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A set S ⊆ V (G) of a (simple) undirected graph G is a locating-dominating set of G if for each v∈V (G) n S, there exists w∈S such tha vw∈E(G) and NG(x) \ S 6= NG(y) \ S for any distinct vertices x and y in V (G) n S. S is a stable locating-dominating set of G if it is a locating-dominating set of G and S n fvg is a locating-dominating set of G for each v∈S. The minimum cardinality of a stable locating-dominating set of G, denoted by s l (G), is called the stable locating-domination number of G. In this paper, we investigate this concept and the corresponding parameter for some graphs. Further, we introduce other related concepts and use them to characterize the stable locating-dominating sets in some graphs. [ABSTRACT FROM AUTHOR]

In this paper we first construct a Lie group structure on n × n Hankel matrices over R + by Hadamard product and then we find its Lie algebra structure and finally calculate dimension of this manifold over R +. Moreover, we discuss topological properties of this manifold using Frobenious norm. We pointed out the relation between Lie group and Lie algebra structures of these matrices by exponential map. It is also shown that the Hadamard product on Hankel matrices over R + is not bounded by Frobenious norm. Lastly, we provide some applications of these manifolds. [ABSTRACT FROM AUTHOR]

Let G be any graph. A sequence L = (w1, . . ., wk) of distinct vertices of G is called a legal hop independent sequence if k = 1 or L is a hop independent and NG[wi ] \ Uj=1i-1 j=1 NG[wj ] ̸= ∅ for every i ∈ {2, · · ·, k}. The maximum length of a legal hop independent sequence in G, denoted by αℓh(G), is called the legal hop independence number of G. In this paper, we investigate its relationships with the hop independence and grundy domination parameter of a graph, respectively. In fact, the legal hop independence parameter is at most equal to the grundy domination (resp. hop independence) parameter on any graph G. Moreover, we derive some formulas and bounds of this parameter on some families of graphs, join, and corona of two graphs. [ABSTRACT FROM AUTHOR]

In this paper, 2-hop domination parameter is introduced and investigated on some special graphs and on the join of two graphs. Characterizations of 2-hop dominating sets in some special graphs are formulated to derive bounds or formulas of the parameter of these graphs. Moreover, new variant of pointwise non-domination is introduced to characterize 2-hop dominating sets in the join of two graphs. This characterization is used to calculate the exact value of 2-hop domination number of the join of two graphs. [ABSTRACT FROM AUTHOR]

Bone fractures are a global public health concern, yet no thorough investigation of low-dose aspirin usage to prevent fractures in the elderly has been conducted. Many interventional human and animal studies have tried to detect the correct role of low-dose aspirin on fractures in elderly persons. The literature doesn't consist of a retrospective observational study that includes a large number of older individuals and evaluates the accurate effect of aspirin on the fractures post falling from low heights. This cross-sectional includes 7132 elderly persons and aimed to detect if there was a link between taking low-dose aspirin to prevent fractures in the elderly. Data was extracted from the National Health and Nutrition Examination Survey (NHANES) database for 2017–2020 and 2013–2014. Demographic and examination data were collected during in-home interviews and study visits to a mobile examination center. Standardized questionnaires were used to collect information such as age, gender, race, educational level, and family income-to-poverty ratio. Body mass index (BMI), weight, standing height, upper leg length, upper arm length, arm circumference, and wrist circumference were all measured during the examination. The study examined 8127 patients, with 7132 elderly patients suitable for data analysis. The odds ratio of fractures due to a fall from standing height or less was 0.963 (95 percent confidence interval 0.08–1.149) in low-dose aspirin users, while having parents with osteoporosis had a related risk of 1.23. (95 percent confidence interval 0.81–1.8). The total number of fractures was 1295; with hip fractures constituting up to 13.82%, wrist fractures of 66.56%, and spine fractures of 19.61%. There was no significant difference in femur and spine bone mineral density (BMD) in the two groups (use low dose aspirin and don't use). Females had a 5.6 times greater fracture risk related to a fall from standing height or less (1 time or more) than males (P-value < 0.001). Furthermore, taking aspirin had no effect on the occurrence of fractures from standing height or less in older people (P-value = 0.468). In addition, the logistic regression after performing the propensity matching score confirmed that there was no impact of taking aspirin on the occurrence of fractures (P-value > 0.05). This cross-sectional study reveals that taking low-dose aspirin to prevent fractures in the elderly is statistically insignificant. However, fractures are more common in older persons, especially in older women; thus, more widespread injury prevention initiatives and access to osteoporosis prevention and diagnosis for older people should improve to minimize the overall burden. [ABSTRACT FROM AUTHOR]

Background: Depression is a prominent cause of mental disability globally, having a severe impact on mental and physical health. Depression rehabilitation and treatment, whether through psychiatric management or counseling therapy, is hampered by stigmatizing attitudes regarding psychiatric illness patients impacted by societal and cultural factors. However, little is known about the stigma toward people with depression among the students in Syria. Methodology: A total of 1,056 students in Syria completed a questionnaire that included a case narrative illustrating depression. A total of 1,056 students in Syria completed a questionnaire that included a case narrative illustrating depression. The survey looked at attitudes toward depression, the desire to keep a safe distance from depressed people, stigma attitudes toward people with depression among college students, perceived beliefs about depressive people, gender (male and female), and the major section (medical and medical and non-medical) differences. Results: Four questionnaires have refused to finish the survey, out of 1259 issued. Around 47.80% of respondents, most of whom were females, felt that sad people might snap out of it. 14.60 percent believe depression isn't even an actual medical condition. Surprisingly, 2% of respondents with a medical background thought the same thing. Regarding more extreme stigmatization, 16.80% of respondents thought depressed persons were harmful. People with depression will be avoided by 19.50 percent of respondents, and people with medical backgrounds will be avoided by 5.20 percent of respondents. Nearly one-fifth of those polled said they would not tell anyone if they were depressed. Only a tiny percentage of respondents (6.90 percent) said they would not hire or vote for a politician who suffers from depression (8.40 percent). Conclusion: According to the study, Syrian college students had a significant level of stigma and social distance toward mentally ill patients. Female students and non-medical students had a higher stigma in most subscale items for people with depression. [ABSTRACT FROM AUTHOR]

Because of the lack of information about injury or malformation when the cryoprotectants agent (CPAs) used as cryoprotective agents in common carp (Cyprinus carpio L.) Larvae that resulting from treated embryos with different concentration of methanol (5, 10 and 15%) in different stages of embryonic development (Gastrula, Heart beat and eyed stage) were used. The results showed that there was negative correlation among the concentrations and hatching rate also malformation status was noticed. Higher defects were observed with 15% followed by 10% and finally 5% concentration for all stages. These experiments and control group were cured out under the same conditions. [ABSTRACT FROM AUTHOR]