Foldings of Difference Sets in Abelian Groups

Maximal sum-free sets in finite Abelian groups, III

Let A be a subset of a finite abelian group G. We say that A is sum-free if there is no solution of the equation x+ y = z, with x, y, z belonging to the set A. Let SF (G) the sel of all sum-free subets of G and σ(G) deonotes the number n(log 2 |SF (G)|). In this article we shall improve the error term in asymptotic formula of σ(G) obtained in [GR05]. The methods used are a slight refinement of methods of [GR05]. Let G be a finite abelian group of order n. A subset A of G is said to be sum-free if there is no solution of the equation x+ y = z, with x, y, z belonging to the set A. Let SF (G) denotes the set of all sum-free subsets of G. This article is motivated by the question of studying the cardinality of the set SF (G). Definition: (I) Let μ(G) denotes the density of a largest sum-free subset of G, so that any such subset has size μ(G)n. (II) Given a set B ⊂ G we say that (x, y, z) ∈ B3 is a Schur triple of the set B if x+ y = z. Observing that all subsets of a sum-free set are sum-free we have the obvious inequality |SF (G)| ≥ 2 (1) Let the symbol σ(G) denotes the number n(log2 |SF (G)|). Then from (1) it follows trivially that σ(G) ≥ μ(G). In this article we improve the results of Ben Green and Imre Ruzsa [GR05] and prove the following two results. The theorem 1 follows immediately from theorem 2 and a result from [GR05], namely theorem 6. The methods used to prove theorem 2 are a slight refinements of methods in [GR05].

Let G be a finite abelian group and A be a subset of G. We say that A is complete if every element of G can be represented as a sum of different elements of A. In this paper, we study the following question What is the structure of a large incomplete set? We show that such a set is essentially contained in a maximal subgroup. As a co-product, we obtain a new proof for several earlier results, including a new proof for Diderrich’s conjecture in large groups.

Low ranks make the difference: How achievement goals and ranking information affect cooperation intentions

objectives: The purpose of this research is to investigate the most common injuries of the players of the national football teams in Afghanistan from the point of view of the coaches of these teams. Methods: The current research has been conducted using a mixed method (quantitative and qualitative), which is descriptive-analytical in terms of its purpose. The statistical population includes all the coaches of Afghanistan's national teams who work at different levels. The samples were selected purposefully and accessible and consisted of all national football team coaches in different age groups. The number of samples was 25 Coaches, in order to collect theoretical bases, the documentary method was used by referring to documents and documents, internet sites, information banks, scientific articles and theses, etc. Field method and questionnaire were also used to collect the data of this study. The data was analyzed using descriptive statistics such as frequency and percentage and inferential statistics such as Friedman in spss software version 26. Results: The qualitative findings of this research, which was conducted with the content analysis approach; It shows that the most common injuries in football sports are injuries of the lower body, upper body injuries, head injuries, shoulder girdle injuries, wrist injuries, foot, toe injuries, knee injuries, lower body muscle injuries, leg and Achilles injuries, and thigh injuries. Injuries, the most common, football And the quantitative findings of this research show that lower body injuries, which include wrist, foot and toe injuries, knee injuries, lower body muscle injuries, leg and Achilles tendon injuries, hip and hip injuries, it is more common than upper body injuries, which include upper body injuries, upper body muscle injuries, head and face injuries, and shoulder girdle injuries, and it has the lowest prevalence among skin injuries. Also among lower body injuries, wrist, foot and toe injuries; The highest rank is followed by knee injuries, lower body muscle injuries, leg and Achilles tendon injuries, and finally thigh and hip injuries have the lowest rank. Among upper body injuries; Injuries around upper; The highest rank is followed by upper body muscle injuries, head and face injuries, and finally shoulder girdle injuries have the lowest rank.

The present study investigated the influence of dominance rank in combination with kinship on age-related differences in social grooming among adult females in a free-ranging group of Japanese monkeys ( Macaca fuscata). Eighty-three adult females were divided into six sub-groups according to age-class (younger: 5-9 years old; middle: 10-14 years old; older: 15-22 years old) and dominance rank (high and low rank). The ratio of the number of unrelated females that each female groomed to the total number of available unrelated females and grooming bouts which she gave to unrelated females decreased with increasing age for both high- and low-ranking females, whereas age did not appear to affect corresponding values for related females. On the other hand, compared with low-ranking females, high-ranking females of all age-classes received grooming more often from a larger number of unrelated females. Moreover, older females of low rank received grooming less often from a smaller number of unrelated females than younger females of low rank. These results indicate that with increasing age females are more likely to concentrate on related females when they have grooming interactions with other females. This tendency seems to be more apparent for low-ranking females. Moreover, the present findings also indicate that older high-ranking females could maintain their social attractiveness as high as younger high-ranking females.

Objective: The research aims [P1] to identify effective learning methods to improve Programme for International Student Assessment (PISA) rankings; this study undertakes a comprehensive analysis of relevant literature. PISA results provide a benchmark for assessing students' reading, mathematics, and science literacy abilities—crucial indicators of a nation's educational success. Most countries within the OECD utilize PISA assessment results to shape their educational policies. As nations strive to enhance their educational frameworks, particularly in teaching methodologies, the pursuit of influencing PISA rankings becomes increasingly competitive. Countries with lower PISA rankings often look to adopt best practices in literacy improvement from those with higher rankings. This study aspires to deliver best practices to bolster students' literacy skills, thereby improving PISA standings. Methods: The systematic literature review (SLR) is designed by the PRISMA diagram flow, encompassing the critical stages of identification, screening, eligibility, and inclusion. The SLR draws from 14 articles sourced from the Scopus database. Findings: The findings reveal that innovative teaching approaches, such as context-based learning and the integration of digital tools, significantly enhance students' performance in reading, mathematics, and science literacy. Notably, reading literacy is improved through the Cooperative Integrated Reading and Composition (CIRC) model, which focuses on collaborative learning. Mathematics literacy benefits from STEM-themed materials that bridge abstract concepts to real-world applications and through oral questioning techniques that foster critical thinking. Science literacy skills are advanced through digital comic materials, simplifying complex concepts, while STEM learning applications enhance students' understanding and engagement. Conclusion: In conclusion, this study underscores the vital role of appropriate teaching methods in improving learning outcomes and boosting student engagement in the international PISA assessment. By strategically adopting effective educational strategies from countries with higher PISA rankings, significant advancements can be made, offering hope for the future of education. Keywords: learning, method, PISA. DOI: http://dx.doi.org/10.23960/jpp.v14.i2.2024100

