It is a classical theorem of Liouville that Hamiltonian systems preserve volume in phase space. Any symplectic Runge–Kutta method will respect this property for such systems, but it has been shown by Iserles, Quispel and ...

This thesis seeks to test and evaluate the effects of in-­network storage in novel proposed Internet architectures in terms of their performance. In a world where more and more people are mobile and connected to the Internet, ...

This project involves learning to predict users' mobility within the network topology. Topological mobility, as opposed to physical mobility, can be substantial as a user switches from LTE to wifi network, while moving ...

We show that the augmented base locus coincides with the exceptional locus (i.e., null locus) for any nef $\Bbb R$-Cartier divisor on any scheme projective over a field (of any characteristic). Next we prove a semi-ampleness ...

We construct the compatible system of $\textit{l}$-adic representations associated to a regular algebraic cuspidal automorphic representation of GL$_{n}$ over a CM (or totally real) field and check local-global compatibility ...

The assumption of separability of the covariance operator for a random image or hypersurface can be of substantial use in applications, especially in situations where the accurate estimation of the full covariance structure ...

Let (M, g) be an analytic, compact, Riemannian manifold with boundary, of dimension n≥2. We study a class of generalized Radon transforms, integrating over a family of hypersurfaces embedded in M, satisfying the Bolker ...

In this article, I summarise Peter Hall’s contributions to high-dimensional data, including their geometric representations and variable selection methods based on ranking. I also discuss his work on classification problems, ...

The Laplace-Beltrami operator on a sphere with a cut arises when considering the problem of wave scattering by a quarter-plane. Recent methods developed for sound-soft (Dirichlet) and sound-hard (Neumann) quarter-planes ...

The peanosphere (or "mating of trees") construction of Duplantier, Miller, and Sheffield encodes certain types of $\gamma$-Liouville quantum gravity (LQG) surfaces ($\gamma \in (0,2)$) decorated with an independent ...

This project lies at the interface between Nonlinear Functional Analysis, unconstrained Optimization and Critical point theory. It concerns mainly the Ambrosetti-Rabinowitz's Mountain Pass Theorem which is a min-max theorem ...

This project is mainly focused on the theory of Monotone (increasing) Operators and its applications. Monotone operators play an important role in many branches of Mathematics such as Convex Analysis, Optimization Theory, ...

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This project is at the interface between Nonlinear Functional Analysis, Convex Analysis and Di erential Equations. It concerns one of the most powerful methods often used to solve optimization problems with constraints; ...

This project is at the interface between Analysis, Natural Sciences and Modeling Theory. It deals with Floquet Theory (also re ered to as Floquet-Lyapunov theory) which is the main tool of the theory of periodic ordinary ...

This work concerns one of the most important tools to solve well-posed problems in the theory of evolution equations (e.g di usion equation, wave equations, ...) and in the theory of stochastic process, namely the semigroups ...

Solution gas drive reservoirs are characterized by rapid and continuous decline of reservoir pressure. This rapid and continuous decline of reservoir pressure causes direct decline of reservoir performance at early stages ...

Hydraulic fracturing is an effective well stimulation technique which is introduced in the 1950s and widely used in the oil and gas industry. Most of the works about hydraulic fracture assumed that the fracture is symmetric ...

A major drawback of directional and horizontal well drilling is the numerous complex computations required to be done while planning a well. These computations are very stressful and time consuming especially when done ...

Failure of offshore oil and gas pipelines occurs under certain conditions due to some applied mechanical forces. These conditions constitute a potential threat to the integrity of in-service life span of the pipelines ...