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Latest Published Articles

Stability in respect of chromatic completion of graphs

ODAM-Vol. 5 (2022), Issue 2, pp. 11 – 18 Open Access Full-Text PDF
Eunice Gogo Mphako-Banda and Johan Kok

Abstract: In an improper coloring, an edge $uv$ for which, \(c(u)=c(v)\) is called a bad edge. The notion of the chromatic completion number of a graph \(G\) denoted by \(\zeta(G),\) is the maximum number of edges over all chromatic colorings that can be added to \(G\) without adding a bad edge. We introduce the stability of a graph in respect of chromatic completion. We prove that the set of chromatic completion edges denoted by \(E_\chi(G),\) which corresponds to \(\zeta(G)\) is unique if and only if \(G\) is stable in respect of chromatic completion. After that, chromatic completion and stability regarding Johan coloring are discussed. The difficulty of studying chromatic completion of graph operations is shown by presenting results for two elementary graph operations.

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Some arguments for the wave equation in Quantum theory 2

OMS-Vol. 6 (2022), Issue 1, pp. 205 – 247 Open Access Full-Text PDF
Tristram de Piro

Abstract: We prove that if the frame \(S\) is decaying surface non-radiating, in the sense of Definition 1, then if \(\left(\rho,\overline{J}\right)\) is analytic, either \(\rho=0\) and \(\overline{J}=\overline{0}\), or \(S\) is non-radiating, in the sense of [1]. In particularly, by the result there, the charge and current satisfy certain wave equations in all the frames \(S_{\overline{v}}\) connected to \(S\) by a real velocity vector \(\overline{v}\), with \(|\overline{v}|

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Note: Vertex stress in generalized Johnson graphs of diameter 2

ODAM-Vol. 5 (2022), Issue 2, pp. 6 – 11 Open Access Full-Text PDF
Johan Kok

Abstract:This note establishes the induced vertex stress, total induced vertex stress, vertex stress and total vertex stress of the generalized Johnson graphs of diameter \(2\). The note serves as the foundation to establish the same parameters for generalized Johnson graphs of diameter greater than or equal to \(3\).

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Sombor indices – back to geometry

ODAM-Vol. 5 (2022), Issue 2, pp. 1 – 5 Open Access Full-Text PDF
Ivan Gutman

Abstract:The Sombor index (\(SO\)) is a vertex-degree-based graph invariant, defined as the sum over all pairs of adjacent vertices of \(\sqrt{d_i^2+d_j^2}\), where \(d_i\) is the degree of the \(i\)-th vertex. It has been conceived using geometric considerations. Numerous researches of \(SO\) that followed, ignored its geometric origin. We now show that geometry-based reasonings reveal the geometric background of several classical topological indices (Zagreb, Albertson) and lead to a series of new \(SO\)-like degree-based graph invariants.

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Comparative study between oxycodone versus morphine, with zofran, to reduce post-operative nausea and vomiting: a monocentric clinical trial

TCMS-Vol. 2 (2022), Issue 2, pp. 24 – 31 Open Access Full-Text PDF
Joseph Maalouli MD, Patricia Nehme MD, Marie Merheb MD and Elie Gharios MD

Abstract: Subjects and methods: A prospective, monocentric clinical trial study was conducted at Mount Lebanon Hospital (MLH) between November 2018 and November 2021. After getting approval from the ethical committee, 237 patients were enrolled on a ratio of 1 to 2 in two groups: the first receiving Oxycodone 5 mg IVP with Zofran 4 mg IVD and the second receiving Morphine 5 mg IVP with Zofran 4mg IVD. Pearson’s Chi-square test and Fisher’s exact test were used to checking for the groups’ differences.
Results: Morphine and Oxycodone had a similar analgesic effect. The use of Zofran lowered PONV incidence rates in both groups. A statistically significant (p-value = 0.047) lower nausea and vomiting incidence in the Morphine group (2.5%) was noted compared to the Oxycodone group (8.8% incidence). Only 10% of Oxycodone group patients and 8.9\% of Morphine group patients had moderate nausea and vomiting, and none of the group’s patients had severe nausea and vomiting. Surgery duration, gender, age, smoking, BMI, pain level, and treatment group were not statistically associated with the severity of NV.
Conclusion: With the same analgesic effect, Zofran injection seemed to lower PONV incidence in both groups, even though the Morphine group had a lower incidence. Zofran seemed effective in lowering the NV severity as well. Therefore, recommending the systematic administration of antiemetic agents in patients receiving Oxycodone or Morphine could enhance patient satisfaction.

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Histopathological patterns in the endometrial biopsy of patients presenting with abnormal uterine bleeding

TCMS-Vol. 2 (2022), Issue 2, pp. 19 – 23 Open Access Full-Text PDF
Akbarova Munisa Abduxalilovna and Sarvar Akbarov Alisherovich

Abstract: Aim: To assess histopathological patterns in the endometrial biopsy of patients presenting with abnormal uterine bleeding.
Methodology: One hundred eight females with the complaint of abnormal uterine bleeding were enrolled. A gynecological examination was done. Dilatation and curettage were carried out. Specimens thus obtained were stored in 10\% formalin. The slides were examined under a microscope, and the various histopathological patterns were assessed.
Results: The age group 20-30 years had 48, 30-40 years had 50, and 40-50 years had ten females. A significant difference was observed. Inflammatory lesions were 28, such as acute endometritis in 12, chronic endometritis in 11, and chorioamnionitis in 5. Proliferative non-neoplastic lesions were 42, such as atypical hyperplasia in 18, typical hyperplasia in 12, and endometrial polyp in 12. Neoplastic lesions in 20 include leiomyoma in 8, a partial mole in 7, the complete mole in 2, and endometroid carcinoma in 3. Normal endometrium in 18, such as proliferative phase in 12 and secretory phase endometrium in 6. A significant difference was observed (P< 0.05).
Conclusion: The most common endometrial biopsy revealed proliferative non-neoplastic lesions such as atypical hyperplasia, typical hyperplasia, and endometrial polyp.

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BOOK - NULL CONTROLLABILITY OF DEGENERATE AND NON-DEGENERATE SINGULAR PARABOLIC