Hemanta Kalita – författare

This book presents contemporary mathematical concepts and techniques including theories of summability, fixed point and non-absolute integration and applications, providing an overview of recent developments in the foundations of the field as well as its applications. It discusses the recent results of double sequence spaces as the four-dimensional forward difference matrix in double sequence spaces, several new fixed point on Hadamard type fractional integral and differential operator related to the qualitative properties of solutions like, existence and uniqueness, stability, continuous dependence, controllability, oscillations, etc. It also includes several new areas of nonabsolute integration theory are introduced and their applications to other fields. This reference text is for researchers, academics, and professionals in the field of pure and applied mathematics.Covers recent research breakthroughs in this field offering new approaches and methods for both theoretical exploration and practical applicationPresents insights into functional analytic methods in summability, absolute and strong summability, direct theorems on summability, special and general summability methods, and their applicationsHighlights fixed-point theory’s application to real-world problems and offers solutions to various complex challengesIntroduces new areas of non-absolute integration theory, such as the Henstock-Kurzweil integral and generalized Riemann integralDiscusses sequence spaces and functional analysis, including the exploration of double sequence spaces and the four-dimensional forward difference matrix, offering valuable contributions to ongoing research

This book presents contemporary mathematical concepts and techniques including theories of summability, fixed point and non-absolute integration and applications, providing an overview of recent developments in the foundations of the field as well as its applications. It discusses the recent results of double sequence spaces as the four-dimensional forward difference matrix in double sequence spaces, several new fixed point on Hadamard type fractional integral and differential operator related to the qualitative properties of solutions like, existence and uniqueness, stability, continuous dependence, controllability, oscillations, etc. It also includes several new areas of nonabsolute integration theory are introduced and their applications to other fields. This reference text is for researchers, academics, and professionals in the field of pure and applied mathematics.

Covers recent research breakthroughs in this field offering new approaches and methods for both theoretical exploration and practical application Presents insights into functional analytic methods in summability, absolute and strong summability, direct theorems on summability, special and general summability methods, and their applications Highlights fixed-point theory’s application to real-world problems and offers solutions to various complex challenges Introduces new areas of non-absolute integration theory, such as the Henstock-Kurzweil integral and generalized Riemann integral Discusses sequence spaces and functional analysis, including the exploration of double sequence spaces and the four-dimensional forward difference matrix, offering valuable contributions to ongoing research

This book presents contemporary mathematical concepts and techniques including theories of summability, fixed point and non-absolute integration and applications, providing an overview of recent developments in the foundations of the field as well as its applications. It discusses the recent results of double sequence spaces as the four-dimensional forward difference matrix in double sequence spaces, several new fixed point on Hadamard type fractional integral and differential operator related to the qualitative properties of solutions like, existence and uniqueness, stability, continuous dependence, controllability, oscillations, etc. It also includes several new areas of nonabsolute integration theory are introduced and their applications to other fields. This reference text is for researchers, academics, and professionals in the field of pure and applied mathematics.

Covers recent research breakthroughs in this field offering new approaches and methods for both theoretical exploration and practical application Presents insights into functional analytic methods in summability, absolute and strong summability, direct theorems on summability, special and general summability methods, and their applications Highlights fixed-point theory’s application to real-world problems and offers solutions to various complex challenges Introduces new areas of non-absolute integration theory, such as the Henstock-Kurzweil integral and generalized Riemann integral Discusses sequence spaces and functional analysis, including the exploration of double sequence spaces and the four-dimensional forward difference matrix, offering valuable contributions to ongoing research

The book focuses on the theory of fixed points, which is a foundation for many branches of pure and applied mathematics. Fixed point theorems have been studied in various function spaces. The book contains modern results on these theorems, investigated in generalized spaces such as S-metric spaces, convex metric spaces, and bipolar metric spaces, with applications in medical imaging. The nonlinear analysis presented in the book is valuable for modeling and solving real-world problems. It includes work on specific nonlinear operators and nonlinear fractional integral equations in Banach spaces. Relevant studies are also included on statistical convergence, inventory model modeling, computational techniques for Sentiment Analysis on Twitter Data, and Blood Management applications. The book is intended for young researchers interested in nonlinear analysis, fixed-point theory, and computational techniques.

