Rectangular-radial drawings of cubic plane graphs

Rectangular drawings and rectangular duals can be naturally extended to other surfaces. In this paper, we extend rectangular drawings and rectangular duals to drawings on a cylinder. The extended drawings are called rectangular-radial drawings and rectangular-radial duals. Rectangular-radial drawings correspond to periodic rectangular tilings of a 1-dimensional strip. We establish a necessary and sufficient condition for plane graphs with maximum degree 3 to have rectangular-radial drawings and a necessary and sufficient condition for triangulated plane graphs to have rectangular-radial duals. Furthermore, we present three linear time algorithms under three different conditions for finding a rectangular-radial drawing for a given cubic plane graph, if one exists.     

Iron Oxychloride/Bovine Serum Albumin Nanosheets as Chemodynamic Therapy Agents

Iron oxychloride (FeOCl) is known for reactive oxygen species (ROS) generation through Fenton chemistry. The activity of FeOCl is preserved in the slightly acidic pH value of the tumor microenvironment (pH 6.5−6.9). Such property can be advantageous in biobased systems, where ROS generation can be modulated in slightly acidic conditions, which is characteristic of the solid tumor microenvironment. In the present study, BSA-stabilized FeOCl nanosheets (NSs) are synthesized and characterized by transmission electron microscope, Fourier transform infrared spectroscopy, zeta potential analysis, dynamic light scattering, and UV–vis spectroscopy. The morphology of the nanoparticles is flake-like, and their hydrodynamic diameter is around 200 nm. MTT, apoptosis assay, and trypan blue staining evaluate the toxicity of FeOCl NSs toward the 4T1 cell line. It is found that the toxicity of the NSs is higher in physiological conditions of solid tumors (pH 6.5, H₂O₂ 100 × 10⁻⁶ m ) than in the conditions of healthy organs (pH 7.4). Specifically, cancer cells are in their late apoptotic stage by more than eight times higher at pH 6.5 than pH 7.4. The toxicity results are in agreement with the in vitro catalytic assay of the NSs. Therefore, the FeOCl NSs can be the building blocks for constructing chemodynamic therapy agents.     

Reversed-phase dispersive liquid-liquid microextraction with central composite design optimization for preconcentration and HPLC determination of oleuropein

A reversed-phase dispersive liquid-liquid microextraction (RP-DLLME) method was developed for the preconcentration and direct HPLC determination of oleuropein in olive's processing wastewater (OPW) and olive leaves extracts. In conventional DLLME, the sedimented phase is a micro-drop of a chlorinated organic solvent that is not compatible with RP-HPLC. Therefore, solvent evaporation and reconstitution with an appropriate solvent is often required. In RP-DLLME, this problem was overcome by overturning the solvent polarity in the ordinary DLLME and replacing the organic solvent with water. A central composite chemometrics design was used for multivariate optimization of the effects of five different parameters influencing the extraction efficiency of the method. In the optimized conditions, a mixture of 1.4 mL of an ethyl acetate extract of sample and 40 μL water (pH 5.0) was rapidly injected into 5.3 mL of cyclohexane. After centrifugation of the formed cloudy mixture, a micro-drop of the aqueous phase was sedimented at the conical bottom of the centrifuge tube. This phase, that contained the preconcentrated and partially purified analyte, was directly injected into an RP-HPLC column for analysis. A mean extraction recovery of 102.5 (±4.5) % with enrichment factors exceeding 38, was obtained for five replicated analysis. The detection limit of the method (3σ) for OE was 0.02 μg L⁻¹ for OPW and 2 × 10⁻³ mg kg⁻¹ for olive leaves samples. The results showed that, RP-DLLME is a promising technique which is quick, easily operated and can be directly coupled to HPLC.     

Annihilator Conditions on Polynomials over Modules

Let R be a ring with unity and M be a right R-module. The system M[x] forms a left near R[x]-module under addition and substitution operations. In this paper we extend the study of annihilator conditions on nearring of polynomials to left near R[x]-module M[x], when M is a reduced Baer module. Also, we give a characterization of reduced modules. As a corollary we obtain some results of Birkenmeier and Huang [3].     

Controlled hydrothermal growth of ZnO nanostructures by sequestering the Zn metal ions with the chelating agent EDTA

In the present work, a controlled growth of ZnO nanostructures by manipulating Zn metal ion concentration by the chelating action of ethylene diaminetetra acetic acid in hydrothermal method is studied. EDTA produces metal–chelate complex by the formation of bidentate ligand with Zn²⁺ in the solution and diminishes the reactivity of Zn metal cations. Concentration of EDTA in the mother solution was varied in different ranges like 3, 5 and 10 mM while retaining the zinc metal salt and the NaOH concentration the same. Three different morphologies of wurtzite structured ZnO nanostructures such as nanorods-bunch, separate/discrete uniformly sized hexagonal nanorods and tapered flower petals like shapes are achieved by 3, 5 and 10 mM strengths of EDTA, respectively. The medium concentration 5 mM of EDTA is found to have moderate control over producing ZnO nanostructures of uniform diameter and a high aspect (length to diameter) ratio. An array of vertically aligned free standing ZnO nanorods with uniform spacing is successfully achieved by the addition of 5 mM of EDTA in the mother solution and the same is studied for its fluorescence property at an excitation of 325 nm and it has exhibited a characteristic UV emission of ZnO around 383 nm.     

An Alternative Mechanism of Non-contact Anterior Cruciate Ligament Injury During Jump-landing: In-vitro Simulation

In the United States, an estimated 100,000 anterior cruciate ligament (ACL) injuries occur every year. Despite decades of research, to this date, the mechanism or mechanisms of non-contact ACL injuries are not well understood. This is primarily because trials cannot be conducted on live subjects to understand the injury mechanism, and it is difficult to instrument a live human knee to measure the response of tissues during dynamic activities. In this paper, we present a dynamic knee injury simulator capable of in-vitro modeling of the ACL injury during jump-landing activity. This system was used to simulate jump-landing on cadaveric knees and to successfully test which conditions would result in isolated ACL injury. A restricted flexion of the hip (a hip that flexes minimally or not at all during landing), combined with low quadriceps and hamstring force levels during landing were found to be conducive to ACL injury. Elevated levels of quadriceps force prevented the injury from occurring even under restricted hip flexion conditions. The measured strain rates in the ACL tissue during injury causing activities were over 250%/s.     

Numerical Solution Based on Hat Functions for Solving Nonlinear Stochastic Itô Volterra Integral Equations Driven by Fractional Brownian Motion

This paper presents a numerical method for solving nonlinear stochastic Itô Volterra integral equations driven by fractional Brownian motion with Hurst parameter \( H \in (0,1)\) via of hat functions. Using properties of the generalized hat basis functions and fractional Brownian motion, new stochastic operational matrix of integration is achieved and the nonlinear stochastic equation is transformed into nonlinear system of algebraic equations which by solving it, an approximation solution with high accuracy is obtained. In addition, error analysis of the method is investigated, and by some examples, efficiency and accuracy of the suggested method are shown.