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.

Modelling and Simulation of ERTMS for Current and Future Mobile Technologies

Nowadays, train control in-lab simulation tools play a crucial role in reducing extensive and expensive on-site railway testing activities. In this paper, we present our contribution in this arena by detailing the internals of our European Railway Train Management System in-lab demonstrator. This demonstrator is built over a general-purpose simulation framework, Riverbed Modeler, previously Opnet Modeler. Our framework models both ERTMS subsystems, the Automatic Train Protection application layer based on movement authority message exchange and the telecommunication subsystem based on GSM-R communication technology. We provide detailed information on our modelling strategy. We also validate our simulation framework with real trace data. To conclude, under current industry migration scenario from GSM-R legacy obsolescence to IP-based heterogeneous technologies, our simulation framework represents a singular tool to railway operators. As an example, we present the assessment of related performance indicators for a specific railway network using a candidate replacement technology, LTE, versus current legacy technology. To the best of our knowledge, there is no similar initiative able to measure the impact of the telecommunication subsystem in the railway network availability.

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.

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.

In Vitro Degradation of Poly(caprolactone)/nHA Composites

The degradation behavior and mechanical properties of polycaprolactone/nanohydroxyapatite composite scaffolds are studied in phosphate buffered solution (PBS), at 37 degrees C, over 16 weeks. Under scanning electron microscopy (SEM), it was observed that the longer the porous scaffolds remained in the PBS, the more significant the thickening of the pore walls of the scaffold morphology was. A decrease in the compressive properties, such as the modulus and the strength of the PCL/nHA composite scaffolds, was observed as the degradation experiment progressed. Samples with high nHA concentrations degraded more significantly in comparison to those with a lower content. Pure PCL retained its mechanical properties comparatively well in the study over the period of degradation. After the twelfth week, the results obtained by GPC analysis indicated a significant reduction in their molecular weight. The addition of nHA particles to the scaffolds accelerated the weight loss of the composites and increased their capacity to absorb water during the initial degradation process. The addition of these particles also affected the degradation behavior of the composite scaffolds, although they were not effective at compensating the decrease in pH prompted by the degradation products of the PCL.

A Novel Scheduling Index Rule Proposal for QoE Maximization in Wireless Networks

This paper deals with the resource allocation problem aimed at maximizing users' perception of quality in wireless channels with time-varying capacity. First of all, we model the subjective quality-aware scheduling problem in the framework of Markovian decision processes. Then, given that the obtaining of the optimal solution of this model is unachievable, we propose a simple scheduling index rule with closed-form expression by using a methodology based on Whittle approach. Finally, we analyze the performance of the achieved scheduling proposal in several relevant scenarios, concluding that it outperforms the most popular existing resource allocation strategies.

Approximate Solutions by Truncated Taylor Series Expansions of Nonlinear Differential Equations and Related Shadowing Property with Applications

This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial condition. The class of differential equations is assumed to be approximated by well-posed truncated Taylor series expansions up to a certain order obtained about certain, in general nonperiodic, sampling points t(i) is an element of [t(0), t(J)] for i = 0, 1, . . . , J of the solution. Two examples are provided.

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.

On Nonnegative Solutions of Fractional q-Linear Time-Varying Dynamic Systems with Delayed Dynamics

This paper is devoted to the investigation of nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic linear time-varying systems involving delayed dynamics with delays. The dynamic systems are described based on q-calculus and Caputo fractional derivatives on any order.

A New Type of Coincidence and Common Fixed Point Theorem with Applications

Coincidence and common fixed point theorems for a class of 'Ciric-Suzuki hybrid contractions involving a multivalued and two single-valued maps in a metric space are obtained. Some applications including the existence of a common solution for certain class of functional equations arising in a dynamic programming are also discussed..

