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This volume consists of a collection of 14 accepted submissions (including several invited feature articles) to the Special Issue of MDPI's journal Symmetry on the general subject area of integral transformations, operational calculus and their applications from many different parts around the world. The main objective of the Special Issue was to gather review, expository, and original research articles dealing with the state-of-the-art advances in integral transformations and operational calculus as well as their multidisciplinary applications, together with some relevance to the aspect of symmetry. Various families of fractional-order integrals and derivatives have been found to be remarka...
Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably wide-spread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences. This Special Issue contains a total of 36 carefully-selected and peer-reviewed articles which are authored by established researchers from many countries. Included in this Special Issue are review, expository and original research articles dealing with the recent advances on the topics of integral transforms and operational calculus as well as their multidisciplinary applications
This issue is a continuation of the previous successful Special Issue “Mathematical Analysis and Applications”
In recent years there has been an increasing interest in problems involving closed form evaluations of (and representations of the Riemann Zeta function at positive integer arguments as) various families of series associated with the Riemann Zeta function ((s), the Hurwitz Zeta function ((s,a), and their such extensions and generalizations as (for example) Lerch's transcendent (or the Hurwitz-Lerch Zeta function) iI>(z, s, a). Some of these developments have apparently stemmed from an over two-century-old theorem of Christian Goldbach (1690-1764), which was stated in a letter dated 1729 from Goldbach to Daniel Bernoulli (1700-1782), from recent rediscoveries of a fairly rapidly convergent se...
The world is becoming more and more competitive. Quality of performance has become the key factor for personal progress. Parents desire that their children climb the ladder of performance to as high a level as possible. This desire for a high level of achievement puts a lot of pressure on students, teachers, and schools and in general the education system itself. In fact, it appears as if the whole system of education revolves round the academic achievement of students, though various other outcomes are also expected from the system. Thus a lot of time and effort of the schools are used for helping students to achieve better in their scholastic endeavors. The importance of scholastic and academic achievement has raised important questions for educational researchers. What factors promote achievement in students? How far do the different factors contribute towards academic achievement? (Ramaswamy, 1990).
Education is the process of developing the capacities and potentials of the individual so as to prepare that individual to be successful in a specific society or culture. From this perspective, education is serving primarily as an individual development function. Education begins at birth and continues throughout life. It is constant and on going. Schooling generally begins some where between the ages four and six when children are gathered together for the purposes of specific guidance related to skills and competencies that society deems important. In the past, once the formal primary and secondary schooling was completed the process was finished. However, in today’s information age, adults are quite often learning in informal setting throughout their working lives and even into retirement.
India is regarded as the most second largest tribal dominated country in the world. The tribal people are intrinsic part of the national life which has been instrumental in contributing to the complex amalgam of national culture by their rich cultural heritage. From thousands of years, they survived in a natural environment with simple lifestyle and developed their cultural pattern which is congenial to their consequent physical and social environment. Even the references of such tribal groups are found in the ancient literature of Ramayana and Mahabharata. At present, the tribal population of India falls into three main zones namely, North Eastern Zone, the Central Zone and the Southern Zone.
This book presents a Paninian perspective towards natural language processing. It has three objectives: (1) to introduce the reader to NLP, (2) to introduce the reader to Paninian Grammar (PG) which is the application of the original Paninian framework to the processing of modern Indian languages using the computer, (3) to compare Paninian Grammar (PG) framework with modern Western computational grammar frameworks.Indian languages like many other languages of the world have relatively free word order. They also have a rich system of case-endings and post-positions. In contrast to this, the majority of grammar frameworks and designed for English and other positional languages. The unique aspe...
This work aims to present, in a systematic manner, results including the existence and uniqueness of solutions for the Cauchy Type and Cauchy problems involving nonlinear ordinary fractional differential equations.