Search results for "mathematical analysis"

showing 9 items of 2409 documents

A comparison theorem for the first Dirichlet eigenvalue of a domain in a Kaehler submanifold

1994

AbstractWe give a sharp lower bound for the first eigenvalue of the Dirichlet eigenvalue problem on a domain of a complex submanifold of a Kaehler manifold with curvature bounded from above. The bound on the first eigenvalue is given as a function of the extrinsic outer radius and the bounds on the curvature, and it is attained only on geodesic spheres of a space of constant holomorphic sectional curvature embedded in the Kaehler manifold as a totally geodesic submanifold.

GeodesicMathematics::Complex VariablesMathematical analysisHolomorphic functionGeneral MedicineKähler manifoldMathematics::Spectral TheorySubmanifoldCurvaturesymbols.namesakeDirichlet eigenvaluesymbolsDirichlet's theorem on arithmetic progressionsMathematics::Differential GeometrySectional curvatureMathematics::Symplectic GeometryMathematicsJournal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics

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A second-order differential equation for the two-loop sunrise graph with arbitrary masses

2011

We derive a second-order differential equation for the two-loop sunrise graph in two dimensions with arbitrary masses. The differential equation is obtained by viewing the Feynman integral as a period of a variation of a mixed Hodge structure, where the variation is with respect to the external momentum squared. The fibre is the complement of an elliptic curve. From the fact that the first cohomology group of this elliptic curve is two-dimensional we obtain a second-order differential equation. This is an improvement compared to the usual way of deriving differential equations: Integration-by-parts identities lead only to a coupled system of four first-order differential equations.

Loop (graph theory)Algebra and Number TheoryGroup (mathematics)Differential equationMathematical analysisFOS: Physical sciencesGeneral Physics and AstronomyMathematical Physics (math-ph)CohomologyMomentumElliptic curveHigh Energy Physics - PhenomenologyMathematics - Algebraic GeometryHigh Energy Physics - Phenomenology (hep-ph)FOS: MathematicsGraph (abstract data type)Algebraic Geometry (math.AG)Hodge structureMathematical PhysicsMathematics

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Statistical Properties of Double Hoyt Fading With Applications to the Performance Analysis of Wireless Communication Systems

2018

In this paper, we investigate the statistical properties of double Hoyt fading channels, where the overall received signal is determined by the product of two statistically independent but not necessarily identically distributed single Hoyt processes. Finite-range integral expressions are first derived for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades of the envelope fading process. A closed-form approximate solution is also deduced for the LCR by making use of the Laplace approximation theorem. Applying the derived PDF of the double Hoyt channel, we then provide analytical expressions for the average…