SOME RESULTS ON THE QUESTIONS OF KIT-WING YU

Majumder, Sujoy Korean Mathematical Society 2016 대한수학회논문집 Vol.31 No.2

The paper deals with the problem of meromorphic functions sharing a small function with its differential polynomials and improves the results of Liu and Gu [9], Lahiri and Sarkar [8], Zhang [13] and Zhang and Yang [14] and also answer some open questions posed by Kit-Wing Yu [16]. In this paper we provide some examples to show that the conditions in our results are the best possible.

Impacts of COVID-19 lockdown on ambient air quality: Statistical analyses of available data on urban West Bengal (India)

Majumder, Rajib Techno-Press 2021 Advances in environmental research Vol.10 No.2

COVID-19 pandemic and consequent unavoidable lockdown left an unprecedented shock on social and economic life. Present study aimed to evaluate the impacts of COVID-19 lockdown on the ambient air quality of urban areas of eastern Indian state West Bengal. During lockdown period, Air Quality Index (AQI) was mostly found in 'Good' or 'Satisfactory' and sometimes, in 'Moderate' categories, and rarely, in 'poor' category. AQI was in 'Good' category for most of the lockdown span at Siliguri (67%) followed by Kolkata (44%), Howrah (38%) and Asansol (25%). Based on average AQI ranges: lockdown period (48.68- 62.12) < same period before 1 year (75.09-89.81) < Period 3 months before lockdown (175-206), it can be stated that AQI category was better during lockdown compared to the other two at all study areas. In Kolkata overall air pollutant levels except ozone (p>0.05) decreased significantly during lockdown. Similarly, PM_2.5, PM₁₀ and NO₂ level reduced in Howrah. Beside, no significant changes observed for NH₃ and SO₂ concentration in Howrah compared to one year before. Apart from PM_2.5, NO₂, NH₃ and SO₂ level of previous year, mean concentration of PM₁₀, CO, O₃ showed significant drop at Siliguri during lockdown. Ambient air quality parameters except SO₂ showed remarkable decline in Asansol also during lockdown. It can be concluded that COVID-19 lockdown exerted positive effects from environmental health perspective. It improved overall ambient air quality parameters of urban areas of West Bengal. Proper planning and policy making should be given utmost priority to control air pollution in the present 'new normal' COVID-19 scenario.

A RESULT ON A CONJECTURE OF W. LÜ, Q. LI AND C. YANG

Majumder, Sujoy Korean Mathematical Society 2016 대한수학회보 Vol.53 No.2

In this paper, we investigate the problem of transcendental entire functions that share two values with one of their derivative. Let f be a transcendental entire function, n and k be two positive integers. If $f^n-Q_1$ and $(f^n)^{(k)}-Q_2$ share 0 CM, and $n{\geq}k+1$, then $(f^n)^{(k)}{\equiv}{\frac{Q_2}{Q_1}}f^n$. Furthermore, if $Q_1=Q_2$, then $f=ce^{\frac{\lambda}{n}z}$, where $Q_1$, $Q_2$ are polynomials with $Q_1Q_2{\not\equiv}0$, and c, ${\lambda}$ are non-zero constants such that ${\lambda}^k=1$. This result shows that the Conjecture given by W. $L{\ddot{u}}$, Q. Li and C. Yang [On the transcendental entire solutions of a class of differential equations, Bull. Korean Math. Soc. 51 (2014), no. 5, 1281-1289.] is true. Also we exhibit some examples to show that the conditions of our result are the best possible.

Manufacturing quality improvement and setup cost reduction in a vendor-buyer supply chain model

Majumder, Arunava,Guchhait, Rekha,Sarkar, Biswajit Inderscience Enterprises Ltd. 2017 European journal of industrial engineering Vol.11 No.5

<P>Quality improvement and setup cost reduction of any production system are endless procedure. Customer's demand is always intended to have the best quality product and the industries always try to improve the quality of products. This paper develops a two-echelon supply chain model with quality improvement of products and setup cost reduction under controllable lead time. The lead time demand follows a normal distribution and in the second case, it does not consider any specific distribution except a mean and standard deviation. Both models are solved analytically to obtain global solution. Two improved iterative algorithms are developed in order to obtain the optimal results of decision variables numerically to minimise the total system cost. The expected value of additional information is calculated to show the financial effect for collecting the information about lead time demand distribution. Some numerical examples and sensitivity analysis are given to illustrate the model.</P>

