Some Results on Fixed and Best Proximity Points of Multivalued

This paper is devoted to investigate the fixed points and best proximity points of multivalued cyclic self-mappings on a set of subsets of complete metric spaces endowed with a partial order under a generalized contractive condition involving a Hausdorff distance. The existence and uniqueness of fixed points of both the cyclic self-mapping and its associate composite self-mappings on each of the subsets are investigated, if the subsets in the cyclic disposal are nonempty, bounded and of nonempty convex intersection. The obtained results are extended to the existence of unique best proximity points in uniformly convex Banach spaces.

Pata contractions and coupled type fixed points

A new coupled fixed point theorem related to the Pata contraction for mappings having the mixed monotone property in partially ordered complete metric spaces is established. It is shown that the coupled fixed point can be unique under some extra suitable conditions involving mid point lower or upper bound properties. Also the corresponding convergence rate is estimated when the iterates of our function converge to its coupled fixed point.

In vitro activities of natural products against oral Candida isolates from denture wearers

Background: Candida-associated denture stomatitis is a frequent infectious disease. Treatment of this oral condition is difficult because failures and recurrences are common. The aim of this study was to test the in vitro antifungal activity of pure constituents of essentials oils. -- Methods: Eight terpenic derivatives (carvacrol, farnesol, geraniol, linalool, menthol, menthone, terpinen-4-ol, and aterpineol), a phenylpropanoid (eugenol), a phenethyl alcohol (tyrosol) and fluconazole were evaluated against 38 Candida isolated from denture-wearers and 10 collection Candida strains by the CLSI M27-A3 broth microdilution method. -- Results: Almost all the tested compounds showed antifungal activity with MIC ranges of 0.03-0.25% for eugenol and linalool, 0.03-0.12% for geraniol, 0.06-0.5% for menthol, a-terpineol and terpinen-4-ol, 0.03-0.5% for carvacrol, and 0.06-4% for menthone. These compounds, with the exception of farnesol, menthone and tyrosol, showed important in vitro activities against the fluconazole-resistant and susceptible-dose dependent Candida isolates. -- Conclusions: Carvacrol, eugenol, geraniol, linalool and terpinen-4-ol were very active in vitro against oral Candida isolates. Their fungistatic and fungicidal activities might convert them into promising alternatives for the topic treatment of oral candidiasis and denture stomatitis.

Fixed and Best Proximity Points of Cyclic Jointly Accretive and Contractive Self-Mappings

p(>= 2)-cyclic and contractive self-mappings on a set of subsets of a metric space which are simultaneously accretive on the whole metric space are investigated. The joint fulfilment of the p-cyclic contractiveness and accretive properties is formulated as well as potential relationships with cyclic self-mappings in order to be Kannan self-mappings. The existence and uniqueness of best proximity points and fixed points is also investigated as well as some related properties of composed self-mappings from the union of any two adjacent subsets, belonging to the initial set of subsets, to themselves.

Fixed Points of Closed and Compact Composite Sequences of Operators and Projectors in a Class of Banach Spaces

Some results on fixed points related to the contractive compositions of bounded operators in a class of complete metric spaces which can be also considered as Banach's spaces are discussed through the paper. The class of composite operators under study can include, in particular, sequences of projection operators under, in general, oblique projective operators. In this paper we are concerned with composite operators which include sequences of pairs of contractive operators involving, in general, oblique projection operators. The results are generalized to sequences of, in general, nonconstant bounded closed operators which can have bounded, closed, and compact limit operators, such that the relevant composite sequences are also compact operators. It is proven that in both cases, Banach contraction principle guarantees the existence of unique fixed points under contractive conditions.

On Best Proximity Point Theorems and Fixed Point Theorems for p-Cyclic Hybrid Self-Mappings in Banach Spaces

This paper relies on the study of fixed points and best proximity points of a class of so-called generalized point-dependent (K-Lambda)hybrid p-cyclic self-mappings relative to a Bregman distance Df, associated with a Gâteaux differentiable proper strictly convex function f in a smooth Banach space, where the real functions Lambda and K quantify the point-to-point hybrid and nonexpansive (or contractive) characteristics of the Bregman distance for points associated with the iterations through the cyclic self-mapping.Weak convergence results to weak cluster points are obtained for certain average sequences constructed with the iterates of the cyclic hybrid self-mappings.

