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Khangembam Bangkim Chandra,Abhinav Singhal 대한핵의학회 2021 핵의학 분자영상 Vol.55 No.6
Purpose Hypermetabolic macrovascular invasion (MVI) and extrahepatic metastasis (EHM) occur in aggressive hepatocellularcarcinoma (HCC) and carry unfavorable prognosis. [18F] FDG PET/CT, despite having low sensitivity in primary HCC,is valuable in patients with aggressive HCC for detection of hypermetabolic MVI and EHM. The study aimed at identifyingthe parameters that could predict hypermetabolic MVI and/or EHM in treatment naive HCC patients for tailored approachto utilize [18F] FDG PET/CT. Methods Data of 131 treatment naive HCC patients (median age, 60 years; range, 21–80 years; 90.8% males) who underwent[18F] FDG PET/CT were retrospectively analyzed to determine the proportion of patients with hypermetabolic MVI and/orEHM. Logistic regression analysis was performed to define independent predictors of hypermetabolic MVI and/or EHM. Results 78/131 (59.5%) patients had hypermetabolic MVI and/or EHM. 52/131 (39.7%) patients had EHM. 56/131 (42.7%)patients had hypermetabolic MVI of which, 30 had concomitant EHM with majority (90%; 27/30) having distant metastasis. 26/131 (19.8%) patients had hypermetabolic MVI without EHM while 22/131 (16.8%) patients had EHM without hypermetabolicMVI of which, majority (95.5%; 21/22) had distant metastasis. Hypermetabolic MVI was associated with EHM( 2=7.868; p value=0.007). AFP>93.7 ng/ml, SUVmax>3.5, and maximum tumor size>5.0 cm were the independentpredictors of hypermetabolic MVI and/or EHM. Conclusion In treatment naive HCC patients with AFP>93.7 ng/ml or maximum tumor size>5.0 cm, [18F] FDG PET/CTcan be valuable.
SOME INEQUALITIES ON POLAR DERIVATIVE OF A POLYNOMIAL
Khangembam Babina Devi 경남대학교 기초과학연구소 2022 Nonlinear Functional Analysis and Applications Vol.27 No.1
In this paper, we extend the above inequality to polar derivative of a polynomial. Further, we also prove an improved version of above inequality into polar derivative.
Women in Conflict in Manipur and the Armed Forces Special Powers Act (AFSPA), 1958
Monika Khangembam 이화여자대학교 아시아여성학센터 2016 이화여자대학교 아시아여성학센터 학술대회자료집 Vol.2016 No.7
Manipur has been suffering for 60 years under an Act called ‘The Armed Forces Special Powers Act, (AFSPA) 1958. Under this Act the armed forces, even the most junior officers, are given the power to arrest and shoot anyone on mere suspicion, to search without any warrant. The act also protects the armed forces from trial and punishment without the sanction of the central government. The Act gives complete impunity to the army personnel even if they are found guilty. This has resulted in huge number of human rights violence and a complete omission of fundamental rights. The act has not only killed a lot of innocent young men but has also left a lot of young widows. Not only they are pushed to extreme impoverishment because their sole bread earner gets killed, sexual violence is also perpetrated on them as a tactic to destabilise the society. At the same time the violence against women by the civilians is very prevalent in the state. This study aims to highlight how the woman’s body is used as playgrounds for war to demoralise the community by raping, torturing and molesting them and also women who are widowed, who’s sons have been killed are the most affected and exploited (economically and sexually). This study will also talk about the various women’s movements and the women leaders that emerged from it in Manipur.
Remark on Some Recent Inequalities of a Polynomial and its Derivatives
Barchand Chanam,Khangembam Babina Devi,Thangjam Birkramjit Singh 경북대학교 자연과학대학 수학과 2022 Kyungpook mathematical journal Vol.62 No.3
We point out a flaw in a result proved by Singh and Shah [Kyungpook Math. J., 57(2017), 537-543] which was recently published in Kyungpook Mathematical Journal. Further, we point out an error in another result of the same paper which we correct and obtain integral extension of the corrected form.
ON AN INEQUALITY OF S. BERNSTEIN
Barchand Chanam,Khangembam Babina Devi,Kshetrimayum Krishnadas,Maisnam Triveni Devi,Reingachan Ngamchui,Thangjam Birkramjit Singh 경남대학교 기초과학연구소 2021 Nonlinear Functional Analysis and Applications Vol.26 No.2
If $p(z)=\sum\limits_{\nu=0}^na_{\nu}z^{\nu}$ is a polynomial of degree $n$ having all its zeros on $|z|=k$, $k\leq 1$, then Govil [3]proved that\begin{align*}\max\limits_{|z|=1}|p'(z)|\leq \dfrac{n}{k^n+k^{n-1}}\max\limits_{|z|=1}|p(z)|. \end{align*} In this paper, by involving certain coefficients of $p(z)$, we not only improve the above inequality but also improve a result provedby Dewan and Mir [2].
