Category: Mathematics
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Edge version of graph inducibility has polynomial growth
This research indicates that the maximum number of induced copies of a graph with a fixed number of edges grows on the order of a power of the edge count, and the paper gives results for cycles and paths.
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Conditional bounds on Dirichlet function arguments and low-lying zeros
This research indicates that, under the generalized Riemann hypothesis, bounds on the argument of Dirichlet L-functions can be used to study low-lying zeros and to show that a positive proportion of Dirichlet L-functions have a first zero unusually close to the central point.
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Paper answers two conjectures on complete evolution algebras
This research indicates that the authors gave positive answers to two conjectures on the classification of complete evolution algebras.
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Continuous solutions for a cohomological equation are characterized
This research indicates that the cohomological equation has a continuous solution exactly when the function has trivial periodic cycle functional.
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Average Nikolskii factors are constant or logarithmic for random trigonometric polynomials
This research indicates that average Nikolskii factors for random trigonometric polynomials with independent Gaussian coefficients are constant for finite q and grow like the square root of the logarithm of n when q equals infinity.
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Existence and uniqueness proved for anisotropic evolution equations
This research indicates that solutions exist, satisfy a comparison principle, and are unique for a class of fully nonlinear anisotropic evolution equations under a closeness assumption on the exponents.
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Equality case for the first Hodge Laplacian eigenvalue on submanifolds
This research indicates that equality in a sharp lower bound for the first p-eigenvalue of the Hodge Laplacian on closed submanifolds in space forms can occur only on topological spheres, assuming positivity.
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Degree bounds for extensions with a given automorphism group
This research indicates that, for certain algebraic number fields, extensions can have degree much larger than the size of their automorphism group while keeping that same group.
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Log-Sobolev inequality holds for some focusing Schrödinger Gibbs measures
This research indicates that the Gibbs measure for the focusing Schrödinger equation satisfies a log-Sobolev inequality when 2 ≤ p ≤ 4, while for p > 4 a convexity-based multiscale approach cannot be applied.
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A right-truncated exponential Rayleigh model fit constrained lifespan data well
This research indicates that a right-truncated [0,1] exponential Rayleigh distribution can model data restricted to the interval [0,1] with improved fit in the datasets examined.
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