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Convolution integrals --- Fractures materials --- Thermodynamics

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Complex analysis --- 512 --- Algebra --- 512 Algebra --- Analyse fonctionnelle --- Functional analysis --- Functional analysis. --- Fourier, Transformations de --- Convolution

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This book provides comprehensive information on the main aspects of Bernstein operators, based on the literature to date. Bernstein operators have a long-standing history and many papers have been written on them. Among all types of positive linear operators, they occupy a unique position because of their elegance and notable approximation properties. This book presents carefully selected material from the vast body of literature on this topic. In addition, it highlights new material, including several results (with proofs) appearing in a book for the first time. To facilitate comprehension, exercises are included at the end of each chapter. The book is largely self-contained and the methods in the proofs are kept as straightforward as possible. Further, it requires only a basic grasp of analysis, making it a valuable and appealing resource for advanced graduate students and researchers alike.

Mathematics. --- Approximation theory. --- Approximations and Expansions. --- Operator theory. --- Bernstein polynomials. --- Convolutions (Mathematics) --- Convolution transforms --- Transformations, Convolution --- Distribution (Probability theory) --- Functions --- Integrals --- Transformations (Mathematics) --- Polynomials, Bernstein --- Convergence --- Probabilities --- Series --- Functional analysis --- Math --- Science --- Theory of approximation --- Polynomials --- Chebyshev systems

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Convolutions (Mathematics) --- Convolucions (Matemàtica) --- Convolution transforms --- Transformations, Convolution --- Distribution (Probability theory) --- Functions --- Integrals --- Transformations (Mathematics) --- Transformacions de convolució --- Transformades de convolució --- Distribució (Teoria de la probabilitat) --- Funcions --- Transformacions (Matemàtica)

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This paper presents different deep neural network architectures designed to forecast the distribution of returns on a portfolio of U.S. Treasury securities. A long short-term memory model and a convolutional neural network are tested as the main building blocks of each architecture. The models are then augmented by cross-sectional data and the portfolio's empirical distribution. The paper also presents the fit and generalization potential of each approach.

Convolution --- Long Short-Term Memory --- LSTM --- Machine Learning --- Macroeconomics and Economic Growth --- Market Risk --- Neural Networks --- Taxation and Subsidies