Results 81 to 90 of about 76,798 (219)
A Banach algebra of generalized functions
Journal of Mathematical Analysis and Applications, 1973 AbstractAn algebraic isomorphism from a convolution algebra of Laplace transformable functions with support on the half-line to a complete discrete normed convolution algebra of sequences is used to construct generalized functions. The extension of this function-to-sequence map to a commutative Banach algebra of generalized functions is shown to be a ...
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DeepSeek in Education: Exploring the Transformative Potential of AI‐Driven Educational Intelligence
Future in Educational Research, EarlyView.ABSTRACT The integration of artificial intelligence into education remains challenged by issues of scalability, interpretability, and multimodal adaptability. DeepSeek's AI‐driven educational tools show potential to improve educational applications through advances in reasoning efficiency, lightweight deployment, and multimodal fusion.
Jian Liao, Fan Sun, Yajie Liu, Yuli Hu
wiley +1 more source
Pointvalue characterizations in multi-parameter algebras [PDF]
We extend classical results from the Colombeau algebra, concerning point-value characterizations of generalized functions, to the more general case of multi-parameter (C,E,P)–algebras. Our investigations include considerations about different definitions
Jean-André Marti, Maximilian Hasler
core
International Journal for Numerical Methods in Fluids, EarlyView.We introduce new efficient and accurate first order finite volume‐type numerical schemes, for the non‐conservative one‐dimensional blood flow equations with transport, taking into account different velocity profiles. The framework is the flux‐vector splitting approach of Toro and Vázquez‐Cendón (2012), that splits the system in two subsystems of PDEs ...
Alessandra Spilimbergo +3 more
wiley +1 more source
Coherent Forecasting of Realized Volatility
Journal of Forecasting, EarlyView.ABSTRACT The QLIKE loss function is the stylized favorite of the literature on volatility forecasting when it comes to out‐of‐sample evaluation and the state of the art model for realized volatility (RV) forecasting is the HAR model, which minimizes the squared error loss for in‐sample estimation of the parameters.
Marius Puke, Karsten Schweikert
wiley +1 more source
Monodromies of generic real algebraic functions
Topology and its Applications, 1999 Consider real holomorphic functions \(f:{\mathcal C}\to\mathbb{P}^1\) (where \({\mathcal C}\) is a compact connected Riemann surface of genus \(g)\) such that \(f\) has at most one non-generic critical value. The monodromies of such functions can be described in terms of labeled graphs.
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Rational points in a family of conics over F2(t)$\mathbb {F}_2(t)$
Mathematische Nachrichten, EarlyView.Abstract Serre famously showed that almost all plane conics over Q$\mathbb {Q}$ have no rational point. We investigate versions of this over global function fields, focusing on a specific family of conics over F2(t)$\mathbb {F}_2(t)$ which illustrates new behavior.
Daniel Loughran, Judith Ortmann
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Generalized Function Algebras Containing Spaces of Periodic Ultradistributions [PDF]
, 2017 We construct differential algebras in which spaces of (one-dimensional) periodic ultradistributions are embedded. By proving a Schwartz impossibility type result, we show that our embeddings are optimal in the sense of being consistent with the pointwise multiplication of ordinary functions.
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Mathematical Methods in the Applied Sciences, EarlyView.We develop a full randomization of the classical hyper‐logistic growth model by obtaining closed‐form expressions for relevant quantities of interest, such as the first probability density function of its solution, the time until a given fixed population is reached, and the population at the inflection point.
Juan Carlos Cortés +2 more
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Mathematical Methods in the Applied Sciences, EarlyView.A highly accurate numerical method is given for the solution of boundary value problem of generalized Bagley‐Torvik (BgT) equation with Caputo derivative of order 0<β<2$$ 0<\beta <2 $$ by using the collocation‐shooting method (C‐SM). The collocation solution is constructed in the space Sm+1(1)$$ {S}_{m+1}^{(1)} $$ as piecewise polynomials of degree at ...
Suzan Cival Buranay +2 more
wiley +1 more source