On a conjecture of Pomerance

We say that k is a P-integer if the first phi(k) primes coprime to k form a reduced residue system modulo k. In 1980 Pomerance proved the finiteness of the set of P-integers and conjectured that 30 is the largest P-integer. We prove the conjecture assuming the Riemann Hypothesis. We further prove that there is no P-integer between 30 and 10^11 and none above 10^3500.Comment: 10 pages. Submitted to Acta Arithmetic

On conjectures and problems of Ruzsa concerning difference graphs of S-units

Given a finite nonempty set of primes S, we build a graph $\mathcal{G}$ with vertex set $\mathbb{Q}$ by connecting x and y if the prime divisors of both the numerator and denominator of x-y are from S. In this paper we resolve two conjectures posed by Ruzsa concerning the possible sizes of induced nondegenerate cycles of $\mathcal{G}$, and also a problem of Ruzsa concerning the existence of subgraphs of $\mathcal{G}$ which are not induced subgraphs.Comment: 15 page

Finding well approximating lattices for a finite set of points

In this paper we address the task of finding well approximating lattices for a given finite set A of points in R-n motivated by practical texture analytic problems. More precisely, we search for o, d(1),..., d(n) is an element of R-n such that a - o is close to Lambda = d(1)Z + ... + d(n)Z for every a is an element of A. First we deal with the one-dimensional case, where we show that in a sense the results are almost the best possible. These results easily extend to the multi-dimensional case where the directions of the axes are given, too. Thereafter we treat the general multidimensional case. Our method relies on the LLL algorithm. Finally, we apply the least squares algorithm to optimize the results. We give several examples to illustrate our approach

Digital Civic Engagement and Youth Participation: Hungarian LIS Students’ Perspective of Political Information

Objective. The research seeks to understand, how Hungarian LIS students use social media as an avenue to express their democratic actions and how social media political information affects the youth’s trust and judgement when interacting with their close family and friends online. Methods. The study employed a quantitative approach to determine the social media engagement of the participants with close family and friends. Convenience sampling was applied in this study (Students of Library and Information Science, University, Hungary), and an online questionnaire was sent to all the potential participants (to 197 students). Results. A total of 43% participated in this research. The youth give a high level of trust to their family members and close friends even if they share, post, like, or comment on something that is different from their point-of-view in social media. Moreover, the youth have a low level of judgement towards family and close friends. Conclusions. Political participation among youth is voluntary and engagement with political information in social media is rare/low

Women’s changing domestic responsibilities in neoliberal Africa: a relational time-space analysis of Lesotho’s garment industry

Since 2001 when Lesotho embraced the neoliberal African Growth and Opportunities Act that offers preferential access to the US market, its garment industry has expanded dramatically to become the nation’s leading employer. Elsewhere, large-scale employment of women in low-paid factory jobs has entailed spatial restructuring of gender and age relations. Lesotho is a distinctive context, with socio-spatial relations historically adjusted to male labour migration, high levels of contemporary male unemployment and alarming AIDS prevalence. Based on semi-structured interviews with 40 female factoryworkers and 37 dependents, this article applies a relational time-space analysis to explore how financial and spatio-temporal aspects of factory employment articulate to alter women’s relationships with those for whom they have culturally determined responsibilities: their children, those suffering from ill health and their (generally rural) home communities. The analysis highlights that such employment is not merely adding to women’s responsibilities, but transforming how they are able to undertake social reproduction, as practical, social and emotional roles are converted to largely financial obligations

Orbital Magnetism and Current Distribution of Two-Dimensional Electrons under Confining Potential

The spatial distribution of electric current under magnetic field and the resultant orbital magnetism have been studied for two-dimensional electrons under a harmonic confining potential V(\vecvar{r})=m \omega_0^2 r^2/2 in various regimes of temperature and magnetic field, and the microscopic conditions for the validity of Landau diamagnetism are clarified. Under a weak magnetic field (\omega_c\lsim\omega_0, \omega_c being a cyclotron frequency) and at low temperature (T\lsim\hbar\omega_0), where the orbital magnetic moment fluctuates as a function of the field, the currents are irregularly distributed paramagnetically or diamagnetically inside the bulk region. As the temperature is raised under such a weak field, however, the currents in the bulk region are immediately reduced and finally there only remains the diamagnetic current flowing along the edge. At the same time, the usual Landau diamagnetism results for the total magnetic moment. The origin of this dramatic temperature dependence is seen to be in the multiple reflection of electron waves by the boundary confining potential, which becomes important once the coherence length of electrons gets longer than the system length. Under a stronger field (\omega_c\gsim\omega_0), on the other hand, the currents in the bulk region cause de Haas-van Alphen effect at low temperature as T\lsim\hbar\omega_c. As the temperature gets higher (T\gsim\hbar\omega_c) under such a strong field, the bulk currents are reduced and the Landau diamagnetism by the edge current is recovered.Comment: 15 pages, 11 figure