Subject
Proofs, structures, equations, geometry, topology, and applied mathematics.
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
The study uses spectral and character-based calculations to separate graph constructions where proper fractional revival is impossible from those where exact algebraic conditions allow it.
Scientific publication4 min read
A mathematical preprint gives conditional existence results for connected partitions of weighted finite and countably infinite graphs. Its ladder examples show that Dirichlet, Neumann and boundaryless rules can select different minimizing shapes—and that unit weights can make parts of the infinite problem ill-defined.
Scientific publication3 min read
A new arXiv preprint presents complementary birational constructions for degree-two marked elliptic surfaces with double fibres, while spelling out where the methods depend on additional assumptions.
Scientific publication5 min read
A new arXiv preprint reports asymptotic upper bounds for integer sets built from Dedekind’s function, Euler’s totient and the sum-of-divisors function. It also establishes density-zero results for repeated applications of Dedekind’s function, while leaving the sharpness of its main bounds open.
Scientific publication5 min read
A mathematical preprint says a refined bound on the common zeros of polynomial systems proves a cited minimum-distance conjecture for evaluation codes on reduced complete intersections. It also derives lower bounds for generalized Hamming weights, but leaves a broader claim about projective Cartesian codes as a conjecture.
Scientific publication3 min read
A new arXiv preprint examines how numerical semigroups are arranged in a rooted tree. Its finite enumerations report more internal than leaf semigroups under several fixed conditions, but the proposed universal and asymptotic patterns remain unproved.
Scientific publication6 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 mathematical preprint reports that the difference in facet counts between chain and order polytopes is exactly the sum of local star-element weights. It also classifies gaps of zero, one and two, and derives a corresponding formula for admissible decompositions in a regular marked setting.
Scientific publication4 min read
A mathematical preprint uses Hamiltonian Floer theory to establish a conditional lower bound for periodic solutions in a stochastic particle-field model. The result concerns a theorem and limiting measures, not experimental observations or a full theory of quantum electrodynamics.
Scientific publication5 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
A mathematics preprint develops exact identities connecting partial permutations, class functions and forgotten symmetric functions. Its formulas lead to ribbon-tiling and rim-hook descriptions of irreducible-character evaluations, while a cancellation argument narrows one set-mapping calculation to partitions with at most two parts.
Scientific publication5 min read
A new arXiv preprint gives a positive answer to a partition question about sets of nice recurrence. The result is a theorem about abstract mathematical systems, not an experiment or a measured effect.
Scientific publication4 min read
A numerical study of a one-dimensional shallow-water model found that a dissipative run produced a dominant soliton in each direction of propagation. The modeled crest-height ratio was about 3, above the study’s reported criterion of greater than 1.25.
Scientific publication6 min read
A mathematical preprint reports a theorem showing that a positive gap below the three-quarter minimum-degree threshold is enough to rule out nonsynchronized local minima in the Kuramoto energy landscape. The result applies to finite simple graphs and does not specify the size of the gap.
Scientific publication4 min read
A mathematical preprint establishes the existence of a degree threshold guaranteeing vertex-disjoint directed cycles with pairwise different lengths. It also gives weighted extensions while leaving the sharpest possible threshold open.
Scientific publication5 min read
A computational study tested ensembles of randomly constructed reservoir computers in three deterministic chaotic systems. It reported a roughly 25-step Hénon-map ensemble horizon and Lorenz 96 ensemble forecasts that remained successful for at least 2.5 Lyapunov times. Performance-weighted averaging outperformed plain averaging.
Scientific publication3 min read
A mathematics preprint describes explicit common-denominator constructions for selected pairs of real numbers, reporting an exponent above one-half and conditional links to the classical and p-adic Littlewood conjectures.
Scientific publication6 min read
A theoretical preprint links quantitative K-stability data with the existence of positive scalar curvature Kähler metrics. Under its stated assumptions, a positive threshold corresponds to such a metric, while a threshold above the average scalar curvature corresponds to a unique constant scalar curvature metric. The boundary case requires additional information.
Scientific publication3 min read
An arXiv preprint reports a universal bound between two graph-theory quantities, presents a constructive approximation algorithm, and gives examples showing why the factor two may be impossible to improve.
Scientific publication4 min read
A theoretical preprint establishes existence and uniqueness for a Dirichlet problem at infinity involving noncompact convex hypersurfaces in Minkowski space. It also reports conditional global existence and local smooth convergence for a normalized inverse curvature flow, while showing that similar conclusions do not generally carry over to certain quotient flows.
Scientific publication5 min read
An arXiv preprint presents a rigidity theorem for complete shrinking gradient Ricci solitons with constant scalar curvature. If the soliton also satisfies a specified curvature inequality outside a compact region and converges smoothly to R² × Sⁿ⁻², the authors conclude that the entire space is isometric to that product. The proof uses curvature estimates, level-set arguments and geometric-spl คน?
Scientific publication6 min read
A theoretical graph-theory preprint identifies an exact finiteness dichotomy for one family of forbidden-induced-subgraph classes, then supplies related finite, infinite and algorithmic results.
Scientific publication4 min read
A theory paper presents a canonical block-triangular decomposition for finite, connected, simple bipartite graphs. Its results connect the characteristic m to matching extension, structural classes and a lattice of independent sets, while leaving practical runtime performance untested.
Scientific publication5 min read
A deterministic graph-theory result identifies the exact minimum semidegree for prescribed directed 3q-cycles in the stated range, while leaving the best size cutoff unresolved.
Scientific publication3 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 classifies four exceptional Deza graph constructions arising from tangent, secant and external-line relations on quadrics. It gives their exact parameters and structural descriptions, but leaves the full classification of relation unions in higher odd dimensions open.
Scientific publication4 min read
A theoretical mathematics manuscript proposes conditional local and global procedures built from ordinary blowups, with its strongest finite result confined to one generation.
Scientific publication4 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
The work compares Selmer and fine Selmer groups across nearby Z_p-extensions. It reports non-increasing μ bounds, conditional λ bounds and a nearby characteristic-ideal relation when the cyclotomic Main Conjecture and zero reference invariants are assumed.
Scientific publication5 min read
A mathematical preprint gives a structural account of hyperbolic-surface entropy, showing that proper-subsurface entropies remain below 1 and that the spectrum has a tightly constrained order.
Scientific publication3 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