https://dspace.iiti.ac.in:8080/jspui/handle/123456789/3645 2026-08-15T14:15:22Z https://dspace.iiti.ac.in:8080/jspui/handle/123456789/18895 Title: Preface Authors: Tanveer, Mohammad Abstract: [No abstract available] 2026-01-01T00:00:00Z https://dspace.iiti.ac.in:8080/jspui/handle/123456789/18866 Title: Rademacher-type exact formula and higher order Turán inequalities for cubic overpartitions Authors: Agarwal, Archit; Garg, Meghali; Maji, Bibekananda Abstract: In 1918, Hardy and Ramanujan made a breakthrough by developing the circle method to deduce an asymptotic formula for the partition function p(n), which was later refined by Rademacher in 1937 to produce an absolutely convergent series representation for p(n). Since then, Rademacher-type exact formulas for various partition functions have been investigated by many mathematicians. The concept of overpartitions was introduced by Lovejoy and Corteel in 2004. Kim, in 2010, studied an overpartition analogue of cubic partitions, termed as cubic overpartitions. The main objective of this paper is to establish a Rademacher-type exact formula for cubic overpartitions and, as an application, to derive an explicit error term that leads to their log-concavity. Furthermore, applying a result of Griffin, Ono, Rolen, and Zagier, we establish higher-order Turán inequalities for cubic overpartitions. In addition, we obtain log-subadditivity and generalized log-concavity properties for cubic overpartitions inspired by the work of Bessenrodt-Ono and DeSalvo-Pak on the ordinary partition function. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2026. 2026-01-01T00:00:00Z https://dspace.iiti.ac.in:8080/jspui/handle/123456789/18833 Title: Heterogeneous oblique double random forest Authors: Tanveer, M.; Hussain, M.A.; Ahmad, Nehal Abstract: The decision tree ensembles use a single data feature at each node for splitting the data. However, splitting in this manner may fail to capture the geometric properties of the data. Thus, oblique decision trees generate the oblique hyperplane for splitting the data at each non-leaf node. Oblique decision trees capture the geometric properties of the data and hence show better generalization. The performance of the oblique decision trees depends on the way oblique hyperplanes are generated and the data used for the generation of those hyperplanes. Recently, multiple classifiers have been used in a heterogeneous random forest (RaF) classifier. However, it fails to generate trees of proper depth. Moreover, double RaF studies highlighted that larger trees can be generated via bootstrapping the data at each non-leaf node and splitting the original data instead of the bootstrapped data recently. The study of heterogeneous RaF lacks the generation of larger trees, while the double RaF based model fails to take over the geometric characteristics of the data. To address these shortcomings, we propose a heterogeneous oblique double RaF. The proposed model employs several linear classifiers at each non-leaf node on the bootstrapped data and splits the original data based on the optimal linear classifier. The optimal hyperplane corresponds to the models based on the optimized impurity criterion. The experimental analysis indicates that the performance of the introduced heterogeneous double random forest is better than the baseline models. To demonstrate the effectiveness of the proposed heterogeneous double random forest, we used it for the diagnosis of Schizophrenia disease. The proposed model predicted the disease with higher accuracy compared to the baseline models. © 2026 Published by Elsevier Ltd. 2027-01-01T00:00:00Z https://dspace.iiti.ac.in:8080/jspui/handle/123456789/18722 Title: INFINITELY DIVISIBLE MODIFIED BESSEL DISTRIBUTIONS Authors: Prabhu, Dhivya K.; Singh, Sanjeev; Vijesh, Antony Abstract: We study certain continuous univariate probability distributions supported on [0,∞) — the McKay distribution and its generalizations, the generalized inverse Gaussian distribution and the K-distribution —, all of which are related to modified Bessel functions of the first and second kinds. In most cases we show that they belong to the class of infinitely divisible distributions, self-decomposable distributions, generalized gamma convolutions and hyperbolically completely monotone densities. Some of the results are known, but new proofs are provided using special functions techniques: Integral representations of quotients of Tricomi hypergeometric functions, Gaussian hypergeometric functions, and modified Bessel functions of the second kind, play an important role in our study. In addition, by using a different approach based on asymptotic properties of modified Bessel functions, we rediscover a Stieltjes transform representation due to Hermann Hankel for the product of modified Bessel functions of the first and second kinds and we deduce a series of new Stieltjes transform representations for products, quotients and their reciprocals concerning modified Bessel functions of the first and second kinds. By using these results we obtain new infinitely divisible modified Bessel distributions with Laplace transforms related to modified Bessel functions of the first and second kind. We show that the new Stieltjes transform representations have some interesting applications and we list some open problems that may be of interest for further research. In addition, we present a new proof, using the Pick function characterization theorem, for the infinite divisibility of the ratio of two gamma random variables and some new Stieltjes transform representations of quotients of Tricomi hypergeometric functions. © 2026 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY) https://creativecommons.org/licenses/by/4.0/. Open Access made possible by subscribing institutions via Subscribe to Open. 2026-01-01T00:00:00Z