Mathematics Insight Digest

Symmetry-based multi-reduction converts the fractional (2+1)-dimensional generalized Boussinesq equation into tractable lower-dimensional problems via...

In bi-objective median location on graphs, consistent paths couple facility placement with routing to avoid contradictory preferences when balancing...

Merging clinical datasets creates structured missingness with deterministic gaps that violate the probabilistic assumptions of standard imputation...

Large bulk viscosity enables the first global strong solutions for arbitrarily large initial data in 2D non-conservative compressible two-fluid...

A deterministic host–vector model incorporates temporary cross-immunity, ADE, secondary-infection mortality, and explicit DENV co-infection in...

Existing benchmarks focus on clean printed documents or isolated expressions, but student answer sheets involve mixed text, formulae, tables, and...

Adaptive monitored circuits harness local mid-circuit measurements and feedback to steer a quantum Bernoulli map toward fixed points, inducing a...

Prescribed ADE singularities in conic-line arrangements force Hirzebruch-type inequalities on any topological realization in 4-manifolds, derived...

Error-aware training via EREAL produces substantial improvements across diverse mathematical reasoning benchmarks under limited-data conditions.

A novel hybrid method, SMOTE-CCU+, delivers the strongest benchmark results for class-imbalance handling in educational data mining.

• Performance...

An open data science competition on a benchmark of over 52,000 labeled math explanations shows that top NLP models can accurately classify responses...

Vertex transitivity and {4,6}-regularity enable exact computation of transmission and average distance in cyclic bipartite graphs.

The classical Borsuk-Ulam conjecture fails precisely for non-trivial torsion-free profinite compact abelian groups, with all p-adic integer groups providing explicit counterexamples through free actions on sphere products admitting equivariant maps.

Interface-aligned Chebyshev integral-tau discretization places monitoring levels and strikes at element faces, enabling geometric convergence where...

Dynamic portfolio optimization extends mean-variance theory to general incomplete markets through time-varying investment decisions and constrained risk-return trade-offs.

For parallel toric arrangements of rank one, the Euler-Poincaré characteristic of the complement manifold equals a sum over the characteristics of the...

Metasurfaces have progressed from wavefront shaping applications to a versatile platform for engineering light–matter interactions across spectral ranges by concentrating light into subwavelength volumes and enabling hybrid polariton states.

OpenAI's announcement of solving the Navier–Stokes existence and smoothness problem remains unverified, drawing sharp criticism for alleged coercive...

• Proved layer: Markov kernels as Kleisli 1-cells, couplings as 2-cells; base-relative posteriors form a fibre; coupling polytopes are Delzant moment...

Markov properties of Gaussian random fields on compact domains extend from combinatorial graphs to metric graphs, with Sections 4.4 and 4.5 delivering new results on field regularity and Cameron–Martin spaces.