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General remarks on dynamic projection method

Leble S.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2016

Vol. 20, No 2

113--130

A brief history and a mathematical description of the dynamic projection operators technique is presented. An example of the general Cauchy problem for evolution equations in 1+ 1 dimensions is studied in detail. A boundary regime propagation is formulated in terms of operators and illustrated by the simplest one-dimensional diffusion equation. The problem of temperature waves is discussed.

A new characterizationof convex Φ-functions with a parameter

Micherda B.

Opuscula Mathematica

2015

Vol. 35, no. 2

191--197

We show that, under some additional assumptions, all projection operators onto latticially closed subsets of the Orlicz-Musielak space generated by Φ are isotonic if and only if Φ is convex with respect to its second variable. A dual result of this type is also proven for antiprojections. This gives the positive answer to the problem presented in Opuscula Mathematica in 2012.

Two-dimensional hp-adaptive algorithm for continuous approximations of material data using space projection

Gurgul P., Sieniek M., Paszyński M., Madej Ł., Collier N.

Computer Science

2013

Vol. 14 (1)

97--112

In this paper we utilize the concept of the L 2 and H 1 projections used to adaptively generate a continuous approximation of an input material data in the finie element (FE) base.This approximation, along with a corresponding FE mesh, can be used as material data for FE solvers. We begin with abrief theoretical background, followed by description of the hp -adaptive algorithm adopted here to improve gradually quality of the projections. We investigate also a few distinct sample problems, apply the aforementioned algorithms and conclude with numerical results evaluation.

B FGMAC : breadth - first frequent subgraph mining with ARC consistency

Douar B., Latiri C., Liquiere M., Slimani Y.

Journal of Artificial Intelligence and Soft Computing Research

2011

Vol. 1, No. 4

269--281

The paper presents a new projection operator for graphs named AC-projection, which exhibits nice theoretical complexity properties unlike to the graph isomorphism operator typically used in graph mining. We study the size of the search space as well as some practical properties of the projection operator. We also introduce a novel breadth-first algorithm for frequent AC-reduced subgraphs mining. Then, we prove experimentally that we can achieve an important performance gain (polynomial complexity projection) without or with non-significant loss of discovered patterns in terms of quality.