Application of the newly \(\varphi^{6}\)-model expansion approach to the nonlinear reaction-diffusion equation

OMS-Vol. 6 (2022), Issue 1, pp. 269 – 280 Open Access Full-Text PDF
Muhammad Abubakar Isah and Asif Yokus

Abstract: In this paper, we use the \(\varphi ^{6}\)-model expansion method to construct the traveling wave solutions for the reaction-diffusion equation. The method of \(\varphi ^{6}\)-model expansion enables the explicit retrieval of a wide variety of solution types, such as bright, singular, periodic, and combined singular soliton solutions. Kink-type solitons, also known as topological solitons in the context of water waves, are another type of solution that can be explicitly retrieved. This study’s results might enhance the equation’s nonlinear dynamical properties. The method proposes a practical and efficient method for solving a sizable class of nonlinear partial differential equations. The dynamical features of the data are explained and highlighted using exciting graphs.

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Ideal theory of interval neutrosophic sets in subtraction algebras

OMS-Vol. 6 (2022), Issue 1, pp. 262 – 268 Open Access Full-Text PDF
V. S. Subha and P. Dhanalakshmi

Abstract: In this paper, we introduce the notion of interval neutrosophic ideals in subtraction algebras. Also, introduce the intersection and union of interval neutrosophic sets in subtraction algebras. We prove intersection of two-interval neutrosophic ideals is also an interval neutrosophic ideal. Some exciting properties and results based on such an ideal are discussed. Moreover, we define the homomorphism and homomorphism of interval neutrosophic sets. We prove the image of an interval neutrosophic subalgebra is also an interval neutrosophic sub-algebra.

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Further on quantum-plank derivatives and integrals in composite forms

OMA-Vol. 6 (2022), Issue 2, pp. 130 – 138 Open Access Full-Text PDF
Ghulam Farid and Zeeshan Afzal

Abstract:In quantum-plank calculus, \(q\)-derivatives and \(h\)-derivatives are fundamental factors. Recently, a composite form of both derivatives is introduced and called \(q-h\)-derivative. This paper aims to present a further generalized notion of derivatives will be called \((q,p-h)\)-derivatives. This will produce \(q\)-derivative, \(h\)-derivative, \(q-h\)-derivative and \((p,q)\)-derivative. Theory based on all aforementioned derivatives can be generalized via this new notion. It is expected, this paper will be useful and beneficial for researchers working in diverse fields of sciences and engineering.

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On the largest real root of the independence polynomial of a unicyclic graph

ODAM-Vol. 5 (2022), Issue 3, pp. 30 – 46 Open Access Full-Text PDF
Iain Beaton and Ben Cameron

Abstract: We find the maximum and minimum connected unicyclic and connected well-covered unicyclic graphs of a given order with respect to \(\preceq\). This extends 2013 work by Csikv’ari where the maximum and minimum trees of a given order were determined and also answers an open question posed in the same work. Corollaries of our results give the graphs that minimize and maximize \(\xi(G)\) among all connected (well-covered) unicyclic graphs. We also answer more related open questions posed by Oboudi in 2018 and disprove a conjecture due to Levit and Mandrescu from 2008. The independence polynomial of a graph \(G\), denoted \(I(G,x)\), is the generating polynomial for the number of independent sets of each size. The roots of \(I(G,x)\) are called the independence roots of \(G\). It is known that for every graph \(G\), the independence root of smallest modulus, denoted \(\xi(G)\), is real. The relation \(\preceq\) on the set of all graphs is defined as follows, \(H\preceq G\) if and only if \(I(H,x)\ge I(G,x)\text{ for all }x\in [\xi(G),0].\)

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A fuzzy solution of nonlinear partial differential equations of fractional order

ODAM-Vol. 5 (2022), Issue 3, pp. 13 – 29 Open Access Full-Text PDF
Mawia Osman, Ahmed Hamoud, Altyeb Mohammed Mustafa, Zengtai Gong, Bchir Mahamat Acyl, Abdoulaye Ali and Bakry Musa

Abstract: In this paper, the fuzzy nonlinear partial differential equations of fractional order are considered. The generalization differential transform method (DTM) and fuzzy variational iteration method (VIM) were applied to solve fuzzy nonlinear partial differential equations of fractional order. The above methods are investigated based on Taylor’s formula, and fuzzy Caputo’s fractional derivative. The proposed methods are also illustrated by some examples. The results reveal the methods are a highly effective scheme for obtaining the fuzzy fractional partial differential equations.

