Results 81 to 90 of about 969 (189)
Invariant Measure and Universality of the 2D Yang–Mills Langevin Dynamic
Communications on Pure and Applied Mathematics, Volume 79, Issue 8, Page 1973-2102, August 2026.ABSTRACT We prove that the Yang–Mills (YM) measure for the trivial principal bundle over the two‐dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge‐fixing and Bourgain's method for invariant measures ...
Ilya Chevyrev, Hao Shen
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Lower semicontinuity, optimization and regularity of variational problems under general PDE constraints [PDF]
, 2018 We investigate variational properties of integral functionals defined on spaces of measures satisfying a general PDE constraint. The study of these properties is motivated by the following three problems: existence of solutions, optimality conditions of ...
Arroyo Rabasa, Adolfo
core
AI in chemical engineering: From promise to practice
AIChE Journal, Volume 72, Issue 7, July 2026.Abstract Artificial intelligence (AI) in chemical engineering has moved from promise to practice: physics‐aware (gray‐box) models are gaining traction, reinforcement learning complements model predictive control (MPC), and generative AI powers documentation, digitization, and safety workflows.
Jia Wei Chew +4 more
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Local and global well-posedness of SPDE with generalized coercivity conditions
, 2013 In this paper we establish the local and global existence and uniqueness of solutions for general nonlinear evolution equations with coefficients satisfying some local monotonicity and generalized coercivity conditions.
Röckner, Michael, Liu, Wei
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Existence of Full Replica Symmetry Breaking for the Sherrington–Kirkpatrick Model at Low Temperature
Communications on Pure and Applied Mathematics, Volume 79, Issue 7, Page 1746-1770, July 2026.ABSTRACT We verify the existence of full replica symmetry breaking (FRSB) for the Sherrington–Kirkpatrick (SK) model and determine the structure of its Parisi measure slightly beyond the high temperature regime. More specifically, we prove that the support of the Parisi measure for the SK model consists of an interval starting at the origin slightly ...
Yuxin Zhou
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Local Polynomial Regression and Filtering for a Versatile Mesh‐Free PDE Solver
International Journal for Numerical Methods in Fluids, Volume 98, Issue 7, Page 804-839, July 2026.A high‐order, mesh‐free finite difference method for solving differential equations is presented. Both derivative approximation and scheme stabilisation is carried out by parametric or non‐parametric local polynomial regression, making the resulting numerical method accurate, simple and versatile. Numerous numerical benchmark tests are investigated for
Alberto M. Gambaruto
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Numerical Methods for Partial Differential Equations, Volume 42, Issue 4, July 2026.ABSTRACT The main purpose of this paper is to design a fully discrete local discontinuous Galerkin (LDG) scheme for the generalized Benjamin–Ono equation. First, we prove the L2$$ {L}^2 $$‐stability for the proposed semi‐discrete LDG scheme and obtained a suboptimal order of convergence for power nonlinear flux.
Mukul Dwivedi, Tanmay Sarkar
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Numerical Methods for Partial Differential Equations, Volume 42, Issue 4, July 2026.ABSTRACT While recent Anderson acceleration (AA) convergence theory [Pollock et al., IMA Num. An., 2021] requires that the AA optimization norm match the Hilbert space norm associated with the fixed point operator, in implementations the ℓ2$$ {\ell}^2 $$ norm is the most common choice. So far there is little research done regarding this discrepancy. To
Elizabeth Hawkins, Leo G. Rebholz
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Journal of Clinical Periodontology, Volume 53, Issue 7, Page 1226-1252, July 2026.ABSTRACT Aim To synthesize evidence on gingival diseases and conditions in children and adolescents (< 18 years) without known systemic disorder involvement, focusing on their distribution, aetiology, diagnosis, management and oral health–related quality of life (OHRQoL).
Georgios Tsilingaridis +4 more
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Symmetries and exact solutions of a (2+1)-dimensional sine-Gordon system
, 1996 We investigate the classical and non-classical reductions of the (2 + 1)-dimensional sine-Gordon system of Konopelchenko and Rogers, which is a strong generalization of the sine-Gordon equation. A family of solutions obtained as a non-classical reduction
Clarkson, Peter +2 more
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