Results 121 to 130 of about 2,499,965 (359)
, 2000 Theorems 1 and 3 corrected (theta replaced by its inverse)
Barton, C. H., Sudbery, A.
openaire +2 more sources
First‐order Sobolev spaces, self‐similar energies and energy measures on the Sierpiński carpet
Communications on Pure and Applied Mathematics, EarlyView.Abstract For any p∈(1,∞)$p \in (1,\infty)$, we construct p$p$‐energies and the corresponding p$p$‐energy measures on the Sierpiński carpet. A salient feature of our Sobolev space is the self‐similarity of energy. An important motivation for the construction of self‐similar energy and energy measures is to determine whether or not the Ahlfors regular ...
Mathav Murugan, Ryosuke Shimizu
wiley +1 more source
A General Approach to Dropout in Quantum Neural Networks
Advanced Quantum Technologies, EarlyView., 2023 Randomly dropping artificial neurons and all their connections in the training phase reduces overfitting issues in classical neural networks, thus improving performances on previously unseen data. The authors introduce different dropout strategies applied to quantum neural networks, learning models based on parametrized quantum circuits.
Francesco Scala +3 more
wiley +1 more source
Communications on Pure and Applied Mathematics, EarlyView.Abstract We consider the global dynamics of finite energy solutions to energy‐critical equivariant harmonic map heat flow (HMHF) and radial nonlinear heat equation (NLH). It is known that any finite energy equivariant solutions to (HMHF) decompose into finitely many harmonic maps (bubbles) separated by scales and a body map, as approaching to the ...
Kihyun Kim, Frank Merle
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Benefits of Open Quantum Systems for Quantum Machine Learning
Advanced Quantum Technologies, EarlyView., 2023 Quantum machine learning (QML), poised to transform data processing, faces challenges from environmental noise and dissipation. While traditional efforts seek to combat these hindrances, this perspective proposes harnessing them for potential advantages. Surprisingly, under certain conditions, noise and dissipation can benefit QML.
María Laura Olivera‐Atencio +2 more
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Vector-Valued Polynomials and a Matrix Weight Function with B2-Action. II
Symmetry, Integrability and Geometry: Methods and Applications, 2013 This is a sequel to [SIGMA 9 (2013), 007, 23 pages], in which there is a construction of a 2×2 positive-definite matrix function K(x) on R^2. The entries of K(x) are expressed in terms of hypergeometric functions. This matrix is used in the formula for a
Charles F. Dunkl
doaj +1 more source
Deformations of Batalin-Vilkovisky algebras
, 1998 We show that a graded commutative algebra A with any square zero odd differential operator is a natural generalization of a Batalin-Vilkovisky algebra. While such an operator of order 2 defines a Gerstenhaber (Lie) algebra structure on A, an operator of ...
Kravchenko, Olga
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Communications on Pure and Applied Mathematics, EarlyView.Abstract We analyse and clarify the finite‐size scaling of the weakly‐coupled hierarchical n$n$‐component |φ|4$|\varphi |^4$ model for all integers n≥1$n \ge 1$ in all dimensions d≥4$d\ge 4$, for both free and periodic boundary conditions. For d>4$d>4$, we prove that for a volume of size Rd$R^{d}$ with periodic boundary conditions the infinite‐volume ...
Emmanuel Michta +2 more
wiley +1 more source
Quasi‐invariance of Gaussian measures for the 3d$3d$ energy critical nonlinear Schrödinger equation
Communications on Pure and Applied Mathematics, EarlyView.Abstract We consider the 3d$3d$ energy critical nonlinear Schrödinger equation with data distributed according to the Gaussian measure with covariance operator (1−Δ)−s$(1-\Delta)^{-s}$, where Δ$\Delta$ is the Laplace operator and s$s$ is sufficiently large. We prove that the flow sends full measure sets to full measure sets. We also discuss some simple
Chenmin Sun, Nikolay Tzvetkov
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