2549 papers
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.
This paper presents a set of course notes designed to introduce undergraduate students to mathematical proofs, covering foundational topics such as logic, proof techniques, induction, set theory, and real analysis, complete with numerous examples and exercises.
This paper investigates the intrinsic geometry of polyhedra by utilizing barycentric algebras to characterize coordinate systems, specifically presenting a coalgebra-based algorithm for computing chordal coordinates in convex polygons that naturally yields the Catalan number enumeration of their triangulations.
This paper develops and analyzes a continuous data assimilation framework using a nudging-based approach and a capped finite element splitting scheme to recover trajectories of a coupled Navier-Stokes-Cahn-Hilliard system with an auxiliary field from coarse spatial observations, demonstrating its effectiveness in synchronizing mismatched initial conditions through numerical experiments.
This paper proposes an efficient, unconditionally stable predictor-corrector algorithm combining orthogonal spline collocation finite elements with variable time stepping to achieve high-order accuracy and suppress numerical oscillations in solving the FitzHugh-Nagumo system.
This paper establishes a structure theorem for -labeled graphs that exclude a fixed -labeled immersion, demonstrating that such graphs admit a tree-cut decomposition where each bag contains either few high-degree vertices or is nearly signed over a proper subgroup of the finite group .
This paper systematically determines the circular chromatic indices of small graphs and multigraphs with maximum degrees up to 6, constructs infinite families of graphs with specific fractional indices, and refutes edge-connectivity variants of the "Upper Gap Conjecture."
For the planar three-body problem with positive masses, non-zero angular momentum, and fixed negative energy, the paper proves the existence of global solutions that maintain an arbitrarily large potential energy by featuring a single close approach to triple collision while evolving into a tight binary configuration with the third body diverging to infinity.
This paper introduces a determinantal method for computing minimal local generalized additive decompositions (GADs) of homogeneous polynomials by minimizing the rank of symbolic inverse systems, proving that this approach guarantees finding all minimal decompositions without tensor extensions whenever the local GAD-rank does not exceed the form's degree.
This paper establishes the existence and combinatorial characterization of the asymptotic v-number for Noetherian graded families of homogeneous ideals via Newton-Okounkov regions, while also proving its eventual quasi-linearity and strict inequalities with regularity and multiplicity.
This paper proposes a robust geometric early warning indicator based on the width of the stochastic separatrix in a two-state ecosystem model, which successfully predicts rapid under-ice phytoplankton blooms in the Arctic where conventional critical slowing down signals fail due to strong noise or limited data.
This paper generalizes the classical discrete -Hardy inequality to arbitrary integer orders to establish optimal discrete -Rellich and -Birman inequalities, utilizing a novel Copson inequality variant with a negative exponent and demonstrating how these results recover the continuous -Birman inequality.
This paper investigates the domination polynomial of the co-maximal graph by deriving explicit formulas for specific cases of , establishing structural connections for general , and analyzing the unimodality, log-concavity, and modulus bounds of its roots.
This paper constructs exotic Hecke correspondences between the special fibers of PEL-type Shimura varieties with potentially bad reduction by utilizing Pappas-Rapoport splitting models, thereby establishing new geometric Jacquet-Langlands correspondences and verifying generic instances of the Tate conjecture.
This paper investigates Max-Cut instances on complete graphs with geometrically decreasing edge weights, establishing a sharp phase diagram for the optimality of isolated cuts based on threshold polynomials and conjecturing their global optimality for sufficiently large .