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Advances in Pure Mathematics 2024年第3期14卷 160-166页

作者： panchanan pramanik Susmita pramanik Sabyasachi Sen Department of Instrument Engineering and Electronics JADAVPUR University Salt Lake Campus Kolkata India Department of Microelectronics & VLSI Technology Maulana Abul Kalam Azad University of Technology West Bengal Haringhata India

The Fermat–pramanik series are like below: .The mathematical principle has been established by factorization principle. The Fermat-pramanik tree can be grown. It produces branched Fermat-pramanik series using same principle making Fermat-pramanik chain. Branched chain can be propagated at any point of the main chain with indefinite length using factorization principle as follows: Same principle is applicable for integer solutions of AM+B2=C2which produces series of the type . It has been shown that this equation is solvable with N{A, B, C, M}. where , , M=M1+M2 and M1>M2. Subsequently, it has been shown that using M= M1+M2+M3+... The combinations of Ms should be taken so that the values of both the parts (Cn+Bn) and (Cn-Bn) should be even or odd for obtaining Z{B,C}. Hence, it has been shown that the Fermat triple can generate a) Fermat-pramanik multiplate, b) Fermat-pramanik Branched multiplate and c) Fermat-pramanik deductive series. All these formalisms are useful for development of new principle of cryptography. .

关键词： Fermat Theorem Fermat-pramanik Tree Solution of AM +B2 =C2 Deductive Series Generation of Fermat’s Triode Generation of Fermat Series

Biocompatibility of folate-modified chitosan nanoparticles

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Asian Pacific Journal of Tropical Biomedicine 2012年第3期2卷 215-219页

作者： Subhankari Prasad Chakraborty Sumanta Kumar Sahu panchanan pramanik Somenath Roy Immunology and Microbiology Laboratory Department of Human Physiology with Community HealthVidyasagar University Nanomaterials Laboratory Department of ChemistryIndian Institute of TechnologyKharagpur

Objective:To evaluate the acute toxicity of carboxymethyl chitosan-2,2' ethylenedioxy bisethylamine-folate(CMC-EDBE-FA) and as well as possible effect on microbial growth and in vitro cell ***:CMC-EDBE-FA was prepared on basis of carboxymethyl chitosan tagged with folic acid by covalently linkage through 2,2' elhylenedioxy bis-ethylamine. In vivo acute toxicity,in vitro cyto-toxicity and antimicrobial activity of CMC-EDBE-FA nanoparticle were ***:Vancomycin exhibited the antibacterial activity against vancomycin sensitive Staphylococcus aureus,but CMC-EDBE-FA nanoparticle did not give any antibacterial activity as evidenced by minimal inhibitory concentration(MIC),minimal bactericidal concentration(MBC),disc agar diffusion(DAD) and killing kinetic ***,the CMC-EDBE-FA nanoparticle showed no signs of in vivo acute toxicity up to a dose level of 1000 mg/kg p.o.,and as well as in vitro cyto-toxicity up to 230 μg/***:These findings suggest that CMC-EDBE-FA nanoparticle is expected to be safe for biomedical applications.

关键词： Carboxymethyl chitosan Folate Staphylococcus aureus Killing kinetic studies MTT assay

Products of Odd Numbers or Prime Number Can Generate the Three Members’ Families of Fermat Last Theorem and the Theorem Is Valid for Summation of Squares of More Than Two Natural Numbers

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Advances in Pure Mathematics 2023年第10期13卷 635-641页

作者： Susmita pramanik Deepak Kumar Das panchanan pramanik Department of Chemistry and Nanoscience GLA University Mathura India Agriculture and Ecology Research Unit Indian Statistical Institute Kolkata India

Fermat’s last theorem, had the statement that there are no natural numbers A, B, and C such that An + Bn = Cn, in which n is a natural number greater than 2. We have shown that any product of two odd numbers can generate Fermat or Pythagoras triple (A, B, C) following n = 2 and also it is applicable A2 + B2 + C2 + D2 + so on =An2 where all are natural numbers.