Some Results on Fixed and Best Proximity Points of Precyclic Self-Mappings

12 p.

Advances in Nonlinear Complexity Analysis for Partial Differential Equations

1 p. -- [Editorial Material]

TWEAK/Fn14 Signaling Is Required for Liver Regeneration after Partial Hepatectomy in Mice

Background & Aims: Pro-inflammatory cytokines are important for liver regeneration after partial hepatectomy (PH). Expression of Fibroblast growth factor-inducible 14 (Fn14), the receptor for TNF-like weak inducer of apoptosis (TWEAK), is induced rapidly after PH and remains elevated throughout the period of peak hepatocyte replication. The role of Fn14 in post-PH liver regeneration is uncertain because Fn14 is expressed by liver progenitors and TWEAK-Fn14 interactions stimulate progenitor growth, but replication of mature hepatocytes is thought to drive liver regeneration after PH. Methods: To clarify the role of TWEAK-Fn14 after PH, we compared post-PH regenerative responses in wild type (WT) mice, Fn14 knockout (KO) mice, TWEAK KO mice, and WT mice treated with anti-TWEAK antibodies. Results: In WT mice, rare Fn14(+) cells localized with other progenitor markers in peri-portal areas before PH. PH rapidly increased proliferation of Fn14(+) cells; hepatocytic cells that expressed Fn14 and other progenitor markers, such as Lgr5, progressively accumulated from 12-8 h post-PH and then declined to baseline by 96 h. When TWEAK/Fn14 signaling was disrupted, progenitor accumulation, induction of pro-regenerative cytokines, hepatocyte and cholangiocyte proliferation, and over-all survival were inhibited, while post-PH liver damage and bilirubin levels were increased. TWEAK stimulated proliferation and increased Lgr5 expression in cultured liver progenitors, but had no effect on either parameter in cultured primary hepatocytes. Conclusions: TWEAK-FN14 signaling is necessary for the healthy adult liver to regenerate normally after acute partial hepatectomy.

