2549 papers
This paper outlines the educational framework and practical examples of the Moscow Mathematical Conference for High School Students, demonstrating how non-novel research projects can effectively guide adolescents through the complete scientific process—from developing intuition and peer review to receiving formal recognition.
This paper proposes a movable-antenna-assisted Rate-Splitting Multiple Access (RSMA) framework integrated with a Reconfigurable Intelligent Surface (RIS) to maximize sum rate by jointly optimizing beamforming, reflection coefficients, rate splitting, and antenna positions, demonstrating significant performance gains over conventional fixed-antenna systems.
This paper investigates the existence of -designs (decompositions of complete graphs into edge-disjoint copies of a grid graph ), proving that such designs exist for toroidal grids when is an odd prime or its square, and for the path-grid (which relates to scrambling Connections puzzles), while showing that admits no such design.
This paper proposes a generalized Fermat's conjecture within the framework of arithmetic dynamics, provides supporting evidence for it, and introduces a multi-indexed version of the conjecture.
This paper establishes sufficient conditions for the infinite direct product of a continuous self-map on a compact metric space to be -chaotic and applies these findings to construct examples of unusual -chaotic maps.
This paper extends the concept of -mixing to set-valued random sequences in Banach spaces and establishes several strong laws of large numbers for such sequences, demonstrating the naturalness and sharpness of the underlying hypotheses through illustrative examples.
This paper establishes improved minimum degree conditions that guarantee the existence of Hamiltonian transversals and Hamiltonian connectivity in both balanced and nearly balanced bipartite graph collections, thereby advancing previous results in the field.
This paper classifies all tame integer tilings and hypertilings by developing a geometric model based on generalised Farey graphs in the hyperbolic plane, which connects these structures to triangulated polygons, friezes, and the Cayley hyperdeterminant.
This paper characterizes the gauge profiles of sets of reals defined by effective dimension and demonstrates a separation between these sets and -well approximable numbers using Hausdorff measure.
This paper proves the long-standing Erdős Matching Conjecture, establishing that the maximum size of a family of -sized subsets of containing no pairwise disjoint sets is bounded by the larger of two canonical extremal constructions.
This paper proves that asymptotically almost all vectorial functions over finite fields possess trivial extended-affine stabilizers, implying that the number of equivalence classes matches the naive estimate and that random sampling is a highly effective strategy for cryptographic primitive design due to the exponential rarity of functions with nontrivial stabilizers.
This paper establishes the existence of global weak solutions for the discrete nonlinear fragmentation equation with degenerate diffusion in arbitrary spatial dimensions by utilizing weak estimates and compactness arguments, thereby extending previous results that were limited to one-dimensional domains with uniformly positive diffusion.
This paper introduces a novel Monte Carlo method for estimating by tossing a coin, which utilizes a new interpretation of derived from Catalan-number series identities.
This paper presents a procedure for efficiently computing cohomological support varieties of certain monomial ideals, which leads to the discovery of new examples that are not unions of linear subspaces and a computer-assisted classification of such varieties for homogeneous monomial ideals with six generators over .
This paper establishes that in raster scan diffraction tomography using focused beams, the object's scattering potential is generically uniquely determined in dimensions higher than two, whereas in two dimensions, only a specific subset of Fourier coefficients can be uniquely recovered while others remain ambiguous.
This paper extends diffraction tomography to accommodate focused beam scanning by modeling incident fields as Herglotz waves, deriving a new Fourier diffraction relation that enables quantitative reconstruction and reveals how different scan geometries impact the imaging results.
This paper demonstrates that the energy-critical co-rotational wave maps equation from into admits finite-time blow-up solutions containing arbitrarily many concentric concentrating bubbles with alternating signs, thereby confirming that all scenarios predicted by the soliton resolution conjecture can occur.
This paper resolves an open problem posed by Heittokangas, Ishizaki, Tohge, and Wen by completely characterizing all finite-order entire solutions of the differential-difference equation , where the coefficients are polynomials and .
This paper extends the recently defined function , which counts multicolored partitions with specific color restrictions for even and odd parts, to the context of overpartitions.
This paper investigates the Cohen-Macaulayness, purity, and shellability of the -th squarefree powers of edge ideals of whisker graphs by characterizing these properties in terms of the structural features of the underlying graph, such as its girth and bipartiteness, while also computing depths and verifying a related conjecture.