An optimal homotopy asymptotic method applied to the steady flow of a fourth-grade fluid past a porous plate

A new analytic approximate technique for addressing nonlinear problems, namely the Optimal Homotopy Asymptotic Method (OHAM), is proposed and used in an application to the steady flow of a fourth-grade fluid. This approach does not depend upon any small/large parameters. This method provides us with a convenient way to control the convergence of approximation series and adjust convergence regions when necessary. The series solution is developed and the recurrence relations are given explicitly. The results reveal that the proposed method is effective and easy to use.     

Yan’s oscillation theorem revisited

Yan’s contribution [J. Yan, Oscillation theorems for second order linear differential equations with damping, Proc. Amer. Math. Soc. 98 (1986) 276–282] was an important breakthrough in the development of the Theory of Oscillation. This frequently cited paper has stimulated extensive investigations in the field. During the last decade, an integral oscillation technique has been developed to such an extent as to allow us to revisit Yan’s fundamental oscillation theorem and remove one of the conditions, leaving the other assumptions and the conclusion intact, thus enhancing this keystone result.     

Stress Response Kinetics of Two Nisin Producer Strains of <Emphasis Type="Italic">Lactococcus lactis</Emphasis> spp. <Emphasis Type="Italic">lactis</Emphasis>

The purpose of this study is to determine the survival and nisin production behaviors of two strains of Lactococcus lactis under different stress conditions that represent the food ecosystem. In this respect, the survival ratios of two nisin producers were determined under different pH, temperature, NaCl, and bile salt concentrations. Then, nisin production levels of the strains were determined at each stress conditions. Both strains had similar growth or inactivation patterns under the same stress conditions. NaCl and bile salt stresses on the survival ratio of the strains could be successfully described by the exponential decay function, whereas Gaussian function produced good fits for temperature and pH stresses. The nisin activity of two nisin producers (in their mid-exponential and/or early stationary phase) decreased dramatically under all stress conditions, except osmotic (NaCl) and low temperature applications. The results of this study showed that two nisin producers had similar adaptive responses under severe stress conditions, which could be described by appropriate mathematical equations. Moreover, the effect of harsh environment on the nisin activity of L. lactis strains depends on the stress factors applied.     

Pyridine-2,5-dicarboxylic acid complexes of nickel(II) with 2,2′-bipyridine and 1,10-phenanthroline coligands; syntheses,crystal structures,spectroscopic and thermal studies

Two pyridine-2,5-dicarboxylic acid (pydcH₂) complexes of nickel(II) with 2,2′-bipyridine and 1,10-phenanthroline were synthesized and characterized by elemental, spectroscopic, thermal analysis, magnetic measurements and single crystal X-ray diffraction techniques. Both [Ni(pydc)(bipy)₂]·7H₂O and [Ni(pydc)(phen)₂]·6.5H₂O crystallize in the monoclinic system and P2₁/c space group. The Ni(II) ions are coordinated by two bidentate bipy or phen ligands and one pydc dianion in a distorted octahedral geometry. The pydc ligand is coordinated through the pyridine nitrogen atom and oxygen atom of carboxyl group as a bidentate ligand. Both carboxylate groups of pydc are deprotonated but only the 2-carboxylate is coordinated to the metal. Thermal decompositions of the complexes have been studied over the range 30–600 °C on heating in a static air atmosphere.     

Synthesis,characterization, and antimicrobial activity of new benzoylthiourea ligands

In this study, new benzoylthiourea derivatives, (E)-N-[(2-benzamidomethyleneamino)ethylcarbamothioyl]benzamide H₃L′, N-(1-(3-benzoylthioureido)propan-2-ylcarbamothioyl)-benzamide H₄L″, (E)-N-[4-(benzamidomethyleneamino)phenylcarbamothioyl]benzamide H₃L‴, were synthesized. Structures of the compounds were identified by spectroscopic techniques. In addition, all synthesized compounds were evaluated for in vitro antibacterial and antifungal activity. Compound H₃L‴ exhibited antibacterial activity.     

