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.

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.

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..

Losses in self-oscillating ballasts for electrode-type compact fluorescent lamps

Commercially available integrated compact fluorescent lamps (CFLs) use self-resonant ballasts on grounds of simplicity and cost. To understand how to improve ballast efficiency, it is necessary to quantify the losses. The losses occurring in these ballasts have been directly measured using a precision mini-calorimeter. In addition, a Pspice model has been used to simulate the performance of an 18 W integrated CFL. The lamp has been represented by a behavioural model and Jiles-Atherton equations were used to model the current transformer core. The total loss is in close agreement with measurements from the mini-calorimeter, confirming the accuracy of the model. The total loss was then disaggregated into component losses by simulation, showing that the output inductor is the primary source of loss, followed by the inverter switches. © 2011 The Institution of Engineering and Technology.

On equations for regular languages, finite automata, and sequential networks

We consider systems of equations of the form where A is the underlying alphabet, the Xi are variables, the Pi,a are boolean functions in the variables Xi, and each δi is either the empty word or the empty set. The symbols υ and denote concatenation and union of languages over A. We show that any such system has a unique solution which, moreover, is regular. These equations correspond to a type of automation, called boolean automation, which is a generalization of a nondeterministic automation. The equations are then used to determine the language accepted by a sequential network; they are obtainable directly from the network.

Effects of temperature and irradiance on early development of Chondrus ocellatus Holm (Gigartinaceae, Rhodophyta)

Chondrus is a type of commercially produced red seaweed that widely used for food and carrageen extraction. Although the natural life history of the alga had been well understood, the factors influencing development of the tetraspore and carpospore remain poorly understood. In the perspective of seedling resources, the regulation of early development is crucial for the seedling nursing; therefore, it is necessary to understand the physiological influences during its early development. In this study, we studied the effects of temperature and irradiance on the early development of Chondrus ocellatus Holm under laboratory conditions. The released tetraspores and carpospores were cultivated at different temperatures (10-28 degrees C) and irradiances ( 10, 60 mu mol photons m(-2)s(-1)) with a photoperiod of 12L:12D. The results indicate that both tetraspores and carpospores are tolerant to temperatures of 10-25 degrees C, and have the highest relative growth rate at 20 degrees C. Irradiance variances influenced the growth of the discoid crusts, and the influence was more significant with increasing temperature; 60 mu mol photons m(-2)s(-1) was more suitable than 10 mu mol photons m(-2)s(-1). The optimum temperature and irradiance for the development of seedlings was 20 degrees C and 60 mu mol photons m(-2)s(-1), respectively.

Creation of a complex butterfly attractor using a novel Lorenz-type system

A novel Lorenz-type system of nonlinear differential equations is proposed. Unlike the original Lorenz system, where the chaotic dynamics remain confined to the positive half-space with respect to the Z state variable due to a limiting threshold effect, the proposed system enables bipolar swing of this state variable. In addition, the classical set of parameters (a, b, c) controlling the behavior of the Lorenz system are reduced to a single parameter, namely a. Two possible modes of operation are admitted by the system; switching between these two modes results in the creation of a complex butterfly chaotic attractor. Numerical simulations and results from an experimental setup are presented

Uniformly convergent finite element and finite difference methods for singularly perturbed ordinary differential equations

This thesis is concerned with uniformly convergent finite element and finite difference methods for numerically solving singularly perturbed two-point boundary value problems. We examine the following four problems: (i) high order problem of reaction-diffusion type; (ii) high order problem of convection-diffusion type; (iii) second order interior turning point problem; (iv) semilinear reaction-diffusion problem. Firstly, we consider high order problems of reaction-diffusion type and convection-diffusion type. Under suitable hypotheses, the coercivity of the associated bilinear forms is proved and representation results for the solutions of such problems are given. It is shown that, on an equidistant mesh, polynomial schemes cannot achieve a high order of convergence which is uniform in the perturbation parameter. Piecewise polynomial Galerkin finite element methods are then constructed on a Shishkin mesh. High order convergence results, which are uniform in the perturbation parameter, are obtained in various norms. Secondly, we investigate linear second order problems with interior turning points. Piecewise linear Galerkin finite element methods are generated on various piecewise equidistant meshes designed for such problems. These methods are shown to be convergent, uniformly in the singular perturbation parameter, in a weighted energy norm and the usual L2 norm. Finally, we deal with a semilinear reaction-diffusion problem. Asymptotic properties of solutions to this problem are discussed and analysed. Two simple finite difference schemes on Shishkin meshes are applied to the problem. They are proved to be uniformly convergent of second order and fourth order respectively. Existence and uniqueness of a solution to both schemes are investigated. Numerical results for the above methods are presented.

Moment decay rates of solutions of stochastic differential equations

The objective of this paper is to investigate the p-ίh moment asymptotic stability decay rates for certain finite-dimensional Itό stochastic differential equations. Motivated by some practical examples, the point of our analysis is a special consideration of general decay speeds, which contain as a special case the usual exponential or polynomial type one, to meet various situations. Sufficient conditions for stochastic differential equations (with variable delays or not) are obtained to ensure their asymptotic properties. Several examples are studied to illustrate our theory.

On subspace lattices I. Closedness type properties and tensor products

We study properties of subspace lattices related to the continuity of the map Lat and the notion of reflexivity. We characterize various “closedness” properties in different ways and give the hierarchy between them. We investigate several properties related to tensor products of subspace lattices and show that the tensor product of the projection lattices of two von Neumann algebras, one of which is injective, is reflexive.

