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6. On $r$-primitive $k$-normal polynomials with two prescribed coefficients

Author

Sharma, Avnish K., Rani, Mamta, Tiwari, Sharwan K., and Panigrahi, Anupama

Subjects
Mathematics - Number Theory, 12E20, 11T23
Abstract

This article investigates the existence of an $r$-primitive $k$-normal polynomial, defined as the minimal polynomial of an $r$-primitive $k$-normal element in $\mathbb{F}_{q^n}$, with a specified degree $n$ and two given coefficients over the finite field $\mathbb{F}_{q}$. Here, $q$ represents an odd prime power, and $n$ is an integer. The article establishes a sufficient condition to ensure the existence of such a polynomial. Using this condition, it is demonstrated that a $2$-primitive $2$-normal polynomial of degree $n$ always exists over $\mathbb{F}_{q}$ when both $q\geq 11$ and $n\geq 15$. However, for the range $10\leq n\leq 14$, uncertainty remains regarding the existence of such a polynomial for $71$ specific pairs of $(q,n)$. Moreover, when $q<11$, the number of uncertain pairs reduces to $16$. Furthermore, for the case of $n=9$, extensive computational power is employed using SageMath software, and it is found that the count of such uncertain pairs is reduced to $3988$., Comment: 27 pages, 3 Tables

Published
2024

11. Loan repayment behavior of beneficiary farmers in primary agricultural cooperative societies in Haryana (India)

Author

Singh Suninder, Singh Abhey, Rani Sumista, and Rani Mamta

Subjects
repayment behavior, beneficiary farmers, loans, pacs, state of haryana, p13, q14, p32, Regional economics. Space in economics, HT388, Economics as a science, HB71-74
Abstract

The study examined the loan repayment behavior of beneficiary farmers in Primary Agricultural Cooperative Societies in the State of Haryana, India.

Published
2024
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16. Chaos-Based Cryptography for Digital Image Security Using Parrondo’s Paradox

Author

Husain, Dildar, Patra, Suparn Padma, Rani, Mamta, Kacprzyk, Janusz, Series Editor, Gomide, Fernando, Advisory Editor, Kaynak, Okyay, Advisory Editor, Liu, Derong, Advisory Editor, Pedrycz, Witold, Advisory Editor, Polycarpou, Marios M., Advisory Editor, Rudas, Imre J., Advisory Editor, Wang, Jun, Advisory Editor, Rathore, Vijay Singh, editor, Tavares, Joao Manuel R. S., editor, Surendiran, B., editor, and Yadav, Anil, editor

Published
2024
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17. Effect and Responses of Lead Toxicity in Plants

Author

Rani, Mamta, Vikas, Kumar, Rohtas, Lathwal, Mamta, Kamboj, Ankush, Bennett, Erin R., Series Editor, Panagiotakis, Iraklis, Series Editor, Chrysochoou, Maria, Advisory Editor, Dermatas, Dimitris, Advisory Editor, di Palma, Luca, Advisory Editor, Lekkas, Demetris Francis, Advisory Editor, Menone, Mirta, Advisory Editor, Metcalfe, Chris, Advisory Editor, Moore, Matthew, Advisory Editor, Kumar, Nitish, editor, and Jha, Amrit Kumar, editor

Published
2024
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21. Blending type Approximations by Kantorovich variant of $\alpha$-Schurer operators

Author

Rao, Nadeem, Rani, Mamta, Kiliçman, Adem, Malik, Pradeep, and Ayman-Mursaleen, Mohammad

Subjects
Mathematics - General Mathematics, 41A10, 41A25, 41A28, 41A35, 41A36
Abstract

In the present manuscript, we present a new sequence of operators, $i.e.$, $\alpha$-Bernstein-Schurer-Kantorovich operators depending on two parameters $\alpha\in[0,1]$ and $\rho>0$ for one and two variables to approximate measurable functions on $[0: 1+q], q>0$. Next, we give basic results and discuss the rapidity of convergence and order of approximation for univariate and bivariate of these sequences in their respective sections. Further, Graphical and numerical analysis are presented. Moreover, local and global approximation properties are discussed in terms of first and second order modulus of smoothness, Peetre's K-functional and weight functions for these sequences in different spaces of functions., Comment: 3 figures

