MAKE MOST OF THE KNOWLEDGE NETWORK, JOIN ACADEMIC RESEARCH FOUNDATION

This study presents a modified one-parameter Ailamujia distribution called the Entropy Transformed Ailamujia distribution (ETAD). The ETAD properties like order and reliability statistics, entropy, moment and moment generating function, quantile function, and its variability measures are derived. The maximum likelihood technique (MLT) method was used in estimating the parameter of ETAD. Through simulation at different sample sizes of between 20 and 1500 with varying parameter values of 0.1, 0.3, 0.5, and 0.7, the MLT was found to be consistent, efficient, and unbiased for estimating the ETAD parameter.

KEYWORDS: Ailamujia distribution, Entropy Transformation, Technique of Maximum likelihood, Simulation.

Financial crises trigger extreme market volatility and sudden price jumps, challenging the accuracy of conventional option pricing models. This study explores the robustness and predictive power of Double-Exponential Jump GARCH (SVDEJGARCH) models in pricing options under extreme market conditions, using NSE Nifty 50 option data. Unlike traditional models such as Black-Scholes, Heston, and Variance-Gamma, which struggle to capture sharp price fluctuations and volatility clustering, the SVDEJ-GARCH model accounts for both heavy-tailed jump distributions and dynamic volatility adjustments. Through an empirical evaluation across different financial crises, we analyze the model’s ability to forecast implied volatility, detect risk asymmetry, and improve option valuation accuracy. The findings provide valuable insights into risk management, hedging strategies, and pricing efficiency in turbulent markets, making this research particularly relevant for traders, policymakers, and financial analysts navigating high-stress market environments.

KEYWORDS: Gamma L´evy process, moments, simulation, martingale fields

In the recent past, the Covid-19 pandemic has caused trouble due to lockdown in their day-to-day life of the people around the world. The risk of exposure of such major source of spread of disease is caused by human interaction with others or touching objects around the infected person, which ultimately creates a chain or clusters of infected people. Graphs are used to model the infected person’s network. In recent past, graph sampling is used to draw sample subgraphs from network(graph) in order to study different network parameters. This paper presents a comparison of clique based procedure (CBP) and shortest path based procedure (SPP) to estimate the average degree of Covid-19 patient network using an overlapping cluster sampling. A probability proportional to size based cluster sampling comparative procedure is used to obtain the lower and upper limit of confidence intervals with the help of multiple samples. Ogive based simulation is also used for single value computation of limits of CI. The results, obtained from simulation, show that the clique based sampling algorithm (CBP) for risk evaluation is more efficient (relative gain of 13.26%) than the shortest path based sampling algorithm (SPP). The estimate of average degree of patient network provides a value about the nature of spread of infection that a patient has generated in society. This estimate also indicates the intensity of risk of spread of disease of a particular type of Covid-19 infection variant. Results of this study showed that this model can be used as a valuable tool for design based sampling on network like structure.

KEYWORDS: Covid-19, Clique, Cluster Sampling, Confidence Interval (CI), Graph, Sampling, Pandemic, Probability proportional to size with replacement(PPSWR), Shortest Path, Social Network.

We construct a surface family possessing a natural lift of a given spacelike curve with spacelike binormal as a line of curvature. We obtain sucient condition for the given curve such that its natural lift is a line of curvature on any member of the surface family. Finally, we present an illustrative example.

KEYWORDS: Minkowski 3-space, Line of curvature, Surface family, Natural lift curve.

This paper intends to develop a new cost-volume-profit (CVP) analysis based on optimization and sphere packing theories [1, 2]. The original cost-volume-profit (CVP) model was first introduced by Hess and Mann in 1903 and generalized later to multiproduct case. It seems a little attention has been paid to the extension of existing models of CVP analysis when its parameters such as sales, prices, and costs vary simultaneously over a given period. For this purpose, we propose a new approach to profitability analysis based on a notion of set of profitability conditions with respect to CVP parameters which is nonconvex. The main difficulty for handling CVP analysis is nonconvexity of the set of profitability conditions. To overcome this, we apply the penalty function method in order to find a feasible point in the nonconvex set of the set of profitability conditions. Finding a feasible point allows to construct other subsets of the set of profitability conditions based on sphere packing theory. The approach also provides practical suggestions and recommendations for managers to choose a set of optimal CVP parameters. The proposed approach is illustrated on some examples providing numerical results.

KEYWORDS: management decison making, CVP analysis, profitability analysis, optimization, penalty method, sphere packing theory.

In this paper we study methods of summability of series. We extend the results of regular summability methods to the domain of multi-index sequences. In particular, we show the relations between Abel's and Cesáro's methods. The main result is a generalization of the well-known Hardy-Littlewood theorem to double sequences.

KEYWORDS: Summability methods, Hardy-Littlewood theorem, Abel method, Cesáro method.

In this paper, we introduce and investgate a new third order recurrence sequence so called generalized co-Padovan sequence and its two special subsequences which are related to generalized padovan numbers and its two subsequences. There are close interrelations between recurrence equations of and roots of characteristic equations of generalized Padovan and generalized co-Padovan numbers. We present Binet’s formulas, generating functions, some identities, Simson’s formulas, recurrence properties, sum formulas and matrices related with these sequences.

2010 Mathematics Subject Classification. 11B37, 11B39, 11B83.
KEYWORDS: Padavon numbers, Perrin numbers, co-Padovan numbers, co-Perrin numbers, third order recurrence relations, Binet’s formula, generating functions.

Some new classes of general mixed inverse quasi variational inclusions are introduced and studied. Several important special cases are highlighted as applications of these problems. The auxiliary principle technique is exploited to suggest some new multi step iterative methods for solving general mixed inverse quasi variational inequalities. We prove that the convergence of the proposed methods only requires the partially relaxed strongly monotonicity of the operator and skew symmetric bifunction, which is weaker than co-coercivity. As special cases, we obtain various known and new results for solving various classes of variational inequalities and related problems. These multi step methods include Mann iteration, Ishikawa (two-step) and Noor (three-step) iterations as special cases.

KEYWORDS: Inverse Quasi variational inequalities, auxiliary principle, multi step iterative methods, convergence, fixed points.