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Study of hemoglobin levels among pregnant women in different trimesters at a tertiary hospital

TCMS-Vol. 2 (2022), Issue 4, pp. 26 – 31 Open Access Full-Text PDF
Sradhamoni Kumbang, Archana Khanikar, Rumi Konwar and Siddhartha Sankar Konwar

Abstract: Background: Pregnancy increases the demand for nutrients and hemoglobin. Besides these, physiological changes in blood parameters also occurs during pregnancy. Anemia in pregnancy is a serious condition contributing to increased maternal and fetal morbidity and mortality. Present study has been undertaken with the knowledge of hemoglobin values and its distribution in different trimesters of pregnancy.
Material and Methods: Present study was single-center, prospective, comparative, parallel-group, observational study, conducted in pregnant women attended the ANC OPD or admitted in antenatal ward and sixty healthy non-pregnant women of same age group.
Results: The mean hemoglobin value was \(12.23\pm1.32 gm\) % throughout pregnancy. In control group the mean value was \(12.59 \pm 2.50 gm\)%. Statistically significant variation was observed between control and each trimester of pregnancy \((p<0.05)\). Significant difference observed between 1st and 2nd trimester \((p < 0.05)\) and 2nd and 3rd trimester \((p < 0.05)\). When compared between 1st and 3rd trimester, difference was not significant \((p>0.05)\) Hemoglobin values are lower in pregnant cases as compared to non-pregnant subjects \((p<0.05)\). Lowest hemoglobin value is observed in 2nd trimester in maximum number of cases. Mean hemoglobin level was found lower in pregnant women with gravidity more than 1 as compared to primigravidae.
Conclusion: A significant association was observed between hemoglobin level and trimester of pregnancy. High occurrence of low hemoglobin level in pregnant women was found belonging to lower socioeconomic class. Maternal hemoglobin value decreases with increase in gestational age.

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COVID 19 associated mucormycosis: A curse in pandemic

TCMS-Vol. 2 (2022), Issue 4, pp. 18 – 25 Open Access Full-Text PDF
Dhruvika Rathva, Mayursinh Dodia, Atisha Modi and Saudhan Desai

Abstract: Aims: Mucormycosis is an acute invasive fungal infection which is rare, opportunistic and can potentially cause fatal complications. This study aimed to evaluate demographic data, disease presentation, medical &/or topical, surgical treatment.
Material and methods: Total twenty five patients with mucormycosis treated at tertiary care hospital in Gujarat during three months duration from May to July 2021. After detailed history thorough Ear, Nose and throat examination was performed. Along with local examination, ophthalmologic and neurologic examination performed in every case. After Functional endoscopic sinus surgery, tissue sent for histopathologic examination.
Results: Twenty five patients diagnosed with Mucormycosis, 18(72%) patients were males and 7(28%) were females. All 25(100%) had past history of COVID 19 infection and Diabetes Mellitus. Out of 25, 23(92%) patients were treated with intravenous or oral steroids and 2(8%) patients were not treated with any steroids. MRI paranasal sinuses with orbit with brain cuts performed for all 25 patients after suspicion of mucormycosis. 12(48%) patients had Sinonasal involvement, 11(44%) were Rhino-orbital involvement, and 2(8%) had Rhino palatal involvement. All 25(100%) patients were given Injection Amphotericin B for 3-4 weeks according to response. 6(24%) Patients were also given Oral Posaconazole. We performed Functional endoscopic sinus surgery in 23(92%) patients. In two (8%) cases Sinus surgery performed along with Maxillectomy. All 25(100%) cases on histopathology confirmed of Mucormycosis.
Conclusion: Prognostic factors we observed in our study were involvement of rhino-orbito-cerebral disease shows poor prognosis. Good Diabetes control showed early recovery. Early identification and early treatment improves prognosis as well as survival rates.