Published
2022

23. Inverses of $r$-primitive $k$-normal elements over finite fields

Author

Rani, Mamta, Sharma, Avnish K., Tiwari, Sharwan K., and Panigrahi, Anupama

Subjects
Mathematics - Number Theory, Mathematics - Rings and Algebras, 12E20\sep 11T23
Abstract

Let $r$, $n$ be positive integers, $k$ be a non-negative integer and $q$ be any prime power such that $r\mid q^n-1.$ An element $\alpha$ of the finite field $\mathbb{F}_{q^n}$ is called an {\it $r$-primitive} element, if its multiplicative order is $(q^n-1)/r$, and it is called a {\it $k$-normal} element over $\mathbb{F}_q$, if the greatest common divisor of the polynomials $m_\alpha(x)=\sum_{i=1}^{n} \alpha^{q^{i-1}}x^{n-i}$ and $x^n-1$ is of degree $k.$ In this article, we define the characteristic function for the set of $k$-normal elements, and with the help of this, we establish a sufficient condition for the existence of an element $\alpha$ in $\mathbb{F}_{q^n}$, such that $\alpha$ and $\alpha^{-1}$ both are simultaneously $r$-primitive and $k$-normal over $\mathbb{F}_q$. Moreover, for $n>6k$, we show that there always exists an $r$-primitive and $k$-normal element $\alpha$ such that $\alpha^{-1}$ is also $r$-primitive and $k$-normal in all but finitely many fields $\mathbb{F}_{q^n}$ over $\mathbb{F}_q$, where $q$ and $n$ are such that $r\mid q^n-1$ and there exists a $k$-degree polynomial $g(x)\mid x^n-1$ over $\mathbb{F}_q$. In particular, we discuss the existence of an element $\alpha$ in $\mathbb{F}_{q^n}$ such that $\alpha$ and $\alpha^{-1}$ both are simultaneously $1$-primitive and $1$-normal over $\mathbb{F}_q$., Comment: 30 pages

Published
2022

24. Primitive Normal Values of Rational Functions over Finite Fields

Author

Sharma, Avnish K., Rani, Mamta, and Tiwari, Sharwan K.

Subjects
Mathematics - Number Theory, Mathematics - Rings and Algebras
Abstract

In this paper, we consider rational functions $f$ with some minor restrictions over the finite field $\mathbb{F}_{q^n},$ where $q=p^k$ for some prime $p$ and positive integer $k$. We establish a sufficient condition for the existence of a pair $(\alpha,f(\alpha))$ of primitive normal elements in $\mathbb{F}_{q^n}$ over $\mathbb{F}_{q}.$ Moreover, for $q=2^k$ and rational functions $f$ with quadratic numerators and denominators, we explicitly find that there are at most $55$ finite fields $\mathbb{F}_{q^n}$ in which such a pair $(\alpha,f(\alpha))$ of primitive normal elements may not exist.

Published
2021

28. Financial Literacy in India: A Review of Literature

Author

Rani Mamta and Siwach Manoj

Subjects
financial literacy, investment, banking, well-being, g21, Regional economics. Space in economics, HT388, Economics as a science, HB71-74
Abstract

The paper aims to understand various concepts and dimensions of financial literacy by using literature-based analysis. The reviews included various parameters, such as the financial literacy of young people, employees, women and college students, and the impact of financial literacy on well-being and investment decisions. Secondary information was gathered from many publications, websites, research papers, and articles. In the context of India, there is still much work to be done in the domain of financial literacy. Numerous studies have revealed low levels of financial literacy among India’s different demographic segments and some studies have revealed moderate levels. Financial literacy is a difficult topic to describe and quantify. The definition and measurement of this idea are the focus of numerous investigations. Policy changes must be made to improve financial literacy at both the fundamental and advanced levels so that people can save and invest money more sensibly in the various market opportunities.

