Wavelet-based robust estimation and variable selection in nonparametric additive models

This article studies M-type estimators for fitting robust additive models in the presence of anomalous data. The components in the additive model are allowed to have different degrees of smoothness. We introduce a new class of wavelet-based robust M-type estimators for performing simultaneous additive component estimation and variable selection in such inhomogeneous additive models. Each additive component is approximated by a truncated series expansion of wavelet bases, making it feasible to apply the method to nonequispaced data and sample sizes that are not necessarily a power of 2. Sparsity of the additive components together with sparsity of the wavelet coefficients within each component (group), results into a bi-level group variable selection problem. In this framework, we discuss robust estimation and variable selection. A two-stage computational algorithm, consisting of a fast accelerated proximal gradient algorithm of coordinate descend type, and thresholding, is proposed. When using nonconvex redescending loss functions, and appropriate nonconvex penalty functions at the group level, we establish optimal convergence rates of the estimates. We prove variable selection consistency under a weak compatibility condition for sparse additive models. The theoretical results are complemented with some simulations and real data analysis, as well as a comparison to other existing methods.

Some Coincidence and Common Fixed Point Results in Fuzzy Metric Space with an Application to Differential Equations

In this paper, we study some coincidence point and common fixed point theorems in fuzzy metric spaces by using three-self-mappings. We prove the uniqueness of some coincidence point and common fixed point results by using the weak compatibility of three-self-mappings. In support of our results, we present some illustrative examples for the validation of our work. Our results extend and improve many results given in the literature. In addition, we present an application of fuzzy differential equations to support our work.

Co-delivery of Simvastatin and Demineralized Bone Matrix Hierarchically from Nanosheet-based Supramolecular Hydrogels for Osteogenesis

Supramolecular hydrogels are widely used as 3D scaffolds and delivery platform in tissue engineering applications. However, hydrophobic therapeutic agents exhibit weak compatibility in hydrogel scaffolds along with aggregation and precipitate....

A General Fixed Point Theorem for Two Pairs of Absorbing Mappings in Gp -Metric Spaces

A general fixed point theorem for two pairs of absorbing mappings satisfying a new type of implicit relation ([37]), without weak compatibility in Gp-metric spaces is proved. As applications, new results for mappings satisfying contractive conditions of integral type and for ϕ-contractive mappings are obtained.

Common Fixed Point Theorems of Compatible Maps in Complex Valued b-Metric Spaces

In a paper Mukheimer established some results regarding common fixed point of two self mappings in a complex valued b-metric space satisfying a rational type contractive condition. In this paper we have established a common fixed point theorem by making use of compatibility and weak compatibility of self mappings satisfying generalized rational inequality of four mappings as opposed to two self mappings in a complex valued b – metric space. Some concrete examples have also been presented to verify the effectiveness and applicability of established results. Towards the end, an application to solution of Urysohn’s integral equations has also been presented to substantiate the usability of the obtained results. Results of this paper generalize the results of Mukheimer and some other earlier results. Theorems approved in this article will be supportable for researchers to work on rational contractions with more than two pair of self mappings.

Fixed Point Theorems for Generalized Kannan-Type Mappings in a New Type of Fuzzy Metric Space

In this paper, first, we introduce a new type of S∗−fuzzy metric space which is a generalization of fuzzy metric spaces. Second, we study the topological properties of S∗−fuzzy metric spaces. Finally, we extend Kannan-type mappings to generalized Kannan-type mappings under ϕ−gauge functions introduced by Fang in S∗−fuzzy metric spaces and prove the existence and uniqueness of fixed point for this kind of mappings. Furthermore, we also obtain the common fixed point theorems for weak compatibility along with E.A. property or CLRg property. Our results extend and improve very recent theorems in the related literature.

Feasibility Study of Chemical Treatments on Sorghum Fibres for Compatibility Enhancement in Polypropylene Composites

Polypropylene (PP) is one of the biggest petro-polymers, which is used in very wide application nowadays. The environment problem due to materials such as plastics having very long time degradability, and critical petroleum sources have promoted some studies to empowerment of natural resources such as natural fibres for substituting or at least modifying petro-polymers. Because of biodegradability obtained from natural source, sorghum fibers are interesting to be used as filler in PP composites, despite of weak compatibility between them. Surface modification on the sorghum fibers through alkalinization prior to acetylation was aimed to improve the fiber compatibility to PP. The treatments were expected to substitute hydroxyl group in the sorghum fibers, into acetic ester group in order to increase their hydrophobicity as the fillers. Moreover, the treatments were able to unbundle single fibers into micro-fibrillated cellulose (MFC) fibres with increase in crystallinity index. Usage of this MFC fiber as filler in PP leads to improvement of the composite performances such as thermal properties. In this study, Fourier Transformation Infra-Red (FTIR) Spectroscopy, X-ray Diffraction (XRD), Differential Scanning Calorimetry (DSC) and Field-Emission Scanning Electron Microscope (FE-SEM) were used to evaluate the performances of the Sorghum fibers after the treatments and as the filler in the Sorghum fibers/PP composites. The experimental results showed the MFC fibers as the smallest sizes in 5.0 microns and the highest crystallinity index up to 79.1 %, obtained from alkalinization with 2.5 M NaOH prior to acetylation with 17.4 M CH3COOH and the glacial (CH3CO2)2. Compatibility study of the treated Sorghum fibers on PP shows an improvement indicated by a strong interaction between the fibers and PP on morphology observation, increase in melting point of PP from 163.4°C (using virgin Shorgum fibers) into 163.6°C (using treated Sorghum fibers) in DSC measurements.

Fixed point theorems for expansive mappings in Gp-metric spaces

In the present paper, we adopt the concept of expansive mapping in the context of Gp-metric spaces in a similar manner expansive mapping in metric spaces. Furthermore, we obtain some results on fixed points of expansive type mappings. Also, we prove some common fixed point results for expansive mappings by using the notion of weak compatibility in Gp-metric space. Our results generalize some comparable results in metric spaces and partial metric spaces to Gp-metric spaces. Moreover, some examples are introduced in order to support our new results.