Subject
Proofs, structures, equations, geometry, topology, and applied mathematics.
A mathematical preprint connects the diagonal F-threshold of a graph's binomial edge ideal to features such as matchings, independent sets and clique matchings.
Scientific publication4 min read
A version 1 arXiv preprint presents a conditional route for excluding non-trivial solutions of a generalized Fermat equation at sufficiently large prime exponents. Its imaginary quadratic example lists three relevant unit solutions and reports relative density 5/6 among squarefree positive integers.
Scientific publication4 min read
A mathematical preprint describes a new family of permutation group polynomials over finite fields of odd characteristic. It pairs the family with an explicit companion, distinguishes it from known families considered in the paper, and gives exact counts for the new and three specified earlier families.
Scientific publication3 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
A theoretical preprint reports a rigorous framework for approximate diagonalization of generalized spin-boson models, with an explicit bound on the remaining operator error.
Scientific publication4 min read
A mathematical preprint shows that associated-prime sets for powers of monomial ideals need not move in one direction: the maximal ideal can appear and later disappear.
Scientific publication4 min read
An exact preprint finds that A4 and B4 admit a special vertex, while D4 and F4 do not. Three intermediate arrangements in the B4 deletion chain also pass the test, while the defect results remain limited to the named cases.
Scientific publication5 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
Researchers propose a formal reduction method for time-dependent Hamiltonian systems whose symmetries can translate time, with worked examples showing how its conserved quantities behave.
Scientific publication4 min read
A mathematical preprint reduces operators on two finite groups to named families and adds structural results on centers, bijectivity, constructions and splitting.
Scientific publication4 min read
A formal mathematical preprint reports equality between the two constructions and traces it through algebraic factors, modules and knot normalization.
Scientific publication3 min read
An arXiv preprint extends the topological Halmos-von Neumann framework to open abelian group bundles, connecting compactifications with dual sheaves, point spectra and dynamical systems while marking clear limits.
Scientific publication4 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 new mathematical preprint gives a conditional route from a well-behaved 2-sphere boundary to a Kleinian group with peripheral subgroups virtually isomorphic to the two-dimensional integer lattice.
Scientific publication4 min read
A new mathematical preprint reports a proof of Mühlherr’s Twist Conjecture and an algorithmic answer to the isomorphism problem for Coxeter groups.
Scientific publication4 min read
A preprint examines the Roberts–Street nerve of the walking coinductive equivalence. It finds the nerve is non-contractible in one formal homotopy theory, while every nonnegative thinification and the left-category reflection are contractible.
Scientific publication3 min read
A mathematical preprint reports unusually large-centroid tensor families, conditional minimal-border-rank theorems and lower reported upper bounds from laser-method calculations for matrix multiplication. The results are algebraic and do not include measured runtimes or an implemented speedup.
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 formal mathematical argument says strong local stability passes to the stated Artin–Schreier base-change when every Frobenius base-change in the required range is already strongly locally stable.
Scientific publication4 min read
A theorem-based analysis links finite Kuramoto manifolds with the Ott-Antonsen and continuum descriptions, while restricting the result to a specific model, parameter range and family of trajectories.
Scientific publication4 min read
A mathematical preprint describes a chain of algorithms that turns subgroup membership in finite-base wreath products into a decidable problem.
Scientific publication3 min read
A mathematical preprint reports unconditional lower and upper certificates for a compact-window version of the Weil quadratic form. Its numerical pattern supports, but does not prove, a Landau–Widom-type law for the true infinite-dimensional profile.
Scientific publication5 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 matching-complement theorem sits at the center of a deductive argument that establishes both the standard 2-Decomposition Conjecture and the 3-Decomposition Conjecture.
Scientific publication4 min read
A proof-based study develops a tree-based route into the integral homology of SL2(Z[1/n]) and gives an explicit intermediate description for the subgroup Γ0(n).
Scientific publication3 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 theoretical arXiv preprint shows that full multigraded regularity preservation fails for some ideals, then uses lower bounds and colored algebraic shifting to settle two colorful fractional Helly conjectures.
Scientific publication5 min read
A preprint constructs one-dimensional hypersurface families where a general reduction bound for generalized Loewy length is exact in some cases and one unit high in others.
Scientific publication4 min read
A prospective Taiwan study found language-specific differences in the Animal Naming Test, while adding serum IL-6 produced a higher but unconfirmed result among Mandarin speakers.
The Kaohsiung journal of medical sciences5 min read
A theoretical preprint reports Devaney chaos for some two-dimensional linear maps under weak topology, but a conflict between a Jordan-block theorem and its proof clouds one part of the classification.
Scientific publication5 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 conditional proof for smooth, closed five-dimensional Riemannian manifolds produces a conformal metric with positive scalar curvature and positive Q-curvature, provided two invariants and an initial metric meet the stated conditions.
Scientific publication4 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 new geometry preprint gives a universal factor-of-two bound for simple polygons, proves the coefficient cannot be increased, and formally checks its main theorems in Lean 4.
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 mathematical preprint proves that uniform Littlewood counterexamples include positive-dimensional families, including pairs whose first coordinate is badly approximable.
Scientific publication4 min read
A mathematical preprint establishes a sharp three-step cover for every 2-colored complete bipartite graph, while constructions show why stronger versions do not always hold.
Scientific publication3 min read
The paper counts bounded products of integer matrices and finds different asymptotic growth laws for fixed targets with nonzero determinant and for the zero matrix. It also proves an upper bound that applies uniformly to nonsingular integer targets.
Scientific publication4 min read