that the linear fragment of continuous logic is maximal with respect to the linear compactness theorem and the linear elementary chain property. We also characterize linear formulas as those preserved by the ultramean construction.     

pH stimuli-responsive and fouling resistance PES membrane fabricated by using photochromic spiropyran and spironaphthoxazine nanofillers for pesticide removal

New fouling resistance and stimulus–responsive nanofiltration membranes were fabricated by adding photochromic spiropyran (SPO) and spironaphthoxazine (SNO) nanofillers to the polyethersulfone (PES) matrix via the phase inversion method. The effect of SPO and SNO, as novel photoresponsive molecule nanofillers, were evaluated in terms of membrane morphology, porosity, wettability, pure water flux (PWF), antifouling resistance, and stimulus–responsive properties. All the modified membranes indicated better performance compared to the bare PES. The membrane PWF was notably enhanced from 7.7 kg/m²h for the bare PES up to 18.68 and 20.58 kg/m²h for the 0.1 wt.% SPO and SNO blended membranes, respectively. Also, the 0.1 wt.% of SNO-based PES membrane indicated the best flux recovery ratio compared to the other membranes. The photo stimulus–responsive assessment showed a color change for both SPO and SNO photochromic in membranes. In the case of variable effect investigation, the response surface methodology at three levels (pressure: 4, 5, 6 bar and flow rate: 50, 100, and 150 L/h) was applied. A suitable flux (23.39 kg/m² h) and high removal efficiency (more than 90%) was achieved at optimum conditions. Also, the modified membranes by photochromic materials were sensitive to environmental variables such as acidic and alkaline conditions by changing their color.     

Crystal structures and in vitro anticancer studies on new unsymmetrical copper(II) Schiff base complexes derived from meso-1,2-diphenyl-1,2-ethylenediamine: a comparison with related symmetrical ones

Two new unsymmetrical copper(II) Schiff base complexes, [CuLⁿ(py)]ClO₄ (n = 1, 2) in which Lⁿ represents a tridentate N₂O type Schiff base ligand, were synthesized. Lⁿs were derived from monocondensation of meso-1,2-diphenyl-1,2-ethylenediamine with salicylaldehyde or 3-methoxysalicylaldehyde. The reaction between [CuLⁿ(py)]ClO₄ and other salicylaldehyde derivatives resulted in new N₂O₂ unsymmetrical tetradentate Cu^II complexes, CuL^3–6. Crystal structures of [CuL¹(py)]ClO₄, CuL⁴, and CuL⁵ were obtained. These new complexes as well as a series of related symmetrical ones (i.e. CuL^7–12) were tested for their in vitro anticancer activity against human liver cancer cell line (Hep-G2) by MTT and apoptosis assay. All of the complexes showed considerable cytotoxic activity against tumor cell lines (IC₅₀ = 5.13–16.24 μg mL^?1). The symmetrical CuL⁷ was the most potent anticancer derivative (IC₅₀ = 5.13 μg mL^?1) compared to the control drug 5-FU (IC₅₀ = 5.4 μg mL^-1, p < 0.05). Flow cytometry experiments showed that the copper derivatives especially [CuL²(py)]ClO₄ and CuL⁷ induced more apoptosis on Hep-G2 tumor cell lines compared to 5-FU.