Güldem Yıldız | Mathematics | Best Paper Award

Published on by Best Achievements

Best Paper Award

Güldem Yıldız
Nigde Omer Halisdemir University

Güldem Yıldız
Affiliation Nigde Omer Halisdemir University
Country Turkey
Article Title Solving the Gardner Equation Through the Sardar Sub-Equation Method and a Hybrid Artificial Neural Network Model
Scopus ID 55735455100
Article Type Research Article
Article Views 192
Reference Count 40
Award Category Best Paper Award
Event Global Best Achievements Awards
ORCID 0000-0002-8120-3525

Güldem Yıldız of Nigde Omer Halisdemir University, Turkey, is associated with the 2026 research article Solving the Gardner Equation Through the Sardar Sub-Equation Method and a Hybrid Artificial Neural Network Model, published by MDPI. The study concerns the Mathematics subject area and combines an analytical sub-equation technique with a hybrid artificial neural network framework. The supplied publication record reports 192 article views and 40 references. The research is presented in connection with the Best Paper Award category of the Global Best Achievements Awards.

Abstract

This article presents the academic recognition of Güldem Yıldız for research on solving the Gardner equation through the Sardar Sub-Equation Method and a hybrid artificial neural network model. The work addresses an analytical and computational treatment of a nonlinear mathematical equation, combining a sub-equation approach with neural-network-based modeling. Such a hybrid framework connects symbolic solution techniques with data-driven approximation, offering a structured basis for examining nonlinear wave equations and related mathematical behavior. The research was published by MDPI in 2026 and is associated with the Mathematics subject area. This page summarizes the researcher, scientific context, methodology, contributions, and recognition academically.

Keywords

Keywords: Gardner equation; Sardar Sub-Equation Method; artificial neural networks; hybrid computational model; nonlinear equations; mathematical physics; analytical solutions; Mathematics.

Introduction to the Research Topic

The Gardner equation is a nonlinear partial differential equation studied in mathematical physics. Analytical methods can provide explicit solution forms, while computational learning approaches can approximate relationships. The reported study combines the Sardar Sub-Equation Method with a hybrid artificial neural network model, linking analytical and computational perspectives in nonlinear research. [1]

Research Profile

Güldem Yıldız is affiliated with Nigde Omer Halisdemir University, Turkey, and is represented in Scopus by Author ID 55735455100 and in ORCID by 0000-0002-8120-3525. The supplied research record identifies Mathematics as the subject area, with six documents, seventeen citations, and an h-index of one at the time of this profile. [2] [3]

Scientific Background

The Gardner equation extends nonlinear wave models by incorporating nonlinear effects, making its solution structure relevant to applied mathematics and mathematical physics. Sub-equation methods seek tractable analytical forms, whereas artificial neural networks provide computational approximation. Combining these perspectives can support comparison between explicit solutions and learned representations for nonlinear research. [1]

Methodology

The approach uses the Sardar Sub-Equation Method to construct analytical solutions of the Gardner equation, followed by a hybrid artificial neural network model computationally. The methodology connects symbolic derivation with numerical or learning-based approximation. The article title establishes this methodological combination, while implementation should be verified in the published article. [1]

Key Findings

The study addresses the Gardner equation through a sub-equation solution method and a hybrid artificial neural network model. This combination indicates an emphasis on complementary analytical and computational treatment rather than one technique. Solution families, numerical results, training procedures, and error measures should be taken directly from the article carefully. [1]

Scientific Contributions

The contribution described by the title is the integration of the Sardar Sub-Equation Method with a hybrid artificial neural network framework for the Gardner equation. This approach connects established analytical solution techniques with computational learning. The work provides context for comparing symbolic formulations and model-based approximations in nonlinear mathematical analysis. [1]

Conclusion

The recognized research focuses on a hybrid treatment of the Gardner equation that combines an analytical sub-equation method with artificial neural network modeling. Its publication in 2026 places the work within current mathematical research. Further assessment of solution accuracy, generalization, and comparative performance requires consultation of the complete published study. [1]

References

    1. MDPI. (2026). Solving the Gardner Equation Through the Sardar Sub-Equation Method and a Hybrid Artificial Neural Network Model. Symmetry.
      https://doi.org/10.3390/sym18091479
    2. Elsevier. (n.d.). Scopus author details: Güldem Yıldız, Author ID 55735455100. Scopus.
      https://www.scopus.com/authid/detail.uri?authorId=55735455100
    3. ORCID. (n.d.). Güldem Yıldız, ORCID iD 0000-0002-8120-3525. ORCID.
      https://orcid.org/0000-0002-8120-3525

Atanu Manna | Mathematical | Best Researcher Award

Published on by Best Achievements

Assist. Prof. Dr. Atanu Manna | Mathematical Analysis | Best Researcher Award

Assist. Prof. Dr. Atanu Manna, Indian Institute of Carpet Technology, India.

Dr. Atanu Manna is an Assistant Professor of Mathematics at the Indian Institute of Carpet Technology, Bhadohi, India. 🎓 He earned his Ph.D. from IIT Kharagpur (2014) and specializes in Geometry of Banach Spaces, Operator Theory, and Inequalities. ✍️ With numerous publications in top-tier journals, his research enhances mathematical frameworks in sequence spaces and numerical radius inequalities. 📚 Dr. Manna actively participates in international conferences and symposiums, contributing significantly to the field of pure and applied mathematics. 🔬

🌟 Professional Profile

🎓 Early Academic Pursuits

Assist. Prof. Dr. Atanu Manna began his academic journey with a Bachelor of Science (B.Sc.) from Vidyasagar University, Midnapore (2006), securing First Class First. He then pursued his Master of Science (M.Sc.) in Mathematics from Jadavpur University, Kolkata (2008), achieving First Class Fifth with a specialization in Pure Mathematics. His academic excellence led him to the Indian Institute of Technology, Kharagpur, where he earned his Doctor of Philosophy (Ph.D.) in 2014. His doctoral research focused on “Modular sequence spaces defined by using de la Valle-Poussin Means, Generalized Means, and Difference operator”.

