Jo Jul 29, 2022
O Un Suk, a lecturer at the Faculty of Applied Mathematics, has studied the relations of core, Weber set and Shapley value to one another under the condition of strong convexity / weak concavity.
A cooperative game with transferable utility, a TU-game for short, is defined as a pair (N, v) , where N is a finite set of players and v is a mapping that assigns a real number v(S) to each coalition S⊆N. v(φ) is set 0.
One of the important problems in the cooperative game theory is to select an efficient payoff vector, i.e., a way of sharing among players the total worth of the game when they all join a grand coalition. For this aim, various solution concepts have been developed.
The solutions playing an important role in selecting efficient payoff vectors include Core, Weber set, and Shapley value.
In many real situations, however, not all subsets of N can be realized as coalitions or they are not feasible. The interest in subcollections of the power set of N is inspired by the fact that in case of restricted communication or cooperation structure, the standard model of a cooperative game is not applicable. A game on concept lattices is a good example.
A game on concept lattices is a cooperative TU-game defined on concepts, where a concept is a pair (S, S') of S, a subset of players or objects, and S' a subset of attributes.
Such games induce a game on extents and a game on intents.
The inclusion of the Weber set in core plays an important role in the studies of the stability of the Shapley value (inclusion of the Shapley value into the core) because the Shapley value is defined as a mean value of all vertices of the Weber set.
The Weber set does not become the subset of the core under convexity in games on concept lattices different from classical cooperative games. Thus, the concept of strong convexity is introduced in games on extents.
Strong convexity means that the larger coalition each player joins in, the greater the average creation value of them gets.
The following theorem shows that the extent Weber set becomes a subset of the extent core in strongly convex games on extents.
Theorem 1. The extent Weber set is included in the extent core if a game on extents is strongly convex.
Corollary 1. The extent Shapley value assigns an element of the extent core if a game on extents is strongly convex.
The condition of strong convexity is a sufficient condition that guarantees the extent Shapley value to be in the extent core in the games on extents. Therefore, in convex games, not strongly convex, the extent Shapley value may belong to the extent core.
Similarly, it becomes possible to define weak concavity in games on intents as they are in dual relation with games on extents. Then, it can be proved that the intent Weber set is the subset of the intent core under weak convexity.
It is concluded that the extent/intent Shapley value can be used as a rational solution to this game if a game on extents/intents is convex/concave.
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Jo Jul 12, 2022
Ri Kwang Hwi, a researcher at the Faculty of Mechanical Science and Technology, has been improving the practical scientific research capability of postgraduate students in close combination of scientific research and education based on a virtual factory.
Universities and research institutes in many countries are in contact with production enterprises so as to bring education and scientific research close to production, resulting in great changes in teaching methods. In particular, they are getting rid of cramming methods to introduce heuristic, inductive and discussion teaching methods.
Introduction of virtual factories allows the contents of selective subjects in postgraduate course to be organized in conformity with the world trend of developing education and pedagogical requirements.
The first step is to let students grasp the actual conditions of the virtual factory in order to combine scientific research and education.
Let’s take “expert system for process planning” as an example. Here the first thing they have to do is to visit the technical department to investigate the work of the technical preparing office, where they learn about the technical process sheet and technical guidance. Then in the technical equipment office they check fixture design and tool design. The next thing to do is to find out about production scheduling in the production department. All these are conducted at the virtual factory, not an actual one.
In real situations, comprehensive investigation is impossible as they do not have everything needed for scientific research and education. This requires the model of a virtual factory, which involves a lot of effort.
The next step is to let students inquire into the trend of development of science and technology and scientific foundations in every element of the production site. Of course, profound scientific inquiry may be impossible, but at least they can get the gist, for they have already finished basic technology subjects and major subjects in undergraduate course.
This part enables them to select a research seed in the course of studying and investigating deep into literature and the world trend of development to break through the cutting edge.
The last step is to let students return to the technical preparing office and the technical equipment office after fixing the direction of scientific research in order to bring their research closer to production. This helps them decide their selective subjects for themselves.
In summary, if virtual factory investigation precedes, postgraduate students can decide their selective subjects after setting the direction of their research before laying scientific foundations for it.
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Jo Jul 4, 2022
Kim Chaek University of Technology is on a winning streak in codechef challenges that take place twice a month. Codechef June Long Challenge witnessed its glory once again.
The first contest that was held on June 10 to 13 produced 32 winners in Division 1, nine of whom are students at KUT.
In the meanwhile, a total of 27 contestants won the first place in Division 1 of the second contest that went on from 24 to 27. Eight out of 27 winners are from KUT.
The number of winners of KUT in Division 1 in the two contests every month in the first half of this year is as follows.
January: first contest ― 7 out of 27, second contest ― 7 out of 29
February: first contest ― 8 out of 38, second contest ― 8 out of 30
March: first contest ― 9 out of 48, second contest ― 5 out of 21
April: first contest ― 10 out of 27, second contest ― 2 out of 5
May: first contest ― 6 out of 14, second contest ― 6 out of 17
June: first contest ― 9 out of 32, second contest ― 8 out of 27
The figures show that many students at KUT have taken part in the codechef challenges and that most of them took the first place.
KUT students are still trying to enlarge their store of knowledge in order to keep the national flag of the DPRK flying over the Internet.
