Markov type equations with solutions in Lucas sequences

Here we look at the Markov equations ax^2 +by^2 +cz 2 = dxyz with integer solutions (x, y, z) which are all members of a Lucas sequence whose characteristic equation has roots which are quadratic units

Employee training to increase efficiency in the Saudi private sector

Saudis in the private sector tend to change employers, and this study sought information on whether training and education experience, and access to these, influenced their career choices. A study of a Saudi conglomerate was used as representative of larger firms who offered training to their employees; and the sample, 105 Saudi nationals, were self-selected for an online survey. Analysis of demographics, and the participants\u27 employment and training experience and intentions are presented. Analysis included medians and percentages of demographic characteristics and employee experiences and intentions, then descriptive analyses for relationships between the main questions and the demographic characteristics. The results were a sample median of 35.5 years of age, with 84.5 percent under the age of 41 years. The participants were well educated with 87.6 percent holding Bachelor\u27s degrees or higher; a further 80 percent had family responsibilities. The median work experience was four years; however, 33.3 percent had two years or less in the workforce, and 42.9 percent had changed their employer three or more times (median 2 employers). Over half (58.1%) attended pre-employment training comprising job skills training (31.4%) and workplace behavior training (12.4%). Upon recruitment, nearly two-thirds (62.1%) attended induction courses and 41 percent of these courses were a week or longer. On-the-job training was conducted by a supervisor (30.5%) or a team member (42.9%). A majority (76.2%) of the participants were in training, predominantly (45.7%) with their employer for promotion or higher pay (23.8%). The remainder were training in other parts of the conglomerate (16.2%) or externally (30.5%). Further, over half (58.1%) of the participants stated that their acquired knowledge and skills were portable and could be used with another employer; nearly a half (47.6%) also stated an intention to change employers. Significant relationships between the demographic variables and survey responses were that older and more experienced employees assisted recruits; whilst older employees, those with family responsibilities and those who had more employers also intended to move. Those with higher qualifications were seeking more pay. In conclusion, experience with, and access to training and education were not associated with intention to stay with their employer

The Effect Of Union Status On Injury Risk And Severity In A Manufacturing Cohort

Objective: This study aimed to investigate the effect of union status on risk of injury among a cohort of aluminum manufacturing workers. Methods: This cohort study included all hourly employees at 19 U.S. plants, which were in operation between 2000 and 2007. Workers were classified into unionized and non-unionized groups. The final dataset combined a human resources database, which includes information about job history and socio-demographic information, and an incident management system, which includes information on work-related injuries. Injuries were classified by severity into four mutually exclusive categories: injuries requiring first aid, medical treatment, work restriction, and lost work time. Descriptive statistics using Chi-square and student’s t-test were calculated. Survival curves and cox-proportional hazard models were used to determine the outcome, which was the individual’s time to first injury within a standardized job category. Results: A total of 27,600 hourly workers included; 19,115 (71%) were unionized while 8,485 (29%) were non-unionized. The cohort of 27,600 persons contributed a total of 41,522 person-jobs (30,360 unionized vs. 11,162 non-unionized). Looking at first injury of any type, union person-jobs incurred 9,290 injuries (30% of union person-jobs) compared to 2,599 injuries in non-union person-jobs (23% of non-union person-jobs). A similar relationship was observed when considering only first OSHA recordable injuries. After adjusting for multiple covariates, union workers had a 27% higher risk of early injury of any type and a 34% higher risk of earlier first recordable injury compared to non-union workers. Conclusion: Our results provide evidence associating union status with higher risk of earlier injuries, whether these injuries were OSHA recordable or first aid only

k-generalized Fibonacci numbers which are concatenations of two repdigits

We show that the k-generalized Fibonacci numbers that are concatenations of two repdigits have at most four digits