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Pap smear: Are we choosing wisely? An observational study of clinicopathologic variables of patients undergoing Pap smear examination

TCMS-Vol. 2 (2022), Issue 4, pp. 12 – 17 Open Access Full-Text PDF
Vani Swapnil Garde

Abstract: Background: Cervical cancer is a major cause of mortality in women. Pap smear is a screening test used in the screening of cervical cancer. There are well defined guidelines regarding its use. It should be offered to all sexually active women between the ages of 30-65 years, irrespective of whether or not they are symptomatic. Moreover, those women who have undergone hysterectomy for reasons other than cervical cancer or precancerous lesions, do not require this test.
Materials and methods: We undertook an observational study to describe the age, presenting complaint, previous history of hysterectomy and reason for hysterectomy in women undergoing Pap smear testing in a private super speciality hospital in Central India in the past 3 years.
Objectives: The objective of this study was to examine how closely the aforementioned guidelines were being followed, so as to deduce how wisely were we choosing the women to whom the test was being offered.
Results: This study found that a significant proportion of tests were being offered to women who did not need them. And more importantly, we were missing the opportunity to screen women who presented with non gynaecologic complaints in our hospital.

Conclusion: Hence we present the findings of this study to reassert the role of Pap smear as a screening test, the primary goal of which is to identify high grade precancerous lesions of the cervix; and to sensitizesensitise specialist physicians other than gynaecologists to offer Pap smear to women presenting with complaints unrelated to the genitourinary tract: so that we can choose wisely as to who should and who should not get the test.
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A clinico-pathological study of colonic biopsies

TCMS-Vol. 2 (2022), Issue 4, pp. 8 – 11 Open Access Full-Text PDF
Alka Dixit Vats and Anubhav Garg

Abstract: Background: To assess clinico-pathological study of colonic biopsies.
Materials and methods: One hundred ten colonic biopsies obtained from Gastroenterology department were collected in 10% neutral buffered formalin processed and embedded with the mucosal surface being uppermost. 4\(\mu\) thick serial sections were prepared and stained with H&E. Detailed study of the sections was done under light microscope and diagnosis rendered accordingly.
Result: Age group 11-20 years had 8, 21-30 years had 22, 31-40 years had 40, 41-50 years had 24 and >50 years had 16 cases. The difference was non- significant (\(P> 0.05\)). Most common clinical features were constipation seen in 36, bleeding PR in 28, bleeding PR weakness in 17, diarrhea in 16 and diarrhea \(+\) pain abdomen \(+\) weakness in 14 patients. The difference was non-significant (\(P> 0.05\)). Non-neoplastic lesions were 74. These were as non-specific colitis in 22, ulcerative colitis in 16, acute inflammation in 14, hyperplastic polyp in 10, inflammatory polyp in 6, retention polyp in 4 and endometriosis in 2 cases. Neoplastic benign lesions were 25. Benign spindle cell lesion was in 3, tubular adenoma in 15, villous adenoma in 5 and tubulovillous adenoma in 2 cases. Neoplastic malignant lesions were well differentiated adenocarcinoma seen in 4, moderately differentiated adenocarcinoma in 6, poorly differentiated adenocarcinoma in 2 and signet ring cell carcinoma in 1 case.
Conclusion: Colonoscopy is a simple and a safe procedure. It helps in assessing the lesions clinically and confirming histopathologicaly through guided biopsy. Colonoscopic biopsies also play a key role not only in diagnosis, but also in follow up and treatment.

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Explicit formula for the \(n\)-th derivative of a quotient

OMA-Vol. 6 (2022), Issue 2, pp. 120 – 129 Open Access Full-Text PDF
Roudy El Haddad

Abstract:Leibniz’s rule for the \(n\)-th derivative of a product is a very well-known and extremely useful formula. This article introduces an analogous explicit formula for the \(n\)-th derivative of a quotient of two functions. Later, we use this formula to derive new partition identities and to develop expressions for some particular \(n\)-th derivatives.

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