A Graph Theoretical Framework for the Strong Gram Classification of Non-negative Unit Forms of Dynkin Type 𝔸n

In the context of signed line graphs, this article introduces a modified inflation technique to study strong Gram congruence of non-negative (integral quadratic) unit forms, and uses it to show that weak and strong Gram congruence coincide among positive unit forms of Dynkin type 𝔸n. The concept of inverse of a quiver is also introduced, and is used to obtain and analyze the Coxeter matrix of non-negative unit forms of Dynkin type 𝔸n. With these tools, connected principal unit forms of Dynkin type 𝔸n are also classified up to strong congruence.

Youth Perceptions, Use and Effects of Social Media on Peace and Conflicts in Tanzania

The article focused on examining how youth perception and use of social media (SM) influences peace and conflicts among Tanzanians, using the Dar es Salaam region as a case study. A qualitative approach was used to collect and analyse data. A purposive sampling technique was used to select respondents, whereby youth, local government officers and community residents were interviewed. The findings revealed that SM has both advantages and disadvantages in promoting peace and activating conflicts, depending on users’ perceptions and interests. SM facilitates conflicts due to the Social Media Networks (SMNs) ability to spread fake news quickly, unfounded claims, and rumours. These promote conflicts between political opponents as well as causing mistrust among citizens and their leaders. Some artists, especially comedians, instigate conflicts in society by editing political and religious leaders’ messages. On the other hand, it was revealed that SM promotes peace due to quicker transfer of relevant information that nurtures positive unit values, solidarity, respect and love among the group, society members, and citizens. These values promote good deeds, such as worshipping God, working and living together amicably. However, the study found out that lack of appropriate education on SM’s use and importance among many youths on youth development seems to have hindered SM use in peace promotion. The study calls for strengthening stakeholders’ initiative to educate and mobilise improved use of SM among youth to sustain peace and security, which is a pre-condition for their self-development and prosperity of their country.

There are no universal ternary quadratic forms over biquadratic fields

We study totally positive definite quadratic forms over the ring of integers $\mathcal {O}_K$ of a totally real biquadratic field $K=\mathbb {Q}(\sqrt {m}, \sqrt {s})$. We restrict our attention to classic forms (i.e. those with all non-diagonal coefficients in $2\mathcal {O}_K$) and prove that no such forms in three variables are universal (i.e. represent all totally positive elements of $\mathcal {O}_K$). Moreover, we show the same result for totally real number fields containing at least one non-square totally positive unit and satisfying some other mild conditions. These results provide further evidence towards Kitaoka's conjecture that there are only finitely many number fields over which such forms exist. One of our main tools are additively indecomposable elements of $\mathcal {O}_K$; we prove several new results about their properties.

How We Get Along

It doesn’t take much of a difference between groups to make in-group–out-group discrimination occur. High schoolers can discriminate on the basis of preference for the paintings of Klee versus Kandinsky. Third-grade children can discriminate on the basis of eye color. The two social identification mechanisms that contribute to discrimination relate to the epistemic and social relational motives underlying shared reality creation. By accentuating similarities within social categories and differences between them, we can order, simplify, and make sense of our complex social world. This epistemic motive, however, is not enough to account for the discrimination of favoring your own group over the other group—in-group favoritism. This comes from the social relational motive of creating a shared reality with others, with wanting a positive connection to those with whom you have a shared reality and experience yourself and others as belonging to the same social category—the we of social identification. Having a common social identity with other in-group members can make interactions relatively smooth, effortless and pleasant, but it does not necessarily make them more productive because the group members often discuss what they share with one another rather than what they don’t share. The roles that we enact are also shared realities that can bias our perception of the world by determining what is relevant and significant. Shared reality perceptions are also critical in close relationships where partners must experience that they are a positive unit who sees and responds to the world in the same way.

Development of Algae Guard Façade Paint with Statistical Modeling under Natural Phenomena