Gene Expression Patterns of Spleen, Lung and Brain with Different Radiosensitivity in C57BL6 Mice

Majumder Md. Zahidur Rahman,Lee, Woo-Jung,Lee, Su-Jae,Bae, Sang-Woo,Lee, Yun-Sil The Korean Association for Radiation Protection 2005 방사선방어학회지 Vol.30 No.4

Although little information is available on the underlying mechanisms, various genetic factors have been associated with tissue-specific responses to radiation. In the present study, we explored the possibility whether organ specific gene expression is associated with radiosensitivity using samples from brain, lung and spleen. We examined intrinsic expression pattern of 23 genes in the organs by semi-quantitative RT-PCR method using both male and female C57BL/6 mice. Expression of p53 and p21, well known factors for governing sensitivity to radiation or chemotherapeutic agents, was not different among the organ types. Both higher expression of sialyltransferase, delta7-sterol reductase, leptin receptor splice variant form 12.1, and Cu/Zn superoxide dismutase (SOD) and lower expression of alphaB crystalline were specific for spleen tissue. Expression level of glutathione peroxidase and APO-1 cell surface antigen gene in lung tissue was high, while that of Na, K-ATPase alpha-subunit, Cu/ZnSOD, and cyclin G was low. Brain, radioresistant organ, showed higher expressions of Na, K-ATPase-subunit, cyclin G, and nucleolar protein hNop56 and lower expression of delta7-sterol reductase. The result revealed a potential correlation between gene expression patterns and organ sensitivity, and Identified genes which might be responsible for organ sensitivity.

Olax psittacorum (Lam.) Vahl. (Olacaceae): current status and future prospects as an herbal plant

Majumder Raja,Adhikari Lopamudra,Dhara Moonmun 경희대학교 융합한의과학연구소 2022 Oriental Pharmacy and Experimental Medicine Vol.22 No.2

Olax psittacorum (Lam.) Vahl. traditionally used by the tribal community of ‘INDIA’ to heal conditions such as pain, psoriasis, mouth-ulcer, anemia, constipation as well as diabetes. Documented scientific shreds of evidence like antipyretic, anti-inflammatory, antimicrobial, anti-viral, anti-cancer, toxicity profile improved its medicinal value. Chromatographic evaluation (GC–MS) proven near about presence of 25 compounds. Among them, hexadecanoic methyl ester, β-sitosterol, phytol, methyl salicylate, 13-docosenamide, and oleanolic acid are significant and contribute to its successful medicinal properties. The toxicity study also revealed the safety of the consumption of the leaf part. Still, consecutive gaps need to be exploring to gather evidence of its contribution to curing different ailments, especially upon the ulcer, anemia, and identification of the presence of lead compounds as an upcoming future research proposal. The ‘Internet Scholar’, ‘Study Guide’, ‘PubMed’, ‘ScienceDirect’, ‘Scopus’, and ‘Sodhganga’ web site have been accessed to gather information about detailed scientific research as well as traditional information from authenticated sources that have been published in the English language. The various folklore claimed medicinal properties like anti-ulcer, aphthous ulcer, analgesic, anti-diabetic, anti-anemic, etc. yet to be justified scientifically with lead compounds that can support the rationality being used as folklore. This plant could be a good choice to explore its importance within the pharmacognostic field of drug development and might be a better source of herbal derived lead compounds which can help to heal ulcer or anemia that can effectively make a credible addition to treatment among the civilization as a natural source of therapeutic compounds.

An innovative vibration barrier by intermittent geofoam - A numerical study

Majumder, Mainak,Ghosh, Priyanka,Sathiyamoorthy, Rajesh Techno-Press 2017 Geomechanics & engineering Vol.13 No.2

A new technique is proposed to obtain more effective screening efficiency against the ground vibration using intermittent geofoam (IF) in-filled trench. The numerical analysis is performed by employing two-dimensional finite element method under dynamic condition. Vertically oscillated strip foundation is considered as the vibration source. In presence of the ground vibration, the vertical displacements at different locations (pick-up points) along the ground surface are captured to determine the amplitude reduction factor (ARF), which helps to assess the efficiency of the vibration screening technique. The efficiency of IF over continuous geofoam (CF) in-filled vibration barriers is assessed by varying the geofoam density, the location of trench and the frequency of excitation. The results from this study indicate that a significant reduction in ARF can be achieved by using intermittent geofoam as compared to continuous geofoam. Further, it is noticed that the efficiency of IF increases with an increase in the frequency of the vibrating source. These encouraging results put forward the potential of utilising intermittent geofoam as a vibration screening material.

