Specialty
A theorem for a planar Neumann reaction-diffusion model finds that sufficiently large diffusion recovers the scalar pattern of decay, threshold behavior and blow-up across bounded H1 data, while the worst-case stabilization cost grows on an exponential scale set by the square of the H1 radius.
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A theorem-driven study gives coefficient, growth and function-space bounds for K-quasiconformal harmonic mappings, while leaving key sharpness questions open.
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A mathematical preprint derives a boundary observability estimate for critically singular wave equations on general domains. The theorem depends on convexity and a sufficiently long observation time, and the authors say it does not establish boundary controllability.
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The results sharply restrict which derivations can remain locally finite, while the differential cases depend on the degree and square-free status of a defining polynomial.
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A mathematical preprint states that locally bounded weak solutions in a class of nonlocal equations are locally Hölder continuous when the interaction measure meets specified structural conditions.
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A mathematical preprint gives a boundary-vanishing test for compactness in a class of single Toeplitz operators, but finds that the test can fail for products.
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A mathematical analysis proves a uniform critical-endpoint regularity bound under uniform equi-integrability, while a constructed counterexample shows bounded source norms alone are insufficient.
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A proof-based analysis on the complex sphere reports uniform bilinear bounds across several exponent ranges, with a lower smoothness threshold for restricted inputs.
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A theoretical preprint examines two abstract Kirchhoff-Pohozaev wave models, reporting global Sobolev results while showing that bounded H^1 data alone cannot ensure uniform control.
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A mathematical preprint ties the exact number of nodes needed for an L2-norm formula to Hadamard-matrix existence, while positive-weight rules can raise the count in some dimensions.
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A new mathematics preprint gives an exact characterization of when a complex symplectic matrix can have a nonzero bounded operator intertwining the complexified Schrödinger representation. The result is formal, with no empirical data or human participants.
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A new arXiv preprint develops a conditional mathematical framework for a fractional one-Laplacian evolution equation. It identifies theorem-based regimes for global weak and strong solutions, finite-time extinction, finite-time blow-up, and selected high-energy outcomes. The work analyzes an abstract model rather than data, participants or real-world cases.
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A mathematical preprint describes linked torsion-theoretic, categorical and quotient-ring characterizations of hereditary QF-3+ rings.
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An arXiv preprint reports polynomial stabilization for a damped, linearized periodic Whitham-Boussinesq system. The sharpest result applies when first-component damping vanishes across an open region.
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A mathematical proof shows that the best coefficient in the three-dimensional lattice Hardy inequality is 1/4, matching the continuous value, while no nonzero finitely supported function achieves equality.
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The conditional theorem applies to a narrowly defined class of almost periodic initial data and also covers a structured analytic quasiperiodic subclass.
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A theoretical analysis identifies the precise symbol classes for metric boundedness of two Volterra-type operators on area Nevanlinna spaces.
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A mathematical theorem reports global existence and uniqueness of strong solutions for a two-dimensional stress-diffusive Oldroyd-B problem under specific domain and initial-data conditions.
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A new arXiv preprint presents geometric refinements of Osgood-type criteria, with conditional theorems for smooth, decaying stationary Navier-Stokes solutions in R3.
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A mathematical preprint finds that the second cohomology of a truncated Novikov algebra changes sharply with the parameter: it vanishes outside the prime field, has dimension three for odd primes inside it, and dimension four in the characteristic-two case.
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A theoretical analysis of the two-component Hunter-Saxton system describes global solutions, an explicit rule for post-breaking energy loss, and a kink-wave profile at large times.
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A preprint develops a theoretical framework for sparse domination, weighted estimates, commutators and duality in abstract Orlicz-Morrey spaces with a ball-basis. Its conclusions are conditional mathematical statements, not results from participants or observational data.
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A mathematical preprint adds a squared relative-distance remainder to Carlson's integral inequality and carries the analysis into discrete and finite-sum settings.
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The result applies to a coupled bulk-surface model under stated assumptions, and its evidence is analytical rather than empirical.
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A mathematical preprint constructs smooth radial kernels that are strictly positive definite in Euclidean space but fail positive definiteness on spheres for every covered even dimension and support radius. Together with a cited odd-dimensional result, it states that direct transfer holds exactly in odd dimensions.
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A preprint reports a nonnegativity result for a spectral quadratic form and applies the framework to curvature and Hessian estimates that remain conditional on strong assumptions.
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A mathematical analysis of a radially symmetric reaction–diffusion model identifies three long-term regimes and a logarithmic correction to the spreading front.
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A theoretical study of a critical quasilinear Schrödinger equation on the Heisenberg group reports existence for positive λ and nonexistence for nonpositive λ, but only within a narrowly defined class of potentials, exponents and weak solutions.
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An arXiv preprint gives an affirmative proof for a question in operator algebra, using unitary, Wiener–Hopf and Mellin-transform representations to build an explicit factorization.
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A mathematical preprint constructs a family of finite rings whose null ideals are not two-sided and proves two-sidedness when the Jacobson radical has nilpotency at most 3.
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A preprint on steady Euler flows finds that smooth far-field profiles can support non-shear solutions under a stated condition, while a dense analytic family is rigid.
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A variational analysis of the divergence equation places the Bogovskii constant at or above the spatial dimension and identifies balls as minimizers. It also examines when variational extrema are attained and how ellipsoids and annuli alter the bounds.
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A mathematics preprint proves that the Cœuré–Loeb fibration can be identified with the complement of an analytic subset in a Stein space. The result changes how this example relates to the smooth open-immersion problem, but it does not show that the original space is Stein or settle the general question.
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A preprint reports that nonnegative concave functions leave the best constant unchanged in a Lee-type Schatten inequality for finite complex matrix families.
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An arXiv preprint presents a weighted Morrey-space bound for sparse operators, extends it under a stated domination condition, and identifies results that still need fuller proof.
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A mathematical preprint presents a Fourier- and distribution-based proof of real-frequency mode stability for a specified Teukolsky class on Kerr, while describing the associated dual modes and the limits of the argument.
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A mathematical analysis finds a direction-specific critical norm profile, exact one-prime equality cases and a certified way to approximate the squared norm with finite matrices.
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A version 1 arXiv preprint presents a real meromorphic function whose preimages of 0, 1 and infinity stay on the real axis, while every other value has a non-Blaschke point divisor in both half-planes.
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A mathematical preprint shows that a known smoothness guarantee is the best possible general bound for isotropic positive definite functions on every even-dimensional sphere.
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A mathematical preprint proves that the free square contains infinitely many pairwise non-unitarily equivalent free extreme points at matrix level 2, and reports related structural results for polygons, graded lifts and polytopes.
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