Rough action on topological rough groups

[EN] In this paper we explore the interrelations between rough set theory and group theory. To this end, we first define a topological rough group homomorphism and its kernel. Moreover, we introduce rough action and topological rough group homeomorphisms, providing several examples. Next, we combine these two notions in order to define topological rough homogeneous spaces, discussing results concerning open subsets in topological rough groups.The authors wish to thank the Deanship for Scientific Research (DSR) at King Abdulaziz University for financially funding this project under grant no. KEP-PhD-2-130-39. Also, we would like to thank the editor and referees for their valuable suggestions which have improved the presentation of the paper.Altassan, A.; Alharbi, N.; Aydi, H.; Özel, C. (2020). Rough action on topological rough groups. Applied General Topology. 21(2):295-304. https://doi.org/10.4995/agt.2020.13156OJS295304212S. Akduman, E. Zeliha, A. Zemci and S. Narli, Rough topology on covering based rough sets, 1st International Eurasian Conference on Mathematical Sciences and Applications (IECMSA), Prishtine, Kosovo, 3ÔÇô7 September 2012.S. Akduman, A. Zemci and C. Özel, Rough topology on covering-based rough sets, Int. J. Computational Systems Engineering 2, no. 2 (2015),107-111. https://doi.org/10.1504/IJCSYSE.2015.077056N. Alharbi, H. Aydi and C. Özel, Rough spaces on covering based rough sets, European Journal of Pure And Applied Mathematics (EJPAM) 12, no. 2 (2019). https://doi.org/10.29020/nybg.ejpam.v12i2.3420N. Alharbi, H. Aydi, C. Park and C. Özel, On topological rough groups, J. Computational Analysis and Applications 29, no. 1 (2021), 117 -122.A. Arhangel'skii and M. Tkachenko, Topological groups and related structures, Atlantis press/ World Scientific, Amsterdam-Paris, 2008. https://doi.org/10.2991/978-94-91216-35-0N. Bagirmaz, I. Icen and A. F. Ozcan, Topological rough groups, Topol. Algebra Appl. 4 (2016), 31-38. https://doi.org/10.1515/taa-2016-0004R. Biswas and S. Nanda, Rough groups and rough subgroups, Bull. Polish Acad. Sci. Math. 42 (1994), 251-254.E. Brynairski, A calculus of rough sets of the first order, Bull. of the Polish Academy Sciences: Mathematics 37, no. 1-6 (1989), 71-78.G. Chiaselotti and F. Infusino, Some classes of abstract simplicial complexes motivated by module theory, Journal of Pure and Applied Algebra 225 (2020), 106471, https://doi.org/10.1016/j.jpaa.2020.106471G. Chiaselotti and F. Infusino, Alexandroff topologies and monoid actions, Forum Mathematicum 32, no. 3 (2020), 795-826. https://doi.org/10.1515/forum-2019-0283G. Chiaselotti, F. Infusino and P. A. Oliverio, Set relations and set systems induced by some families of integral domains, Advances in Mathematics 363 (2020), 106999, https://doi.org/10.1016/j.aim.2020.106999G. Chiaselotti, T. Gentile and F. Infusino, Lattice representation with algebraic granular computing methods, Electronic Journal of Combinatorics 27, no. 1 (2020), P1.19. https://doi.org/10.37236/8786S. Hallan, A. Asberg and T. H. Edna, Additional value of biochemical tests in suspected acute appendicitis, European Journal of Surgery 163, no. 7 (1997), 533-538.R. R. Hashemi, F. R. Jelovsek and M. Razzaghi, Developmental toxicity risk assessment: A rough sets approach, Methods of Information in Medicine 32, no. 1 (1993), 47-54. https://doi.org/10.1055/s-0038-1634890A. Huang, H. Zhao and W. Zhu, Nullity-based matroid of rough sets and its application to attribute reduction, Information Sciences 263 (2014), 153-165. https://doi.org/10.1016/j.ins.2013.11.014A. Kusiak, Decomposition in data mining: An industrial case study, IEEE Transactions on Electronics Packaging Manufacturing 23 (2000), 345-353. https://doi.org/10.1109/6104.895081A. Kusiak, Rough set theory: A data mining tool for semiconductor manufacturing, IEEE Transactions on Electronics Packaging Manufacturing 24, no. 1(2001), 44-50. https://doi.org/10.1109/6104.924792C. A. Neelima and P. Isaac, Rough anti-homomorphism on a rough group, Global Journal of Mathematical Sciences: Theory and Practical 6, no. 2, (2014), 79-80.M. Novotny and Z. Pawlak, On rough equalities, Bulletin of the Polish Academy of Sciences, Mathematics 33, no. 1-2 (1985), 99-104.N. Paul, Decision making in an information system via new topology, Annals of fuzzy Mathematics and Informatics 12, no. 5 (2016), 591-600.Z. Pawlak,Rough sets, Int. J. Comput. Inform. Sci. 11, no. 5 (1982), 341-356. https://doi.org/10.1007/BF01001956J. Pomykala, The stone algebra of rough sets, Bulletin of the Polish Academy of Sciences, Mathematics 36, no. 7-8 (1988), 495-508.J. Tanga, K. Shea, F. Min and W. Zhu, A matroidal approach to rough set theory, Theoretical Computer Science 471 (2013), 1-11. https://doi.org/10.1016/j.tcs.2012.10.060S. Wang, Q. Zhu, W. Zhu and F. Min, Graph and matrix approaches to rough sets through matroids, Information Sciences 288 (2014), 1-11. https://doi.org/10.1016/j.ins.2014.07.023S. Wang, Q. Zhu, W. Zhu and F. Min, Rough set characterization for 2-circuit matroid, Fundamenta Informaticae 129 (2014), 377-393. https://doi.org/10.3233/FI-2013-97

