نشریه ریاضی و جامعه
سال هفتم شماره 4 (زمستان 1401)

The outstanding Russian mathematician Aleksandr M. Lyapunov passed away one hundred years ago, on November 6, 1918. Honouring his memory, we recall the main events of his life when he was a student, then from the years in Saint Petersburg until 1885, from the Kharkov period, finally from his second period in Saint Petersburg from 1902. We recount the main fields of his scientific activity (stability theory, potential theory, probability theory, shape of planets) concerning stability theory and chaos in details.

There are many topics in graph theory that can be called ``moving objects around a graph". For example; In network optimization, shipments are transferred from some vertices (resources) to other vertices (demand) according to the costs allocated to the edges, so that this can be done in the cheapest way. A pebble motion in a graph involves removing two pebbles from the vertex of a graph and then placing a pebble at the adjacent vertex. If a distribution (or configuration) of pebbles allows us to move at least one pebble to each vertex by repeatedly applying pebble movements, then that distribution is called a pebble of the graph. One of the most basic questions is how many pebbles are needed to ensure that any configuration with this number can target a pebble at any particular target. The smallest number of stones that meet this condition is called the graph pebble number. In this paper, after examining the roots of the number theory of the pebble graph model, which in turn is a productive subject, we will study the pebble number for specific graphs and also consider an optimization approach to this subject called weight functions.

Suppose $G$ is a finite non-abelian group and $\Gamma(G)$ is a simple graph with the non-central conjugacy classes of $G$ as its vertex set. Two different non-central conjugacy classes $A$ and $B$ are assumed to be adjacent if and only if there are elements $a,b \in G$ such that $a \in A$, $b \in B$ and $ab = ba$. This graph is called the commuting conjugacy class graph of G. In this paper, the structure of the commuting conjugacy class graph of the generalized dihedral group $D_{(m,n)}$ and the generalized dicyclic group $Dic (A, y, x)$ are completely determined.

In this paper, we analyze the eighth grade students performance in Fars province in cognitive and content domains in mathematics by TIMSS 2019 assessment results. Due to the cultural, social and economic proximity of Fars and Isfahan provinces, corresponding results have been obtained for students of Isfahan province and comparisons have been made in each domain by using appropriate tests. Also, gender analysis has been derived in both cognitive and content dimensions and in all of their domains in mathematics for students of both provinces

The vital role of education in a successful and good life is undeniable. Education improves the value and ascendency of both personal and social life. The basic foundation of development in every country is determined by its educational system. It is so important that neglecting this crucial matter leads to catastrophic effects on development and improvement of any country in various dimensions. Children and teenagers are the greatest and the most valuable resources of a society and the more we try to preserve these resources, the wealthier and the more successful our society will be in the future. Through entrepreneurial education, students learn how to be innovative and how to create new methods in every profession and business by identifying their own abilities, capabilities and ambitions. Benefiting from operational and practical educations in workshops and labs, they can attempt to find strong and weak points and threats and opportunities in their own field of study and also in their environment and try to create new opportunities. Through entrepreneurial educations, not only will the students be equipped with skills such as decision making, problem solving, goal setting, critical thinking, creative thinking and etc., but also, they learn scientific, practical and demand-driven skills and abilities. When empowered with entrepreneurial awareness and knowledge, skilled and capable individuals create occupational opportunities in economic, social and cultural grounds. In other words, they analyze environmental problems, difficulties, needs and opportunities through different and new thoughts and views and eventually use them to create values. In this line, given the importance of this topic, in this article, developing creativity and education for entrepreneurship at schools will be examined

In this note we show that if every codegree of real-valued irreducible characters of a finite group $G$ is either a $2$-number or $2'$-number, then $G$ is solvable