On the concept of solution for fractional differential equations with uncertainty

We consider a differential equation of fractional order with uncertainty and present the concept of solution. It extends, for example, the cases of first order ordinary differential equations and of differential equations with uncertainty. Some examples are presented.     

Viscoelastic flow in a two-dimensional collapsible channel

We compute the flow of three viscoelastic fluids (Oldroyd-B, FENE-P, and Owens blood model) in a two-dimensional channel partly bounded by a tensioned membrane, a benchmark geometry for fluid–structure interactions. The predicted flow patterns are compared to those of a Newtonian liquid. We find that computations fail beyond a limiting Weissenberg number. Flow fields and membrane shape differ significantly because of the different degree of shear thinning and molecular extensibility underlying the three different microstructural models.     

Positive and maximal positive solutions of singular mixed boundary value problem

The paper is concerned with existence results for positive solutions and maximal positive solutions of singular mixed boundary value problems. Nonlinearities h(t;x;y) in differential equations admit a time singularity at t=0 and/or at t=T and a strong singularity at x=0.     

Study of size dependent features of swift heavy ion irradiation in nanosized zinc ferrite

In the present work zinc ferrite nanoparticles of different crystallite size were irradiated with 200 MeV Ag¹⁵⁺ ion beam. The structural and magnetic characterization performed for these samples indicate the presence of size dependent irradiation induced changes in the nanoparticles. The superparamgnetic nanoparticles do not alter their behavior after irradiation; however paramagnetic samples exhibit weak ferrimagnetism in the irradiated specimen. Results obtained from these measurements are in agreement with results obtained from the electron paramagnetic resonance spectroscopy.     

Thermal conductance of nanofluids: is the controversy over?

Over the last decade nanofluids (colloidal suspensions of solid nanoparticles) sparked excitement as well as controversy. In particular, a number of researches reported dramatic increases of thermal conductivity with small nanoparticle loading, while others showed moderate increases consistent with the effective medium theories on well-dispersed conductive spheres. Accordingly, the mechanism of thermal conductivity enhancement is a hotly debated topic. We present a critical analysis of the experimental data in terms of the potential mechanisms and show that, by accounting for linear particle aggregation, the well established effective medium theories for composite materials are capable of explaining the vast majority of the reported data without resorting to novel mechanisms such as Brownian motion induced nanoconvection, liquid layering at the interface, or near-field radiation. However, particle aggregation required to significantly enhance thermal conductivity, also increases fluid viscosity rendering the benefit of nanofluids to flow based cooling applications questionable.     

Release studies on niosomes containing fatty alcohols as bilayer stabilizers instead of cholesterol

Monomers of some amphiphiles organize into bilayers to form liposomes and niosomes. Such bilayers are unstable or leaky and hence cholesterol is a common ingredient included to stabilize them. Cholesterol stabilizes bilayers, prevents leakiness, and retards permeation of solutes enclosed in the aqueous core of these vesicles. Other than cholesterol a material with good bilayer-stabilizing properties is yet to be identified. We have substituted cholesterol with fatty alcohols in niosomes containing polyglyceryl-3-di-isostearate (PGDS) and polysorbate-80 (PS-80) to explore their membrane-stabilizing property via permeation studies. Niosomes of polyglyceryl-3-di-isostearate, fatty alcohol/cholesterol, and polysorbate were prepared by ether injection method. Aqueous solution of ketorolac tromethamine (KT) was entrapped in them. The effects of alkyl chain length of fatty alcohols (C(12), C(14), C(16), C(18), and C(16+18)), of acyl chain length of polyoxyethylene sorbitan monoester surfactants, and of the molar ratio of lipid mixture on the release rate of ketorolac from niosomes were assessed by employing modified dissolution-dialysis method. Niosomes with cholesterol or fatty alcohols have exhibited a common release pattern. Niosomes containing fatty alcohol showed a considerably slower release rate of KT than those containing cholesterol. Based on the release rate, fatty alcohols can be ranked as stearyl相似文献   

The Existence of Positive Solutions to Neutral Differential Equations

In this paper, we shall consider a class of neutral differential equations of the form

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where τ (0, ∞), σ [0, ∞), Q(t) C([t₀, ∞), R ⁺ ), r(t) C([t₀, ∞), (0, ∞)) with r(t) nondecreasing on [t₀ − τ, ∞). We shall show that all positive solutions of ( * ) can be classified into four types, A, B, C, and D, and we shall obtain sufficient and necessary conditions for the existence of A-type, B-type, and D-type positive solutions of ( * ), respectively. A sufficient condition for the existence of C-type positive solutions of ( * ) is also given. Finally, we shall offer a sharp oscillation result for all solutions of ( * ). Our results generalize and improve those established in B. Yang and B. G. Zhang (Funkcial. Ekvac.39 (1996), 347–362).     

Contraction and approximate contraction with an application to multi-point boundary value problems

The paper deals with some general iterative methods in n-metric spaces. The obtained results are more explicit than those known in the literature and provides error estimates when the sequence obtained on a floating-point system starts oscillating. A stopping criteria and error estimates at that stage are provided. An application to multi-point boundary value problems is also given.     

Origin of charge density wave formation in insulators from a high resolution photoemission study of BaIrO3

We investigate the origin of charge density wave (CDW) formation in insulators by studying BaIrO3 using high-resolution (1.4 meV) photoemission spectroscopy. The spectra reveal the existence of localized density of states at the Fermi level, E(F), in the vicinity of room temperature. These localized states are found to vanish as the temperature is lowered, thereby, opening a soft gap at E(F), as a consequence of CDW transition. In addition, the energy dependence of the spectral density of states reveals the importance of magnetic interactions, rather than well-known Coulomb repulsion effect, in determining the electronic structure thereby implying a close relationship between ferromagnetism and CDW observed in this compound. Also, Ba core level spectra surprisingly exhibit an unusual behavior prior to CDW transition.