Microencapsulation of omega-3 fatty acid rich oil via complex coacervation

The overall goal of this thesis was to use plant-based materials to encapsulate omega-3 oils to produce microencapsulated powders with improved stability against oxidative stresses. This research includes four studies (Chapter 3, 4, 5 & 6). Chapter 3 examined the complexation behaviour of lentil protein isolate (LPI) and carboxymethyl cellulose (CMC) with different degree of substitution (DS; 0.7, 0.9, and 1.2) and molar mass (MM; 90 and 250 kDa), and their thermodynamic properties. For complexation behaviour, max optical density was conducted at 4:1 LPI: CMC mixing ratio. MM and DS had no significant effect on critical pH values but impacted the size and number of complexes formed. The complexation reactions of all LPI-CMC mixtures at pH 3 was energetically favorable. Chapter 4 and 5 compared the complexation behaviour of LPI with various polysaccharides, including CMC, gum Arabic (GA), alginate (AL), ι-carrageenan (ι-C), and κ-carrageenan (κ-C), and the resulting emulsifying properties. For chapter 4, at 4:1 LPI-polysaccharide mixing ratio, LPI-GA and LPI-CMC mixtures formed coacervate-type of complexes, while precipitate-type of complexes were formed with LPI-AL and LPI-ι-C systems. Their resulting complexes at pHopt were used to make emulsions. LPI-ι-C emulsion displayed the highest emulsion stability (ES) due to its high emulsion viscosity, lower mean droplet sizes, and highly negative-charged droplets. For chapter 5, incorporating ι-C and κ-C into the LPI solution led to suppression of complexes formed. Emulsions prepared with the resulting soluble complexes at pH 6 showed significantly higher stability than those made with insoluble complexes at pH 3.5 for each sample. The greatest ES was attributed to 4:1 LPI-κ-C and LPI-ι-C emulsions at pH 6. Chapter 6 developed the LPI-polysaccharide based microcapsules to encapsulate flaxseed oil. LPI-κ-C and LPI-ι-C emulsions with maltodextrin at pH 6 were prepared, followed by spray-drying or freeze-drying to yield the dried capsules. Spray-dried capsules showed higher oil encapsulation efficiency, but the encapsulated oil was oxidized significantly due to heat effect during drying and lower water activity of the capsules. Flaxseed oil was stable in all freeze-dried capsules during 8 weeks of storage. For in vitro oil release profile, more oil was released from LPI-κ-C powders under simulated gastric fluid, but more oil was released from LPI-ι-C powders under subsequent simulated gastric fluid and simulated intestinal fluid regardless of drying method and oil content. This research suggested that there is great potential to use the resulting emulsions to make plant-based microcapsules to deliver omega-3 oils

Nontrivial solutions of systems of Hammerstein integral equations with first derivative dependence

By means of classical fixed point index, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for systems of Hammerstein integral equations where the nonlinearities are allowed to depend on the first derivative. As a byproduct of our theory we discuss the existence of positive solutions of a system of third order ODEs subject to nonlocal boundary conditions. Some examples are provided in order to illustrate the applicability of the theoretical results.Comment: 18 page

Existence, uniqueness, and numerical approximations for stochastic Burgers equations

In this paper we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities. The proof of this result exploits the properties of an existent fully explicit space-time discrete approximation scheme and, in particular, the fact that it satisfies suitable a priori estimates. As a byproduct we obtain almost sure and strong convergence of the approximation scheme to the mild solutions of the considered SPDEs. We conclude by applying the main result of the paper to the stochastic Burgers equations with space-time white noise.Comment: 23 page

On the solvability of third-order three point systems of differential equations with dependence on the first derivative

This paper presents sufficient conditions for the solvability of the third order three point boundary value problem \begin{equation*} \left\{ \begin{array}{c} -u^{\prime \prime \prime }(t)=f(t,\,v(t),\,v^{\prime }(t)) \\ -v^{\prime \prime \prime }(t)=h(t,\,u(t),\,u^{\prime }(t)) \\ u(0)=u^{\prime }(0)=0,u^{\prime }(1)=\alpha u^{\prime }(\eta ) \\ v(0)=v^{\prime }(0)=0,v^{\prime }(1)=\alpha v^{\prime }(\eta ). \end{array} \right. \end{equation*} The arguments apply Green's function associated to the linear problem and the Guo--Krasnosel'ski\u{\i} theorem of compression-expansion cones. The dependence on the first derivatives is overcome by the construction of an adequate cone and suitable conditions of superlinearity/sublinearity near $0$ and $+\infty .$ Last section contains an example to illustrate the applicability of the theorem.Comment: 21 page