The goal of these notes is to give an accessible introduction to the structure theory of linear transformations. We want to develop enough of the theory for use in differential equations, with only basic linear algebra as a prerequisite. In a following set of notes, we will show how these results can be applied to differential equations. In the rest of the section, we will cover some topics tha...

Introduction. If the numbers of vertices and edges of a (linear) graph are suitably restricted, it is to be expected that something can be said about the configurations which the graph contains. As far as we know the first result in this direction is due to Turân. He proved that a graph with kn vertices and Ck,2n+1 edges always contains a complete graph of order k + 1. We shall here prove one s...

Graphs are an integral data structure for many parts of computation. They are highly effective at modeling many varied and flexible domains, and are excellent for representing the way humans themselves conceive of the world. Nowadays, there is lots of interest in working with large graphs, including social network graphs, “knowledge” graphs, and large bipartite graphs (for example, the Netflix ...

In this paper we analyse the structure of the BRST charge of nonlinear superalgebras. We consider quadratic non-linear superalgebras where a commutator (in terms of (super) Poisson brackets) of the generators is a quadratic polynomial of the generators. We find the explicit form of the BRST charge up to cubic order in Faddeev-Popov ghost fields for arbitrary quadratic nonlinear superalgebras. W...

We initiate the study of graph sketching, i.e., algorithms that use a limited number of linear measurements of a graph to determine the properties of the graph. While a graph on n nodes is essentially O(n2)-dimensional, we show the existence of a distribution over random projections into d-dimensional "sketch" space (d « n2) such that several relevant properties of the original graph can be inf...

one of the reasons that companies avoid paying their taxes is that they choose to use debts for their funding. in other words, tax saving, an activity of companies to avoid taxpaying, can be used to finance corporate projects. furthermore, since institutional owners are more inclined to supervise, they may shrink managerial behaviors to avoid taxpaying. in this study, institutional owners’ supe...

evolving models have found applications in many real world systems. in this paper, potentials of the evolving linear models (elms) in tracking control design for nonlinear variable structure systems are introduced. at first, an elm is introduced as a dynamic single input, single output (siso) linear model whose parameters as well as dynamic orders of input and output signals can change through ...

Evolving models have found applications in many real world systems. In this paper, potentials of the Evolving Linear Models (ELMs) in tracking control design for nonlinear variable structure systems are introduced. At first, an ELM is introduced as a dynamic single input, single output (SISO) linear model whose parameters as well as dynamic orders of input and output signals can change through ...