On Solution and Stability of a Two-Variable Functional Equations

The main purpose of this paper is to investigate the stability of the functional equation f(x+y,y+z)=2f(x/2,y/2)+2f(y/2,z/2) in normed spaces. The solutions of such functional equations are considered

Comparision of Density Measurement Methods for Unidirectional Flax-Epoxy Polymer Composites

Density is a decisive factor in determining one of the most important advantages of flax fiber-reinforced polymer (FFRP) composites, i.e. their relatively low weight leading to high specific properties. As a fundamental physical property of composites, density enters in many engineering design and quality control calculations and its value is a determining factor for several applications. Especially, we need precise material properties including density so as to develop efficient numerical models to these materials. In this work, three density measurement methods were evaluated and compared: Helium-gas pycnometry and Archimedes with two different immersing liquids, water and ethanol. The results show that Helium-gas pycnometry and Archimedes with ethanol gave similar and repeatable results, whereas using water resulted in much lower values. The density values were all in the range of reported values. However, Helium-gas pycnometry or Archimedes using ethanol are recommended for more precision in measuring the density of FFRP composites

Comparision of density measurement methods for unidirectional flax-epoxy polymer composites

Density is a decisive factor in determining one of the most important advantages of flax fiber-reinforced polymer (FFRP) composites, i.e. their relatively low weight leading to high specific properties. As a fundamental physical property of composites, density enters in many engineering design and quality control calculations and its value is a determining factor for several applications. Especially, we need precise material properties including density so as to develop efficient numerical models to these materials. In this work, three density measurement methods were evaluated and compared: Helium-gas pycnometry and Archimedes with two different immersing liquids, water and ethanol. The results show that Helium-gas pycnometry and Archimedes with ethanol gave similar and repeatable results, whereas using water resulted in much lower values. The density values were all in the range of reported values. However, Helium-gas pycnometry or Archimedes using ethanol are recommended for more precision in measuring the density of FFRP composites

A Note to Paper “On the Stability of Cubic Mappings and Quartic Mappings in Random Normed Spaces” (Erratum)

Recently, Baktash et al. (2008) proved the stability of the cubic functional equation f(2x+y)+f(2x−y)=2f(x+y)+2f(x−y)+12f(x) and the quartic functional equation f(2x+y)+f(2x−y)=4f(x+y)+4f(x−y)+24f(x)−6f(y) in random normed spaces. In this note, we correct the proofs

Coupled Fixed Point Theorems under Weak Contractions

Cho et al. [Comput. Math. Appl. 61(2011), 1254–1260] studied common fixed point theorems on cone metric spaces by using the concept of c-distance. In this paper, we prove some coupled fixed point theorems in ordered cone metric spaces by using the concept of c-distance in cone metric spaces

A Study of the interlaminar fracture toughness of unidirectional flax/epoxy composites

Having environmental and economic advantages, flax fibers have been recognized as a potential replacement for glass fibers as reinforcement in epoxy composites for various applications. Its widening applications require employing failure criteria and analysis methods for engineering design, analysis, and optimization of this material. Among different failure modes, delamination is known as one of the earliest ones in laminated composites and needs to be studied in detail. However, the delamination characteristics of unidirectional (UD) flax/epoxy composites in pure Mode I has rarely been addressed, while Mode II and Mixed-mode I/II have never been addressed before. This work studies and evaluates the interlaminar fracture toughness and delamination behavior of UD flax/epoxy composite under Mode I, Mode II, and Mixed-mode I/II loading. The composites were tested following corresponding ASTM standards and fulfilled all the requirements. The interlaminar fracture toughness of the composite were determined and validated based on the specific characteristics of natural fibers. Considering the variation in the composite structure configuration and its effects, the results of interlaminar fracture toughness fit in the range of those reported for similar composites in the literature and provide a basis for the material properties of this composite