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A simple proof of Ramanujan's reciprocity theorem
P. S. Guruprasad,N. Pradeep 장전수학회 2006 Proceedings of the Jangjeon mathematical society Vol.9 No.2
In this note, we give a simple proof of Ramanujan's reciprocity theorem using q-binomial theorem.
Shankar Bhaumik,A. Kumaraswamy,S. Guruprasad,P. Bhandari 대한기계학회 2015 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.29 No.11
Contact based FE simulations have been carried out to estimate the contact pressure distribution at seal/rod interface at sealed oil pressuresof 10, 20 and 30 MPa and constant rod velocity of 0.12 m/s. Oil film thickness at the interface was then computed analytically atvarious combinations of oil pressures and rod velocities. Seal contact pressure and oil film thickness data along with surface roughness,intermolecular interaction between seal/rod interfaces has been perused to estimate the friction in Nitrile-Butadiene Rubber (NBR) rectangularhydraulic rod seals using theoretical models such as Inverse hydrodynamic lubrication (IHL), Greenwood-Williamson (GW)and Wassink’s models. The friction at seal/rod interface was also measured experimentally using a specially designed test rig. The comparisonof theoretical and experimental data revealed that, friction computed from GW and Wassink’s models had good agreement withthe experimental results.
R. RAJENDRA,P. S. Guruprasad,K. BHARGAVA,P. SIVA KOTA REDDY 장전수학회 2021 Proceedings of the Jangjeon mathematical society Vol.24 No.2
In this paper, we present a new representation of partitions of positive integers using labeled trees. Labeled trees representing a partition of an integer n is called a partition-tree of n. We discuss some results involving partition-trees, energy of an integer with respect to partition-trees, and gracefulness of the default labeling of partition trees.
Some edge degree based topological indices of graphene
K. B. Sudhakara,P. S. Guruprasad,M. A. Sriraj 장전수학회 2020 Proceedings of the Jangjeon mathematical society Vol.23 No.2
Graphene is a two dimensional material consisting of a single layer of carbon atom arranged in a honeycomb structure. Its properties include high strength and good conductivity of heat and electricity. In this paper, we compute some edge degree based topological indices namely, Generalized Zagreb index, Atom Bond Connectivity index, Augmented Zagreb Index, Geometric Arithmetic index, Harmonic index, ,Symmetric division degree index, Modified first multiple Zagreb index, second multiple Zagreb index, first, second and third Zagreb polynomial of Graphene.
New Modular Relations for the Ratio’s of Ramanujan Function χ(−q) of degree 9
B. N. DHARMENDRA,P. S. Guruprasad 장전수학회 2020 Proceedings of the Jangjeon mathematical society Vol.23 No.3
In this paper, we establish some new modular equations of Ramanujan’s function χ(−q) of degree 9. Further, we obtain some explicit evaluations of class invariant gn from them.
On Certain New Modular Relations for the Rogers-Ramanujan type functions of order Twelve
K. R. Vasuki,P. S. Guruprasad 장전수학회 2010 Advanced Studies in Contemporary Mathematics Vol.20 No.3
In this paper, we define the Rogers-Ramanujan type functions M(q) and N(q) of order twelve and obtain some modular relations involving these identities, which are analogues to Ramanujan’s well known forty identities for Rogers-Ramanujan functions. Further, we establish certain color partition identities from them.
Vishnu G. Nair,Adarsh Rag S.,Jayalakshmi K. P.,Dileep M. V.,K. R. Guruprasad 제어·로봇·시스템학회 2023 International Journal of Control, Automation, and Vol.21 No.7
In this paper, a dynamic workspace allocation methodology for coverage path planning using multiple robots in the presence of obstacles is presented. The entire workspace is initially partitioned using the Manhattan Voronoi partitioning method, without considering the obstacles present, and the robots execute Multi-Robot Simultaneous Exploration and Coverage (MRSimExCoverage) using the Spanning Tree Coverage (STC) algorithm and cover the workspace. A dynamic workspace re-allocation strategy to optimize the area covered by each robot, whenever obstacles are detected, so as to avoid certain obstacle-induced coverage issues is studied. Simulation experiments within the Matlab/V-rep environment are used to demonstrate and validate the performance of the proposed algorithm. Though the authors used the STC algorithm for path planning for demonstration, any suitable coverage algorithm may be used.