Outcome of 82 cases of nasal polyposis undergoing functional endoscopic sinus surgery

TCMS-Vol. 1 (2021), Issue 1, pp. 6 – 10 Open Access Full-Text PDF
Ankush Sathiyan, Hari Mahajan Jain, Sarfaraz Alam Khan
Abstract: Aim: To study 82 cases of nasal polyposis undergoing functional endoscopic sinus surgery (FESS). Methodology: Our study comprised of 82 patients presenting with the symptoms of nasal polyposis (38 male patient, 44 female patients). All managed with FESS. Parameters assessed were NOSE score and nasal endoscopy score pre- operatively which was compared with post- operative score at 6 months and 12 months. Results: We found pre- operative NOSE score was \(65.2\pm 5.7,\) at 6 months was \(28.4\pm 4.1\) and at 12 months post- operatively was \(24.2\pm 3.6.\) We found pre- operative nasal endoscopic score was 6.02, 6 months score was 3.1 and 12 months score was 2.5. Conclusion: Patients nasal endoscopy score and NOSE symptom score was improved after treatment. Functional endoscopic sinus surgery is treatment of choice in patients with chronic rhinosinusitis with nasal polyps.
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Internet’s handprint

EASL-Vol. 4 (2021), Issue 1, pp. 80 – 97 Open Access Full-Text PDF
Anders S.G. Andrae
Abstract: In this decade there will an unprecedented growth of generated data, computations, instructions, and operations. This growth may not compromise clean air, clean water and a sustainable energy and material usage, but rather facilitate these prerequisites for flora and fauna. There are many indications (expected trends and estimates) showing that the Internet Sector will be able to provide solutions to other Sectors such as Buildings, Transportation and Industry which will help reduce the total global consumption of energy and materials. For instance, products are replaced by virtual services e.g. by using e-readers instead of paperbacks, and transportation is avoided by online shopping or Internet meetings. This is more resource and energy efficient than before and entire sectors, like transport, industry, and agriculture can be optimized. Internet may foster new sustainable lifestyles which can lower the affluence despite certain rebound effects. The underlying idea is that e.g. human-related global greenhouse gas (GHG) supply can be significantly halted if existing and developing ICT Solutions are used in other sectors (and in the Internet infrastructure itself) to cause a handprint. Such solutions include products-sold-as-services, smart Grid and smart metering. Compared to earlier approaches, the 2020 transformative effects on smart work, land use and smart circularity are included in the discussion, as well as consequential LCA modelling. Internet’s handprint will be 4-7 times its footprint in 2030. The handprint is highly dependent e.g. on how large share of the buildings can adopt smart metering and the product to service rate. Internet will in itself use intelligent ICT solutions as well as neuromorphic, reversible and superconducting computing as well as nanophotonics to mitigate its own material and energy use. However, more importantly the intelligent ICT solutions should be used in the rest of the society to reach efficiency goals. Power saving is a highly efficient strategy for cost reduction in the Internet Sector itself and beyond.
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Graph energy and nullity

ODAM-Vol. 4 (2021), Issue 1, pp. 25 – 28 Open Access Full-Text PDF
Ivan Gutman
Abstract: The energy of a graph is the sum of absolute values of its eigenvalues. The nullity of a graph is the algebraic multiplicity of number zero in its spectrum. Empirical facts indicate that graph energy decreases with increasing nullity, but proving this property is difficult. In this paper, a method is elaborated by means of which the effect of nullity on graph energy can be quantitatively estimated.
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A morphometric analysis of shape, size and position of mental foramen in dry human mandibles

TCMS-Vol. 1 (2021), Issue 1, pp. 1 – 5 Open Access Full-Text PDF
Nidhi Sharma
Abstract: Aim: To calculate size, shape and position of mental foramen. Materials & Methods: 50 dry human mandibles of either gender (20- females, 30- males) were included. The position of mental foramen in horizontally was calculated based on classification proposed by Bokhari. The vertical position was divided into six types using the modified Ngeow and Yuzawati criteria. Size was measured both vertically and horizontally with the help of vernier caliper and expressed as mean. Results: Most common horizontal position was II seen in both males (left- 56%, right- 50%) and females (left- 60%, right- 58%). Most common vertical position was 2 seen in males (left- 62%, right- 65%) and females (left- 55%, right- 52%). Most common shape was oval seen in both genders (males- 68% left, 62% right) and (females- 70% left, 72% right). A significant difference was observed \((P<0.05)\). Conclusion: Variation in shape, size and position was observed both males and females, however, most common shape found to be oval and position was II horizontally and 2 vertically in both genders.
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On parametric equivalent, isomorphic and unique sets

