Current Topics on Mathematics and Computer Science Vol. 11

Korea is one of the leading countries across the world to have promoted education through ICT using smart school practices. Using the Analytical Hierarchy Process (AHP) method, this paper aims to identify the determinants affecting the success of the smart schooling system in Korea; prioritise the indicators necessary for the success of the smart schooling system in terms of weight; and provide policy implications for policymakers and practitioners involved in smart school and education policy. The indicator teacher dedication has the greatest weight score, followed by attitudes toward e-learning and IT, meaning that the individual involved in the smart schooling system's activities should be viewed as more significant than any other indication.

In this chapter,I introduce a modified Ishikawa iteration for a countable family of multi-valued Mappings under the SC- Conditions and Condition (A). The best approximation operator to obtain weak and strong convergence of the modified Ishikawa iteration in a Banach spaces. Main results to the problem of finding a common fixed point of a countable family of I-Nonexpansive multi-valued mappings.

Elliptic Curve Scalar multiplication is the process of repeatedly adding a point on a curve to itself [1]. Many scholars working in the field of cryptography have been drawn to studies in Scalar Multiplication over Elliptic Curves (EC) over finite fields in recent years to see how elliptic curves cryptography (ECC) may be implemented and how to reduce its complexity [2].  Elliptic curve scalar multiplication utilising the point-halving algorithm [3], then the double-base (DB) chain algorithm, and finally step multi-base representation (SMBR) are the most efficient approaches used in Elliptic curve cryptography, however each technique has its own set of drawbacks. As a result, it is critical to develop a new approach that may be used to effectively deploy ECC while also decreasing its complexity. For affine coordinates, the study introduces the Treble algorithm, which is a new algorithm. We kept working with the binary concept or double and add operation with the help of the treble technique to make it more efficient, which refers to the use of all input values in producing any form of output, including how much time and energy is necessary. The results demonstrate that our contribution can improve EC scalar multiplication significantly. Elliptic Curve Scalar Multiplication is diverse aspect of Cryptography.

In Korea, the unemployment rate is not improving, the income disparity between rich and poor is widening, and a large percentage of young university graduates are unemployed (the employment rate is approximately 58 percent as of 2014). Ordinary people's demands for additional jobs and social benefits are becoming more vocal and serious. In this context, social businesses in Korea emerged as a means of addressing the problem of unemployment, particularly among disadvantaged social groups, and boosting the supply of social services. Since the establishment of the Social Enterprise Promotion Act in 2007, the number of social enterprises has been steadily expanding, and as of December 2014, there were 1251 in total. However, critics have questioned the viability of social enterprises, claiming that they fail to continue operating or shrink in size once the benefits and government subsidies they receive as certified businesses expire.The purpose of this study is to look at the elements that influence the long-term viability of social enterprises in Korea, as well as to propose theoretical and policy implications on how to improve social enterprise viability.

Text Summarization has been an area of interest for many years. It refers to creating a concise text of a document without any lose of information. Researchers in the area of natural language processing have developed many abstractive and extractive methods for creating summary. Abstractive summaries modifies the sentences and creates a modified concise form, while extractive summaries pick relevant sentences. The extractive method used in this work is a novel one which models the document as an Intuitionistic Fuzzy Hypergraph (IFHG). The main objectives of the work are to convert a document in to an IFHG, apply morphological operations to it and to create a summary filter. This is the premier work which applies morphological operations on IFHG that is modeled on a text. The method has generated summary which is almost similar to a human generated summary and showed more accuracy when compared with other machine generated summaries. An attempt to apply skelton operation on text hypergraph is also made.

We describe alternative ways to present the famous Klein four-group.

A comprehensive statistical model is developed for the correct evaluation of contraception effectiveness with a double objective: first, to contribute to a better understanding by statisticians of the general subject of inference, by means of an interesting particular example, and second, to help clinical practitioners when dealing with human contraception. From the probability of a woman, using some contraceptive procedure, conceiving in a single cycle, the pregnant woman rate and the pregnancy rate are defined and calculated. This is used to infer the values of these rates from experimental trials, accounting for the number of followed women and for the period they are followed for, whatever kind of events may be counted up in the trials, either pregnant women or pregnancies. However, computing pregnancies can bias the results of a trial, since the conceiving women, supposedly with a greater risk of pregnancy, should be replaced in the sample by new ones, whereas computing pregnant women allows more objectivity, since those pregnant women stay in the sample up to the end of the trial. Thus, a more realistic effectiveness rate can be deduced from the investigation.

