On The Existence of Multiple Solutions of a Class of Third-Order Nonlinear Two-Point Boundary Value Problems

A general approach is presented for proving existence of multiple solutions of the third-order nonlinear differential equation

$$Au^{\prime\prime\prime}(x) + u^{\prime\prime}(x)u^\prime(x) + u^\prime(x)f(u(x))=0,\quad x \in [0,1] ,$$

subject to given proper boundary conditions. The proof is constructive in nature, and could be used for numerical generation of the solution or closed-form analytical solution by introducing some special functions. The only restriction is about f(u), where it is supposed to be differentiable function with continuous derivative. It is proved the problem may admit no solution, may admit unique solution or may admit multiple solutions.

     

The effect of real viscosity on the heat transfer of water based Al2O3 nanofluids in a two-sided lid-driven differentially heated rectangular cavity

The heat transfer and fluid flow behavior of water based Al₂O₃ nanofluids are numerically investigated inside a two-sided lid-driven differentially heated rectangular cavity. Physical properties which have major effects on the heat transfer of nanofluids such as viscosity and thermal conductivity are experimentally investigated and correlated and subsequently used as input data in the numerical simulation. Transport equations are numerically solved with finite volume approach using SIMPLEC algorithm. It was found that not only the thermal conductivity but also the viscosity of nanofluids has a key role in the heat transfer of nanofluids. The results show that at low Reynolds number, increasing the volume fraction of nanoparticles increases the viscosity and has a deteriorating effect on the heat transfer of nanofluids. At high Reynolds number, the increase in the viscosity is compensated by force convection and the increase in the volume fraction of nanoparticles which results in an increase in heat transfer is in coincidence with experimental results.     

Students’ ways of understanding a proof

We present a model for describing the growth of students’ understandings when reading a proof. The model is composed of two main paths. One is focused on becoming aware of the deductive structure of the proof, in other words, understanding the proof at a semantic level. Generalization, abstraction, and formalization are the most important transitions in this path. The other path focuses on the surface-level form of the proof, and the use of symbolic representations. At the end of this path, students understand how and why symbolic computations formally establish a claim, at a syntactic level. We make distinctions between states in the model and illustrate them with examples from early secondary students’ mathematical activity. We then apply the model to one student’s developing understanding in order to show how the model works in practice. We close with some suggestions for further research.     

A new scheme for solving nonlinear Stratonovich Volterra integral equations via Bernoulli’s approximation

In this paper, an efficient method for solving nonlinear Stratonovich Volterra integral equations is proposed. By using Bernoulli polynomials and their stochastic operational matrix of integration, these equations can be reduced to the system of nonlinear algebraic equations with unknown Bernoulli coefficient which can be solved by numerical methods such as Newton’s method. Also, an error analysis is valid under fairly restrictive conditions. Furthermore, in order to show the accuracy and reliability of the proposed method, the new approach is compared with the block pulse functions method by some examples. The obtained results reveal that the proposed method is more accurate and efficient than the block pulse functions method.     

A hybrid legendre tau method for the solution of a class of nonlinear wave equations with nonlinear dissipative terms

This article presents a technique based on the hybrid Legendre tau‐finite difference method to solve the fourth order wave equation which arises in the elasto‐plastic‐microstructure models for longitudinal motion of an elasto‐plastic bar. Illustrative examples and numerical results obtained using new technique demonstrate that the proposed approach is efficient in treating longitudinal equation of ealsto‐plastic bar. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1055–1071, 2011     

Study of Coulomb collisional effects on the propagation of electromagnetic waves in a turbulent plasma

The presence of Weibel instability in laser-irradiated fuel could be detrimental to the process of ablative implosion, which is necessary for achieving thermonuclear fusion reactions. In this paper, the effect of the Coulomb collisional within the turbulent plasma on the Weibel instability growth rate has been investigated for linear and circular polarization. The results indicate that the Weibel instability growth rate at circular polarization near the ignition centre of the fuel fusion (collisional plasma) is about 10⁵ times higher than the collisional Weibel instability growth rate at linear polarization. The Weibel instability growth rate is observed near the critical density of the fuel fusion (collisionless plasma) at linear polarization and enhancement near the foot of the heat in front of the fuel fusion. By increasing the steps of the density gradient plasma in the low-density corona, electromagnetic instability occurs at a higher stress flow. Therefore, the deposition condition of electron beam energy in circular polarization of turbulent plasma can be shifted to the fuel core for suitable ignition.     

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.     

Design and synthesis of phenoxymethybenzoimidazole incorporating different aryl thiazole-triazole acetamide derivatives as α-glycosidase inhibitors

Molecular Diversity - A novel series of phenoxymethybenzoimidazole derivatives (9a-n) were rationally designed, synthesized, and evaluated for their α-glycosidase inhibitory activity. All...     

NE102A Plastic Scintillator Response to 3He Ions

Physics of Particles and Nuclei Letters - Plastic scintillators are widely used in detecting nuclear radiation due to their low construction cost, the ability to be produced in nearly any shape and...