• Education of Primary School Mathematics
• /
• v.7 no.1
• /
• pp.15-29
• /
• 2003

The present study examined the 7th national elementary school mathematics curriculum from a perspective of mathematical creativity. The study investigated to what extent the activities in the Pattern and Function lessons in the national elementary school mathematics textbooks promoted the development of mathematical creativity. The results indicated that the current elementary school mathematics curriculum was limited in many ways to promote the development of mathematical creativity. Regarding the activities in Pattern lessons, for example, most activities presented closed tasks involving finding and extending patterns. The lesson provided little opportunities to explore the relationships among various patterns, apply patterns to different situations, or create ones own patterns. In regard to the Function lessons, the majority of activities were about computing the rate. This showed that the function was taught from an operational perspective, not a relational perspective. It was unlikely that students would develop the basic understanding of function through the activities involving the computing the rate. Further, the lessons had students use exclusively the numbers in representing the function. Students were provided little opportunities to use various representation methods involving pictures or graphs, explore the strengths and limitations of various representation methods, or to choose more effective representation methods in particular contexts. In conclusion, the lesson activities in the current elementary school mathematics textbooks were unlikely to promote the development of mathematical creativity.

• Journal of the Korean Mathematical Society
• /
• v.45 no.4
• /
• pp.1057-1073
• /
• 2008

We present an explicit Eta pairing approach for computing the Tate pairing on general divisors of hyperelliptic curves $H_d$ of genus 2, where $H_d\;:\;y^2+y=x^5+x^3+d$ is defined over ${\mathbb{F}}_{2^n}$ with d=0 or 1. We use the resultant for computing the Eta pairing on general divisors. Our method is very general in the sense that it can be used for general divisors, not only for degenerate divisors. In the pairing-based cryptography, the efficient pairing implementation on general divisors is significantly important because the decryption process definitely requires computing a pairing of general divisors.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.15 no.12
• /
• pp.4275-4291
• /
• 2021

With the unprecedented growth of textual information on the Internet, an efficient automatic summarization system has become an urgent need. Recently, the neural network models based on the encoder-decoder with an attention mechanism have demonstrated powerful capabilities in the sentence summarization task. However, for paragraphs or longer document summarization, these models fail to mine the core information in the input text, which leads to information loss and repetitions. In this paper, we propose an abstractive document summarization method by applying guidance signals of key sentences to the encoder based on the hierarchical encoder-decoder architecture, denoted as KI-HABS. Specifically, we first train an extractor to extract key sentences in the input document by the hierarchical bidirectional GRU. Then, we encode the key sentences to the key information representation in the sentence level. Finally, we adopt key information representation guided selective encoding strategies to filter source information, which establishes a connection between the key sentences and the document. We use the CNN/Daily Mail and Gigaword datasets to evaluate our model. The experimental results demonstrate that our method generates more informative and concise summaries, achieving better performance than the competitive models.

• International Journal of Computer Science & Network Security
• /
• v.22 no.10
• /
• pp.374-388
• /
• 2022

Cloud computing has been one of the most critical technology in the last few decades. It has been invented for several purposes as an example meeting the user requirements and is to satisfy the needs of the user in simple ways. Since cloud computing has been invented, it had followed the traditional approaches in elasticity, which is the key characteristic of cloud computing. Elasticity is that feature in cloud computing which is seeking to meet the needs of the user's with no interruption at run time. There are traditional approaches to do elasticity which have been conducted for several years and have been done with different modelling of mathematical. Even though mathematical modellings have done a forward step in meeting the user's needs, there is still a lack in the optimisation of elasticity. To optimise the elasticity in the cloud, it could be better to benefit of Machine Learning algorithms to predict upcoming workloads and assign them to the scheduling algorithm which would achieve an excellent provision of the cloud services and would improve the Quality of Service (QoS) and save power consumption. Therefore, this paper aims to investigate the use of machine learning techniques in order to predict the workload of Physical Hosts (PH) on the cloud and their energy consumption. The environment of the cloud will be the school of computing cloud testbed (SoC) which will host the experiments. The experiments will take on real applications with different behaviours, by changing workloads over time. The results of the experiments demonstrate that our machine learning techniques used in scheduling algorithm is able to predict the workload of physical hosts (CPU utilisation) and that would contribute to reducing power consumption by scheduling the upcoming virtual machines to the lowest CPU utilisation in the environment of physical hosts. Additionally, there are a number of tools, which are used and explored in this paper, such as the WEKA tool to train the real data to explore Machine learning algorithms and the Zabbix tool to monitor the power consumption before and after scheduling the virtual machines to physical hosts. Moreover, the methodology of the paper is the agile approach that helps us in achieving our solution and managing our paper effectively.

• Journal of the Chungcheong Mathematical Society
• /
• v.25 no.3
• /
• pp.475-489
• /
• 2012

A plateau in a Motzkin path is a sequence of three steps: an up step, a horizontal step, then a down step. We find three different forms for the bivariate generating function for plateaus in Motzkin paths, then generalize to longer plateaus. We conclude by describing a further generalization: a continued fraction form from which one can easily derive new multivariate generating functions for various kinds of path statistics. Several examples of generating functions are given using this technique.

• Journal of Computing Science and Engineering
• /
• v.6 no.4
• /
• pp.310-319
• /
• 2012

Next generation wireless receivers demand low computational complexity algorithms with high computing power in order to perform fast signal detections and error estimations. Several signal detection and estimation algorithms have been proposed for next generation wireless receivers which are primarily designed to provide reasonable performance in terms of signal to noise ratio (SNR) and bit error rate (BER). However, none of them have been chosen for direct implementation as they offer high computational complexity with relatively lower computing power. This paper presents a low-complexity power-efficient algorithm that improves the computing power and provides relatively faster signal detection for next generation wireless multiuser receivers. Measurement results of the proposed algorithm are provided and the overall system performance is indicated by BER and the computational complexity. Finally, in order to verify the low-complexity of the proposed algorithm we also present a formal mathematical proof.

• Honam Mathematical Journal
• /
• v.16 no.1
• /
• pp.103-109
• /
• 1994

Piezoceramic patches as collocated actuator and sensors are widely used in mechanical control systems. An approximation scheme for computing feedback gains arising in heat flux stabilization problem with such control mechanism is introduced. The scheme is based on a finite element method and a variational approach.

• Journal of the Chungcheong Mathematical Society
• /
• v.28 no.3
• /
• pp.443-449
• /
• 2015

In this paper we propose a method of computing the number of points on the reduction of non-hyperelliptic modular curves of genus greater than or equal to 3 over finite fields.

• Journal of the Korean Mathematical Society
• /
• v.52 no.6
• /
• pp.1195-1207
• /
• 2015

Lagrange multiplier method for solving the contact problem in elasticity is considered. Based on lower semicontinuity of sensitivity functional we prove the convergence of modified dual scheme to corresponding saddle point.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.1
• /
• pp.263-272
• /
• 2016

By using the finite projective geometry method, the separating properties of linear constant-weight codes are presented. An algorithm is given for computing the cardinality of separating coordinate positions of certain disjoint codeword sets of linear constant-weight codes.