Hybrid GR-SVM for prediction of surface roughness in abrasive water jet machining

This paper presents a hybridization model of support vector machine (SVM) and grey relational analysis (GRA) in predicting surface roughness value of abrasive water jet (AWJ) machining process. The influential factors of five process parameters in AWJ, namely traverse speed, water jet pressure, standoff distance, abrasive grit size and abrasive flow rate, need to be analyzed using GRA approach. Then, the irrelevance factors of process parameters are eliminated. There is a need of determining the influential factors of process parameters to the surface roughness as to develop a robust prediction model. GRA acts as feature selection method in preprocessing process of hybrid grey relational-support vector machine (GR-SVM) prediction model. Efficiency of the proposed model is demonstrated. GR-SVM presents more accurate result than conventional SVM as it removes the redundant features and irrelevant element from the experimental datasets.     

A derivative concept with respect to an arbitrary kernel and applications to fractional calculus

In this paper, we propose a new concept of derivative with respect to an arbitrary kernel function. Several properties related to this new operator, like inversion rules and integration by parts, are studied. In particular, we introduce the notion of conjugate kernels, which will be useful to guaranty that the proposed derivative operator admits a right inverse. The proposed concept includes as special cases Riemann‐Liouville fractional derivatives, Hadamard fractional derivatives, and many other fractional operators. Moreover, using our concept, new fractional operators involving certain special functions are introduced, and some of their properties are studied. Finally, an existence result for a boundary value problem involving the introduced derivative operator is proved.     

On an inverse problem of reconstructing a subdiffusion process from nonlocal data

We consider a problem of modeling the thermal diffusion process in a closed metal wire wrapped around a thin sheet of insulation material. The layer of insulation is assumed to be slightly permeable. Therefore, the temperature value from one side affects the diffusion process on the other side. For this reason, the standard heat equation is modified, and a third term with an involution is added. Modeling of this process leads to the consideration of an inverse problem for a one‐dimensional fractional evolution equation with involution and with periodic boundary conditions with respect to a space variable. This equation interpolates heat equation. Such equations are also called nonlocal subdiffusion equations or nonlocal heat equations. The inverse problem consists in the restoration (simultaneously with the solution) of the unknown right‐hand side of the equation, which depends only on the spatial variable. The conditions for overdefinition are initial and final states. Existence and uniqueness results for the given problem are obtained via the method of separation of variables.     

Applications purement semi-affines et tressages

In this Note, we show essentially two results which complete the article by Ait Mokhtar et al., 2008. The first one, having defined the maps purement semi-affines, consists in looking the writing clarify of the compound of these maps. The second result, having defined the tressage, consists in showing that the compound of two tressages is also a tressage.     

On the convergence of a class of algorithms using linearly independent search directions

Powell has shown that the cyclic coordinate method with exact searches may not converge to a stationary point. In this note we consider a more general class of algorithms for unconstrained minimization, and establish their convergence under the assumption that the objective function has a unique minimum along any line.     

Abundant Exact Traveling Wave Solutions of Generalized Bretherton Equation via Improved (G′/G)-Expansion Method

In this article, we construct abundant exact traveling wave solutions involving free parameters to the generalized Bretherton equation via the improved (G′/G)-expansion method. The traveling wave solutions are presented in terms of the trigonometric, the hyperbolic, and rational functions. When the parameters take special values, the solitary waves are derived from the traveling waves.     

Transparent and flexible field emission display device based on single‐walled carbon nanotubes

A fully transparent and flexible field emission device (FED) has been demonstrated. Single‐walled carbon nanotubes (SWCNTs) coated on arylite substrate were used as electron emitters for the FED and a novel metavanadate phosphor coated on the SWCNTs/arylite film was used as transparent and flexible screen. The SWCNTs/arylite based emitters and the SWCNTs/arylite/metal‐vanadate‐based phosphor showed a transmittance value of 92.6% and 54%, respectively. The assembled device also showed satisfactory transparency and flexibility as well as producing significant current. Metavanadate phosphor is considered to be an excellent candidate due to its superior luminescence properties and easy fabrication onto transparent and flexible conductive substrate at room temperature while retaining reasonable transparency of the substrate. Thus, its transparency and flexibility will open the door to next‐generation FEDs. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)