The primary goal of this study is to determine object boundaries in outdoor scenes of photographs using only some general attributes of real-world objects. Segmentation and recognition should not be separated in this case and should be treated as an interleaving procedure. The goal of this project is to develop an adaptive global clustering technique that can capture non-accidental structural links among the constituent parts of structured objects, which typically have several constituent parts. The colour and texture information is also used to distinguish background items such as the sky, tree, and ground. This method categories them according to their properties without requiring any prior knowledge of the items. On two demanding outdoor databases and in distinct outside natural scene contexts, the suggested method outperformed two state-of-the-art image segmentation approaches, improving segmentation quality. It is possible to overcome significant reflection and excessive segmentation by employing this clustering strategy. This work proposes to increase performance and background identification capacity.

Mobile Computing is a new paradigm aimed at providing users with constant network connectivity regardless of their location. Computer networking removed the physical barrier between computers, allowing users connected to the system from one computer to access resources on another. This paved the path for distributed computing, in which a group of connected computers works together to achieve a common goal. However, the access points to such a distributed system were still tethered machines and a user did not have the flexibility to move while accessing such a system. Mobile computing expands distributed computing in the direction of making a system's services available to a user regardless of their location or, more significantly, their location changes. Wireless networking removed the requirement to be linked to a cable, static infrastructure in order to benefit from distributed system services. A cable infrastructure of static hosts (representing a conventional distributed system) connects areas of wireless coverage ('cells') to mobile computers in a distributed system with mobile hosts.

Two symbols are defined in this study utilising the Hankel type transform, as well aspseudo-differential type operators M(x,D) and N(x,D) associated with the Bessel type operator \(\Delta\)_{\(\alpha\),\(\beta\)} defined by equation (2.1) in terms of these symbols.. Further product of M(x,D) and N(x,D) is defined. Sobolev type space is also defined. It is demonstrated that the pseudo-differential type operators M(x,D) , N(x,D) and the product of pseudo-differential type operators are bounded in a certain Sobolev type space associated with the Hankel type transform. Finally, certain unique cases are investigated.

Mathematics is the science that is structured and deductive object of study that includes an abstract form of facts, concepts, principles and procedures rests on an agreement, deductive thinking patterns, have an empty symbol of sense, pay attention to the universe of discourse and consistent system. Mathematics has a language and a well-defined rules, a clear and systematic reasoning, and the structure and the linkages between the concept is strong. Mathematics is a language of symbols that must be understood as a representation of statements. The main elements of the mathematical work is deductive reasoning which works on the basis of assumptions and have a consistent truth. So that mathematics is known as a deductive science, which means that the mathematics starts from an undefined elements, axioms / postulates and ultimately lowering the theorem. Math formed as a result of human thinking which relate to the idea,Mathematics is the fruit of human thought that the truth of a general nature which does not rely on the scientific method that contains the inductive process. Mathematics is one of the most important auxiliary science and useful in everyday life as well as in supporting the development of human resources and the development of science and technology. Such formal mathematics taught since elementary school through college. Therefore, school mathematics learning should take place effectively and with quality.

This chapter presented a procedure and tables for a Bayesian single sampling plan based on the Gamma-Zero Inflated Poisson distribution involving minimum angle method to reduce the producer's risk and consumer’s risk for specified acceptance quality level and limiting quality level. In recent years, every manufacturing industry using technological advancements to detect product defects and rectifying them in the initial stages of production. It is possible to reduce the number of defective products early on using such technologies. Therefore, the occurrence of non-defects would be more frequent in the sampling inspection. However, random fluctuations in the production processes may lead some products to an imperfect state. In this case, one can consider the appropriate probability distribution of the number of defects to be a Gamma-Zero Inflated Poisson (G-ZIP) distribution. The optimal plan parameters for the proposed sampling plan are given to determine its minimum angle values, which are illustrated with suitable examples. Necessary tables are constructed to facilitate quality control engineers.