The fixed point theory provides a very powerful tool in mathematics and many other scientific fields such as nonlinear analysis, integral equations and differential equations. What is interesting in a recent study on the fixed point theory is the generalization of metric space (MS).

By generalizing the concept of MS in the fixed point theory, many mathematicians presented new concepts such as b-metric space, triple controlled metric type space and triple-composed metric space. Some other authors defined a new notion called S-metric space (S-MS). Later, some mathematicians introduced new concepts for generalizing S-MS by using the ideas of earlier space concepts. S_b-MS and triple controlled S-metric type space (TC-S-MTS) are typical examples.

Kil Chol Jin, a lecturer at the Faculty of Applied Mathematics, proposed a new concept of triple-composed S-metric space (TCS-MS). He got motivation from the concepts of TCMS and S-MS while analyzing the recent research results on S-MS.

TCS-MS is a new concept that uses the composition of three functions rather than the multiplication of three functions, unlike the recently introduced TC-S-MTS.

He presented some meaningful examples showing that triple-composed S-metric space is a real generalization of S-metric space and S_b-metric space. In addition, he proved a fixed point result for Proinov-type contractive mappings in triple-composed S-metric spaces.

For more information, please refer to his paper “Triple-Composed S-Metric Spaces and Related Fixed Point Results” in “Proceedings of KUTIC-2025”.

Due to the frequent occurrence of accidents in the sea, it is an important requirement to predict accidents in advance and take safety measures from an early stage.

At present, assessment of accident risks is referred to as the question of how to predict risks and take measures. Intensifying research on the global regulatory tool, the Formal Safety Assessment (FSA), is important in finding and reducing ship accident risks from early stages by taking safety measures.

Jon Kwang Sik, a researcher at the Faculty of Naval Architecture and Ocean Engineering, proposed a methodology for evaluating ship safety and providing safety measures with a focus on the risk of possible collision accidents by applying the FSA method, which has been widely adopted.

He established a measure scheme for avoiding or minimizing damage by predicting damage results based on the identification of many risk indexes associated with collision accidents, and conducted a comparative analysis to propose the most appropriate measures to prevent collision accidents.

The proposed method will play an important role in planning regulations for assessing the safety of ships and taking safety measures in relation to possible marine accidents as well as collision accidents in all ships in the future.

Tantalum and niobium are the most important materials for various sectors of the national economy. They are used for structural steel, superconducting, electron tubes, cemented carbide, steel modifiers, scientific lens additives, dental prosthetic materials, etc.

Tantalum and niobium are found in over 130 kinds of minerals, composed of tantalate and niobate or complex oxide of titanium-niobium-tantalate. The widely used minerals in the production of metallic tantalum and niobium are tantalum-columbite, pyrochlore, rare-earth perovskite, etc. Among them, pyrochlore is a very valuable mineral due to its high content of rare earth elements as well as tantalum and niobium.

The separation methods of tantalum and niobium include fractional crystallization of fluoride complexes, solvent extraction, ion exchange, distillation of chlorides, and selective reduction of NbCl₅. Among them, those that have been commercialized for many years are fractional crystallization and solvent extraction.

Recently, the development of inexpensive and efficient solvent extractants by many researchers has led to the separation of tantalum and niobium by solvent extraction methods. Although the use of neutral extractants such as MIBK and TBP in hydrofluoric or hydrofluoric-sulfuric acid media is common for the separation of tantalum and niobium, the separation of tantalum and niobium from sulfuric acid decomposition has been rarely studied so far.

Kang Chung Su, a section head at the Faculty of Chemical Engineering, conducted a study to separate the impurities from the aqueous leachate of pyrochlore sulfate decomposition product and to separate tantalum and niobium with octanol as the extractant.

After keeping the pH of the sulfate leaching solution at 2 and mixing 100% octanol to an aqueous phase/organic phase ratio (A/O) of 1:1, the extraction at room temperature for 15min resulted in more than 99% tantalum extraction, but no niobium extraction. After stripping of the tantalum-loaded octanol with distilled water at room temperature for 20min at a phase ratio of 1:1, more than 99% tantalum was stripped. When ammonia solution is added to the tantalum pregnant strip solution to pH 4.5-5.5, tantalum hydroxide is precipitated and when ammonia solution is added to the raffinate to pH 6-7, niobium hydroxide is precipitated.