2888 papers
This paper establishes critical exponents that determine whether solutions to a degenerate and singular parabolic equation with a time-dependent forcing term exhibit finite-time blow-up or global existence, proving that blow-up is inevitable for positive forcing exponents while identifying specific thresholds for global solvability under smallness conditions when the forcing is constant or subcritical.
This paper investigates rate-induced tipping in a moving habitat using a non-autonomous reaction-diffusion model, demonstrating that populations face extinction if the habitat's displacement rate exceeds a unique critical threshold, a phenomenon analytically characterized by heteroclinic connections between stable and unstable states.
This paper demonstrates that the focusing effect of rare fluctuations onto an optimal path, previously established in Langevin dynamics, also persists in discrete-time Markov jump processes through a framework combining large deviation theory and time reversal.
This paper presents a two-stage stochastic optimization framework, implemented in the open-source tool *OptBio*, to guide risk-adjusted investment and operational planning for diversified sugarcane-based biofuel and bioelectricity facilities under market uncertainty, demonstrating through a Brazilian case study that risk-averse strategies favor diversification while highlighting the potential viability of biomethane, hydrogen, and biochar.
This paper proposes a distributionally robust free energy principle that unifies exploration and uncertainty-aware learning to enable reliable, zero-shot robotic manipulation in real-world environments without task-specific fine-tuning.
This paper establishes a sharp criterion for the global existence versus finite-time blow-up dichotomy of solutions to an inhomogeneous coupled nonlinear Schrödinger system with quadratic interactions by utilizing variational methods, conservation laws, and sharp Gagliardo-Nirenberg inequalities relative to ground state solutions.
This paper generalizes the classical multiplicity of an ideal to graded families of ideals on Noetherian local rings, establishing that many fundamental theorems (such as Rees' theorem and the Minkowski inequality) hold for this new invariant through simple proofs based on intersection products on blow-up schemes, independent of volume theory and Okounkov bodies.
This paper introduces an extended 3-manifold topological model for high-contrast optical flow that resolves the limitations of previous torus-based approaches by identifying that the most significant motion patches are concentrated near binary step-edge circles rather than the torus, thereby offering new insights into the topological and geometric structures underlying visual data inference.
This paper presents a unified framework that proves the equivalence of variational, Green's function, and characteristic-based methods for constructing reproducing kernels, enabling a data-driven, mesh-free approach to learning kernels that accurately approximate Koopman eigenfunctions and solve various linear transport equations.
This paper classifies central extensions for the loop group of area-preserving diffeomorphisms of the 2-sphere and demonstrates that their associated Lie algebra cocycles emerge as fuzzy sphere limits of Kac-Moody cocycles for large in (twisted) loop algebras of , provided a specific rescaling by $6/k^3$.
This paper establishes the scattering rigidity of positively homogeneous Hamiltonian systems on manifolds with boundary by proving that the Hamiltonian is uniquely determined up to boundary-fixing canonical transformations via the inversion of X-ray and light ray transforms on Hamiltonian curves, a result applied to demonstrate semiglobal lens rigidity for non-trapping Finsler manifolds.
This paper proves that in a general round-robin tournament model with equally strong players, the largest scores are asymptotically almost surely distinct provided that grows to infinity while satisfying the condition .
This paper investigates sign changes in summatory functions of arithmetic functions and their Dirichlet inverses, demonstrating that convolving with specific "magic partition function" encodings can smooth oscillatory behavior to produce sequences with predictable sign properties under reasonable asymptotic bounds.
This paper proposes an efficient algorithm for minimizing total squared rate deviation in parallel Gaussian channels under a sum-power constraint by deriving a closed-form solution using the Lambert W function and a one-dimensional bisection method, which outperforms classical waterfilling and general-purpose solvers in both speed and target-tracking accuracy.
This paper introduces a Gauss-Newton method for large-scale PDE-constrained inverse problems, such as Full-Waveform Inversion, that achieves fast convergence without requiring additional PDE solves beyond those needed for gradient evaluation.
This paper establishes that the theory of lovely pairs of any complete strongly geometric field theory with quantifier elimination admits quantifier elimination when expanded with predicates for linear independence and corresponding coordinate functions, thereby generalizing Delon's results to include dense pairs of real closed and -adically closed fields.
This paper establishes conditional stability estimates and derives a priori error estimates for a finite element-based least-squares reconstruction of parameter identification problems governed by elliptic equations with power-type nonlinearity, extending and sharpening previous linear results under weaker regularity assumptions.
This paper extends the Stockwell transform to the setting of Gelfand pairs, investigates its key properties, and analyzes the associated localization operators within this framework.
This paper derives explicit formulas for general position polynomials of complete multipartite graphs and investigates their unimodality and log-concavity, demonstrating that these properties hold for balanced complete multipartite graphs with small part sizes and for coronas of various graph classes, while failing for larger part sizes.
This paper resolves an open question in convex optimization by proving that the gradient-evaluation sequence in Nesterov's accelerated gradient descent method, including in projection-based and non-Euclidean settings, achieves the optimal convergence rate for the objective function value, matching the performance of the standard solution sequence.