Influence of coal thermoplastic properties on coking pressure generation: Part 2 – A study of binary coal blends and specific additives

OBJECTIVE-To assess the knowledge and use of infection control practices (ICPs) among US veterinarians. DESIGN-Anonymous mail-out population survey. PROCEDURES-In 2005 a questionnaire was mailed to US small animal, large animal, and equine veterinarians who were randomly selected from the AVMA membership to assess precaution awareness (PA) and veterinarians' perceptions of zoonotic disease risks. Respondents were assigned a PA score (0 to 4) on the basis of their responses (higher scores representing higher stringency of ICPs); within a practice type, respondents' scores were categorized as being within the upper 25% or lower 75% of scores (high and low PA ranking, respectively). Characteristics associated with low PA rankings were assessed. RESULTS-Generally, respondents did not engage in protective behaviors or use personal protective equipment considered appropriate to protect against zoonotic disease transmission. Small animal and equine veterinarians employed in practices that had no written infection control policy were significantly more likely to have low PA ranking. Male gender was associated with low PA ranking among small animal and large animal veterinarians; equine practitioners not working in a teaching or referral hospital were more likely to have low PA ranking than equine practitioners working in such institutions. CONCLUSIONS AND CLINICAL RELEVANCE-Results indicated that most US veterinarians are not aware of appropriate personal protective equipment use and do not engage in practices that may help reduce zoonotic disease transmission. Gender differences may influence personal choices for ICPs. Provision of information and training on ICPs and establishment of written infection control policies could be effective means of improving ICPs in veterinary practices.

Cow traffic in relation to social rank and motivation of cows in an automatic milking system with control gates and an open waiting area

BackgroundMetagenomics has a great potential to discover previously unattainable information about microbial communities. An important prerequisite for such discoveries is to accurately estimate the composition of microbial communities. Most of prevalent homology-based approaches utilize solely the results of an alignment tool such as BLAST, limiting their estimation accuracy to high ranks of the taxonomy tree.ResultsWe developed a new homology-based approach called Taxonomic Analysis by Elimination and Correction (TAEC), which utilizes the similarity in the genomic sequence in addition to the result of an alignment tool. The proposed method is comprehensively tested on various simulated benchmark datasets of diverse complexity of microbial structure. Compared with other available methods designed for estimating taxonomic composition at a relatively low taxonomic rank, TAEC demonstrates greater accuracy in quantification of genomes in a given microbial sample. We also applied TAEC on two real metagenomic datasets, oral cavity dataset and Crohn’s disease dataset. Our results, while agreeing with previous findings at higher ranks of the taxonomy tree, provide accurate estimation of taxonomic compositions at the species/strain level, narrowing down which species/strains need more attention in the study of oral cavity and the Crohn’s disease.ConclusionsBy taking account of the similarity in the genomic sequence TAEC outperforms other available tools in estimating taxonomic composition at a very low rank, especially when closely related species/strains exist in a metagenomic sample.Electronic supplementary materialThe online version of this article (doi:10.1186/1471-2105-15-242) contains supplementary material, which is available to authorized users.

A chemical kinetic model of vitrinite maturation and reflectance

Twenty-five studies which reported WISC subtest scores of disabled readers were reviewed. The subtests were reclassified into categories labeled Spatial, Conceptual, and Sequential, and disabled readers were ranked as to their relative strength in these three categories. Disabled readers were highest in the Spatial category, intermediate in the Conceptual category, and lowest in the Sequential category. The high rank in the Spatial category suggests that disabled readers are strong in visual-spatial skills. The low rank in the Sequential category can be accounted for by deficits in short-term memory processes and attentional processes.

An attempt was made to replicate findings of positive telepathic influence on dream content where the sender views audio-visual programs in a “sensory bombardment” chamber and the recipient's dreams are collected on experimental arousals in an EEG sleep laboratory. In the original study (Krippner, Honorton, Ullman, Masters, & Houston, 1971), agent- S distance was 14 miles; here it was approximately 2000 miles: the agent viewed programs in New York City while S slept in Wyoming. 8 female Ss were selected on the basis of prior telepathic experience, favorable attitudes toward telepathy, good dream recall, and rapport with the agent, who was a well-known “psychic.” Each slept for one experimental night, during which the agent viewed an audio-visual program randomly selected from a pool of such programs and constructed around a single theme. At the conclusion of the study, 3 judges were given the dreams, grouped by S, viewed the 8 audio-visual programs the agent had seen, and ranked the 8 programs for their correspondence to each S‘s dreams. High rankings (1–4) of the true target were considered “hits,” low rankings (5–8) “misses.” Median judge rankings of true targets failed to reveal a significant long-distance, “sensory bombardment” telepathic influence on Ss' dreams.

Influence of surface chemistry on interfacial properties of low to high rank coal seams