A generalized orthogonality relation via norm derivatives in real normed linear spaces

Aequationes mathematicae - We introduce a generalized orthogonality relation in real normed linear spaces via norm derivatives. The relation between this concept and other types of orthogonalities...     

Stochastic functional evolution equations with monotone nonlinearity: Existence and stability of the mild solutions

In this paper, we study a class of semilinear functional evolution equations in which the nonlinearity is demicontinuous and satisfies a semimonotone condition. We prove the existence, uniqueness and exponentially asymptotic stability of the mild solutions. Our approach is to apply a convenient version of Burkholder inequality for convolution integrals and an iteration method based on the existence and measurability results for the functional integral equations in Hilbert spaces. An Itô-type inequality is the main tool to study the uniqueness, p-th moment and almost sure sample path asymptotic stability of the mild solutions. We also give some examples to illustrate the applications of the theorems and meanwhile we compare the results obtained in this paper with some others appeared in the literature.     

Synergistic effect of graphene oxide nanoplatelets and cellulose nanofibers on mechanical,thermal, and barrier properties of thermoplastic starch

In recent years, because of the limited availability of oil resources and the increasing concerns regarding environment protection, much attention has been drawn to produce packaging films based on degradable biopolymers instead of synthetic polymers. On the other hand, because of the high costs of oil extraction, raw materials and film production, and disposing of the waste products of synthetic films, the need to replace these films with less pollutant and more cost‐effective films is growing globally. In this study, to answer the need for replacing synthetic polymer films, nanocomposite films based on thermoplastic starch reinforced with cellulose nanofibers and graphene oxide nanoplatelets were produced and characterized. The results implied that the synergistic effect of cellulose nanofibers and graphene oxide nanoplatelets has played an important role in improving the mechanical properties of the films. The results showed that with the addition of cellulose nanofibers and graphene oxide nanoplatelets, the tensile strength and elastic modulus of starch film were increased from 3 and 32 MPa to 13 and 436 MPa, which corresponds to 438% and 1435% improvement, respectively. In addition, the oxygen permeability resistance and the water vapor transmission for samples containing 3 wt% of graphene oxide nanoplatelets was decreased by 78% and 30% compared with the thermoplastic starch film, respectively. The permeability coefficient of the samples containing 3 wt% graphene oxide nanoplatelets for oxygen, nitrogen, and carbon dioxide have proved to be 0.051, 0.054, and 0.047 barrer, which shows that these films can perform well as packaging films.     

Location of a semi-obnoxious facility with elliptic maximin and network minisum objectives

This paper considers the problem of locating a single semi-obnoxious facility on a general network, so as to minimize the total transportation cost between the new facility and the demand points (minisum), and at the same time to minimize the undesirable effects of the new facility by maximizing its distance from the closest population center (maximin). The two objectives employ different distance metrics to reflect reality. Since vehicles move on the transportation network, the shortest path distance is suitable for the minisum objective. For the maximin objective, however, the elliptic distance metric is used to reflect the impact of wind in the distribution of pollution. An efficient algorithm is developed to find the nondominated set of the bi-objective model and is implemented on a numerical example. A simulation experiment is provided to find the average computational complexity of the algorithm.     

Nonlinear functional differential equations of monotone-type in Hilbert spaces

In this paper, we study a class of semilinear functional evolution equations with finite delay in which the nonlinearity satisfies the weak condition of demicontinuity with respect to functional variable and also a semimonotone condition. We will prove the existence, uniqueness and measurability of the mild solutions based on an extension of the analogous results for non-delay initial value problems on Banach spaces and a version of recently developed random Schauder’s fixed point theorem. This will be done first for the generalized solutions and then we follow an approximating procedure to obtain the same results for the mild solutions.