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Investigation of Special Type-Π Smarandache Ruled Surfaces Due to Rotation Minimizing Darboux Frame
This study begins with the construction of type-Π Smarandache ruled surfaces, whose base curves are Smarandache curves derived by rotation-minimizing Darboux frame vectors of the curve in E3. The direction vectors of these surfaces are unit vectors that convert Smarandache curves. The Gaussian and mean curvatures of the generated ruled surfaces are then separately calculated, and the surfaces are required to be minimal or developable. We report our main conclusions in terms of the angle between normal vectors and the relationship between normal curvature and geodesic curvature. For every surface, examples are provided, and the graphs of these surfaces are produced.
Contact Geometry of Slant Submanifolds
This book contains an up-to-date survey and self-contained chapters on contact slant submanifolds and geometry, authored by internationally renowned researchers. The notion of slant submanifolds was introduced by Prof. B.Y. Chen in 1990, and A. Lotta extended this notion in the framework of contact geometry in 1996. Numerous differential geometers have since obtained interesting results on contact slant submanifolds. The book gathers a wide range of topics such as warped product semi-slant submanifolds, slant submersions, semi-slant ξ┴ -, hemi-slant ξ┴ -Riemannian submersions, quasi hemi-slant submanifolds, slant submanifolds of metric f-manifolds, slant lightlike submanifolds, geometric inequalities for slant submanifolds, 3-slant submanifolds, and semi-slant submanifolds of almost paracontact manifolds. The book also includes interesting results on slant curves and magnetic curves, where the latter represents trajectories moving on a Riemannian manifold under the action of magnetic field. It presents detailed information on the most recent advances in the area, making it of much value to scientists, educators and graduate students.
Inequalities in Geometry and Applications
This book presents the recent developments in the field of geometric inequalities and their applications. The volume covers a vast range of topics, such as complex geometry, contact geometry, statistical manifolds, Riemannian submanifolds, optimization theory, topology of manifolds, log-concave functions, Obata differential equation, Chen invariants, Einstein spaces, warped products, solitons, isoperimetric problem, Erdös–Mordell inequality, Barrow’s inequality, Simpson inequality, Chen inequalities, and q-integral inequalities. By exposing new concepts, techniques and ideas, this book will certainly stimulate further research in the field.
International Journal of Mathematical Combinatorics, Volume 1, 2018
The mathematical combinatorics is a subject that applying combinatorial notion to all mathematics and all sciences for understanding the reality of things in the universe. The International J. Mathematical Combinatorics is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly, which publishes original research papers and survey articles in all aspects of mathematical combinatorics, Smarandache multi-spaces, Smarandache geometries, non-Euclidean geometry, topology and their applications to other sciences.
MATHEMATICAL COMBINATORICS, Vol. 1 / 2018
The Mathematical Combinatorics (International Book Series) is a fully refereed international book series with ISBN number on each issue, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 110-160 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences.
MATHEMATICAL COMBINATORICS
The Mathematical Combinatorics (International Book Series) is a fully refereed international book series with ISBN number on each issue, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 110-160 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences.
Manifolds
Differential geometry is a very active field of research and has many applications to areas such as physics and gravity, for example. The papers in this book cover a number of subjects which will be of interest to workers in these areas. It is hoped that the papers here will be able to provide a useful resource for researchers with regard to current fields of research in this important area.
Sixties Radicalism and Social Movement Activism
'Sixties Radicalism and Social Movement Activism' explores and re-analyses major events, debates and themes from the radical developments of the nineteen sixties and relates them to contemporary social movements and issues.
THE INDIAN LISTENER
The Indian Listener (fortnightly programme journal of AIR in English) published by The Indian State Broadcasting Service,Bombay ,started on 22 December, 1935 and was the successor to the Indian Radio Times in english, which was published beginning in July 16 of 1927. From 22 August ,1937 onwards, it was published by All India Radio,New Delhi.In 1950,it was turned into a weekly journal. Later,The Indian listener became "Akashvani" in January 5, 1958. It was made a fortnightly again on July 1,1983. It used to serve the listener as a bradshaw of broadcasting ,and give listener the useful information in an interesting manner about programmes,who writes them,take part in them and produce them alo...
The Lady of Two Nations
A casual encounter between an Oxford University-educated scion of a Nawabi family and a comely young woman belonging to a Christian family of Kumaon transformed into a ‘happily ever after’ alliance. Their romantic entanglement had as its backdrop of the tug-of-war between Congress and Muslim League in undivided India. When Irene converted to Islam, her family ostracised her. Liaqat Ali Khan (1896-1951) went on to become the first Prime Minister of Pakistan and his wife Irene Pant (1905-90) attained fame as his wife and fondly came to be known as Gul-e-Ra’ana. In the 1930s, women were not easily allowed to get an education or work. The writer Raj Gopal Singh Verma narrates the fascinati...