Advanced Reaction Systems for Hydrogen Production

[EN] This PhD work started in March 2010 with the support of the University of the Basque Country (UPV/EHU) under the program named “Formación de Personal Investigador” at the Chemical and Environmental Engineering Department in the Faculty of Engineering of Bilbao. The major part of the Thesis work was carried out in the mentioned department, as a member of the Sustainable Process Engineering (SuPrEn) research group. In addition, this PhD Thesis includes the research work developed during a period of 6 months at the Institut für Mikrotechnik Mainz GmbH, IMM, in Germany. During the four years of the Thesis, conventional and microreactor systems were tested for several feedstocks renewable and non-renewable, gases and liquids through several reforming processes in order to produce hydrogen. For this purpose, new catalytic formulations which showed high activity, selectivity and stability were design. As a consequence, the PhD work performed allowed the publication of seven scientific articles in peer-reviewed journals. This PhD Thesis is divided into the following six chapters described below. The opportunity of this work is established on the basis of the transition period needed for moving from a petroleum based energy system to a renewable based new one. Consequently, the present global energy scenario was detailed in Chapter 1, and the role of hydrogen as a real alternative in the future energy system was justified based on several outlooks. Therefore, renewable and non-renewable hydrogen production routes were presented, explaining the corresponding benefits and drawbacks. Then, the raw materials used in this Thesis work were described and the most important issues regarding the processes and the characteristics of the catalytic formulations were explained. The introduction chapter finishes by introducing the concepts of decentralized production and process intensification with the use of microreactors. In addition, a small description of these innovative reaction systems and the benefits that entailed their use were also mentioned. In Chapter 2 the main objectives of this Thesis work are summarized. The development of advanced reaction systems for hydrogen rich mixtures production is the main objective. In addition, the use and comparison between two different reaction systems, (fixed bed reactor (FBR) and microreactor), the processing of renewable raw materials, the development of new, active, selective and stable catalytic formulations, and the optimization of the operating conditions were also established as additional partial objectives. Methane and natural gas (NG) steam reforming experimental results obtained when operated with microreactor and FBR systems are presented in Chapter 3. For these experiments nickel-based (Ni/Al2O3 and Ni/MgO) and noble metal-based (Pd/Al2O3 and Pt/Al2O3) catalysts were prepared by wet impregnation and their catalytic activity was measured at several temperatures, from 973 to 1073 K, different S/C ratios, from 1.0 to 2.0, and atmospheric pressure. The Weight Hourly Space Velocity (WHSV) was maintained constant in order to compare the catalytic activity in both reaction systems. The results obtained showed a better performance of the catalysts operating in microreactors. The Ni/MgO catalyst reached the highest hydrogen production yield at 1073 K and steam-to-carbon ratio (S/C) of 1.5 under Steam methane Reforming (SMR) conditions. In addition, this catalyst also showed good activity and stability under NG reforming at S/C=1.0 and 2.0. The Ni/Al2O3 catalyst also showed high activity and good stability and it was the catalyst reaching the highest methane conversion (72.9 %) and H2out/CH4in ratio (2.4) under SMR conditions at 1073 K and S/C=1.0. However, this catalyst suffered from deactivation when it was tested under NG reforming conditions. Regarding the activity measurements carried out with the noble metal-based catalysts in the microreactor systems, they suffered a very quick deactivation, probably because of the effects attributed to carbon deposition, which was detected by Scanning Electron Microscope (SEM). When the FBR was used no catalytic activity was measured with the catalysts under investigation, probably because they were operated at the same WHSV than the microreactors and these WHSVs were too high for FBR system. In Chapter 4 biogas reforming processes were studied. This chapter starts with an introduction explaining the properties of the biogas and the main production routes. Then, the experimental procedure carried out is detailed giving concrete information about the experimental set-up, defining the parameters measured, specifying the characteristics of the reactors used and describing the characterization techniques utilized. Each following section describes the results obtained from activity testing with the different catalysts prepared, which is subsequently summarized: Section 4.3: Biogas reforming processes using γ-Al2O3 based catalysts The activity results obtained by several Ni-based catalysts and a bimetallic Rh-Ni catalyst supported on magnesia or alumina modified with oxides like CeO2 and ZrO2 are presented in this section. In addition, an alumina-based commercial catalyst was tested in order to compare the activity results measured. Four different biogas reforming processes were studied using a FBR: dry reforming (DR), biogas steam reforming (BSR), biogas oxidative reforming (BOR) and tri-reforming (TR). For the BSR process different steam to carbon ratios (S/C) from 1.0 to 3.0, were tested. In the case of BOR process the oxygen-to-methane (O2/CH4) ratio was varied from 0.125 to 0.50. Finally, for TR processes different S/C ratios from 1.0 to 3.0, and O2/CH4 ratios of 0.25 and 0.50 were studied. Then, the catalysts which achieved high activity and stability were impregnated in a microreactor to explore the viability of process intensification. The operation with microreactors was carried out under the best experimental conditions measured in the FBR. In addition, the physicochemical characterization of the fresh and spent catalysts was carried out by Inductively Coupled Plasma Atomic Emission Spectroscopy (ICP-AES), N2 physisorption, H2 chemisorption, Temperature Programmed Reduction (TPR), SEM, X-ray Photoelectron Spectroscopy (XPS) and X-ray powder Diffraction (XRD). Operating with the FBR, conversions close to the ones predicted by thermodynamic calculations were obtained by most of the