Reform of the Doctrine of Utmost Good Faith: A Comparative Study between the UK and Saudi Arabia

In the UK and Saudi Arabia, it is necessary for the contracting parties in insurance contracts to comply with the requirement of the doctrine of utmost good faith. In recent years, the doctrine of utmost good faith and the mutual duties of the contracting parties have developed in different ways in each jurisdiction. Both jurisdictions provide consumer protection in insurance markets by Consumer Insurance (Disclosure and Representation) Act 2012 in the UK and Insurance Consumer Protection Principles 2014 in Saudi Arabia. However, there are many differences between the conduct of each jurisdiction since the coming into force of the Insurance Act 2015 in the UK, which revolutionised the insurance law in several key areas. This thesis particularly aims to critically analyse the reform of the doctrine of utmost good faith and looks at how the current reform impacts on the interpretation of this doctrine between the UK and Saudi jurisdictions. This study critically analyses the insureds’ pre-contractual duties for consumers and businesses in the UK with a comparison to Saudi la

New topologies between the usual and Niemytzki

[EN] We use the technique of Hattori to generate new topologies on the closed upper half plane which lie between the usual metric topology and the  Niemytzki topology. We study some of their fundamental properties and weaker versions of normality.Abuzaid, D.; Alqahtani, M.; Kalantan, L. (2020). New topologies between the usual and Niemytzki. Applied General Topology. 21(1):71-79. https://doi.org/10.4995/agt.2020.12042OJS717921

Three new soft separation axioms in soft topological spaces

Soft $\omega$-almost-regularity, soft $\omega$ -semi-regularity, and soft $\omega$-$T_{2\frac{1}{2}}$ as three novel soft separation axioms are introduced. It is demonstrated that soft $\omega$ -almost-regularity is strictly between "soft regularity" and "soft almost-regularity"; soft $\omega$-$T_{2\frac{1}{2}}$ is strictly between "soft $T_{2\frac{1}{2}}$" and "soft $T_{2}$", and soft $\omega$ -semi-regularity is a weaker form of both "soft semi-regularity" and "soft $\omega$-regularity". Several sufficient conditions for the equivalence between these new three notions and some of their relevant ones are given. Many characterizations of soft $\omega$-almost-regularity are obtained, and a decomposition theorem of soft regularity by means of "soft $\omega$ -semi-regularity" and "soft $\omega$-almost-regularity" is obtained. Furthermore, it is shown that soft $\omega$-almost-regularity is heritable for specific kinds of soft subspaces. It is also proved that the soft product of two soft $\omega$-almost regular soft topological spaces is soft $\omega$-almost regular. In addition, the connections between our three new conceptions and their topological counterpart topological spaces are discussed

A classification of the point spectrum of constant length substitution tiling spaces and general fixed point theorems for tilings

We examine the point spectrum of the various tiling spaces that result from different choices of tile lengths for substitution of constant length on a two or a three letter alphabet. In some cases we establish insensitivity to changes in length. In a wide range of cases, we establish that the typical choice of length leads to trivial point spectrum. We also consider a problem related to tilings of the integers and their connection to fixed point theorems. Using this connection, we prove a generalization of the Banach Contraction Principle

Propagation dynamics of elliptical super-Gaussian bullets in nonlinear metamaterial waveguide

The characteristics of an optical beam propagating in a medium should be preserved for many applications related to fiber optic communication. The phenomenon of self-trapping due to adequate balance among linear and nonlinear effects may preserve the characteristics of an optical beam. In this work, we perform a theoretical investigation on the propagation of a spatiotemporal elliptical super-Gaussian beam in a Kerr nonlinear metamaterial waveguide. We follow the Lagrangian variational method and numerical analysis using the appropriate trial function for the input elliptical super-Gaussian beam and analyze the self-trapping and deformation of the propagating beam in metamaterials. We obtain special conditions to observe the self-trapping and stabilize the dynamics of the elliptical super-Gaussian beam in both negative and positive index regimes of the metamaterial. It is found that in the negative index regime of metamaterial, the phenomenon of self-trapping may exist in the normal dispersion regime with defocusing Kerr nonlinearity. However similar to the conventional medium, the robust balance among the anomalous dispersion and focussing Kerr nonlinearity supports the self-trapping in the positive index regime. There is a critical optical power for the input beam to observe the pulse trapping phenomena. This power is found to be a function of the super-Gaussian parameter as well as the ellipticity of the input beam. The period of self-trapping is also a function of the super-Gaussian parameter and the ellipticity of the input beam

On <i>q</i>-Hermite-Hadamard Inequalities via <i>q</i> − <i>h</i>-Integrals

This paper aims to find Hermite–Hadamard-type inequalities for a generalized notion of integrals called q−h-integrals. Inequalities for q-integrals can be deduced by taking h=0 and are connected with several known results of q-Hermite–Hadamard inequalities. In addition, we analyzed q−h-integrals, q-integrals, and the corresponding inequalities for symmetric functions

On q-Hermite-Hadamard Inequalities via q &minus; h-Integrals

This paper aims to find Hermite&ndash;Hadamard-type inequalities for a generalized notion of integrals called q&minus;h-integrals. Inequalities for q-integrals can be deduced by taking h=0 and are connected with several known results of q-Hermite&ndash;Hadamard inequalities. In addition, we analyzed q&minus;h-integrals, q-integrals, and the corresponding inequalities for symmetric functions

Some Seminormed Difference Sequence Spaces over n-Normed Spaces Defined by a Musielak-Orlicz Function of Order (α,β)

We first define the notion of lacunary statistical convergence of order (α,β), and taking this notion into consideration, we introduce some seminormed difference sequence spaces over n-normed spaces with the help of Musielak-Orlicz function M=(Mk) of order (α,β). We also examine some topological properties and prove inclusion relations between the resulting sequence spaces