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A universal labeling of a graph G is a labeling of the edge set in G such that in every orientation \(\ell \) of G for every two adjacent vertices v and u, the sum of incoming edges of v and u in the oriented graph are different from each other. The universal labeling number of a graph G is the minimum number k such that G has universal labeling from \(\{1,2,\ldots , k\}\) denoted it by \(\overrightarrow{\chi _{u}}(G) \). We have \(2\Delta (G)-2 \le \overrightarrow{\chi _{u}} (G)\le 2^{\Delta (G)}\), where \(\Delta (G)\) denotes the maximum degree of G. In this work, we offer a provocative question that is: “Is there any polynomial function f such that for every graph G, \(\overrightarrow{\chi _{u}} (G)\le f(\Delta (G))\)?”. Towards this question, we introduce some lower and upper bounds on their parameter of interest. Also, we prove that for every tree T, \(\overrightarrow{\chi _{u}}(T)={\mathcal {O}}(\Delta ^3) \). Next, we show that for a given 3-regular graph G, the universal labeling number of G is 4 if and only if G belongs to Class 1. Therefore, for a given 3-regular graph G, it is an \( {{\mathbf {N}}}{{\mathbf {P}}} \)-complete to determine whether the universal labeling number of G is 4. Finally, using probabilistic methods, we almost confirm a weaker version of the problem. 相似文献
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Atefeh Vaezi Fatemeh Soojoodi Arash Tehrani Banihashemi Marzieh Nojomi 《Women and birth : journal of the Australian College of Midwives》2019,32(2):e238-e242
Background
Prevalence of postpartum depression is estimated to be about 10–15% worldwide. Many risk factors are supposed to play a role leading a new mother to maternal postpartum depression which can considerably affect the baby, mother, family and also the society.Objective
To investigate the prevalence of maternal postpartum depression and its association with social support.Methods
Using a cross-sectional study, 200 new mothers who attended three teaching hospitals in Tehran, Iran were selected with a convenience sampling. Postpartum depression was assessed using the Iranian version of Edinburgh Postpartum Depression Scale and women’s levels of social support were measured using the Iranian version of Social Support Questionnaire.Results
Prevalence of postpartum depression was 43.5% in new mothers. The mean (±Standard Deviation) score of social support network was 2.09 ± 0.99; which is lower in depressed mothers in comparison to non-depressed mothers (1.78 ± 0.87 vs. 2.33 ± 1.00 respectively, P < 0.001). A reverse significant association was found between social support and postpartum depression after adjusting for confounding variables such as past history of depression, illness of baby and medication consumption during pregnancy (Odds Ratio = 0.47, 95% Confidence Interval = 0.33–0.67).Conclusion
The bigger the social network of a mother, the less postpartum depression occurs. It is suggested to educate the family about the very important role of social support and improve it in every aspect of health care in order to prevent postpartum depression. 相似文献3.
Mary J. Waller Gerardo A. Okhuysen Marzieh Saghafian 《The Academy of Management Annals.》2016,10(1):561-598
In this review, we aim to advance work on group and team dynamics by examining how important elements of dynamism are embedded in the current literature on emergent states in groups. We use the concept of emergence as an organizing frame, building block, and critical lens, first summarizing key aspects of the extant literature on emergence, and then drawing four core characteristics of emergent phenomena from this literature. We use these characteristics to organize our review and examine how emergent states are portrayed in the past decade of groups literature. We end by exploring challenges to the development of a more dynamic perspective and by offering specific suggestions to guide and advance future work on groups and teams. 相似文献
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It is well-known, in the literature, that most of the characterization results on exponential distribution are based on the solution of Cauchy functional equation and integrated Cauchy functional equation. In the present paper, we consider the functional equation $$F(x) = F(xy) + F(xQ(y)), \quad x, xQ(y) \in [0, \theta),\; y \in [0,1],$$ where F and Q satisfy certain conditions, to give some new characterization results on the generalized Pareto distributions based on progressively Type-II right censored order statistics. We prove the main results without restricting to distributions that are absolutely continuous with respect to Lebesgue measure. 相似文献
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