Analytic Continual
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Simultaneous recovery of multiple parameters in nonlocal diffusion equations from internal measurements
Announce Type: new Abstract: This paper is devoted to simultaneously recovering multiple parameters from internal measurements for nonlocal diffusion equations. The uniqueness of the inverse problem is established by employing the asymptotic behavior of solutions, analytic continuation, the Laplace transform, and properties of analytic functions. For numerical reconstruction, we apply the Levenberg-Marquardt method to obtain a stable approximate solution of the inverse problem.
A Unified Framework for Virtual Wave Transform: From Generalized Formulation to Excitation-Specific Projection
Announce Type: cross Abstract: We present a unified theoretical framework for the mapping between diffusive and wave-like dynamics, formulated as a spectral integral operator acting on temporal fields. By introducing an analytic continuation in the complex frequency plane, we establish an explicit correspondence between thermal diffusion and a virtual wave field governed by a hyperbolic equation. This mapping is shown to define a causal, compact Fredholm operator that acts as a nonstationary...
‘Coal power has lost its status’: Solar power outstrips coal in US despite Trump's attacks
States won by Trump in the 2024 election accounted for 74 per cent of all solar capacity installed in the first quarter of 2026. Even as President Donald Trump boosts coal over clean energy, solar power is hitting new milestones in the US and remains the leading source of new power. Data released on 10 June by global energy think tank Ember, along with a report by the Solar Energy Industries Association (SEIA) and analytics firm Wood Mackenzie, show the continued growth of solar and decline...
The Whitney method of fundamental solutions with Lusin wavelets
Announce Type: replace Abstract: We establish the theoretical foundation for a variant of the method of fundamental solutions (MFS), where the source points $\{q_j\}_{j=1}^\infty$ accumulate towards the domain in a Whitney fashion, meaning that their separation is proportional to the distance to the domain. We prove that the normalized Lusin wavelets $\psi_j(w) = b_j(w-q_j)^{-2}$ constitute a generalized basis, known as a frame, for the Hardy subspace of $L_2$-traces of holomorphic functions...
Towards Efficient and Exact Forgetting Services in Pre-Trained-Model-based Continual Learning
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Improving Heart-Focused Medical Question Answering in LLMs via Variance-Aware Rubric Rewards with GRPO
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Exterior complex scaling enables physics-informed neural networks for quantum scattering
arXiv:2602.04553v2 Announce Type: replace-cross Abstract: Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving differential equations, yet their application to nuclear scattering has been hindered by the oscillatory, non-decaying nature of scattering wave functions. In this work, I demonstrate that exterior complex scaling (ECS) transforms scattering boundary conditions into exponentially decaying waves suitable for neural network solutions, enabling PINNs to...
Brain scans reveal two distinct types of autism
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Russian crude here to stay? Why India-US energy ties may be more about LPG, LNG than oil
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Baby items, meal deliveries: ATO warns taxpayers to stop 'unusual' claims
Tax time 2026: ATO warns millions of Aussies chasing tax deductions to stop with 'unusual' claims Tue 2 Jun 2026 at 4:48am The tax office is warning Australians to stop claiming private expenses on their tax returns, with some attempting to claim baby expenses, personal gifts and meal deliveries as work-related. More than 10 million Australians have claimed about $31 billion worth of work-related expenses in their 2024-25 tax returns so far, many relating to working from home. The average...