catalysts tested. The Rh-Ni/Ce-Al2O3 catalyst obtained the highest hydrogen production yield in DR. In BSR process, the Ni/Ce-Al2O3 catalyst achieved the best activity results operating at S/C=1.0. In the case of BOR process, the Ni/Ce-Zr-Al2O3 catalyst showed the highest reactants conversion values operating at O2/CH4=0.25. Finally, in the TR process the Rh-Ni/Ce-Al2O3 catalyst obtained the best results operating at S/C=1.0 and O2/CH4=0.25. Therefore, these three catalysts were selected to be coated onto microchannels in order to test its performance under BOR and TR processes conditions. Although the operation using microreactors was carried out under considerably higher WHSV, similar conversions and yields as the ones measured in FBR were measured. Furthermore, attending to other measurements like Turnover Frequency (TOF) and Hydrogen Productivity (PROD), the values calculated for the catalysts tested in microreactors were one order of magnitude higher. Thus, due to the low dispersion degree measured by H2-chemisorption, the Ni/Ce-Al2O3 catalyst reached the highest TOF and PROD values. Section 4.4: Biogas reforming processes using Zeolites L based catalysts In this section three type of L zeolites, with different morphology and size, were synthesized and used as catalyst support. Then, for each type of L zeolite three nickel monometallic and their homologous Rh-Ni bimetallic catalysts were prepared by the wetness impregnation method. These catalysts were tested using the FBR under DR process and different conditions of BSR (S/C ratio of 1.0 and 2.0), BOR (O2/CH4 ratio of 0.25 and 0.50) and TR processes (at S/C=1.0 and O2/CH4=0.25). The characterization of these catalysts was also carried out by using the same techniques mentioned in the previous section. Very high methane and carbon dioxide conversion values were measured for almost all the catalysts under investigation. The experimental results evidenced the better catalytic behavior of the bimetallic catalysts as compared to the monometallic ones. Comparing the catalysts behavior with regards to their morphology, for the BSR process the Disc catalysts were the most active ones at the lowest S/C ratio tested. On the contrary, the Cylindrical (30–60 nm) catalysts were more active under BOR conditions at O2/CH4=0.25 and TR processes. By the contrary, the Cylindrical (1–3 µm) catalysts showed the worst activity results for both processes. Section 4.5: Biogas reforming processes using Na+ and Cs+ doped Zeolites LTL based catalysts A method for the synthesis of Linde Type L (LTL) zeolite under microwave-assisted hydrothermal conditions and its behavior as a support for heterogeneously catalyzed hydrogen production is described in this section. Then, rhodium and nickel-based bimetallic catalysts were prepared in order to be tested by DR process and BOR process at O2/CH4=0.25. Moreover, the characterization of the catalysts under investigation was also carried out. Higher activities were achieved by the catalysts prepared from the non-doped zeolites, Rh-Ni/D and Rh-Ni/N, as compared to the ones supported on Na+ and Cs+ exchanged supports. However, the differences between them were not very significant. In addition, the Na+ and Cs+ incorporation affected mainly to the Disc catalysts. Comparing the results obtained by these catalysts with the ones studied in the section 4.4, in general worst results were achieved under DR conditions and almost the same results when operated under BOR conditions. In Chapter 5 the ethylene glycol (EG) as feed for syngas production by steam reforming (SR) and oxidative steam reforming (OSR) was studied by using microchannel reactors. The product composition was determined at a S/C of 4.0, reaction temperatures between 625°C and 725°C, atmospheric pressure and Volume Hourly Space Velocities (VHSV) between 100 and 300 NL/(gcath). This work was divided in two sections. The first one corresponds to the introduction of the main and most promising EG production routes. Then, the new experimental procedure is detailed and the information about the experimental set-up and the measured parameters is described. The characterization was carried out using the same techniques as for the previous chapter. Then, the next sections correspond to the catalytic activity and catalysts characterization results. Section 5.3: xRh-cm and xRh-np catalysts for ethylene glycol reforming Initially, catalysts with different rhodium loading, from 1.0 to 5.0 wt. %, and supported on α-Al2O3 were prepared by two different preparation methods (conventional impregnation and separate nanoparticle synthesis). Then, the catalysts were compared regarding their measured activity and selectivity, as well as the characterization results obtained before and after the activity tests carried out. The samples prepared by a conventional impregnation method showed generally higher activity compared to catalysts prepared from Rh nanoparticles. By-product formation of species such as acetaldehyde, ethane and ethylene was detected, regardless if oxygen was added to the feed or not. Among the catalysts tested, the 2.5Rh-cm catalyst was considered the best one. Section 5.4: 2.5Rh-cm catalyst support modification with CeO2 and La2O3 In this part of the Chapter 5, the catalyst showing the best performance in the previous section, the 2.5Rh-Al2O3 catalyst, was selected in order to be improved. Therefore, new Rh based catalysts were designed using α-Al2O3 and being modified this support with different contents of CeO2 or La2O3 oxides. All the catalysts containing additives showed complete conversion and selectivities close to the equilibrium in both SR and OSR processes. In addition, for these catalysts the concentrations measured for the C2H4, CH4, CH3CHO and C2H6 by-products were very low. Finally, the 2.5Rh-20Ce catalyst was selected according to its catalytic activity and characterization results in order to run a stability test, which lasted more than 115 hours under stable operation. The last chapter, Chapter 6, summarizes the main conclusions achieved throughout this Thesis work. Although very high reactant conversions and rich hydrogen mixtures were obtained using a fixed bed reaction system, the use of microreactors improves the key issues, heat and mass transfer limitations, through which the reforming reactions are intensified. Therefore, they seem to be a very interesting and promising alternative for process intensification and decentralized production for remote application.

