In the paper we consider an Ising model with four competing interactions (external field, nearest neighbor, second neighbors and triples of neighbors) on the Cayley tree of order two.We show that for some parameter values of the model there is a phase transition. Our second result gives complete description of the periodic Gibbs measures for the mo

In the paper, the one-dimensional model with nearest-neighbor interactions In, n ∈ Z, and the s pin values ±1 is considered. It is known that, under some conditions on parameters of In, a phase transition occurs for this model. We define the notion of a phase separation point between two phases. We prove that the expectation value of this point

The physical phenomenon of phase transition is reflected in mathematical model by non-uniqueness of the Gibbs measures and phase diagram of the model describes a morphology of phases, stability of phases, different transitions from one phase to another and corresponding transition lines. We study the phase diagram for the Potts model on a Cayley tr

This paper is concerned with the surface roughness and surface integrity of titanium alloy Ti- 6AI-4V after end milling under room temperature and preheated conditions. End milling experiments were carried out on a Vertical Machining Centre, using 20 mm uncoated WC-Co inserts. High frequency induction heating was utilized for preheated experiments.

الحمد لله الذي أنزل القرآن بلسان عربي مبين، والصلاة والسلام على أفصح من نطق بالضاد، سيدنا محمد صلى الله عليه وسلم، وعلى آله وصحبه أجمعين. فإنه يسرنا أن نقدّم لأبنائنا التلاميذ كتاب التلميذ ضمن

Previous report indicated that sponge voucher number (1L82008) possessed the highest antimicrobial activity among four sponges and three corals species investigated. A large amount of sponge tissue (287 g dry weight) was extracted with methanol and followed with water. The methanol and water extracts were examined against two Gram-Positive bacteria

Malaysian experts have warned that several major cities, including the capital Kuala Lumpur, could face serious water shortages due to over-pollution of the country's rivers by problems brought about by over-development. As 97 per cent of Malaysia’s water supply is sourced from surface water, the main aim of this study was to identify a relat

This paper presents the investigation of tool life improvement in end-milling of Titanium Alloy Ti-6Al-4V through workpiece preheating. End milling tests were conducted on Vertical Machining Centre with full immersion cutting. Induction heating was utilized during end milling for preheating. The titanium alloy Ti-6Al-4V bar was used as the workpiec

This paper aims at studying the differences between Arabic and Malay cultures from the perspective of translation studies. Thus, it is intended to uncover the problems of translating the culture-specific items between the two said languages. It also aims to shed some light on the related theories from the realm of translation studies with regard to

We study the phase diagram for Potts model on a Cayley tree with competing nearest-neighbor interactions J1, prolonged next-nearest-neighbor interactions Jp and one-level next-nearest-neighbor interactions Jo. Vannimenus proved that the phase diagram of Ising model with Jo=0 contains a modulated phase, as found for similar models on periodic lattic