Third-order tensors are widely used as a mathematical tool for modeling physical properties of media in solid state physics. In most cases, they arise constitutive proportionality between basic physics quantities. The tensor can be considered complete set parameters medium. algebraic features the seen proper identification natural material, crystals, and design artificial nano-materials with pr...

We present algorithms for higher-order dependency parsing that are “third-order” in the sense that they can evaluate substructures containing three dependencies, and “efficient” in the sense that they require only O(n4) time. Importantly, our new parsers can utilize both sibling-style and grandchild-style interactions. We evaluate our parsers on the Penn Treebank and Prague Dependency Treebank,...

Iterative differential equations provide a new idea to study functional equations. The of iterative can methods for the with state-dependent delays. In this paper, we are concerned proving existence infinitely many positive solutions nonlinear first-order systems singular BVPs on time scales by using Krasnoselskii’s cone fixed point theorem in Banach space. It is worth pointing out that use sym...

We develop a data-driven model discovery and system identification technique for spatially-dependent boundary value problems (BVPs). Specifically, we leverage the sparse of nonlinear dynamics (SINDy) algorithm group regression techniques with set forcing functions corresponding state variable measurements to yield parsimonious system. The approach models forced systems governed by linear or ope...