Hole-Phonon Relaxation and Photocatalytic Properties of Titanium Dioxide and Zinc Oxide: First-Principles Approach

First-principles calculations for the temporal characteristics of hole-phonon relaxation in the valence band of titanium dioxide and zinc oxide have been performed. A first-principles method for the calculations of the quasistationary distribution function of holes has been developed. The results show that the quasistationary distribution of the holes in TiO2 extends to an energy level approximately 1eV below the top of the valence band. This conclusion in turn helps to elucidate the origin of the spectral dependence of the photocatalytic activity of TiO2. Analysis of the analogous data for ZnO shows that in this material spectral dependence of photocatalytic activity in the oxidative reactions is unlikely.

Influence of Humidity on Fiber Bragg Grating Sensors

We demonstrate the influence of the relative humidity (RH) on the wavelength of fiber Bragg grating sensors (FBGS), performing tests with five FBGS at different humidity and temperature conditions. These tests were performed in a climate chamber whose RH changes according to a scheduled profile from 30% to 90%, in steps of 10%. These profiles were repeated for a wide range of temperatures from 10 degrees C to 70 degrees C, in steps of 10 degrees C. Two different types of instrumentation methods have been tested, spot welding and epoxy bonding, in two different materials, steel and carbon fiber reinforced polymer (CFRP). We discuss the results for each type of sensor and instrumentation method by analyzing the linearity of the Bragg wavelength with RH and temperature.

Stability analysis and observer design for discrete-time SEIR epidemic models

This paper applies Micken's discretization method to obtain a discrete-time SEIR epidemic model. The positivity of the model along with the existence and stability of equilibrium points is discussed for the discrete-time case. Afterwards, the design of a state observer for this discrete-time SEIR epidemic model is tackled. The analysis of the model along with the observer design is faced in an implicit way instead of obtaining first an explicit formulation of the system which is the novelty of the presented approach. Moreover, some sufficient conditions to ensure the asymptotic stability of the observer are provided in terms of a matrix inequality that can be cast in the form of a LMI. The feasibility of the matrix inequality is proved, while some simulation examples show the operation and usefulness of the observer.

An approach version of fuzzy metric spaces including an ad hoc fixed point theorem

In this paper, inspired by two very different, successful metric theories such us the real view-point of Lowen's approach spaces and the probabilistic field of Kramosil and Michalek's fuzzymetric spaces, we present a family of spaces, called fuzzy approach spaces, that are appropriate to handle, at the same time, both measure conceptions. To do that, we study the underlying metric interrelationships between the above mentioned theories, obtaining six postulates that allow us to consider such kind of spaces in a unique category. As a result, the natural way in which metric spaces can be embedded in both classes leads to a commutative categorical scheme. Each postulate is interpreted in the context of the study of the evolution of fuzzy systems. First properties of fuzzy approach spaces are introduced, including a topology. Finally, we describe a fixed point theorem in the setting of fuzzy approach spaces that can be particularized to the previous existing measure spaces.

Efficient Synthesis of Single-Chain Polymer Nanoparticles via Amide Formation

Single-chain technology (SCT) allows the transformation of individual polymer chains to folded/collapsed unimolecular soft nanoparticles. In this work we contribute to the enlargement of the SCT toolbox by demonstrating the efficient synthesis of single-chain polymer nanoparticles (SCNPs) via intrachain amide formation. In particular, we exploit cross-linking between active methylene groups and isocyanate moieties as powerful "click" chemistry driving force for SCNP construction. By employing poly(methyl methacrylate)- (PMMA-) based copolymers bearing beta-ketoester units distributed randomly along the copolymer chains and bifunctional isocyanate cross-linkers, SCNPs were successfully synthesized at r.t. under appropriate reaction conditions. Characterization of the resulting SCNPs was carried out by means of a combination of techniques including size exclusion chromatography (SEC), infrared (IR) spectroscopy, proton nuclear magnetic resonance (H-1 NMR) spectroscopy, dynamic light scattering (DLS), and elemental analysis (EA).