关键词： Fermat Last Theorem Generation of Fermat’s Numbers Extension of Fermat’s Expression Fermat’s Expression from Products of Odd Numbers

Antioxidative effect of folate-modified chitosan nanoparticles

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Asian Pacific Journal of Tropical Biomedicine 2011年第1期1卷 29-38页

作者： Subhankari Prasad Chakraborty Santanu Kar Mahapatra Sumanta Kumar Sahu panchanan pramanik Somenath Roy Immunology and Microbiology Laboratory Department of Human Physiology with Community HealthVidyasagar University Nanomaterials Laboratory Department of ChemistryIndian Institute of Technology

Objective:To evaluate the potency of carboxymethyl chitosan-2,2' ethylenedioxy bisethylamine-folate(CMC-EDBE-FA) on tissue injury,antioxidant status and glutathione system in tissue mitochondria and serum against nicotine-induced oxidative stress in ***: CMC-EDBE-FA was prepared on basis of carboxymethyl chitosan tagged with folic acid by covalently linkage through 2,2' ethylenedioxy *** were divided into four groups,i.e.,control,nicotine(1 mg/kg bw/day),CMC-EDBE-FA(1 mg/kg bw/day) and nicotine(1 mg/kg bw/day) and CMC-EDBE-FA(1 mg/kg bw/day) for 7 *** of lipid peroxidation, oxidized glutathione level,antioxidant enzyme status and DNA damage were observed and ***:The significantly increase of lipid peroxidation,oxidized glutathione levels and DNA damage was observed in nicotine treated group as compared with control group;those were significantly reduced in CMC-EDBE-FA supplemented ***,significantly reduced antioxidant status in nicotine treated group was effectively ameliorated by the supplementation of *** CMC-EDBE-FA treated groups showed no significant change as compared with control group;rather than it repairs the tissue damage of nicotine treated ***:These findings suggest that CMC-EDBE-FA is non-toxic and ameliorates nicotine-induced toxicity.

关键词： Carboxymethyl chitosan Nicotine Glutathione Antioxidants Deoxyribonucleic acid fragmentation Antioxidative effect Folate Lipid peroxidation Oxidized

Nitric oxide mediated Staphylococcus aureus pathogenesis and protective role of nanoconjugated vancomycin

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Asian Pacific Journal of Tropical Biomedicine 2011年第2期1卷 102-109页

作者： Subhankari Prasad Chakraborty Santanu Kar Mahapatra Sumanta Kumar Sahu Sourav Chattopadhyay panchanan pramanik Somenath Roy Immunology and Microbiology laboratory Department of Human Physiology with Community HealthVidyasagar University Nanomaterials Laboratory Department of ChemistryIndian Institute of Technology

Objective:To investigate the relation between fruit seeds,plants residuals and appendicitis. Methods:Among cases that underwent appendectomy,the appendicitis cases having fruit seeds and undigested plant residuals in their etiology were examined ***, histopathological features,age,sex,and parameters of morbidity and mortality were used. Results:Fruit seed was found in one case(0.05%) with presence of pus in appendix lumen, undigested plant residuals in 7 cases(0.35%).It was determined that there were appendix inflammation in 2 of the plant residuals cases,while there were obstruction and lymphoid hyperplasia in the appendix lumen of 5 *** mortality was ***:The ratio of acute appendicitis caused by plants is minimal among all appendectomised patients, but avoidence of eating undigested fruit seeds and chewing plants well may help to prevent appendicitis.

关键词： Staphylococcus aureus Lymphocyte Nanoconjugated vancomycin Antioxidant enzymes TNF-α IL-10 Infection Anti-inflammatory Antioxidative effect Bacteremia Oxidative stress Nitric oxide Inflammatory parameter Pathogenesis