Daily Papers

We investigate the first-order differential calculus over extended metric-topological measure spaces. The latter are quartets mathbb X=(X,τ,{sf d},mathfrak m), given by an extended metric space (X,{sf d}) together with a weaker topology τ (satisfying suitable compatibility conditions) and a finite Radon measure mathfrak m on (X,τ). The class of extended metric-topological measure spaces encompasses all metric measure spaces and many infinite-dimensional metric-measure structures, such as abstract Wiener spaces. In this framework, we study the following classes of objects: - The Banach algebra {rm Lip}_b(X,τ,{sf d}) of bounded τ-continuous {sf d}-Lipschitz functions on X. - Several notions of Lipschitz derivations on X, defined in duality with {rm Lip}_b(X,τ,{sf d}). - The metric Sobolev space W^{1,p}(mathbb X), defined in duality with Lipschitz derivations on X. Inter alia, we generalise both Weaver's and Di Marino's theories of Lipschitz derivations to the extended setting, and we discuss their connections. We also introduce a Sobolev space W^{1,p}(mathbb X) via an integration-by-parts formula, along the lines of Di Marino's notion of Sobolev space, and we prove its equivalence with other approaches, studied in the extended setting by Ambrosio, Erbar and Savaré. En route, we obtain some results of independent interest, among which are: - A Lipschitz-constant-preserving extension result for τ-continuous {sf d}-Lipschitz functions. - A novel and rather robust strategy for proving the equivalence of Sobolev-type spaces defined via an integration-by-parts formula and those obtained with a relaxation procedure. - A new description of an isometric predual of the metric Sobolev space W^{1,p}(mathbb X).

Synthesizing physically plausible articulated human-object interactions (HOI) without 3D/4D supervision remains a fundamental challenge. While recent zero-shot approaches leverage video diffusion models to synthesize human-object interactions, they are largely confined to rigid-object manipulation and lack explicit 4D geometric reasoning. To bridge this gap, we formulate articulated HOI synthesis as a 4D reconstruction problem from monocular video priors: given only a video generated by a diffusion model, we reconstruct a full 4D articulated scene without any 3D supervision. This reconstruction-based approach treats the generated 2D video as supervision for an inverse rendering problem, recovering geometrically consistent and physically plausible 4D scenes that naturally respect contact, articulation, and temporal coherence. We introduce ArtHOI, the first zero-shot framework for articulated human-object interaction synthesis via 4D reconstruction from video priors. Our key designs are: 1) Flow-based part segmentation: leveraging optical flow as a geometric cue to disentangle dynamic from static regions in monocular video; 2) Decoupled reconstruction pipeline: joint optimization of human motion and object articulation is unstable under monocular ambiguity, so we first recover object articulation, then synthesize human motion conditioned on the reconstructed object states. ArtHOI bridges video-based generation and geometry-aware reconstruction, producing interactions that are both semantically aligned and physically grounded. Across diverse articulated scenes (e.g., opening fridges, cabinets, microwaves), ArtHOI significantly outperforms prior methods in contact accuracy, penetration reduction, and articulation fidelity, extending zero-shot interaction synthesis beyond rigid manipulation through reconstruction-informed synthesis.

In this paper, a mathematical model is developed to describe the evolution of the concentration of compounds through a gas chromatography column. The model couples mass balances and kinetic equations for all components. Both single and multiple-component cases are considered with constant or variable velocity. Non-dimensionalisation indicates the small effect of diffusion. The system where diffusion is neglected is analysed using Laplace transforms. In the multiple-component case, it is demonstrated that the competition between the compounds is negligible and the equations may be decoupled. This reduces the problem to solving a single integral equation to determine the concentration profile for all components (since they are scaled versions of each other). For a given analyte, we then only two parameters need to be fitted to the data. To verify this approach, the full governing equations are also solved numerically using the finite difference method and a global adaptive quadrature method to integrate the Laplace transformation. Comparison with the Laplace solution verifies the high degree of accuracy of the simpler Laplace form. The Laplace solution is then verified against experimental data from BTEX chromatography. This novel method, which involves solving a single equation and fitting parameters in pairs for individual components, is highly efficient. It is significantly faster and simpler than the full numerical solution and avoids the computationally expensive methods that would normally be used to fit all curves at the same time.

The analytical formulae for the phase space factors and the three-momenta of three- and four-body final states are derived for all sets of independent kinematic variables containing invariant mass variables. These formulae will help experimental physicist to perform the data analysis. As an example, we show how to use these formulae to distinguish the different mechanisms of e+pto e+J/ψ+ p process for searching the signals of P_c states at the energy region of Electron-Ion collider at China (EicC).