Results 31 to 40 of about 33,042 (127)

ON CERTAIN RESULTS INVOLVING SQUARE OF RAMANUJAN'S MOCK THETA FUNCTIONS

South East Asian Journal of Mathematics and Mathematical Sciences, 2023
In this paper, making use of an identity deduced from Bailey's transform, certain results have been established involving the square of Ramanujan's mock theta functions.
Satya Prakash Singh, Ashish Pratap Singh
semanticscholar   +1 more source

Holomorphic projections and Ramanujan’s mock theta functions [PDF]

Proceedings of the National Academy of Sciences, 2014
Significance Mock theta functions were introduced by Ramanujan in 1920. They have become a vivid area of research, and they continue to play important roles in different parts of mathematics and physics. In this paper, we extend the concept of holomorphic projection, which allows us to prove identities for the Fourier series ...
Imamoğlu Ö, Raum M, Richter OK
openaire   +4 more sources

Irrational Behaviour of Bilateral Mock Theta Functions of Order Seven at Infinite Number of Points

International Journal of Science and Social Science Research, 2023
At the beginning of 1920, three months before his demise, Ramanujan addressed mock theta functions in his last letter to G. H. Hardy. He presented seventeen examples, and assigned them to orders three, five, and seven.
J. Singh
semanticscholar   +1 more source

On string functions of the generalized parafermionic theories, mock theta functions, and false theta functions [PDF]

Advances in Mathematics
Kac and Wakimoto introduced the admissible highest weight representations in order to classify all modular invariant representations of the Kac--Moody algebras. For the Kac--Moody algebra $A_1^{(1)}$ the string functions of admissible representations are
Nikolay Borozenets, E. Mortenson
semanticscholar   +1 more source

New parameterized mock theta functions and Hecke-type double sums

New Zealand Journal of Mathematics
In this paper we express two new mock theta functions with one parameter as the Appell-Lerch sums using the Bailey mechanism. Meanwhile, we also obtain some Hecke-type double sums for some new $q$-series.
Li-Jun Hao, Liang-Liang Xu
semanticscholar   +1 more source

Adaptive Collision Sensitivity for Efficient and Safe Human–Robot Collaboration

Advanced Intelligent Systems, EarlyView.
An adaptive collision‐sensitivity framework uses each robot link's effective mass to estimate contact forces online and decide when collaborative robots should stop or continue. Tested on simulated and real UR10e and simulated KUKA arms, it maintains conservative force estimates while reducing unnecessary stops and increasing task productivity. What is
Lukas Rustler, Matej Misar, Matej Hoffmann   +2 more
wiley   +1 more source

Irrational Behavior of Bilateral Mock Theta Functions

International Journal of Science and Engineering Science Research
Ramanujan was the first who introduced the mock theta functions in his last letter to G. H. Hardy in January 1920. Shukla and Ahmad obtained bilateral mock theta functions of order 7, 9, …, 2r + 1, and they have shown that these functions meet the mock ...
J. Singh
semanticscholar   +1 more source

Deep Reinforcement Learning Based Autonomous Decision‐Making for Cooperative Uncrewed Aerial Vehicles: A Search and Rescue Real World Application

Journal of Field Robotics, EarlyView.
ABSTRACT This paper presents the first end‐to‐end framework that combines guidance, navigation, and centralized task allocation for multiple UAVs performing autonomous search‐and‐rescue (SAR) in GNSS‐denied indoor environments. A twin delayed deep deterministic policy gradient controller is trained with an artificial potential field (APF) reward that ...
Thomas Hickling, Maxwell Hogan, Abdulla Tammam, Nabil Aouf   +3 more
wiley   +1 more source

Dietary selectivity mediates niche overlap and interspecific competition in a reedbed warbler community in southern Europe

Ibis, EarlyView.
Sympatric species are expected to use resources differently along one or more ecological dimensions. This can be complex when there is partial separation along multiple dimensions, such as where bird species exhibit similarities in habitat use and diet.
S. R. Davies, I. P. Vaughan, R. J. Thomas, P. Josa, S. Bateman Posse, W. O. C. Symondson   +5 more
wiley   +1 more source

New Mock Theta Function Identities via Fractional q-Calculus and Bilateral ₂ψ₂ Series

Fractal and Fractional
Mock theta functions, introduced by Ramanujan in his last letter to Hardy, play a significant role in q-series theory and have natural connections to fractional q-calculus. In this paper, we study bilateral hypergeometric series of the form ψ22= ∑n=−∞∞(a,
Qiuxia Hu, Bilal Khan
doaj   +1 more source