Fractional Calculus and Quantum Calculus presents a focused collection of contemporary research on fractional calculus, quantum (q-) calculus, and generalized calculus, highlighting recent theoretical developments and their emerging applications across mathematics, science, and engineering.The volume brings together contributions on analytical and computational methods for fractional differential and integro-differential equations, addressing fundamental topics such as existence, uniqueness, stability, controllability, and nonlocal and delay effects. It explores advances in quantum calculus through q-Sturm–Liouville theory and q-matrix generated sequence spaces, with emphasis on operator theory, summability, and geometric properties in functional analysis. The book further develops generalized fractional and nonlocal integral operators with novel kernels, broadening the mathematical framework for modelling complex systems.Additional chapters present recent progress in statistical and rough convergence within fuzzy normed spaces, fractional difference sequence spaces, and SUM integral transforms, providing powerful tools for convergence analysis and computational techniques. The inclusion of fractional-order gradient descent methods also demonstrates the growing impact of fractional calculus in machine learning, optimization, and data-driven computation.Overall, the book offers a concise yet rigorous resource for researchers in fractional and quantum calculus, functional analysis, numerical methods, and interdisciplinary applications involving memory, nonlocality, and discrete–continuous dynamics.

Document from the year 2020 in the subject Chemistry - Macromolecular Chemistry, Polymer Chemistry, grade: 2, , language: English, abstract: This work gives an overview over core modified Porphyrinoids. Specifically: Smaragdyrins, Expanded Porphyrinoids and Corroles. It does so by, in two chapters, defining each of the aforementioned chemical combinations' synthesis and characterization, properties and respective dyads. Smaragdyrin is a pentapyrrolic 22p-electron expanded porphyrin system bearing two direct pyrrole-pyrrole bonds. This macrocycle and its core modified derivative i.e. 25-oxasmaragdyrin have received upsurge interest in recent years due to their notable optical and electrochemical properties. Corroles are aromatic tetrapyrrolic macrocycles containing one meso carbon less compared to porphyrins and have one direct pyrrole-pyrrole linkage. This class of macrocycle possesses novel spectral, electrochemical and luminescence properties that can be exploited in material applications. In this book, we have discussed the synthesis, properties and their limited coordination chemistry of expanded porphyrinoid 25-oxasmaragdyrin and core-modified corroles. Corroles, on the other hand, are tetrapyrrolic contracted porphyrins, fully conjugated 18p electron macrocyles containing three methine bridges and one direct pyrrole-pyrrole linkage.

Document from the year 2022 in the subject Chemistry - Macromolecular Chemistry, Polymer Chemistry, grade: 17, Gauhati University, language: English, abstract: Porous coordination polymers, also known as metal organic frameworks are a new type of hybrid material constructed via self-assembly of metal ions/metal clusters which function as nodes and organic ligands which act as bridges or linkers. They are one of the earliest developed classes of metal containing polymers. They extend infinitely one, two or three dimensional framework through coordination bonding, hydrogen bonding, p-p stacking, C-H-p interactions as well as van der Waal forces. These weaker non-covalent interactions, are important for the packing of the one dimensional chains, two-dimensional nets and three-dimensional frameworks. In view of the tunable structures and promising properties shown by these systems various complexities have been prepared and thoroughly investigated over last decade. MOFs are currently flourishing fields of research owing to their intriguing structural motifs and various potential applications, in the field of gas storage, gas separation, catalysis, ion exchange, microelectronics, non linear optics, sensors, medicine and molecular magnetism etc. They possess structural regularity, high porosity, high surface area resulting in greater potential applications than conventional zeolites or activated carbons and mesoporous silica. For the construction of porous coordination polymers with diverse structures and properties selection of the special inorganic and organic building blocks is one of the important factors. Multicarboxylate organic ligands have proved to be an excellent choice for the construction of MOFs of higher nuclearity due to their different coordination modes with the metals, molecular flexibilities and structural stabilities. Metal carboxylate linker in combination with cross linked or pillered polypyridine have generated many interesting coordination architecture. Making use of transition metal carboxylate and linear bridging auxiliary ligands it is possible to construct 1-D, 2-D and 3-D porous coordination polymer of different pore structures and porosities. Aside from coordination bonding interactions, various non-covalent bonding or some weak intra- or intermolecular interactions, such as hydrogen-bonding, p p stacking and C H p interactions or van der Waals interactions also influence the formation of final architectures.