Common Fixed Points of Generalized Rational Type Cocyclic Mappings in Multiplicative Metric Spaces

The aim of this paper is to present fixed point result of mappings satisfying a generalized rational contractive condition in the setup of multiplicative metric spaces. As an application, we obtain a common fixed point of a pair of weakly compatible mappings. Some common fixed point results of pair of rational contractive types mappings involved in cocyclic representation of a nonempty subset of a multiplicative metric space are also obtained. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature.

Coincidence and common fixed point theorems for Suzuki type hybrid contractions and applications

Coincidence and common fixed point theorems for a class of Suzuki hybrid contractions involving two pairs of single-valued and multivalued maps in a metric space are obtained. In addition, the existence of a common solution for a certain class of functional equations arising in a dynamic programming is also discussed.

On contractive cyclic fuzzy maps in metric spaces and some related results on fuzzy best proximity points and fuzzy fixed points

This paper investigates some properties of cyclic fuzzy maps in metric spaces. The convergence of distances as well as that of sequences being generated as iterates defined by a class of contractive cyclic fuzzy mapping to fuzzy best proximity points of (non-necessarily intersecting adjacent subsets) of the cyclic disposal is studied. An extension is given for the case when the images of the points of a class of contractive cyclic fuzzy mappings restricted to a particular subset of the cyclic disposal are allowed to lie either in the same subset or in its next adjacent one.

TWEAK/Fn14 Signaling Is Required for Liver Regeneration after Partial Hepatectomy in Mice

Background & Aims: Pro-inflammatory cytokines are important for liver regeneration after partial hepatectomy (PH). Expression of Fibroblast growth factor-inducible 14 (Fn14), the receptor for TNF-like weak inducer of apoptosis (TWEAK), is induced rapidly after PH and remains elevated throughout the period of peak hepatocyte replication. The role of Fn14 in post-PH liver regeneration is uncertain because Fn14 is expressed by liver progenitors and TWEAK-Fn14 interactions stimulate progenitor growth, but replication of mature hepatocytes is thought to drive liver regeneration after PH. Methods: To clarify the role of TWEAK-Fn14 after PH, we compared post-PH regenerative responses in wild type (WT) mice, Fn14 knockout (KO) mice, TWEAK KO mice, and WT mice treated with anti-TWEAK antibodies. Results: In WT mice, rare Fn14(+) cells localized with other progenitor markers in peri-portal areas before PH. PH rapidly increased proliferation of Fn14(+) cells; hepatocytic cells that expressed Fn14 and other progenitor markers, such as Lgr5, progressively accumulated from 12-8 h post-PH and then declined to baseline by 96 h. When TWEAK/Fn14 signaling was disrupted, progenitor accumulation, induction of pro-regenerative cytokines, hepatocyte and cholangiocyte proliferation, and over-all survival were inhibited, while post-PH liver damage and bilirubin levels were increased. TWEAK stimulated proliferation and increased Lgr5 expression in cultured liver progenitors, but had no effect on either parameter in cultured primary hepatocytes. Conclusions: TWEAK-FN14 signaling is necessary for the healthy adult liver to regenerate normally after acute partial hepatectomy.

Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability

This paper investigates the boundedness and convergence properties of two general iterative processes which involve sequences of self-mappings on either complete metric or Banach spaces. The sequences of self-mappings considered in the first iterative scheme are constructed by linear combinations of a set of self-mappings, each of them being a weighted version of a certain primary self-mapping on the same space. The sequences of self-mappings of the second iterative scheme are powers of an iteration-dependent scaled version of the primary self-mapping. Some applications are also given to the important problem of global stability of a class of extended nonlinear polytopic-type parameterizations of certain dynamic systems.