Sol–gel doped TiO<Subscript>2</Subscript> nanomaterials: a comparative study

Among the great number of sol–gel prepared nanomaterials, TiO₂ has attracted significant interest due to its high photocatalytic activity, excellent functionality, thermal stability and non-toxicity. The photocatalytic degradation of pollutants using un-doped and doped TiO₂ nanopowders or thin films is very attractive for applications in environmental protection, as a possible solution for water purification. The present work describes a comparative structural and chemical study of un-doped TiO₂ and the corresponding S- and Ag-doped materials. The photocatalytic activity was established by testing the degradation of organic chloride compounds from aqueous solutions. Sol–gel Ag-doped TiO₂ coatings, prepared by co-gelation and sol–gel Ag-doped TiO₂ coatings obtained from nanopowders were also compared. Their structural evolution and crystallization behaviour (lattice parameters, crystallite sizes, internal strains) with thermal treatment were followed by thermal analysis, X-ray diffraction, transmission electron microscopy, atomic force microscopy and specific surface areas measurements. X-ray photoelectron spectroscopy analyses were performed to characterize the surface composition and S or Ag speciation, which was used to interpret the catalytic data.     

Fixed point results for multivalued contractions on ordered gauge spaces

The purpose of this article is to present fixed point results for multivalued E _≤-contractions on ordered complete gauge space. Our theorems generalize and extend some recent results given in M. Frigon [7], S. Reich [12], I.A. Rus and A. Petruşel [15] and I.A. Rus et al. [16].      

Utilization of blast furnace slag nano-fluids in two-phase closed thermos-syphon heat pipes for enhancing heat transfer

This article deals with utilization of blast furnace slag nano-fluids in two-phase closed thermo-syphon heat pipes for enhancing heat transfer at various states of operation. The utilization of nano-fluids obtained from X₂O₃-, XO-, XO₂-, and X₂O-type oxides, such as Al₂O₃, Fe₂O₃, CaO, SiO₂, MgO, MnO, K₂O, and Na₂O, on the improvement of heat pipe performance has been separately reported in a number of studies in the literature. The present study experimentally demonstrated the effect of using a nano-fluid obtained from blast furnace slag comprised of various types of metal oxides in varying ratios on improving the performance of a heat pipe. The slag was obtained from the iron blast furnace of Karabük Iron Steel Workings (Turkey). Triton X-100 (Dow Chemical Company) dispersant was used in the study to produce the blast furnace slag/water nano-fluid via direct-synthesis. The 2 wt% concentration of blast furnace slag/water nano-fluid was used as the working fluid in heat pipes. A straight copper tube with an inner diameter of 13 mm, outer diameter of 15 mm, and length of 1 m was used as the heat pipe in the present experimental study. The nano-fluid filled 33.3% (44.2 ml) of the volume of the two-phase closed thermo-syphon. Three heating power levels (200, 300, and 400 W) were used in the experiments with three different flow rates of cooling water (5, 7.5, and 10 g/s) used in the condenser for cooling the system. An increase of 22% was achieved in thermal performance of the two-phase closed thermo-syphon when 2 wt% blast furnace slag containing nano-fluid was used to replace pure water at a heat load of 200 W with a cooling water flow rate of 5 g/s.     

A Note on the Relative Equilibria Bifurcations in the $$$$-Body Problem

Consider the planar Newtonian \((2N+1)\)-body problem, \(N\ge 1,\) with \(2N\) bodies of unit mass and one body of mass \(m\). Using the discrete symmetry due to the equal masses and reducing by the rotational symmetry, we show that solutions with the \(2N\) unit mass points at the vertices of two concentric regular \(N\)-gons and \(m\) at the centre at all times form invariant manifold. We study the regular \(2N\)-gon with central mass \(m\) relative equilibria within the dynamics on the invariant manifold described above. As \(m\) varies, we identify the bifurcations, relate our results to previous work and provide the spectral picture of the linearization at the relative equilibria.