The celebrated 1975 Kuramoto model of $N$ identical oscillators with phase angle vector $\boldsymbol{\vartheta}=(\vartheta_1,\ldots,\vartheta_N)$ and all-to-all coupling reads \begin{equation} \label{*} \dot\vartheta_j\,=\tfrac{1}{N}\sum_{k=1}^N \sin...
We describe a task and motion planning architecture for highly dynamic systems that combines a domain-independent sampling-based deliberative planning algorithm with a global reactive planner. We leverage the recent development of a reactive, vector...
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I'm in Linear Algebra right now and we're mostly just working with vector spaces, but they're introducing us to the basic concepts of fields and groups in preparation taking for Abstract Algebra la...
We define Dorfman connections, which are to Courant algebroids what connections are to Lie algebroids. Several examples illustrate this analogy. A linear connection $\nabla\colon \mathfrak{X}(M)\timesΓ(E)\toΓ(E)$ on a vector bundle $E$ over a smoot...
In mathematics, a Hermitian connection ∇ {\displaystyle \nabla } is a connection on a Hermitian vector bundle E {\displaystyle E} over a smooth manifold
Building upon previous works characterizing GRW space-times using concircular and torse-forming vectors, this paper investigates a Lorentzian manifold equipped with a concircularly semi-symmetric metric connection. We demonstrate that such a manifold...
Random vector functional link (RVFL), a variant of single-layer feedforward neural network (SLFN), has garnered significant attention due to its lower computational cost and robustness to overfitting. Despite its advantages, the RVFL network's relian...
Support vector regression (SVR) has garnered significant popularity over the past two decades owing to its wide range of applications across various fields. Despite its versatility, SVR encounters challenges when confronted with outliers and noise, p...
Quantum models based on the mathematics of quantum mechanics (QM) have been developed in cognitive sciences, game theory and econophysics. In this work a generalization of credit loans is introduced by using the vector space formalism of QM. Operator...
H. Cartan in his book on differential calculus proved a theorem generalizing a Cauchy's mean-value theorem to the case of functions taking values in a Banach space. Cartan used this theorem in a masterful way to develop the entire theory of diffe...
In this paper, we demonstrate the emergence of non-degenerate bright solitons and summarize their several interesting features in a completely integrable two-component long-wave-short-wave resonance interaction model with a general form of nonlineari...
In recent times, bound soliton states have often been referred to as soliton molecules in the nonlinear optics literature. The striking analogies between photonic bound states and matter molecular structures in chemistry and physics have intensified...
In this paper, we investigate the problem of electromagnetic wave propagation in hyperbolic nonlinear media. To address this problem, we consider the scalar hyperbolic nonlinear Schrödinger system and its coupled version, namely hyperbolic Manakov t...
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Magneto conductance oscillations periodic in flux with periodicity $Φ_{0}$ and $Φ_{0}/2$ are seen in asymmetric Aharonov-Bohm rings as a function of density of electrons or Fermi wave vector. Dephasing of these oscillations is incorporated using...