Spectral characterization of the quadratic variation of mixed Brownian–fractional Brownian motion

Dzhaparidze and Spreij (Stoch Process Appl, 54:165–174, 1994) showed that the quadratic variation of a semimartingale can be approximated using a randomized periodogram. We show that the same approximation is valid for a special class of continuous stochastic processes. This class contains both semimartingales and non-semimartingales. The motivation comes partially from the recent work by Bender et al. (Finance Stoch, 12:441–468, 2008), where it is shown that the quadratic variation of the log-returns determines the hedging strategy.     

Numerical solution of fractional differential equations via a Volterra integral equation approach

The main focus of this paper is to present a numerical method for the solution of fractional differential equations. In this method, the properties of the Caputo derivative are used to reduce the given fractional differential equation into a Volterra integral equation. The entire domain is divided into several small domains, and by collocating the integral equation at two adjacent points a system of two algebraic equations in two unknowns is obtained. The method is applied to solve linear and nonlinear fractional differential equations. Also the error analysis is presented. Some examples are given and the numerical simulations are also provided to illustrate the effectiveness of the new method.     

A numerical method for solving linear integral equations of the second kind on the non-rectangular domains based on the meshless method

The main purpose of this article is to describe a numerical scheme for solving two-dimensional linear Fredholm integral equations of the second kind on a non-rectangular domain. The method approximates the solution by the discrete collocation method based on radial basis functions (RBFs) constructed on a set of disordered data. The proposed method does not require any background mesh or cell structures, so it is meshless and consequently independent of the geometry of domain. This approach reduces the solution of the two-dimensional integral equation to the solution of a linear system of algebraic equations. The error analysis of the method is provided. The proposed scheme is also extended to linear mixed Volterra–Fredholm integral equations. Finally, some numerical examples are presented to illustrate the efficiency and accuracy of the new technique.     

Algebraic Characterization of Dense-Separability Among Compact Spaces

In this note, we show that a compact Hausdorff space X is dense-separable if and only if every family of ideals of C(X) with zero intersection has a countable subfamily with zero intersection. As a consequence of this characterization we observe that every compact dense-separable space whith Soc(C(X)) = 0 has a countable dense and co-dense subset.     

2D Poly(arylene vinylene) Covalent Organic Frameworks via Aldol Condensation of Trimethyltriazine

Designing structural order in electronically active organic solids remains a great challenge in the field of materials chemistry. Now, 2D poly(arylene vinylene)s prepared as highly crystalline covalent organic frameworks (COFs) by base‐catalyzed aldol condensation of trimethyltriazine with aromatic dialdehydes are reported. The synthesized polymers are highly emissive (quantum yield of up to 50 %), as commonly observed in their 1D analogues poly(phenylene vinylene)s. The inherent well‐defined porosity (surface area ca. 1000 m² g^?1, pore diameter ca. 11 Å for the terephthaldehyde derived COF‐1) and 2D structure of these COFs also present a new set of properties and are likely responsible for the emission color, which is sensitive to the environment. COF‐1 is highly hydrophilic and reveals a dramatic macroscopic structural reorganization that has not been previously observed in framework materials.     

Nanofluid Today

Journal of Thermal Analysis and Calorimetry -     

Self‐Healing Polyester Urethane Supramolecular Elastomers Reinforced with Cellulose Nanocrystals for Biomedical Applications

Stretchable self‐healing urethane‐based biomaterials have always been crucial for biomedical applications; however, the strength is the main constraint of utilization of these healable materials. Here, a series of novel, healable, elastomeric, supramolecular polyester urethane nanocomposites of poly(1,8‐octanediol citrate) and hexamethylene diisocyanate reinforced with cellulose nanocrystals (CNCs) are introduced. Nanocomposites with various amounts of CNCs from 10 to 50 wt% are prepared using solvent casting technique followed by the evaluation of their microstructural features, mechanical properties, healability, and biocompatibility. The synthesized nanocomposites indicate significantly higher tensile modulus (approximately 36–500‐fold) in comparison to the supramolecular polymer alone. Upon exposure to heat, the materials can reheal, but nevertheless when the amount of CNC is greater than 10 wt%, the self‐healing ability of nanocomposites is deteriorated. These materials are capable of rebonding ruptured parts and fully restoring their mechanical properties. In vitro cytotoxicity test of the nanocomposites using human dermal fibroblasts confirms their good cytocompatibility. The optimized structure, self‐healing attributes, and noncytotoxicity make these nanocomposites highly promising for tissue engineering and other biomedical applications.     

A proper orthogonal decomposition variational multiscale meshless interpolating element-free Galerkin method for incompressible magnetohydrodynamics flow

In the recent decade, the meshless methods have been handled for solving most of PDEs due to easiness of the meshless methods. One of the popular meshless methods is the element-free Galerkin (EFG) method that was first proposed for solving some problems in the solid mechanics. The test and trial functions of the EFG are based on the special basis. Recently, some modifications have been developed to improve the EFG method. One of these improvements is the variational multiscale EFG procedure. In the current article, the shape functions of interpolation moving least squares approximation have been applied to the variational multiscale EFG technique for solving the incompressible magnetohydrodynamics flow. In order to reduce the elapsed CPU time of simulation, we employ a reduced-order model based on the proper orthogonal decomposition technique. The current combination can be referred to as the reduced-order variational multiscale EFG technique. To illustrate the reduction in CPU time used as well as the efficiency of the proposed method, we applied it for the two-dimensional cases.     

Transmission dynamics of novel coronavirus SARS-CoV-2 among healthcare workers,a case study in Iran

One of the main concerns during the COVID-19 pandemic was the protection of healthcare workers against the novel coronavirus. The critical role and vulnerability of healthcare workers during the COVID-19 pandemic leads us to derive a mathematical model to express the spread of coronavirus between the healthcare workers. In the first step, the SECIRH model is introduced, and then the mathematical equations are written. The proposed model includes eight state variables, i.e., Susceptible, Exposed, Carrier, Infected, Hospitalized, ICU admitted, Dead, and finally Recovered. In this model, the vaccination, protective equipment, and recruitment policy are considered as preventive actions. The formal confirmed data provided by the Iranian ministry of health is used to simulate the proposed model. The simulation results revealed that the proposed model has a high degree of consistency with the actual COVID-19 daily statistics. In addition, the roles of vaccination, protective equipment, and recruitment policy for the elimination of coronavirus among the healthcare workers are investigated. The results of this research help the policymakers to adopt the best decisions against the spread of coronavirus among healthcare workers.