On the arithmetic of generalized Fekete polynomials

For each prime number $p$ one can associate a Fekete polynomial with coefficients $-1$ or $1$ except the constant term, which is 0. These are classical polynomials that have been studied extensively in the framework of analytic number theory. In a recent paper, we showed that these polynomials also encode interesting arithmetic information. In this paper, we define generalized Fekete polynomials associated with quadratic characters whose conductors could be a composite number. We then investigate the appearance of cyclotomic factors of these generalized Fekete polynomials. Based on this investigation, we introduce a compact version of Fekete polynomials as well as their trace polynomials. We then study the Galois groups of these Fekete polynomials using modular techniques. In particular, we discover some surprising extra symmetries which imply some restrictions on the corresponding Galois groups. Finally, based on both theoretical and numerical data, we propose a precise conjecture on the structure of these Galois groups.Comment: To appear in Experimental Mathematic

APMEC: An Automated Provisioning Framework for Multi-access Edge Computing

Novel use cases and verticals such as connected cars and human-robot cooperation in the areas of 5G and Tactile Internet can significantly benefit from the flexibility and reduced latency provided by Network Function Virtualization (NFV) and Multi-Access Edge Computing (MEC). Existing frameworks managing and orchestrating MEC and NFV are either tightly coupled or completely separated. The former design is inflexible and increases the complexity of one framework. Whereas, the latter leads to inefficient use of computation resources because information are not shared. We introduce APMEC, a dedicated framework for MEC while enabling the collaboration with the management and orchestration (MANO) frameworks for NFV. The new design allows to reuse allocated network services, thus maximizing resource utilization. Measurement results have shown that APMEC can allocate up to 60% more number of network services. Being developed on top of OpenStack, APMEC is an open source project, available for collaboration and facilitating further research activities

Experimental Evaluation of Geopolymer Concrete Strength Using Sea Sand and Sea Water in Mixture

This paper presents the experimental strength evaluation of geopolymer concrete and ordinary concrete using sea sand and seawater in the mixture. A series of 30 cubic samples with a 150 mm side length and 12 rectangular specimens with a dimension of 100 × 100 × 400 mm (width × thickness × length) were cast and tested in this study. Specimens were divided equally into two groups. The first group of specimens was cast using geopolymer as the main binder (GPC), while the second group of samples was made using ordinary Portland Cement (OPC). While the compression tests were performed for specimens in two groups at the ages of 3, 7, 28, 60, and 120 days, the tensile tests were only performed for specimens at 7 and 28 days. The testing results revealed that the compression strength of GPC specimens using sea sand and seawater was significantly higher than that of OPC samples using the same type of salted sand and water. Besides, the use of sea sand and seawater for replacing river sand and fresh water in the production of GPC is feasible in terms of compressive strength since GPC produces a higher compressive strength than that of conventional concrete. Doi: 10.28991/CEJ-2022-08-08-03 Full Text: PD

The congruence effect between product emotional appeal and country-based emotion: The moderating role of country-of-origin

Previous research has suggested that country-based emotions (i.e., emotions associated with a country) can influence consumer evaluations of a product from thatcountry. However, it remains unclear when and how country-based emotions can be influential in consumer decision making. The results from an experiment revealthat only for a destination with a less favorable country-of-origin image will the match (vs. mismatch) between the country-based emotion and the emotional appealof the product advertisement increase the purchase likelihood of the product. Thesefindings are beneficial for local brands in that they can promote tourist spendingat their destination by cooperating with destination marketers in developing integrated promotional campaigns that elicit congruent emotions

On the Paley graph of a quadratic character

Paley graphs form a nice link between the distribution of quadratic residues and graph theory. These graphs possess remarkable properties which make them useful in several branches of mathematics. Classically, for each prime number $p$ we can construct the corresponding Paley graph using quadratic and non-quadratic residues modulo $p$. Therefore, Paley graphs are naturally associated with the Legendre symbol at $p$ which is a quadratic Dirichlet character of conductor $p$. In this article, we introduce the generalized Paley graphs. These are graphs that are associated with a general quadratic Dirichlet character. We will then provide some of their basic properties. In particular, we describe their spectrum explicitly. We then use those generalized Paley graphs to construct some new families of Ramanujan graphs. Finally, using special values of $L$-functions, we provide an effective upper bound for their Cheeger number.Comment: To appear in Mathematica Slovac