Published
2023
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46. Design and Synthesis of Neutral Density Filter in Visible Range for Color Sorting Applications.

Author

Yadav, Mini, Yadav, Sandeep, Shankar, Ajay, Bala, Renu, and Rani, Mamta

Subjects
NEUTRAL density filters, X-ray spectroscopy, OPTICAL coatings, THIN films, ELECTRONIC attenuators
Abstract

This paper provides the design, construction, and characterization of a neutral density filter (NDF) for the visible spectrum and investigate the thickness effect on their various properties. In this work, Nichrome single layer was designed by the Essential Macleod modelling software. The Co-evaporation ofss nickel and chromium was used to construct a filter on a glass substrate by thermal vacuum coating unit under high vacuum. Low thickness supports amorphous nature examined by XRD diffractogram. Energy-Dispersive X-ray Spectroscopy (EDAX) examinations of the thin films revealed that high thickness has slight variation in constant stoichiometry for the chosen Nickel/Chromium ratio (80:20) during co-evaporation and confirm the deposition is successfully done. Additionally, Atomic Force Microscopy (AFM) analysis revealed that surface roughness decreased from 6.034 to 2.895 in correlation with increased layer thickness. These methods made it possible to produce NDFs with optical densities ranging from 0.5 OD at 10 nm film thickness to 2.7 OD at 70 nm thickness. As a result, for steady and long-lasting NDF, the spectral fluctuation of thin filters in our case is lowest at 10 nm (OD= 0.08). A good match data was found between optical transmission and absorption spectra of the designed and the deposited films. The designed NDF's applicability and effectiveness for color sorting tasks were subsequently examined, marking a promising step towards advancing optical engineering solutions in this specific application domain. [ABSTRACT FROM AUTHOR]

Published
2024
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47. MEASUREMENT OF FINANCIAL INCLUSION DISPARITY AMONG INDIAN STATES: AN EMPIRICAL STUDY USING WROCLAW TAXONOMIC METHODOLOGY.

Author

Garg, Aman, Rani, Mamta, Siwach, Manoj, and Garg, Shubham

Subjects
FINANCIAL inclusion, FINANCIAL policy, ECONOMIC activity, ECONOMIC expansion, FINANCIAL performance
Abstract

Financial inclusion is an essential aspect of economic growth. A well-designed financial system significantly aids in the development of a nation, encourages individuals to save, combats poverty and lessens inequality. Finance inclusion is usually accepted as the primary gauge for the expansion of any economic activity. Therefore, this article aims to provide more exhaustive insight into the performance of financial inclusion at the sub-national level in India. The study has adopted the Wroclaw taxonomic method for developing the composite index of financial inclusion in India, covering the period from 2012 to 2022. The Financial Inclusion Index (FII) is a multidimensional phenomenal index that measures many aspects of financial inclusion on a scale from zero to one, where “zero” represents total financial exclusion and “one” means complete financial inclusion in an economy. The results show that Chandigarh is ranked 1st out of the 34 states and UTs with an FII value of 0.09. Bihar has the lowest FII score of 0.75, placing it at 34th in India. The current study will assist the policymakers, government and Reserve Bank of India in formulating policies on financial inclusion in India. [ABSTRACT FROM AUTHOR]

Published
2024
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48. Microexpression Analysis: A Review

Author

Rani, Mamta, Rathee, Neeru, Kacprzyk, Janusz, Series Editor, Gomide, Fernando, Advisory Editor, Kaynak, Okyay, Advisory Editor, Liu, Derong, Advisory Editor, Pedrycz, Witold, Advisory Editor, Polycarpou, Marios M., Advisory Editor, Rudas, Imre J., Advisory Editor, Wang, Jun, Advisory Editor, Abraham, Ajith, editor, Castillo, Oscar, editor, and Virmani, Deepali, editor

Published
2021
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