Asymptotic layer-type model of high pressure direct current glow discharge in electronegative gases

Here a self-consistent one-dimensional continuum model is presented for a narrow gap plane-parallel dc glow discharge. The governing equations consist of continuity and momentum equations for positive and negative ions and electrons coupled with Poisson's equation. A singular perturbation method is developed for the analysis of high pressure dc glow discharge. The kinetic processes of the ionization, electron attachment, and ion-ion recombination are included in the model. Explicit results are obtained for the asymptotic limits: delta=(r(D)/L)(2)--> 0, omega=(r(S)/L)(2)--> 0, where r(D) is the Debye radius, r(S) is recombination length, and L is the gap length. The discharge gap divides naturally into four layers with multiple space scales: anode fall region, positive column, transitional region, cathode fall region and diffusion layer adjacent to the cathode surface, its formation is discussed. The effects of the gas pressure, gap spacing and dc voltage on the electrical properties of the layers and its dimension are investigated. (C) 2000 American Institute of Physics. [S0021-8979(00)00813-6].

Time-dependent three-dimensional spectrum synthesis for Type Ia supernovae

A Monte Carlo code (artis) for modelling time-dependent three-dimensional spectral synthesis in chemically inhomogeneous models of Type Ia supernova ejecta is presented. Following the propagation of ?-ray photons, emitted by the radioactive decay of the nucleosynthesis products, energy is deposited in the supernova ejecta and the radiative transfer problem is solved self-consistently, enforcing the constraint of energy conservation in the comoving frame. Assuming a photoionization-dominated plasma, the equations of ionization equilibrium are solved together with the thermal balance equation adopting an approximate treatment of excitation. Since we implement a fully general treatment of line formation, there are no free parameters to adjust. Thus, a direct comparison between synthetic spectra and light curves, calculated from hydrodynamic explosion models, and observations is feasible. The code is applied to the well-known W7 explosion model and the results tested against other studies. Finally, the effect of asymmetric ejecta on broad-band light curves and spectra is illustrated using an elliptical toy model. © 2009 RAS.

Retinal vascular geometry predicts incident renal dysfunction in young people with type 1 diabetes

OBJECTIVE - To examine the relationship between retinal vascular geometry parameters and development of incident renal dysfunction in young people with type 1 diabetes. RESEARCH DESIGN AND METHODS - This was a prospective cohort study of 511 adolescents with type 1 diabetes of at least 2 years duration, with normal albumin excretion rate (AER) and no retinopathy at baseline while attending an Australian tertiary-care hospital. AER was quantified using three overnight, timed urine specimen collections and early renal dysfunction was defined as AER >7.5 µg/min. Retinal vascular geometry (including length-to-diameter ratio [LDR] and simple tortuosity [ST]) was quantified from baseline retinal photographs. Generalized estimating equations were used to examine the relationship between incident renal dysfunction and baseline venular LDR and ST, adjusting for age, diabetes duration, glycated hemoglobin (A1C), blood pressure (BP), BMI, and cholesterol. RESULTS - Diabetes duration at baseline was 4.8 (IQR 3.3-7.5) years. After amedian 3.7 (2.3-5.7) years follow-up, 34% of participants developed incident renal dysfunction. In multivariate analysis, higher retinal venular LDR (odds ratio 1.7, 95% CI 1.2-2.4; quartile 4 vs. 1-3) and lower venular ST (1.6, 1.1-2.2; quartile 1 vs. 2-4) predicted incident renal dysfunction. CONCLUSIONS - Retinal venular geometry independently predicted incident renal dysfunction in young people with type 1 diabetes. These noninvasive retinal measures may help to elucidate early mechanistic pathways for microvascular complications. Retinal venular geometry may be a useful tool to identify individuals at high risk of renal disease early in the course of diabetes. © 2012 by the American Diabetes Association.

Rocking behaviour of multi-block columns subjected to pulse-type ground motion accelerations

Ancient columns, made with a variety of materials such as marble, granite, stone or masonry are an important part of the
European cultural heritage. In particular columns of ancient temples in Greece and Sicily which support only the architrave are
characterized by small axial load values. This feature together with the slenderness typical of these structural members clearly
highlights as the evaluation of the rocking behaviour is a key aspect of their safety assessment and maintenance. It has to be noted
that the rocking response of rectangular cross-sectional columns modelled as monolithic rigid elements, has been widely investigated
since the first theoretical study carried out by Housner (1963). However, the assumption of monolithic member, although being
widely used and accepted for practical engineering applications, is not valid for more complex systems such as multi-block columns
made of stacked stone blocks, with or without mortar beds. In these cases, in fact, a correct analysis of the system should consider
rocking and sliding phenomena between the individual blocks of the structure. Due to the high non-linearity of the problem, the
evaluation of the dynamic behaviour of multi-block columns has been mostly studied in the literature using a numerical approach
such as the Discrete Element Method (DEM). This paper presents an introductory study about a proposed analytical-numerical
approach for analysing the rocking behaviour of multi-block columns subjected to a sine-pulse type ground motion. Based on the
approach proposed by Spanos (2001) for a system made of two rigid blocks, the Eulero-Lagrange method to obtain the motion
equations of the system is discussed and numerical applications are performed with case studies reported in the literature and with a
real acceleration record. The rocking response of single block and multi-block columns is compared and considerations are made
about the overturning conditions and on the effect of forcing function’s frequency.
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