IMPROVEMENT AND GENERALIZATION OF A THEOREM OF T. J. RIVLIN
Mahajan Pritika,Khangembam Babina Devi,N. Reingachan,Barchand Chanam 경남대학교 기초과학연구소 2022 Nonlinear Functional Analysis and Applications Vol.27 No.3
In this paper, we generalize as well as sharpen the above inequality. Also our results not only generalize, but also sharpen some known results proved recently.
SOME Lq INEQUALITIES FOR POLYNOMIAL
Barchand Chanam,N. Reingachan,Khangembam Babina Devi,Maisnam Triveni Devi,Kshetrimayum Krishnadas 경남대학교 기초과학연구소 2021 Nonlinear Functional Analysis and Applications Vol.26 No.2
Let $p(z)$be a polynomial of degree n. Then Bernstein's inequality [12,18] is$$ \max_{|z|=1}|p^{'}(z)|\leq n\max_{|z|=1}|(z)|.$$For $q>0$, we denote$$\|p\|_{q}=\left\{\frac{1}{2\pi}\int^{2\pi}_{0}|p(e^{i\theta})|^{q}d\theta\right\}^{\frac{1}{q}},$$and a well-known fact from analysis [17] gives$$\lim_{q\rightarrow \infty} \left\{\frac{1}{2\pi} \int^{2\pi}_{0}|p(e^{i\theta})|^{q} d\theta\right\}^{\frac{1}{q}} = \max_{|z|=1}|p(z)|. $$ Above Bernstein's inequality was extended by Zygmund [19] into $L^{q}$ norm by proving\begin{equation*}\|p^{'}\|_{q}\leq n\|p\|_{q}, \;\;q\geq 1. \end{equation*} Let $p(z)=a_{0}+\sum^{n}_{\nu=\mu}a_{\nu}z^{\nu}$, $1\leq\mu\leq n$, be a polynomial of degree n having no zero in $|z|<k, k\geq 1$. Then for $0< r\leq R\leq k$, Aziz and Zargar [4] proved$$\max_{|z|=R}|p^{'}(z)|\leq \frac{nR^{\mu-1}(R^{\mu}+k^{\mu})^{\frac{n}{\mu}-1}}{(r^{\mu}+k^{\mu})^{\frac{n}{\mu}}}\max_{|z|=r}|p(z)|. $$ In this paper, we obtain the $L^{q}$ version of the above inequality for $q>0$. Further, we extend a result of Aziz and Shah [3] into $L^{q}$ analogue for $q>0$. Our results not only extend some known polynomial inequalities, but also reduce to some interesting results as particular cases.
HIGHER DERIVATIVE VERSIONS ON THEOREMS OF S. BERNSTEIN
Thangjam Birkramjit Singh,Khangembam Babina Devi,N. Reingachan,Robinson Soraisam,Barchand Chanam 경남대학교 기초과학연구소 2022 Nonlinear Functional Analysis and Applications Vol.27 No.2
In this paper, we first prove a result concerning the sth derivative where 1 ≤ s < n of the polynomial involving some of the co-efficients of the polynomial. Our result not only improves and generalizes the above inequality, but also gives a generalization to higher derivative of a result due to Dewan and Mir [2] in this direction. Further, a direct generalization of the above inequality for the sth derivative where 1 ≤ s < n is also proved.
IMPROVED VERSION ON SOME INEQUALITIES OF A POLYNOMIAL
Rashmi Rekha Sahoo,N. Reingachan,Robinson Soraisam,Khangembam Babina Devi,Barchand Chanam 경남대학교 기초과학연구소 2023 Nonlinear Functional Analysis and Applications Vol.28 No.4
Let $P(z)$ be a polynomial of degree $n$ and $P(z)\neq0$ in $|z|<1$. Then for every real $\alpha$ and $R>1$,Aziz \cite{Aziz1} proved that$$ \max_{|z|=1}|P(Rz)-P(z)|\leq \frac{R^{n}-1}{2}\left(M_{\alpha}^{2}+M_{\alpha+\pi}^{2}\right)^{\frac{1}{2}},$$where\begin{equation*}M_{\alpha}=\max_{1\leq k\leq n}|P(e^{i(\alpha+2k\pi) n})|. \end{equation*}\par In this paper, we establish some improvements and generalizations of the above inequality concerning the polynomials and their ordinary derivatives.