Algaecides are chemicals that cause serious health problems. Conventional paints contain algaecides to improve the algae resistance on the paint film. Present research has suggested an environment-friendly paint formulation that focuses on developing algae resistance without having algaecides. In this research, algae growth on newly developed paint is modeled by incorporating dirt resistance of paint and natural phenomena including humidity, temperature, and time, respectively. The fitted Model revealed explained variation of 59.65% in the average algae growth, of which, dirt resistance, humidity, temperature, and some of their interactions play significant role in this variation. The model suggests that the proposed newly developed paint without algaecides is more resistant to algae growth and significantly decreased the average algae growth rate by 0.53% as compared to conventional paints. Keeping the effect of all other factors constant, if dirt resistance of paint (Dc value) increases by one percent, average algae growth decreases by 12.98%; when temperature increases by 1 °C, average algae growth decreases by 22.4%; a positive unit change in the joint linear effect of dirt resistance, temperature, and humidity caused a decrease in average algae growth by 0.0031%. It was also observed that the individual effect of the humidity variable was inversely related with average algae growth. However, the combination of humidity and temperature, humidity and dirt resistance, humidity and time, and the quadratic effect of humidity were found to increase the average algae growth rate. The cubic effect of temperature variable by one degree centigrade resulted in decrease of average algae growth by 0.000907%.

Development of Algae Guard Façade Paint with Statistical Modeling under Natural Phenomena

Algaecides are chemicals that cause serious health problems. Conventional paints contain algaecides to improve the algae resistance on the paint film. Present research has suggested an environmental friendly paint formulation that focuses on developing algae resistance without having algaecides. In this research, Algae growth on newly developed paint is modeled by incorporating dirt resistance of paint and natural phenomena including humidity, temperature and time respectively. The fitted Model revealed explained variation of 59.65% in the average algae growth, of which, Dirt Resistance, Humidity and temperature and some of their interactions play significant role in this variation. Model suggests that the proposed newly developed paint without algaecides is more resilient to algae growth and significantly decreased the average algae growth rate by 0.53% as compared to conventional paints. Keeping the effect of all other factors constant, if dirt resistance of paint (Dc value) increases by one percent, average algae growth decreases by 12.98%; when temperature increases by 1oC, average algae growth decreases by 22.4%; a positive unit change in the joint linear effect dirt resistance, temperature and humidity caused a decrease in average algae growth by 0.0031%. It was also observed that the individual effect of humidity variable was inversely related with average algae growth. However the combination of humidity and temperature, humidity and dirt resistance, humidity and time, and the quadratic effect of humidity were found to increase the average algae growth rate. The cubic effect of temperature variable by one degree centigrade resulted in decrease of average algae growth by 0.000907%.

Transformational leadership influence on unit performance

PurposeThe purpose of this paper is to explore the role of mediation and moderation mechanisms between firm-level effects of transformational leadership (TFL) on unit-level performance across levels.Design/methodology/approachThe authors used surveys to collect data from 800 senior managers at the firm level and 1,377 unit managers from 800 units of 100 firms from semiconductors, optoelectronics, computer electronics, and telecommunications industries. The industries were chosen because these firms focus on expanding their businesses and encourage extensive knowledge sharing among the firms and at all levels within the organizations.FindingsIn this study, the authors theorized that firm-level effects of TFL on unit-level performance across levels were positively related to unit-level performance. Unit-level knowledge sharing mediates the positive relationship between firm-level TFL and unit-level performance. A cross-level interaction effect of firm-level TFL and unit-level absorptive capacity showed that a positive unit-level absorptive capacity enhanced firm-level influence of TFL on unit-level knowledge sharing. Unit-level absorptive capacity moderates the positive relationship between unit-level knowledge sharing and unit-level performance.Originality/valueFirst, the authors attempt to integrate the leadership and knowledge management research by exploring the critical mediator of unit-level knowledge sharing in explaining the effects of firm-level TFL on employees’ performance at the unit level. This approach is important because it extends the research areas of the two fields, and also clarifies issues regarding how and why TFL at the top of the organization positively impacts the performance of employees at a lower level of the organizational hierarchy. Second, the effectiveness of firm-level TFL depends on the absorptive capacity of each unit. The importance of absorptive capacity and the consequences of leadership behaviors have been emphasized in studies.

Study on the Improvement of Microprism Retroreflective Material

In this paper, the microprism reflective structure is optimized by theoretical research and simulation calculations, and based on the current technology of V-shaped diamond blade manufacturing mode, an improved microprism retroreflective material is designed. By adjusting the intensity distribution and angle of the light cone, we can control the style of light cone which is formed by the reflected light for optimal reflective effect. The microprism reflective structure contains the positive unit and negative unit. The negative unit relative to the positive unit is rotated 60° for producing phase superposition to reduce the non-uniform of the material orientation. Cutting along a straight line by V-shaped diamond blade, the technology creates a plurality of higher-precision and smaller reflective elements and enhances the retroreflective performance. Meanwhile, the overall processing technology which reduces labor force greatly is beneficial to the cost control and highly practical during the fabrication process. Keywords: microprism retroreflective material, improvement and optimization