The construction of algebraic structure of central molecular chirality is provided starting from the empirical Fischer projections for tetrahedrons. A matrix representation is given and the algebra of O(4) orthogonal group for rotations and inversions is identified. The result can be generalized to chains of connected tetrahedrons.
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http://dx.doi.org/10.1002/chir.10239 | DOI Listing |
Cogn Neurodyn
December 2025
Department of Mathematics, Quaid-I-Azam University, Islamabad, Pakistan.
Algebraic structures are highly effective in designing symmetric key cryptosystems; however, if the key space is not sufficiently large, such systems become vulnerable to brute-force attacks. To address this challenge, our research focuses on enlarging the key space in symmetric key schemes by integrating the non-chain ring with a four-dimensional chaotic system. While chaotic maps offer significant potential for data processing, relying solely on them does not fully leverage their operational advantages.
View Article and Find Full Text PDFNeural Netw
December 2024
Department of Earth Science and Engineering, Imperial College London, Prince Consort Road, London SW7 2BP, UK; Centre for AI-Physics Modelling, Imperial-X, White City Campus, Imperial College London, W12 7SL, UK.
Machine learning (ML) has benefited from both software and hardware advancements, leading to increasing interest in capitalising on ML throughout academia and industry. There have been efforts in the scientific computing community to leverage this development via implementing conventional partial differential equation (PDE) solvers with machine learning packages, most of which rely on structured spatial discretisation and fast convolution algorithms. However, unstructured meshes are favoured in problems with complex geometries.
View Article and Find Full Text PDFSci Rep
January 2025
Department of Mathematics, College of Science, King Khalid, University, Abha, 61413, Saudi Arabia.
Algebraic structures play a vital role in securing important data. These structures are utilized to construct the non-linear components of block ciphers. Since constructing non-linear components through algebraic structures is crucial for the confusion aspects of encryption schemes, relying solely on these structures can result in limited key spaces.
View Article and Find Full Text PDFData Brief
February 2025
Institut Camille Jordan, UMR-CNRS 5208, École Centrale de Lyon, 36 Avenue Guy de Collongue, 69134, Écully, France.
The dataset presented contains the experimental structural response, in the frequency domain, of a suspended steel plate to a point force excitation. The plate is excited by a mechanical point force generated by a Brüel & kJær shaker with a white noise signal input from 3.125 Hz to 2000 Hz.
View Article and Find Full Text PDFRep Prog Phys
January 2025
SISSA, via Bonomea 265, 34136 Trieste, Trieste, 34136, ITALY.
We review recent progress regarding the double scaled Sachdev-Ye-Kitaev model and other p-local quantum mechanical random Hamiltonians. These models exhibit an expansion using chord diagrams, which can be solved by combinatorial methods. We describe exact results in these models, including their spectrum, correlation functions, and Lyapunov exponent.
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