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The utilisation of plastic waste as a modifier in asphalt mixtures has inflicted significant impacts on the cracking resistance of the produced mixtures. Whilst many studies have evaluated the cracking resistance of asphalt mixtures incorporating plastic waste using wet method, limited studies have used the dry method are available. The current study aims to evaluate the effect of plastic waste incorporation on the fracture properties of conventional asphalt mixture. In addition, the impact of ageing and moisture damage on the fracture properties of modified asphalt was also investigated. Indirect tensile strength test was carried out to assess the CT-index, tensile strength, and fracture energy of the asphalt mixtures before and after exposure to ageing and moisture conditioning. The finding revealed that the asphalt mixture incorporating plastic waste demonstrated superior resistance to thermal and fatigue cracking compared to the control mixture, thus proving the capability of plastic waste in increasing the resistance of asphalt against ageing and moisture damage.

The sigma field is a branch of mathematics that refers to the gathering of subsets includes sample space. It is useful in establishing a formal mathematical probability definition. The sets that occur in the sigma field are responsible for constituting various events in the presence of available sample space. In this paper, we focus on sigma fields. The main aim of this paper is to define the sigma field. Different types of sigma fields, along with the basic mathematics and examples, are also elaborated upon.

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تعد المخالفة الصوتية إحدى الظواهر الصوتية التي يتغير فيها الصوتان المتشابهان إلى صوتين مختلفين لأسباب تاريخية وسياقية. ونظراً لما تؤديه المخالفة الصوتية من دور في تلفظ الكلمات،ـ مما أدى الى قيام الباحثتين إلى دراسة تجريبية على طالبات الماجستير في قسمي اللغة العربية والانكليزية لمعرفة مدى فهم وإدراك هذه الظاهرة. لذا اختيرت (10) كلمات في كل من اللغتين العربية والانكليزية وبعد عرضها على محكمين ، طبّق الاختبار على الطالبات باستعمال النسبة المئوية لحساب الفرق في الاداء الصوتي. وقد توصلت الباحثتان إلى عدد من التوصيات والمقترحات.