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The Boolean Hierarchy I: Structural Properties
The complexity of sets formed by boolean operations (union, intersection, and complement) on NP sets are studied, showing that in some relativized worlds the boolean hierarchy is infinite, and that for every k there is a relativization world in which the Boolean hierarchy extends exactly k levels. Expand
A survey on counting classes
The authors prove P/sup EP(log)/ 25 PP, investigate the Boolean closure BC( EP) of EP, and give a relativization principle which allows them to completely separate BC(EP) in a suitable relativized world and to give simple proofs for known relativizing results. Expand
XμCT analysis of magnetic field-induced phase transitions in magnetorheological elastomers
The phase behavior of polymer solutions and composites is a complex issue and is of both technological and fundamental interest. For a better understanding of the microstructure formation inExpand
The Boolean Hierarchy II: Applications
The Boolean Hierarchy I: Structural Properties explores the structure of the boolean hierarchy, the closure of NP with respect to boolean hierarchies, and the role of symbols in this hierarchy. Expand
Counting classes with finite acceptance types
Perfectionnement de la hierarchie de Hausdorff generee par NP. Les nouvelles classes permettent une exacte classification de la complexite de certains problemes de denombrement. Les classes sontExpand
Investigation of the motion of particles in magnetorheological elastomers by X-μCT
The behavior of magnetic particles inside elastomeric matrices is a complex issue and can be influenced in many ways, e.g. by applying a magnetic field or external mechanical stimuli. It is ofExpand
Statistical analysis of magnetically soft particles in magnetorheological elastomers
The physical properties of magnetorheological elastomers (MRE) are a complex issue and can be influenced and controlled in many ways, e.g. by applying a magnetic field, by external mechanicalExpand
Tunable dynamic moduli of magnetic elastomers: from characterization by x-ray micro-computed tomography to mesoscopic modeling.
This work uses data extracted from real magnetoelastic samples as input for coarse-grained dipole-spring modeling and calculations to investigate internal restructuring, stiffening, and changes in the normal modes spectrum of ferrogels and magnetorheological elastomers. Expand
Nondeterministic Turing Machines with Modified Acceptance
In this paper an extremely fine hierarchy within BC(NP) is proposed, characterized by nondeter-ministic polynomial time Turing machines with suitably modified acceptance notions. Expand
Importance of matrix inelastic deformations in the initial response of magnetic elastomers
The initial magnetic response of magnetic elastomers can be explained by irreversible polymer matrix deformations under first external field application.