💼 Professional Endeavors

Currently serving as an Assistant Professor in Mathematics at the Indian Institute of Carpet Technology, Bhadohi, India, Dr. Manna plays a pivotal role in academic and research advancements. His expertise extends to subjects like Calculus, Linear Algebra, Functional Analysis, Applied Statistics, and Complex Analysis. His teaching philosophy integrates theoretical concepts with real-world applications, fostering a deep understanding among students.

🔬 Contributions and Research Focus On Mathematical 

Dr. Atanu Manna, an esteemed Assistant Professor at the Indian Institute of Carpet Technology, specializes in Functional Analysis, Operator Theory, and Inequalities. His pioneering work on Orlicz and Musielak-Orlicz spaces 📐, Hardy-type inequalities 📊, and Numerical Radius bounds 🔢 has led to groundbreaking improvements in mathematical inequalities. His contributions include refining Hardy, Copson, and Rellich inequalities, extending operator theory in Banach spaces, and developing new geometric properties of modular spaces. With numerous high-impact journal publications 📖, he actively participates in international conferences 🌍, sharing insights on mathematical analysis. His research bridges pure and applied mathematics, influencing theoretical advancements and practical applications in mathematical sciences. 🎓

🌍 Impact and Influence

Dr. Manna’s scholarly works have made a significant impact on Mathematical Analysis and Inequalities. His research outputs include numerous peer-reviewed journal articles and conference proceedings, enhancing the field’s understanding of functional spaces and operator inequalities. His international collaborations and participation in prestigious conferences underscore his influence in the global mathematical community.

🏅 Awards and Honors 

Dr. Manna has been recognized for his outstanding contributions to mathematics through multiple conference invitations, research fellowships, and academic distinctions. His First Class First rank in B.Sc. and prestigious conference presentations highlight his academic excellence.

📚 Academic Citations

With a growing presence in the academic world, Dr. Manna has authored and co-authored over 20 research papers in esteemed journals such as Linear Algebra and its Applications, Glasgow Mathematical Journal, Revista de la Real Academia de Ciencias, and Journal of Mathematical Analysis and Applications. His Google Scholar profile reflects his research impact, with a steadily increasing citation count, validating the significance of his work.

🚀 Legacy and Future Contributions

Dr. Manna’s research continues to shape the field of Mathematical Inequalities and Operator Theory. His future endeavors include further advancements in Banach space geometry and numerical radius inequalities. With a strong dedication to teaching and research, he aims to mentor aspiring mathematicians, leaving a lasting impact on the academic landscape.

Publications Top Notes

📖 Numerical radius and Berezin number inequality
📌 Journal of Mathematical Analysis and Applications (2023) – Cited by: 7 🔢

📖 Difference sequence spaces derived by using generalized means
📌 Journal of the Egyptian Mathematical Society (2015) – Cited by: 6 📊

📖 Some mth-order Difference Sequence Spaces of Generalized Means and Compact Operators
📌 Annals of Functional Analysis (2015) – Cited by: 6 🧮

📖 On the improvements of Hardy and Copson inequalities
📌 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales (2023) – Cited by: 3 📈

📖 Norm inequalities involving upper bounds of certain matrix operators in Orlicz-type sequence spaces
📌 The Journal of Analysis (2019) – Cited by: 3 🔣

📖 Factorized enhancement of Copson’s inequality
📌 Tamkang Journal of Mathematics (2018) – Cited by: 3 🏆

📖 Norm inequalities involving upper bounds for operators in Orlicz-Taylor sequence spaces
📌 4th International Conference in Mathematics and Computing (2018) – Cited by: 2 🔢

📖 Some geometric properties of Musielak-Orlicz sequence spaces generated by de la Vallee-Poussin means
📌 Mathematical Inequalities & Applications (2015) – Cited by: 2 📏

📖 On improvements of the Hardy, Copson and Rellich inequalities
📌 arXiv preprint (2023) – Cited by: 1 🔬

📖 Orlicz extension of Numerical radius inequalities
📌 arXiv preprint (2022) – Cited by: 1 📚

📖 Bigeometric Cesàro difference sequence spaces and Hermite interpolation
📌 Asian-European Journal of Mathematics (2020) – Cited by: 1 ✏️

📖 New Hardy-type integral inequalities
📌 Acta Sci. Math. (Szeged) (2020) – Cited by: 1 🎯

📖 Property (k-beta) of Musielak-Orlicz and Musielak-Orlicz-Cesaro spaces
📌 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales (2019) – Cited by: 1 📐

📖 Some geometric properties of generalized Cesaro-Musielak-Orlicz spaces equipped with the Amemiya norm
📌 Acta Mathematica Vietnamica (2016) – Cited by: 1 📉

📖 Some paranormed difference sequence spaces derived by using Generalized means
📌 Kyungpook Mathematical Journal (2015) – Cited by: 1 📘

📖 On (K-NUC)-property in Musielak-Orlicz spaces defined by de la Vallee-Poussin means and some countably modulared spaces
📌 DCDIS, Series A: Mathematical Analysis (2014) – Cited by: 1 🔢

📖 Some Geometric Properties of Generalized Cesàro–Musielak–Orlicz Sequence Spaces
📌 Mathematics and Computing Conference (Haldia, India) – Cited by: N/A 🏅