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Jo Jun 11, 2022
Ro Yong Sim, a researcher at the Faculty of Electrical Engineering, has applied, in her subject Servo Motor Design, a new examination method in which students are given questions in multimedia and allowed to consult references, in contrast with traditional examination methods in which only theoretical problems and complicated design calculations were given, in order to evaluate correctly their theoretical and practical abilities to design different servo motors.
Primarily, in order to evaluate students’ design ability she gives questions for the characteristic parameters of servo motors whose dimensional structures difficult to be expressed in words are shown in movies and images and allows them to consult all available references to calculate them.
The questions are made to be solved only when they have gone through several steps of calculation while grasping the correct meaning of all the variables in complicated design equations.
Then the students, on the basis of the decision of what kind of servo motor it is from the images and movies, calculate the characteristic parameters such as time constant or inertia, which makes it possible to evaluate their design ability for a particular object.
Secondly, she presents questions in images to evaluate the practical ability to understand design plans.
In other words, she blanks or makes errors in some parts of the plan of a servo motor shown in image to make the students correct them.
The students are supposed to write on their exam paper which parts contain errors and how the errors should be corrected.
Thirdly, she uses questions to estimate the computer aided design ability of the students.
For example, to test the analysis ability of the students by Ansoft Maxwell software, she distributes to students’ computers a program file which has analysis conditions beforehand and encounters an error because of some mistakes made during modeling and analyzing. The students come to use some software tools to correct the errors. She makes them write or draw on the paper the cause of errors, the resultant parameter values and graphs.
Fourthly, she uses multimedia for questions to estimate their theoretical knowledge, too.
For example, while showing a movie in which a three-phase hybrid-type stepper motor is rotating, she pauses the movie at any moment and asks students to draw an equivalent magnetic circuit at that point. This enables her to evaluate if they have a correct understanding in detail of the operating principle of the stepper motor.
Finally, she uses multimedia to evaluate the creative ability of the students.
For example, in the past she used to ask, “What methods to decrease the cogging torque of a permanent magnet electric machine are there?”, but now she first shows the parts and assemblies of a permanent magnet synchronous motor in multimedia and then gives questions like how this motor could decrease cogging torque and what else could be done for that.
So she can evaluate on the basis of a particular object if the students grasp the theory and know how to apply it to the practice.
Besides, by giving a task to design permanent magnet about that object, she could test the creative design ability of the students in a comprehensive way such as if they select the optimal pole embrace to minimize the cogging torque, if they set reasonable air gap, if they choose proper material for permanent magnet or if they rationally design dimensions like the width and the thickness of the poles.
She makes such questions with PowerPoint software, sends them to every computer of the students, and allows them to use all the materials such as computers, textbooks and reference books during the test while she prevents them from exchanging information through the network.
Applying this testing method she has been able to correctly evaluate the practical ability as well as the theoretical knowledge of the students and fully stimulate the interest in their study.
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Jo Jun 3, 2022
The contests lasted from 6 to 23 May, 2022.
The first contest was held on May 6 to 9. It drew over 17 000 contestants from tens of countries and regions including our country, and India. More than 90 participants competed in Division 1, over 800 in Division 2, some 2 900 in Division 3 and over 13 900 in Division 4.
A total of 14 contestants won the first place in Division 1 ― 10 from the DPRK, 2 from India, 1 from Italy and 1 from Japan. 6 out of the 10 winners of our country are students at Kim Chaek University of Technology. As much as 71.4287% of the world winners are from the DPRK, and 42.857% are from Kim Chaek University of Technology. KUT students add up to 60% of the 10 DPRK winners.
The second contest went on from 20 to 23. Over 18 000 contestants from tens of countries and regions including our country and India took part. Some 110 contestants competed in Division 1, more than 1 100 in Division 2, over 2 900 in Division 3 and more than 14 200 in Division 4.
A total of 17 winners in Division 1 include 7 from the DPRK, 4 from India, 2 from China, 1 from Singapore, 1 from Taipeh, China and 2 from Japan.
6 out of the 7 DPRK winners are students from Kim Chaek University of Technology. Our country and KUT make up 41.176% and 35.294% of the world winners, respectively. KUT students account for 85.714% of the DPRK winners.
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Jo May 3, 2022
The contests came to an end on April 25, 2022.
The first contest, which was held on April 8 to 11, drew 20 000-odd contestants from tens of countries and regions including our country, China and India. More than 130 participants competed in Division 1, over 600 in Division 2, over 4 600 in Division 3 and over 15 500 in Division 4. Division 1 set forth 5 problems, none of which were challenge problems.
A total of 27 contestants won the first place in Division 1 ― 19 from the DPRK, 3 from China, 2 from India, 2 from Japan and 1 from the US.
10 out of the 19 winners of our country are students at Kim Chaek University of Technology.
As much as 70.37% of the world winners are from the DPRK, and 37.037% are from KUT. KUT students add up to 52.63% of the 19 DPRK winners.
In the meantime, a student from KUT took the first place in Division 2.
Several KUT students who were absent from the Codechef March Long Challenge due to the national coding challenge held in the same period took part in this contest, which bestowed on KUT the honour of having many winners.
The second contest went on from 22 to 25. 18 000-odd contestants from tens of countries and regions including our country, China and India took part. Over 70 contestants competed in Division 1, more than 900 in Division 2, over 3 300 in Division 3 and over 14 000 in Division 4.
4 from our country and 1 from Japan made a total of 5 winners in Division 1.
Half the 4 DPRK winners are students from Kim Chaek University of Technology.
Our country and KUT make up 80% and 40% of the world winners, respectively.
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