This book contains proceedings of select chapters presented at the International Conference on Nonlinear Analysis & Computational Techniques (ICNACT-2024), held at VIT Bhopal University, Madhya Pradesh, India, from 8 to 10 August 2024. It discusses advances, emerging trends and theoretical developments in topics related to nonlinear analysis and computational techniques, including the introduction to new function spaces, such as a generalized Orlicz with Rao and Ren’s norm, the s-Young space and the controlled G-metric spaces. The book explains some relationships among different types of near linear spaces and introduces the strongly λ-summable functions.Nonlinear systems frequently require convergence and fixed point theorems. In this sense, the concept of q-lacunary almost statistical convergence is exposed. The book proposes a common coupled fixed point theorems, a few fixed point theorems for compatible mappings of type P and some applications on dynamic programming. In differential equations, some works extend Ostrowski-type inequalities; solution of the fractal nonlinear Klein–Gordon equation, study of a hybrid differential equation and the problem of exponential stability of the nonlinear Saint–Venant equation, finally provides a study of some properties for Cayley transform of operators. The book is useful to researchers in mathematics and applied sciences, engineers, graduate students, computational scientists, software developers and educators. They will benefit from this theory, which is essential for efficiently solving complex equations via the understanding, modeling and solving nonlinear problems and their theoretical and practical domains.

This book contains proceedings of select chapters presented at the International Conference on Nonlinear Analysis & Computational Techniques (ICNACT-2024), held at VIT Bhopal University, Madhya Pradesh, India, from 8 to 10 August 2024. It discusses advances, emerging trends and theoretical developments in topics related to nonlinear analysis and computational techniques, including the introduction to new function spaces, such as a generalized Orlicz with Rao and Ren’s norm, the s-Young space and the controlled G-metric spaces. The book explains some relationships among different types of near linear spaces and introduces the strongly λ-summable functions.Nonlinear systems frequently require convergence and fixed point theorems. In this sense, the concept of q-lacunary almost statistical convergence is exposed. The book proposes a common coupled fixed point theorems, a few fixed point theorems for compatible mappings of type P and some applications on dynamic programming. In differential equations, some works extend Ostrowski-type inequalities; solution of the fractal nonlinear Klein–Gordon equation, study of a hybrid differential equation and the problem of exponential stability of the nonlinear Saint–Venant equation, finally provides a study of some properties for Cayley transform of operators. The book is useful to researchers in mathematics and applied sciences, engineers, graduate students, computational scientists, software developers and educators. They will benefit from this theory, which is essential for efficiently solving complex equations via the understanding, modeling and solving nonlinear problems and their theoretical and practical domains.

This book presents a systematic treatment of Henstock–Orlicz (or H-Orlicz) spaces with minimal assumptions on the Young function. H-Orlicz spaces contain non-absolute integrable functions called Henstock–Kurzweil integrable functions. Results from classical functional analysis are presented in detail, and new material is included on classical analysis. Extrapolation is used to prove, for example, the countable additivity of Henstock–Dunford integrable functions on H-Orlicz spaces are included. Relationships of modular convergence and norm convergence of H-Orlicz spaces are discussed. Finally, central geometrical results are provided for H-spaces, including uniformly convexity, reflexivity and the Radon–Nikodym property of the H–Orlicz spaces. Primarily aimed at researchers and PhD students interested in Orlicz spaces or generalized Orlicz spaces, this book can be used as a basis for advanced graduate courses in analysis.

This book presents a systematic treatment of Henstock–Orlicz (or H-Orlicz) spaces with minimal assumptions on the Young function. H-Orlicz spaces contain non-absolute integrable functions called Henstock–Kurzweil integrable functions. Results from classical functional analysis are presented in detail, and new material is included on classical analysis. Extrapolation is used to prove, for example, the countable additivity of Henstock–Dunford integrable functions on H-Orlicz spaces are included. Relationships of modular convergence and norm convergence of H-Orlicz spaces are discussed. Finally, central geometrical results are provided for H-spaces, including uniformly convexity, reflexivity and the Radon–Nikodym property of the H–Orlicz spaces. Primarily aimed at researchers and PhD students interested in Orlicz spaces or generalized Orlicz spaces, this book can be used as a basis for advanced graduate courses in analysis.