Specialty
A mathematical preprint proposes a Fourier-based proof for real-frequency mode stability in subextremal Kerr, using dual solutions and a boundary calculation to show that the specified quasinormal modes are the zero solution.
Scientific publication4 min read
A mathematical preprint constructs special small initial data for a quasilinear Schrödinger equation whose high-regularity Sobolev norm later becomes arbitrarily large. The result is an existence proof for selected data, not a claim about typical solutions.
Scientific publication4 min read
A mathematical preprint adapts a refined Schreyer workflow to exterior-algebra resolutions, states that its lifting procedures terminate and that the resulting algorithm returns the required syzygy basis, and illustrates a BGG cohomology route. A proposed parallel formulation remains untested for speed and scale.
Scientific publication3 min read
A theoretical preprint maps the spectral conditions behind β0(H), identifies the largest class that survives every compact perturbation, and proves that β(H) is dense in the full bounded-operator algebra.
Scientific publication4 min read
A mathematical analysis finds that prey can spread at one model threshold, while predator expansion varies by direction and is limited by the smaller of two modeled speeds.
Scientific publication4 min read
A mathematical preprint reports that the cone's frequency separates two regimes: global solutions are ruled out at or above it and form an ordered family below it.
Scientific publication3 min read
The paper classifies a diagonal operator, separates two geometric tests, and extends its stochastic-convolution analysis to the Laplacian.
Scientific publication4 min read
A proof-based analysis of stratified Lie groups finds uniform control for the full horizontal Riesz transform through p = 2, but no universal high-p bound.
Scientific publication4 min read
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.
Scientific publication4 min read
A theorem-driven study gives coefficient, growth and function-space bounds for K-quasiconformal harmonic mappings, while leaving key sharpness questions open.
Scientific publication4 min read
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.
Scientific publication5 min read
A symbolic study of real Cayley-Dickson algebras constructs a six-cycle and a double-hexagon graph, then sets out conditional rules for subalgebras and basis-form zero divisors.
S. Zhilina, Orthogonality graphs of real Cayley-Dickson algebras. Part I: Doubly alternative zero divisors and their hexagons, Int. J. Algebra Comput. 31(4) (2021) 663-6894 min read
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.
Scientific publication5 min read
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.
Scientific publication4 min read
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.
Scientific publication3 min read
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.
Scientific publication4 min read
A proof-based analysis on the complex sphere reports uniform bilinear bounds across several exponent ranges, with a lower smoothness threshold for restricted inputs.
Scientific publication4 min read
A mathematical study finds that a carefully defined graph built from selected zero divisors can recover key parameters of real Cayley-Dickson algebras, although the result does not apply unchanged to the full graph or the lowest dimensions.
S. Zhilina, Orthogonality graphs of real Cayley-Dickson algebras. Part II: The subgraph on pairs of basis elements, Int. J. Algebra Comput. 31(4) (2021) 691-7253 min read
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.
Scientific publication4 min read
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.
Scientific publication4 min read
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.
Scientific publication3 min read
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.
Scientific publication5 min read
A mathematical preprint describes linked torsion-theoretic, categorical and quotient-ring characterizations of hereditary QF-3+ rings.
Scientific publication4 min read
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.
Scientific publication4 min read
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.
Scientific publication3 min read
The conditional theorem applies to a narrowly defined class of almost periodic initial data and also covers a structured analytic quasiperiodic subclass.
Scientific publication4 min read
A theoretical analysis identifies the precise symbol classes for metric boundedness of two Volterra-type operators on area Nevanlinna spaces.
Scientific publication3 min read
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.
Scientific publication3 min read
A new arXiv preprint presents geometric refinements of Osgood-type criteria, with conditional theorems for smooth, decaying stationary Navier-Stokes solutions in R3.
Scientific publication4 min read
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.
Scientific publication3 min read
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.
Scientific publication4 min read
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.
Scientific publication4 min read
A mathematical preprint adds a squared relative-distance remainder to Carlson's integral inequality and carries the analysis into discrete and finite-sum settings.
Scientific publication3 min read
The result applies to a coupled bulk-surface model under stated assumptions, and its evidence is analytical rather than empirical.
Scientific publication3 min read
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.
Scientific publication3 min read
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.
Scientific publication4 min read
A mathematical analysis of a radially symmetric reaction–diffusion model identifies three long-term regimes and a logarithmic correction to the spreading front.
Scientific publication4 min read
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.
Scientific publication3 min read
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.
Scientific publication3 min read
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.
Scientific publication4 min read