On ABC energy and its application to anticancer drugs

For a simple connected graph $\Gamma$ with node set $V(\Gamma) = \{w_{1}, w_{2}, \dots, w_{n}\}$ and degree sequence $d_{i}$, the atom-bond connectivity ($ABC$) matrix of $\Gamma$ has an $(ij)$-th entry $\sqrt{\frac{d_{i}+d_{j}-2}{d_{i}d_{j}}}$ if $w_{i}$ is adjacent to $w_{j}$ and $0$, otherwise. The multiset of all eigenvalues of $ABC$ matrix is known as the $ABC$ spectrum and their absolute sum is known as the $ABC$ energy of $\Gamma.$ Two graphs of same order are known as $ABC$ equienergetic if they have the same $ABC$ energy but share different $ABC$ spectrum. We describe the $ABC$ spectrum of some special graph operations and as an application, we construct the $ABC$ equienergetic graphs. Further, we give linear regression analysis of $ABC$ index/energy with the physical properties of anticancer drugs. We observe that they are better correlated with $ABC$-energy

Association of the angiotensinogen gene polymorphism with atherosclerosis and its risk traits in the Saudi population

BACKGROUND: Angiotensinogen (AGT) constitutes a central component of the renin-angiotensin system that controls the systemic blood pressure and several other cardiovascular functions and may play an important role in atherosclerosis pathways. In this study, we employed TaqMan genotyping assays to evaluate the role of 8 AGT variants in primary hypertension (HTN), type 2 diabetes mellitus (T2DM), and obesity as a possible trigger of coronary artery disease (CAD) in a population of 4615 angiographed native Saudi individuals. METHODS: Linkage analysis was done by using the Affymetrix Gene Chip array, sequencing by using the MegaBACE DNA analysis system and genotyping accomplished by TaqMan chemistry using the Applied Biosystem real-time Prism 7900HT Sequence Detection System. RESULTS: Six variants, rs2067853 GG [Odds ratio(95% Confidence Interval) = 1.44(1.17-1.78); p = 0.001], rs7079 [1.49(1.20-1.85); p < 0.0001], rs699 G [1.19(1.08-1.13); p < 0.0001], rs3789679 A [1.51(1.14-1.99); p = 0.004], rs2148582 GG [1.31(1.11-1.55); p = 0.002] and rs5051 TC + CC [1.32(1.13-1.60); p = 0.001] conferred risk for HTN (3521 cases versus 1094 controls). The rs2067853 (p = 0.042), rs699G (p = 0.007) and rs5051 (p = 0.051) also conferred risk for myocardial infarction (MI; 2982 vs 1633), while rs3789679 A (p < 0.0001) and GA + AA (p < 0.0001) as well as rs4762G (p = 0.019) were associated with obesity (1576 vs 2458). However, while these variants appeared to be also associated with CAD (2323 vs 2292), only the rs7079G (p = 0.035) retained its significant relationship. Interestingly, among the haplotypes constructed from these SNPs, the baseline 8-mer haplotype, GGTGGGGT (χ(2) = 7.02; p = 0.0081) and another GGCGGAGT (χ(2) = 5.10; p = 0.024), together with several of their derivatives were associated with HTN. T2DM was associated with two 8-mer haplotypes, GGTAGGAC (χ(2) = 5.66; p = 0.017) and ATTGAGAC (χ(2) = 5.93; p = 0.015), obesity with GGCGGAGT (χ(2) = 9.49; p = 0.0021) and MI was linked to ATTGGGAC (χ(2) = 6.68; p = 0.010) and GGTGGGAT (χ(2) = 4.25; p = 0.039). Furthermore, several causative haplotypes were also shared among the risk traits as well as with CAD. CONCLUSION: These results point to AGT as independently conferring risk for various cardiovascular traits, and possibly interacting with these traits in events leading to atherosclerosis

New Insights into Immunological Involvement in Congenital Disorders of Glycosylation (CDG) from a People-Centric Approach

SFRH/BD/124326/2016 SFRH/BD/138647/2018Congenital disorders of glycosylation (CDG) are rare diseases with variable phenotypes and severity. Immunological involvement remains a largely uncharted topic in CDG, mainly due to lack of robust data. To better characterize immune-related manifestations' prevalence, relevance, and quality-of-life (QoL) impact, we developed electronic questionnaires targeting (1) CDG patients and (2) the general "healthy" population. Two-hundred and nine CDG patients/caregivers and 349 healthy participants were included in this study. PMM2-CDG was the most represented CDG (n = 122/209). About half of these participants (n = 65/122) described relevant infections with a noteworthy prevalence of those affecting the gastrointestinal tract (GI) (63.1%, n = 41/65). Infection burden and QoL impact were shown as infections correlated with more severe clinical phenotypes and with a set of relevant non-immune PMM2-CDG signs. Autoimmune diseases had only a marginal presence in PMM2-CDG (2.5%, n = 3/122), all being GI-related. Allergy prevalence was also low in PMM2-CDG (33%, n = 41/122) except for food allergies (26.8%, n = 11/41, of PMM2-CDG and 10.8%, n = 17/158, of controls). High vaccination compliance with greater perceived ineffectiveness (28.3%, n = 17/60) and more severe adverse reactions were described in PMM2-CDG. This people-centric approach not only confirmed literature findings, but created new insights into immunological involvement in CDG, namely by highlighting the possible link between the immune and GI systems in PMM2-CDG. Finally, our results emphasized the importance of patient/caregiver knowledge and raised several red flags about immunological management.publishersversionpublishe