Abstract In this study, an initial-value problem for a nonlinear Volterra functional integro-differential equation on finite interval was considered. The term in the contains multiple time delays. addition to giving some new theorems existence and uniqueness of solutions equation, authors also prove Hyers-Ulam-Rassias stability Hyers-Ulam equation. proofs use several different tools including B...

In even space-time dimensions the multi-loop Feynman integrals are of rational function in projective space. By using an algorithm that extends Griffiths--Dwork reduction for case hypersurfaces with singularities, we derive Fuchsian linear differential equations, Picard--Fuchs respect to kinematic parameters a large class massive integrals. With this approach obtain operator high multiplicities...

We classify the smooth projective symmetric G-varieties with Picard number one (and G semisimple). Moreover we prove a criterion for the smoothness of the simple (normal) symmetric varieties whose closed orbit is complete. In particular we prove that, given a such variety X which is not exceptional, then X is smooth if and only if an appropriate toric variety contained in X is smooth. keywords:...

A new nonlinear iterative method for nonlinear parabolic equation is developed and applied to a multimaterial nonequilibrium radiation diffusion problem on distorted meshes. The new iterative method is named by Picard-Newton method (PN for short). Solution process of the method is as follows. First, by linearizing the time-discretized nonlinear partial differential equation(PDE), we can get an ...

Orders on surfaces provided a rich source of examples of noncommutative surfaces. In [HS05] the authors prove the existence of the analogue of the Picard scheme for orders and in [CK11] the Picard scheme is explicitly computed for an order on P ramified on a smooth quartic. In this paper, we continue this line of work, by studying the Picard and Hilbert schemes for an order on P ramified on a u...

Orders on surfaces provided a rich source of examples of noncommutative surfaces. In [HS05] the authors prove the existence of the analogue of the Picard scheme for orders and in [CK11] the Picard scheme is explicitly computed for an order on P ramified on a smooth quartic. In this paper, we continue this line of work, by studying the Picard and Hilbert schemes for an order on P ramified on a u...

We begin by considering second order dynamical systems of the from ẍ(t) + Γ(ẋ(t)) + λ(t)B(x(t)) = 0, where Γ : H → H is an elliptic bounded self-adjoint linear operator defined on a real Hilbert space H, B : H → H is a cocoercive operator and λ : [0,+∞)→ [0,+∞) is a relaxation function depending on time. We show the existence and uniqueness of strong global solutions in the framework of the Cau...

This paper considers an enhancement of the classical iterated penalty Picard (IPP) method for incompressible Navier-Stokes equations, where we restrict our attention to $O(1)$ parameter, and Anderson acceleration (AA) is used significantly improve its convergence properties. After showing fixed point operator associated with IPP iteration Lipschitz continuous continuously (Frechet) differentiab...

This paper considers an enhancement of the classical iterated penalty Picard (IPP) method for incompressible Navier-Stokes equations, where we restrict our attention to $O(1)$ parameter, and Anderson acceleration (AA) is used significantly improve its convergence properties. After showing fixed point operator associated with IPP iteration Lipschitz continuous continuously (Frechet) differentiab...

A bstract We study complex saddles of the Lorentzian path integral for 4D axion gravity and its dual description in terms a 3-form flux, which include Giddings-Strominger Euclidean wormhole. Transition amplitudes are computed using with help Picard-Lefschetz theory. The number nature is shown to qualitatively change presence bilocal operator that could arise, example, as result considering high...