ODAM-Vol. 4 (2021), Issue 1, pp. 19 – 24 Open Access Full-Text PDF
J. Kok, J. Shiny
Abstract: This short paper introduces the notions of parametric equivalence, isomorphism and uniqueness in graphs. Results for paths, cycles and certain categories (or types) of trees with regards to minimum confluence sets are presented.
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On the exponential Diophantine equation \((2^{2m+1}-1)+(13)^n=z^2\)

EASL-Vol. 4 (2021), Issue 1, pp. 77 – 79 Open Access Full-Text PDF
Sudhanshu Aggarwal
Abstract: Nowadays, scholars are very interested to determine the solution of different Diophantine equations because these equations have numerous applications in the field of coordinate geometry, cryptography, trigonometry and applied algebra. These equations help us for finding the integer solution of famous Pythagoras theorem and Pell’s equation. Finding the solution of Diophantine equations have many challenges for scholars due to absence of generalize methods. In the present paper, author studied the exponential Diophantine equation \((2^{2m+1}-1)+(13)^n=z^2\), where \(m,n\) are whole numbers, for its solution in whole numbers. Results show that the exponential Diophantine equation \((2^{2m+1}-1)+(13)^n=z^2\), where \(m\), \(n\) are whole numbers, has no solution in whole number.
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Mathematical analysis of a delayed HIV/AIDS model with treatment and vertical transmission

OMS-Vol. 5 (2021), Issue 1, pp. 128 – 146 Open Access Full-Text PDF
Gratien Twagirumukiza, Edouard Singirankabo
Abstract: None can underestimate the importance of mathematical modelling for their role in clarifying dynamics of epidemic diseases. They can project the progress of the disease and demonstrate the result of the epidemic to public health in order to take precautions. HIV attracts global attention due to rising death rates and economic burdens and many other consequences that it leaves behind. Up to date, there is no medicine and vaccine of HIV/AIDS but still many researches are conducted in order to see how to mitigate this epidemic and reduce the death rate or increase the life expectancy of those who are infected. A delayed HIV/AIDS treatment and vertical transmission model has been investigated. The model took into account both infected people from the symptomatics group and asymptomatic group to join AIDS group. We considered that a child can be infected from the mother to an embryo, fetus or childbirth. Those who are infected, it will take them some time to get mature and spread the disease. By using mathematical model, reproduction number, positivity, boundedness, and stability analysis were determined. The results showed that the model is much productive if time delay is considered.
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Atomic localization via superposition of three standing wave fields in a four level tripod atomic configuration

EASL-Vol. 4 (2021), Issue 1, pp. 69 – 76 Open Access Full-Text PDF
Anwar Hussain, Muhammad Izhar, Mian Azhar Uddin, Muhammad Wahab, Anwar Ali Khan, Masood Rauf Khan
Abstract: We theoretically present the physical realization of one dimensional (1D) atom localization by superposition of three standing wave fields in a four-level tripod atomic configuration. The most interesting result that we observe is the variation of the bandwidth of the localization peaks with the intensity of the space independent Rabi frequency. A sharp single and double localized peaks are observed at different direction of the wave numbers. The bandwidth of a localized peak is reduced as the intensity of the space independent Rabi frequency goes on increasing, which corresponds to the reduction in the uncertainty. These results will hopefully contribute to the development of current high tech-applications.
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A note on Jeśmanowicz’ conjecture for non-primitive Pythagorean triples

OMS-Vol. 5 (2021), Issue 1, pp. 115 – 127 Open Access Full-Text PDF
Van Thien Nguyen, Viet Kh. Nguyen, Pham Hung Quy
Abstract: Let \((a, b, c)\) be a primitive Pythagorean triple parameterized as \(a=u^2-v^2,\ b=2uv,\ c=u^2+v^2\), where \(u>v>0\) are co-prime and not of the same parity. In 1956, L. Jeśmanowicz conjectured that for any positive integer \(n\), the Diophantine equation \((an)^x+(bn)^y=(cn)^z\) has only the positive integer solution \((x,y,z)=(2,2,2)\). In this connection we call a positive integer solution \((x,y,z)\ne (2,2,2)\) with \(n>1\) exceptional. In 1999 M.-H. Le gave necessary conditions for the existence of exceptional solutions which were refined recently by H. Yang and R.-Q. Fu. In this paper we give a unified simple proof of the theorem of Le-Yang-Fu. Next we give necessary conditions for the existence of exceptional solutions in the case \(v=2,\ u\) is an odd prime. As an application we show the truth of the Jeśmanowicz conjecture for all prime values \(u < 100\).
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