scholarly journals Mathematical Problems for Complex Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-2
Author(s):  
Haijun Jiang ◽  
Haibo He ◽  
Jianlong Qiu ◽  
Qiankun Song ◽  
Jianquan Lu
Keyword(s):  
Complex Systems ◽  
Mathematical Problems

The mathematical problems of complex systems investigation under uncertainties

2017 ◽  
pp. 135-171
Author(s):  
K. Atoyev ◽  
P. Knopov ◽  
V. Pepeliaev ◽  
P. Kisała ◽  
R. Romaniuk ◽  
...  
Keyword(s):  
Complex Systems ◽  
Mathematical Problems

scholarly journals Mathematical Problems of Managing the Risks of Complex Systems under Targeted Attacks with Known Structures

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2468
Author(s):  
Alexander Shiroky ◽  
Andrey Kalashnikov
Keyword(s):  
Complex Systems ◽  
Optimal Allocation ◽  
Risk Function ◽  
Chain Structure ◽  
System Structure ◽  
Optimal Placement ◽  
Targeted Attacks ◽  
Mathematical Problems ◽  
Local Risk ◽  
Simple Chain

This paper deals with the problem of managing the risks of complex systems under targeted attacks. It is usually solved by using Defender–Attacker models or similar ones. However, such models do not consider the influence of the defending system structure on the expected attack outcome. Our goal was to study how the structure of an abstract system affects its integral risk. To achieve this, we considered a situation where the Defender knows the structure of the expected attack and can arrange the elements to achieve a minimum of integral risk. In this paper, we consider a particular case of a simple chain attack structure. We generalized the concept of a local risk function to account for structural effects and found an ordering criterion that ensures the optimal placement of the defending system’s elements inside a given simple chain structure. The obtained result is the first step to formulate the principles of optimally placing system elements within an arbitrarily complex network. Knowledge of these principles, in turn, will allow solving the problems of optimal allocation of resources to minimize the risks of a complex system, considering its structure.

scholarly journals The complexity of the four colour theorem

2010 ◽  
Vol 13 ◽  
pp. 414-425 ◽  
Author(s):  
Cristian S. Calude ◽  
Elena Calude
Keyword(s):  
Complex Systems ◽  
Planar Graph ◽  
Riemann Hypothesis ◽  
Logic Program ◽  
Formal Proof ◽  
Complexity Class ◽  
Computational Method ◽  
Equational Logic ◽  
Four Color Theorem ◽  
Mathematical Problems

AbstractThe four colour theorem states that the vertices of every planar graph can be coloured with at most four colours so that no two adjacent vertices receive the same colour. This theorem is famous for many reasons, including the fact that its original 1977 proof includes a non-trivial computer verification. Recently, a formal proof of the theorem was obtained with the equational logic program Coq [G. Gonthier, ‘Formal proof–the four color theorem’,Notices of Amer. Math. Soc.55 (2008) no. 11, 1382–1393]. In this paper we describe an implementation of the computational method introduced by C. S. Calude and co-workers [Evaluating the complexity of mathematical problems. Part 1’,Complex Systems18 (2009) 267–285; A new measure of the difficulty of problems’,J. Mult. Valued Logic Soft Comput.12 (2006) 285–307] to evaluate the complexity of the four colour theorem. Our method uses a Diophantine equational representation of the theorem. We show that the four colour theorem is in the complexity class ℭU,4. For comparison, the Riemann hypothesis is in class ℭU,3while Fermat’s last theorem is in class ℭU,1.

STUDI DESKRIPTIF MINAT CALON GURU SEKOLAH DASAR TERHADAP PENGGUNAAN ALAT PERAGA MATEMATIKA SETELAH PERKULIAHAN MEDIA DAN MODEL PEMBELAJARAN MATEMATIKA SD

2015 ◽  
Vol 8 (1) ◽  
pp. 19
Author(s):  
Isna Rafianti ◽  
Etika Khaerunnisa
Keyword(s):  
Elementary Teachers ◽  
Elementary Mathematics ◽  
Mathematics Learning ◽  
Learning Model ◽  
Prospective Elementary Teachers ◽  
Descriptive Research ◽  
Learning Mathematics ◽  
Mathematical Problems ◽  
The Subject ◽  
Object Of Study

This research is motivated by the lack of interest of teachers in the use of props in the process of learning mathematics in elementary school. In accordance with the demands of the curriculum in 2013 and supported by the developed learning theory, learning mathematics is abstract object of study, students need an intermediary that props math-ematics, so that students can more easily understand the concepts that will be pre-sented, and in the end it can deliver students to solve mathematical problems, not only that proposed by the teacher but also the problems in life. The purpose of this study was to determine the interest of prospective elementary teachers on the use of props mathematics after getting lectures media and elementary mathematics learning model. By knowing the interest of prospective elementary teachers will be developed further realization of the state of the subject being studied. The method used is descriptive research, then the instruments used were questionnaires and interviews. The results of this study stated that the interest of prospective elementary teachers on the use of props after attending lectures media and elementary mathematics learning model is high over-all with a percentage of 76.70%.Keywords : Interest, Props Mathematics

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