This paper describes a program that solves elementary mathematical problems, mostly in metric space theory, and presents solutions that are hard to distinguish from solutions that might be written by human mathematicians.

A time-domain boundary condition is derived that accounts for the acoustic impedance of a thin boundary layer over an impedance boundary, based on the asymptotic frequency-domain boundary condition of Brambley [2011, AIAA ...

We report the results of computations for two–dimensional dambreaks of viscoplastic fluid, focusing on the phenomenology of the collapse, the mode of initial failure, and the final shape of the slump. The volume-of-fluid ...

In his 2005 review, $\textit{Gravity and the Thermodynamics of Horizons}$, Paddy suggested that a vacuum in thermal equilibrium with a bath of radiation should have a gradually diminishing energy. We work through the ...

We study the space of oriented genus $\textit{g}$ subsurfaces of a fixed manifold $\textit{M}$, and in particular its homological properties. We construct a “scanning map” which compares this space to the space of sections ...

We construct algebras of endomorphisms in the derived category of the cohomology of arithmetic manifolds, which are generated by Hecke operators. We construct Galois representations with coefficients in these Hecke algebras ...

We propose a new theory of higher spin gravity in three spacetime dimensions. This is defined by what we will call a Nambu-Chern-Simons (NCS) action; this is to a Nambu 3-algebra as an ordinary Chern-Simons (CS) action is ...

This article presents a comparative analysis of the diachronic evolution of Romance clausal structure from Classical Latin through to the late medieval period, with particular reference to the Verb Second (V2) property. ...

In this paper, we prove a conjecture published in 1989 and also partially address an open problem announced at the Conference on Learning Theory (COLT) 2015. For an expected loss function of a deep nonlinear neural network, ...

In the world today, the size of complex problems and systems has increased, due to the advances in technology and the area of computer design and architecture. Modeling and predicting the behaviour of complex systems ...

The estimation of a log-concave density on $\Bbb R$$^d$ represents a central problem in the area of nonparametric inference under shape constraints. In this paper, we study the performance of log-concave density estimators ...

We review recent progress in the application of numerical relativity techniques to astrophysics and high-energy physics. We focus on recent developments regarding the spin evolution in black hole binaries, high-energy black ...

Uncertainty analysis of flow performance predictions involves identifying significant reservoir parameters impacting the flow response. Uncertainty analysis often requires conducting large number of reservoir simulation ...

It is well know that many physically significant problems in different areas of re- search can be transformed into an equation of the form Au = 0, (0.0.1) where A is a nonlinear monotone operator from a real Banach space ...

• Let H be a real Hilbert space. Let K, F : H → H be bounded, continuous and monotone mappings. Let {un }∞ and {vn }∞ be n=1 n=1 sequences in E defined iteratively from arbitrary u1 , v1 ∈ H by un+1 = un − βn (F un − ...

Algorithms for single-valued and multi-valued nonexpansive-type mappings have continued to attract a lot of attentions because of their remarkable utility and wide applicability in modern mathematics and other reasearch ...

This thesis is a contribution to Control Theory of some Partial Functional Integrodifferential Equations in Banach spaces. It is made up of two parts: controllability and existence of optimal controls. In the first part, ...

This dissertation presents an overview of the research work with the above caption. This research is divided into five major sections or parts. Part one deals with interfacial adhesion studies of the layers relevant to ...

This work presents the results of experimental and theoretical studies of the biodegradation of polyethylene, recycling of polyethylene into strong and tough earth-based composite building materials and the statistical ...

Current standard of care treatment modalities for early-stage breast cancer typically involve mastectomy or lumpectomy followed by radiation therapy to remove any residual cancer cells. Although mastectomy has a low ...