n-Tupled Coincidence Point Theorems for Probabilistic ψ-Contractions in Menger Spaces

We introduced n-tupled coincidence point for a pair of maps T:Xn→X and A:X→X in Menger space. Utilizing the properties of the pseudometric and the triangular norm, we will establish n-tupled coincidence point theorems under weak compatibility as well as n-tupled fixed point theorems for hybrid probabilistic ψ-contractions with a gauge function. Our main results do not require the conditions of continuity and monotonicity of ψ. At the end of this paper, an example is given to support our main theorem.

Numerical Solvability and Solution of an Inverse Problem Related to the Gibbs Phenomenon

We report on the inverse problem for the truncated Fourier series representation of fx∈BV-L,L in a form with a quadratic degeneracy, revealing the existence of the Gibbs-Wilbraham phenomenon. A new distribution-theoretic proof is proposed for this phenomenon. The paper studies moreover the iterative numerical solvability and solution of this inverse problem near discontinuities of fx.

Building Expert Medical Prognostic Systems Using Voronoi Diagram

The method of building expert systems for medical prediction of severity in patients is purposed. The method is based on using Voronoi diagrams. Examples of using the method are described in the paper.

A New Study of Blind Deconvolution with Implicit Incorporation of Nonnegativity Constraints

The inverse problem of image restoration to remove noise and blur in an observed image was extensively studied in the last two decades. For the case of a known blurring kernel (or a known blurring type such as out of focus or Gaussian blur), many effective models and efficient solvers exist. However when the underlying blur is unknown, there have been fewer developments for modelling the so-called blind deblurring since the early works of You and Kaveh (1996) and Chan and Wong (1998). A major challenge is how to impose the extra constraints to ensure quality of restoration. This paper proposes a new transform based method to impose the positivity constraints automatically and then two numerical solution algorithms. Test results demonstrate the effectiveness and robustness of the proposed method in restoring blurred images.

Interval-Valued Neutrosophic Soft Rough Sets

We first defined interval-valued neutrosophic soft rough sets (IVN-soft rough sets for short) which combine interval-valued neutrosophic soft set and rough sets and studied some of its basic properties. This concept is an extension of interval-valued intuitionistic fuzzy soft rough sets (IVIF-soft rough sets).

Modified Eccentric Connectivity of Generalized Thorn Graphs

The thorn graph GT of a given graph G is obtained by attaching t(>0) pendent vertices to each vertex of G. The pendent edges, called thorns of GT, can be treated as P2 or K2, so that a thorn graph is generalized by replacing P2 by Pm and K2 by Kp and the respective generalizations are denoted by GPm and GKp. The modified eccentric connectivity index of a graph is defined as the sum of the products of eccentricity with the total degree of neighboring vertices, over all vertices of the graph in a hydrogen suppressed molecular structure. In this paper, we give the modified eccentric connectivity index and the concerned polynomial for the thorn graph GT and the generalized thorn graphs GKp and GPm.

Computation of a Canonical Form for Linear 2D Systems

Symbolic computation techniques are used to obtain a canonical form for polynomial matrices arising from discrete 2D linear state-space systems. The canonical form can be regarded as an extension of the companion form often encountered in the theory of 1D linear systems. Using previous results obtained by Boudellioua and Quadrat (2010) on the reduction by equivalence to Smith form, the exact connection between the original polynomial matrix and the reduced canonical form is set out. An example is given to illustrate the computational aspects involved.

Computational Modelling of Couette Flow of Nanofluids with Viscous Heating and Convective Cooling

The combined effect of viscous heating and convective cooling on Couette flow and heat transfer characteristics of water base nanofluids containing Copper Oxide (CuO) and Alumina (Al2O3) as nanoparticles is investigated. It is assumed that the nanofluid flows in a channel between two parallel plates with the channel’s upper plate accelerating and exchange heat with the ambient surrounding following the Newton’s law of cooling, while the lower plate is stationary and maintained at a constant temperature. Using appropriate similarity transformation, the governing Navier-Stokes and the energy equations are reduced to a set of nonlinear ordinary differential equations. These equations are solved analytically by regular perturbation method with series improvement technique and numerically by an efficient Runge-Kutta-Fehlberg integration technique coupled with shooting method. The effects of the governing parameters on the dimensionless velocity, temperature, skin friction, pressure drop and Nusselt number are presented graphically, and discussed quantitatively.

Multiresolution Analysis Based on Coalescence Hidden-Variable Fractal Interpolation Functions

Multiresolution analysis arising from Coalescence Hidden-variable Fractal Interpolation Functions (CHFIFs) is developed. The availability of a larger set of free variables and constrained variables with CHFIF in multiresolution analysis based on CHFIFs provides more control in reconstruction of functions in L2(R) than that provided by multiresolution analysis based only on Affine Fractal Interpolation Functions (AFIFs). Our approach consists of introduction of the vector space of CHFIFs, determination of its dimension and construction of Riesz bases of vector subspaces Vk, k∈Z, consisting of certain CHFIFs in L2(R)∩C0(R).

Combined Effect of Surface Roughness and Slip Velocity on Jenkins Model Based Magnetic Squeeze Film in Curved Rough Circular Plates

This paper aims to discuss the effect of slip velocity and surface roughness on the performance of Jenkins model based magnetic squeeze film in curved rough circular plates. The upper plate’s curvature parameter is governed by an exponential expression while a hyperbolic form describes the curvature of lower plates. The stochastic model of Christensen and Tonder has been adopted to study the effect of transverse surface roughness of the bearing surfaces. Beavers and Joseph’s slip model has been employed here. The associated Reynolds type equation is solved to obtain the pressure distribution culminating in the calculation of load carrying capacity. The computed results show that the Jenkins model modifies the performance of the bearing system as compared to Neuringer-Rosensweig model, but this model provides little support to the negatively skewed roughness for overcoming the adverse effect of standard deviation and slip velocity even if curvature parameters are suitably chosen. This study establishes that for any type of improvement in the performance characteristics the slip parameter is required to be reduced even if variance (−ve) occurs and suitable magnetic strength is in force.