The fourth known primitive solution to
This paper presents the fourth known primitive solution to the Diophantine equation , detailing the methodology used to discover it.
🔢 Category
math
6080 papers
Waring-Goldbach problems for one square and higher powers
This paper proves that every sufficiently large odd integer can be expressed as the sum of one square and fourteen fifth powers of primes, while every sufficiently large even integer can be written as the sum of one square, one biquadrate, and twelve fifth powers of primes.
Reductification of parahoric group schemes
This paper demonstrates that any parahoric group scheme over a henselian discretely valued field becomes reductive after a finite Galois extension, allowing it to be recovered as the smoothening of Galois invariants of a reductive model, a result that extends prior work to the wildly ramified case and confirms the Grothendieck–Serre conjecture for generically trivial parahoric torsors in sufficiently good residue characteristics.
Sobolev regularity of the symmetric gradient of solutions to a class of -Laplacian systems
This paper establishes the Sobolev regularity of a nonlinear function of the symmetric gradient for weak solutions to -Laplacian systems with Lipschitz coefficients and Orlicz-Sobolev data, utilizing uniform higher differentiability estimates derived from approximating problems with singular perturbations.
On the approximation of Weierstrass function via superoscillations
This paper investigates the convergence properties of M.V. Berry's superoscillating approximation to the truncated Weierstrass function, providing sharp error estimates and analyzing the associated double limits.
Joint Linnik problems
This paper proves a conjecture by Michel and Venkatesh regarding the joinings of distinct Linnik problems through simultaneous quaternionic embeddings of imaginary quadratic fields, while also addressing a related non-equivariant conjecture by Aka, Einsiedler, and Shapira.
Decision-dependent distributionally robust standard quadratic optimization with Wasserstein ambiguity
This paper proposes a distributionally robust framework for standard quadratic optimization under Wasserstein ambiguity, demonstrating its equivalence to a modified deterministic StQP instance while providing out-of-sample performance guarantees and empirical validation.
Mean-field games with unbounded controls: a weak formulation approach to global solutions
This paper establishes the existence of equilibria for non-Markovian mean-field games with unbounded controls and quadratic running costs using a weak formulation approach grounded in new stability results for quadratic-growth generalized McKean-Vlasov BSDEs, thereby removing previous restrictions on model parameter boundedness and time horizons.
The Impact of Neglecting Vaccine Unwillingness in Epidemiology Models
This study demonstrates that neglecting vaccine unwillingness in epidemiological models introduces significant errors in both long-term equilibrium predictions and short-term epidemic wave simulations, with the magnitude of error depending on the disease's infectivity and the speed of vaccination programs.
A Survey on Stacked Intelligent Metasurfaces: Fundamentals, Recent Advances, and Challenges
This survey provides a comprehensive overview of stacked intelligent metasurfaces (SIMs), detailing their physical principles, modeling frameworks, and hardware realizations while examining their role in enabling advanced 6G functionalities like wave-domain signal processing, integrated sensing, and cell-free networks, alongside identifying key challenges for future research.
On nonmatrix varieties of associative rings
This paper extends known results on nonmatrix varieties of associative algebras from the case of infinite fields to the more general setting of unital commutative rings, specifically characterizing varieties of -algebras that do not contain the algebra of matrices.
Fluctuations for the Sherrington--Kirkpatrick spin glass model near the critical temperature
This paper establishes the precise asymptotic variance and a Gaussian central limit theorem for the log-partition function of the Sherrington-Kirkpatrick spin glass model in the critical regime where the inverse temperature approaches the critical point at a rate of .
A refined 1-cocycle for regular isotopies and the refined tangle equations
This paper introduces a refined combinatorial 1-cocycle with Laurent polynomial coefficients to define refined tangle equations, providing a quantitative method to analyze knot isotopies and distinguish knot diagrams based on the solvability of these equations.
Algebraic Invariants of Edge Ideals Under Suspension
This paper investigates how algebraic invariants of edge ideals change under selective graph suspensions, demonstrating that while suspensions over minimal vertex covers consistently preserve regularity and increase projective dimension by one, suspensions over maximal independent sets exhibit uniform behavior only for paths and cycles, with a specific extremal family of paths showing increases in both regularity and the -invariant.
Graph labellings and external difference families
This paper establishes a systematic framework for constructing digraph-defined external difference families by combining graph blow-up techniques with generalized vertex labellings, resulting in new combinatorial families—including the first infinite construction for specific 2-circular external difference families—and novel results on graph labellings such as -valuations for sun graphs.
A homological generalized Property R conjecture is false
This paper disproves a homological generalization of the generalized Property R conjecture by demonstrating the existence of 2-component framed links in that surger to a connected sum of homology manifolds yet are not handleslide equivalent to a split link.
Lipschitz Bounds and Uniform Convergence for Sequences of Bounded Rough Riemannian Metrics
This paper investigates the minimal conditions required to establish Lipschitz and uniform bounds for sequences of bounded rough Riemannian metrics, providing counterexamples to demonstrate the sharpness of these conditions while exploring their underlying geometric intuition.
Blackwells Demon: Postdiction and Prediction in Random Walks
This paper introduces "Blackwells Demon," a thought experiment demonstrating that under specific restrictive conditions involving a complex environment, one can predict the direction of a random walk with a success probability greater than 1/2 by exploiting inhomogeneities in a statistically homogeneous system, analogous to how Maxwell's Demon exploits molecular speed variations.
Extremal degree-based indices of general polyomino chains via dynamic programming
This paper introduces a dynamic programming framework to identify extremal general polyomino chains for degree-based topological indices, specifically resolving a 2015 open problem by characterizing the chains that maximize the generalized Randić index with based on the number of squares modulo 4.
Fully-Dualizable and Invertible -Algebras
This paper proves a conjecture by Brochier, Jordan, Safronov, and Snyder that characterizes fully-dualizable and invertible -algebras within higher Morita categories, thereby identifying the specific algebraic structures that generate -dimensional and invertible topological quantum field theories.