A RESULT ON AN OPEN PROBLEM OF LÜ, LI AND YANG

Majumder, Sujoy,Saha, Somnath Korean Mathematical Society 2021 대한수학회보 Vol.58 No.4

In this paper we deal with the open problem posed by Lü, Li and Yang [10]. In fact, we prove the following result: Let f(z) be a transcendental meromorphic function of finite order having finitely many poles, c₁, c₂, …, c_n ∈ ℂ\{0} and k, n ∈ ℕ. Suppose fⁿ(z), f(z+c₁)f(z+c₂) ⋯ f(z+c_n) share 0 CM and fⁿ(z)-Q₁(z), (f(z+c₁)f(z+c₂) ⋯ f(z+c_n))^(k) - Q₂(z) share (0, 1), where Q₁(z) and Q₂(z) are non-zero polynomials. If n ≥ k+1, then $(f(z+c_1)f(z+c_2)\;{\cdots}\;f(z+c_n))^{(k)}\;{\equiv}\;{\frac{Q_2(z)}{Q_1(z)}}f^n(z)$. Furthermore, if Q₁(z) ≡ Q₂(z), then $f(z)=c\;e^{\frac{\lambda}{n}z}$, where c, λ ∈ ℂ \ {0} such that e^{λ(c₁+c₂+⋯+c_n)} = 1 and λ^k = 1. Also we exhibit some examples to show that the conditions of our result are the best possible.

Completeness and compactness in fuzzy cone metric spaces

A. Majumder,T. Bag 원광대학교 기초자연과학연구소 2019 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.18 No.3

In this paper, some basic results in complete fuzzy cone metric space are studied and Cantor's Intersection Theorem is established in fuzzy setting. On the other hand some results in compact fuzzy cone metric spaces are developed.

Toxicological evaluation, brine shrimp lethality assay, in vivo and ex vivo antioxidant assessment followed by GC–MS study of the extracts obtained from Olax psittacorum (Lam.) Vahl

Raja Majumder,Lopamudra Adhikari,Chowdhury Mobaswar Hossain,Moonmun Dhara,Jinamitra Sahu 경희대학교 융합한의과학연구소 2020 Oriental Pharmacy and Experimental Medicine Vol.20 No.3

Olax psittacorum (Lam.) Vahl. has versatile ethnopharmacological healing property in addition with incomplete research are adequate pieces of information to support the choice of the plant to build up proper data in acute and sub-chronic toxicological, cytotoxicity with ex vivo and in vivo antioxidant profile as well as qualitative analytical illustration through GC–MS of the selected extracts obtained from different parts of the plant. We have extracted leaf methanolic extract (LME), stem methanolic extract (SME), stem aqueous extract (SAE) and fruits aqueous extract (FrAE) for the above mentioned respective studies. OECD guideline 420 and 407, brine shrimp lethality (BSLA), lipid peroxidation, catalase assay was conducted to gather information on toxicity, cytotoxicity, and antioxidant properties respectively. BSLA study indicates that LME may be a good choice to develop as an anticancer drug for future perspective ( LC50 = 41.88 μg/ml). Both LME and SME have been selected for ex vivo and in vivo antioxidant analysis on the basis of their low toxicity and GCMS analysis. Moreover, in vivo lipidperoxidation as well as catalase assay both having significant difference (P < 0.05) between the groups except LME 200 and positive control (P = 0.084) as well as LME 200 and SME 100 (P = 0.054) respectively. This study justifies that high dose exposure of FrAE, SAE, and SME could be so toxic due to changes in biochemical parameters and in comparison, LME is safer according to the significant (P < 0.05) outcome statistically. LME and SME are safe to consume at a dose of ≤ 200 mg/kg/bw as herbal supplements with antioxidant property.