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Category: Mathematics

  • Tensor nuclear norm is fully decomposable on specific subspaces

    Tensor nuclear norm is fully decomposable on specific subspaces

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    What the study found The study shows that the tensor nuclear norm can be fully decomposed over specific subspaces, and it identifies the largest subspaces for which this full decomposability holds. It also derives new inclusions for the subdifferential, which is the set of all valid subgradients, of the tensor nuclear norm. Why the authors…

  • Fourier bounds for Kakeya sets in finite fields

    Fourier bounds for Kakeya sets in finite fields

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    What the study found The study shows that a Kakeya set in a finite field vector space supports a probability measure with a bounded Fourier transform at every non-zero frequency. The authors also report that this bound is sharp in all dimensions at least 2. What the authors say this matters The authors state that…

  • Extremal signed complete graphs with K2,2-minor-free negative subgraphs

    Extremal signed complete graphs with K2,2-minor-free negative subgraphs

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    What the study found The authors characterize the extremal signed complete graphs that achieve the maximum and second maximum index when the negative-edge-induced subgraph is a K2,2-minor-free spanning subgraph of Kn. Why the authors say this matters The abstract says this work addresses an extremum problem for the index of a signed complete graph based…

  • Minimal partitions can exist in unbounded domains

    Minimal partitions can exist in unbounded domains

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    What the study found The study finds that for unbounded domains, including domains of infinite volume, spectral minimal partitions can exist below a threshold determined by the essential spectrum and the best “k-1” partition energy. The behavior at the threshold differs by the choice of p: for p < ∞, minimizing partitions may or may…

  • Hermite process distributions are shown to admit densities

    Hermite process distributions are shown to admit densities

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    What the study found Finite-dimensional distributions of Hermite processes of order q ge 1 with self-similarity parameter H in (1/2, 1) are shown to admit a density with respect to Lebesgue measure. This result is stated for any distinct times t_1, …, t_n. Why the authors say this matters The authors note that the Gaussian…

  • Weighted Neumann eigenvalues are established for outward cuspidal domains

    Weighted Neumann eigenvalues are established for outward cuspidal domains

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    What the study found The study establishes Sobolev-space embeddings into weighted Lebesgue spaces for a nonlinear Neumann eigenvalue problem in outward cuspidal domains. These embeddings are used to show solvability of the Neumann spectral problem and to estimate the associated weighted Neumann eigenvalues. Why the authors say this matters The authors say these embedding results…

  • Repetition thresholds for rich sequences tend to 2

    Repetition thresholds for rich sequences tend to 2

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    What the study found The authors verify a conjecture that the repetition threshold for the class of rich sequences over d symbols tends to 2 as d grows. A repetition threshold is the smallest number r such that sequences in the class avoid repetitions with exponent greater than r. Why the authors say this matters…

  • Edge version of graph inducibility is determined by fractional independence number

    Edge version of graph inducibility is determined by fractional independence number

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    What the study found The study shows that the edge version of inducibility for any graph H satisfies ρ(H,m) = Θ(m^α_f(H)), where α_f(H) is the fractional independence number of H. The authors also give additional bounds and conjectures for paths and cycles. Why the authors say this matters The authors indicate that this result shifts…

  • Conditional bounds for Dirichlet L-function arguments and low-lying zeros

    Conditional bounds for Dirichlet L-function arguments and low-lying zeros

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    What the study found Under the generalized Riemann hypothesis, the study gives conditional bounds on the mean and mean square of the argument of Dirichlet L-functions for large prime modulus. It also reports applications to low-lying zeros and a new lower bound on the proportion of Dirichlet L-functions with zeros close to the central point.…

  • Modified conjugate gradient method showed better numerical performance

    Modified conjugate gradient method showed better numerical performance

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    What the study found The paper reports that a modified conjugate gradient coefficient method was developed for solving unconstrained optimization problems. The authors state that the method uses a strong Wolfe line search and that numerical results showed improved performance compared with other conjugate gradient methods. Why the authors say this matters The study suggests…