Specialty
A theorem-driven mathematical analysis identifies the regime for positive classical global solutions of a singular elliptic equation and classifies every solution in that regime.
Scientific publication3 min read
A new arXiv preprint presents a conditional mathematical theorem: every weakly stable solution of Serrin’s problem is a connected ball of radius 1. The proof handles both finite- and infinite-volume cases and extends the stated result across Euclidean dimensions n≥2.
Scientific publication4 min read
A preprint examines when a strictly increasing mapping can be given a monotone, continuous generalized inverse. It reports a unique construction under closed convexity, a whole-space extension for compact domains, and a counterexample on an open half-disk.
Scientific publication4 min read
A mathematical preprint proves one-sided semiconvexity and local mean-curvature bounds for free boundaries in the classical obstacle problem, while identifying limits on stronger geometric control.
Scientific publication3 min read
An arXiv preprint develops a visco-elastic Mullins–Sekerka system with a prescribed constant contact angle. It builds the model around perimeter, capillary, elastic and second-gradient energy terms, then constructs weak solutions through implicit time discretization.
Scientific publication4 min read
A new arXiv preprint develops a categorical version of Bayesian reversal for faithful states on infinite-dimensional von Neumann algebras. The authors show that the Petz recovery map satisfies the proposed retrodiction axioms and matches ordinary Bayesian inversion in commutative cases. They do not prove that it is the only map with those properties.
Scientific publication5 min read
An arXiv preprint presents a theorem for an isothermal van der Waals fluid model. Under tightly constrained small initial disturbances, the model has a global weak solution that converges uniformly to a selected liquid–vapor steady state. The result is mathematical, not experimental evidence about real fluids.
Scientific publication5 min read
An arXiv preprint presents a convex-integration construction for the three-dimensional incompressible Navier–Stokes equations. The result allows approximate endpoint flexibility and establishes distinct weak solutions for a dense subset of finite-energy initial data, but it does not establish exact endpoint control or nonuniqueness in the Leray–Hopf class.
Scientific publication5 min read
An arXiv preprint presents conditional Calderón–Zygmund estimates for nonlinear parabolic systems. The result concerns local mathematical regularity, not human health or experimental outcomes.
Scientific publication3 min read
A mathematical analysis finds that a restricted class of focusing nonlinear Schrödinger solutions approaches free radiation outside finitely many exceptional velocity directions. If residual mass remains, its mass and current measures settle into finitely many point-supported velocity components, while the dynamics inside the exceptional cones remain unresolved.
Scientific publication3 min read
A theoretical operator-algebra analysis gives conditional characterizations of positive contractive projections and rectangular projection ranges. It also shows why positivity and complete isometry cannot be dropped from the main result.
Scientific publication5 min read
A numerical preprint reports that TDPSAC remained stable across a larger simulated canal-flow deviation and achieved the strongest results among the learning-based controllers tested.
Scientific publication5 min read
An arXiv preprint presents a mathematical construction in which a smooth random flow is linked to sustained exponential growth of a specified magnetic field. The proof uses selected Fourier modes, a tridiagonal solution operator and probabilistic bounds, while the authors stress that the result is not a general theory.
Scientific publication4 min read
An arXiv preprint proposes a nested-derivative method for identifying when certain nonlinear partial differential equations may have elementary solutions in space. The paper develops conditional criteria and symbolic examples rather than testing measurements or physical systems.
Scientific publication3 min read
A version-one arXiv preprint presents an elementary maximum-principle proof for bounding the largest principal curvature inside solutions to prescribed curvature quotient equations. The result is conditional, local and theoretical: it does not provide an empirical measurement or a global or boundary estimate.
Scientific publication4 min read
A theoretical analysis turns a one-dimensional infiltration–hydration problem into explicit formulas and describes how the moving front changes its behavior across mathematical parameter regimes.
Scientific publication5 min read
A new arXiv preprint develops necessary-and-sufficient capacity criteria for bounded and compact embeddings from QK spaces into L2(μ), and uses them to characterize Volterra and multiplication operators.
Scientific publication3 min read
A mathematical preprint reports that finite lower order is enough to make one-third-power Nevanlinna defect sums converge for general-position hyperplanes, with a corresponding result for bounded-degree divisors.
Scientific publication5 min read
A new arXiv preprint identifies the exact leading constant in Schäffer’s determinant–inverse matrix inequality. The authors prove that the optimal universal constant, divided by √n, tends to √e, and construct explicit norms and matrices that reach the same asymptotic ratio.
Scientific publication5 min read
A new arXiv preprint studies what happens to one-dimensional run-and-tumble models as diffusivity approaches zero. The analysis finds that one moving component can retain a concentrated mass at the boundary and derives a dynamic law for that mass under stated assumptions.
Scientific publication5 min read
An arXiv preprint develops sharp regularity bounds for stable stationary harmonic maps into round spheres. It also proves rigidity for certain tangent maps and gives a lower bound for the Morse index of nonconstant harmonic maps between spheres.
Scientific publication5 min read
An arXiv preprint gives a mathematical proof that the full horizontal Riesz transform has weak-type constant at most 2 for real-valued inputs on stratified Lie groups. The result is uniform across the groups’ listed dimension and structural parameters, but the paper is theoretical rather than empirical and does not establish optimality or broader generality.
Scientific publication5 min read
A mathematical arXiv preprint finds that a bounded H∞-calculus alone need not deliver stochastic maximal regularity for a constructed operator, while deriving exact conditions for selected operators and spaces.
Scientific publication3 min read
A new arXiv preprint develops asymptotic formulas for recovering phase-related far-field information from intensity measurements at two points. It also examines recovery on a distant plane, but the method depends on geometry and has not been tested with physical or noisy data.
Scientific publication5 min read